Seamless Precise Positioning through the Integration of Satellite, Terrestrial Ranging and Inertial Technologies
By
Wei Jiang
A thesis in fulfilment of the requirements for the Degree of Doctor of Philosophy
School of Civil and Environmental Engineering Faculty of Engineering UNSW Sydney NSW 2052, Australia
June, 2015
ABSTRACT
The integration of Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) technologies is a very useful navigation option for high accuracy positioning in support of many applications, including airborne mapping, urban positioning and sensor georeferencing. An integrated GNSS/INS system provides navigation solutions by taking advantage of the complementary characteristics of each component technology. However its performance is still limited by the quality of GNSS measurements (when available) and the geometric configuration of the visible satellites. To address this limitation, an alternative, non-GNSS-based positioning technology can augment the traditional integrated GNSS/INS multi-sensor system. Locata is a terrestrial-based technology which can transmit GNSS-like ranging signals. This research is focused on the integration of GNSS, Locata and INS technologies so as to provide accurate and reliable navigation coverage. The main research contributions are:
(a) An “on-the-fly” (OTF) Locata resolution algorithm that takes advantage of geometry change via an Extended Kalman filter is proposed. Single-differenced Locata carrier phase measurements are utilised for accurate and reliable solutions. A “loosely-coupled” decentralised Locata/INS integration architecture based on the Kalman filter is used for data processing. To evaluate the performance of the proposed system a field trial was conducted on Sydney Harbour. The experiment demonstrated that the Locata OTF algorithm was effective and could improve the system accuracy in comparison with the conventional “known point initialisation” method. Furthermore, the experiment confirmed that Locata/INS integration could achieve centimetre-level accuracy for position solutions, and centimetre-per-second accuracy for velocity determination. (b) A new Precise Point Positioning (PPP) technique, augmented by Locata measurements is proposed. In the Locata-augmented PPP-GNSS approach the Locata and GNSS carrier phase measurements are processed simultaneously in a “tightly-combined” mode, and the carrier phase ambiguities are resolved as floating- point values on an epoch-by-epoch basis. A field experiment indicated that the initial convergence time of the integrated Locata/GNSS filter was only 10 seconds, which was significantly faster than using the conventional PPP-GNSS algorithm. I
Abstract
Moreover, the proposed Locata-augmented PPP-GNSS technique could achieve centimetre-level accuracy for horizontal positioning, which was superior to both the Locata-only and PPP-GNSS techniques. (c) A “loosely-coupled” integration algorithm scheme for PPP-GNSS, Locata and INS is developed. To satisfy both accuracy and reliability requirements, three integration algorithms – Centralised Kalman filtering, Federated Kalman filtering and Global Optimal filtering (GOF) – are investigated and implemented within a “triple- integrated” GNSS/Locata/INS navigation system. A preliminary performance assessment, based on the analysis of real data, concluded that all three integration algorithms were able to achieve positioning solutions at centimetre-level accuracy. (d) A novel adaptive fault-tolerant multi-sensor integrated navigation system is proposed, which can ensure a reliable positioning service in complex situations. The proposed system implements a decentralised filtering architecture to fuse the INS, GNSS and Locata measurements. In order to improve the system accuracy, the GOF algorithm is used to implement the proposed multi-sensor navigation system. The adaptive technique is based on the innovation covariance discrepancy, which mainly adapts to the changes in the statistical properties of the sensor measurements, and mitigates the adverse influence caused by these changes. To evaluate the fault- tolerance capability of the proposed system, a series of typical GNSS failures were simulated. The results confirmed that the proposed system was not affected by the failures, and that the reliability and fault tolerant capability were improved. (e) Locata technology could not only be used in outdoor environments as a GNSS “augmentation”, it also can enable precise indoor navigation. In this research, a new multipath mitigating antenna “V-Ray” developed by Locata Corporation is used to address the challenges of making terrestrial ranging measurements in an indoor environment with severe multipath. A new navigation methodology – the position and attitude modelling system (PAMS) – is proposed for processing carrier phase and azimuth measurements via an Unscented Kalman filter. The PAMS can output the complete set of navigation parameters – position, velocity, acceleration and attitude – simultaneously via an OTF initialisation. The indoor test was conducted in a metal warehouse and the results confirmed that the horizontal positioning solution had an accuracy of better than 5cm and an orientation accuracy of better than 0.7 degrees.
II
ACKNOWLEDGEMENT
I would like to gratefully acknowledge the enthusiastic supervision of Professor Chris Rizos during this work. His help, support, and guidance from initial step to the final level enabled me to complete this work. I am also deeply grateful to my co-supervisor Dr. Yong Li for his invaluable help. His knowledge and experience have been a tremendous help for me during my PhD period. Sincere thanks to Associate Professor Samsung Lim, Dr. Binghao Li and Dr. Alex NG for reviewing my work each year and providing me with constructive feedback. I would like to acknowledge to China Scholarship Council (CSC) and the University of New South Wale (UNSW) for awarding me research scholarship and allowing me to enjoy this challenging but extremely interesting research work.
I also would like to express my thanks to all the other staff members, especially Associate Dr. Mohammad Choudhury, Dr. Craig Roberts, and Professor Jinling Wang for their valuable advice on my research and their continuous encouragements. Special thanks to Dr. Joel Barnes, Dr. Steve Hewitson, Dr. David Small and Mr. Nunzio Gambale from Locata Company for their tremendous help in terms of Locata technology and field experiments. Thanks are also given to visiting academic staff, particular Associate Professor Liangqing Lu from National University of Defense Technology and Associate Professor Gongmin Yan from Northwestern Polytechnical University. I am also thankful to Dr. Tao Li, Dr. Ling Yang, Dr. Sara Shirowzhan, Dr. Wei Li, Dr. Yiping Jiang, Mr. Yang Yang, Mr. Zeyu Li, Ms. Liran Sun and Mr. You Shao for their years of friendship.
Last, but far from least, I would like to express my deepest appreciation to my family. Sincere gratitude is given to my father Sizhe Jiang and my mother Yanqiong Cao, for their unconditional love, understanding, and support which motivated me on my PhD journey. A special thanks and much love to my husband, Kaibin Zong, for his love and consideration for the four years, and keep me smiling and energetic all the time.
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TABLE OF CONTENTS
ABSTRACT ...... I
ACKNOWLEDGEMENT ...... III
TABLE OF CONTENTS ...... IV
LIST OF FIGURES ...... VIII
LIST OF TABLES ...... XI
CHAPTER 1 ...... 1
INTRODUCTION ...... 1
1.1 Background ...... 1
1.2 Research Motivation and Objective ...... 3
1.3 Contributions of the Research ...... 5
1.4 Thesis Outline ...... 7
1.5 List of Publications ...... 9
1.5.1 Peer-reviewed Journal Publications ...... 9
1.5.2 Full Paper Peer-reviewed Conference Publications ...... 9
1.5.3 Abstract Reviewed Conference Publications ...... 10
CHAPTER 2 ...... 11
REVIEW THE GEO-REFERENCING TECHNOLOGIES AND NAVIGATION ALGORITHMS ...... 11
2.1 Overview of GNSS Positioning Technology ...... 11
2.1.1 GNSS Introduction ...... 11
2.1.2 GNSS Measurements ...... 14
2.1.3 GNSS Error Sources ...... 17
2.1.4 Precise GNSS Positioning Methods ...... 20
2.2 Overview of the Terrestrial Ranging Technology ...... 23
2.2.1 Locata Introduction ...... 23
IV
Table of Contents
2.2.2 Locata Measurements and Measurement Equations ...... 26
2.3 Overview of Inertial Navigation Technology ...... 28
2.3.1 Coordinate Systems ...... 29
2.3.2 INS Mechanisation ...... 30
2.3.3 INS Error Characteristics ...... 34
2.3.4 INS Error Model ...... 35
2.4 Integration Overview ...... 36
2.4.1 Integration Strategy ...... 36
2.4.2 Integration Data Filtering ...... 38
CHAPTER 3 ...... 43
LOCATA POSITIONING AND LOCATA/INS INTEGRATION FOR PRECISE MARITIME APPLICATION ...... 43
3.1 Introduction ...... 43
3.2 Locata On-The-Fly Positioning Method ...... 44
3.2.1 Dynamic Model ...... 45
3.2.2 Measurement Model...... 47
3.2.3 Calculation of Approximate Initial State ...... 48
3.3 Locata/INS Integration ...... 48
3.3.1 INS Error Dynamic Model ...... 48
3.3.2 Integration Measurement Model ...... 51
3.4 Experiment and Result Analysis ...... 52
3.5 Summary ...... 62
CHAPTER 4 ...... 64
LOCATA AUGMENTED PRECISE POINT POSITIONING FOR KINEMATIC APPLICATIONS ...... 64
4.1 Introduction ...... 64
4.2 GNSS Precise Point Positioning Technology ...... 66
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Table of Contents
4.2.1 Error Sources and Mitigation Techniques in PPP ...... 66
4.2.2 PPP-GNSS Mathematical Model ...... 70
4.3 Locata Augmented PPP-GNSS System ...... 73
4.4 Experiment and Result Analysis ...... 75
4.5 Summary ...... 84
CHAPTER 5 ...... 85
OPTIMAL DATA FUSION ALGORITHM FOR NAVIGATION USING TRIPLE INTEGRATION OF PPP-GNSS, LOCATA AND INS ...... 85
5.1 Introduction ...... 85
5.2 Multi-sensor Filtering Algorithms ...... 88
5.2.1 Centralised Kalman Filtering ...... 88
5.2.2 Federated Kalman Filtering...... 90
5.2.3 Global Optimal Filtering ...... 93
5.3 PPP-GNSS/Locata/INS Integration System ...... 98
5.4 System Evaluation and Result Analysis ...... 101
5.5 Summary ...... 106
CHAPTER 6 ...... 108
MULTI-SENSOR NAVIGATION SYSTEM BASED ON AN ADAPTIVE FAULT- TOLERANT GOF ALGORITHM ...... 108
6.1 Introduction ...... 108
6.2 Adaptive Fault-tolerant Filtering Algorithm ...... 109
6.2.1 Adaptive Sensor Fusion Strategy ...... 109
6.2.2 Adaptive Fault-tolerant Multi-sensor Navigation System ...... 112
6.3 Experiment and Simulation Analysis ...... 115
6.3.1 System Performance of GOF based Triple Integration System ...... 116
6.3.2 Evaluation of Adaptive GOF Method ...... 120
6.4 Summary ...... 126
VI
Table of Contents
CHAPTER 7 ...... 128
PRECISE INDOOR POSITIONING AND ATTITUDE DETERMINATION USING TERRESTRIAL RANGING SIGNALS ...... 128
7.1 Introduction ...... 128
7.2 Locata Multipath-mitigation Technology...... 130
7.3 Locata Position and Attitude Computation Model ...... 132
7.3.1 Locata Indoor Position Computation Model ...... 132
7.3.2 Locata Attitude Computation Model ...... 134
7.4 Locata Position and Attitude Modelling System (PAMS) Mechanisation ..... 135
7.4.1 UKF Introduction ...... 135
7.4.2 PAMS Estimation Process ...... 138
7.5 Experiment and Analyses ...... 140
7.6 Summary ...... 149
CHAPTER 8 ...... 151
CONCLUSIONS AND RECOMMENDATIONS ...... 151
8.1 Concluding Remarks ...... 151
8.1.1 Locata Positioning and Integration of Locata and INS Technology ...... 152
8.1.2 Locata-augmented GNSS Precise Point Positioning...... 154
8.1.3 GNSS/Locata/INS Multi-sensor Navigation System ...... 155
8.1.4 Locata Indoor Navigation ...... 157
8.2 Recommendations for Future Work ...... 159
REFERENCES ...... 161
VII
LIST OF FIGURES
Figure 2.1 GNSS positioning based on measurement double-differencing...... 22 Figure 2.2 The Locata technology positioning concept (Barnes et al. 2003)...... 24 Figure 2.3 LocataLite: receiver (left) and transmitter (right)...... 24 Figure 2.4 LocataLite antenna setup with two transmit antennas and one receive antenna ...... 26 Figure 3.1 LocataNet configuration and rover trajectory for Sydney Harbour test ...... 53 Figure 3.2 Test vessel and experimental setup...... 54 Figure 3.3 Signal availabilities and DOP values for the Sydney Harbour test ...... 55 Figure 3.4 Periods of poor geometry for the Sydney Harbour tests...... 55 Figure 3.5 Position differences between Locata and reference solutions ...... 56 Figure 3.6 Velocity differences between Locata and reference solutions ...... 57 Figure 3.7 Comparison of Locata stand-alone OTF and KPI solutions ...... 58 Figure 3.8 INS stand-alone solutions ...... 59 Figure 3.9 Position difference between Locata/INS and reference solution ...... 59 Figure 3.10 Velocity difference between Locata/INS and reference solution ...... 60 Figure 3.11 Lever arm estimation ...... 61 Figure 4.1 Test vessel and installed Locata and GNSS antennas used for the Sydney Harbour test ...... 76 Figure 4.2 Sydney Harbour experiment configuration and vessel trajectories ...... 77 Figure 4.3 Geometric conditions for GNSS positioning for the Sydney Harbour test ... 78 Figure 4.4 PPP-GNSS solution accuracy with respect to the ground-truth solution ...... 79 Figure 4.5 Geometric conditions for Locata augmented PPP-GNSS system and horizontal geometry for the Locata standalone system ...... 80 Figure 4.6 Locata augmented PPP-GNSS accuracy with respect to the ground-truth solution ...... 81 Figure 4.7 Horizontal accuracy comparison of PPP-GNSS, Locata standalone, and Locata augmented PPP-GNSS systems ...... 83 Figure 5.1 System configuration of CKF ...... 89 Figure 5.2 System configuration of FKF ...... 90 Figure 5.3 System configuration of GOF ...... 96
VIII
List of Figures
Figure 5.4 Position and velocity error of the CKF system ...... 102 Figure 5.5 Position and velocity error of the FKF system ...... 103 Figure 5.6 Position and velocity error of the GOF system ...... 103 Figure 5.7 Position and velocity precision evaluation of the CKF system ...... 104 Figure 5.8 Position and velocity precision evaluation of the FKF system...... 105 Figure 5.9 Position and velocity precision evaluation of the GOF system ...... 105 Figure 5.10 Fault-tolerance evaluation of GOF-based triple integration system ...... 106 Figure 6.1 Adaptive fault-tolerant filtering algorithm in the local filter. The ˆ measurement noise covariance i kR is adjusted in each epoch by matching the ˆ innovation covariance r kC and its pre-defined value r kC ...... 112 Figure 6.2 Adaptive fault-tolerant multi-sensor navigation system based on GOF decentralised estimation filtering. The measurements 1kz and 2 kz of Locata/INS and GNSS/INS subsystems are input to the local adaptive filters to achieve the local ˆ estimation, the GOF algorithm is then applied to fuse the local estimation ˆi kx , i kP , and global prediction kx , kP ...... 113 Figure 6.3 Trajectory of the triple-integration system at the Locata Numerella Test Facility ...... 116 Figure 6.4 Position solution comparison between the FKF and the GOF-based triple- integrated solutions ...... 117
Figure 6.5 Position and velocity precision comparison ( ˆkP ) between the FKF (blue line) and the GOF (red line) results during the last 100 seconds ...... 118 Figure 6.6 Position solution difference comparison between the GOF-based triple- integration system, local GNSS/INS system and local Locata/INS system...... 119 Figure 6.7 Position and velocity precision comparison between the GOF-based triple- integration (red line), local GNSS/INS system (blue line) and local Locata/INS system (green line) during the last 100 seconds ...... 120 Figure 6.8 Comparison of the GOF and the AGOF with outlier failure simulation ..... 122 Figure 6.9 Comparison of the GOF and the AGOF with constant bias simulation ...... 123 Figure 6.10 Comparison of the GOF and the AGOF with “stuck bias” simulation ..... 124 Figure 6.11 Comparison of the GOF and the AGOF with GNSS stop working simulation ...... 125
IX
List of Figures
Figure 6.12 Comparison of the AFKF-based system with and without failure simulation ...... 125 Figure 6.13 Comparison of the AGOF-based system with and without failure simulation ...... 126 Figure 7.1 Locata V-Ray principle (LaMance and Small 2011) ...... 131 Figure 7.2 Locata beam-forming V-Ray antenna ...... 132 Figure 7.3 Geometry of Locata azimuth angle measurement ...... 134 Figure 7.4 Indoor testing environment at the NTF ...... 141 Figure 7.5 Comparison of calculated carrier phase error between V-Ray antenna (top) and conventional omni-directional antenna (bottom) ...... 142 Figure 7.6 Locata trajectory and LocataLite installations for indoor testing ...... 143 Figure 7.7 DD carrier phase measurements and cycle slip detection ...... 144 Figure 7.8 Mean and STD of the position difference in the north component ...... 145 Figure 7.9 Mean and STD of the position difference in the east component...... 145 Figure 7.10 Mean and STD of orientation differences ...... 146 Figure 7.11 Comparison of horizontal position differences calculated using the EKF and UKF ...... 147 Figure 7.12 DRMS comparison between typical range-based system and the integrated range-azimuth system...... 148 Figure 7.13 Orientation RMS comparison between azimuth-based system and the integrated range-azimuth system...... 149
X
LIST OF TABLES
Table 3.1 Specifications of the Applanix POS-MV (Applanix Corporation 2009) ...... 54 Table 3.2 Comparison of Locata stand-alone OTF and KPI solutions ...... 58 Table 3.3 Comparison of Locata OTF stand-alone and Locata/INS integration solutions ...... 62 Table 4.1 IGS satellite orbit and clock products ...... 67 Table 4.2 PPP-GNSS errors and corresponding mitigation methods ...... 69 Table 4.3 Error statistics of the PPP-GNSS solution ...... 79 Table 4.4 DOP comparison of geometries for different sensor configurations ...... 80 Table 4.5 Error statistics of the Locata augmented PPP-GNSS solution ...... 82 Table 4.6 Error statistics of PPP-GNSS, Locata standalone and Locata augmented PPP- GNSS ...... 83 Table 5.1 Position and velocity analysis of the three filtering systems ...... 102 Table 6.1 Specifications of the Honeywell H764 IMU...... 115 Table 6.2 MRSE of triple-integrated system and local systems ...... 120 Table 6.3 Simulated GNSS failures and periods ...... 121 Table 6.4 RMS of the AFKF and the AGOF solutions with and without failure simulation ...... 126 Table 7.1 Overview of indoor positioning technology ...... 128 Table 7.2 Configuration of LocataLites for indoor testing ...... 141 Table 7.3 RMS comparison of positioning differences ...... 147
XI
CHAPTER 1 INTRODUCTION
1.1 Background
Modern precise positioning and navigation technologies support many applications including geodesy, surveying, mapping, machine control and guidance, image georeferencing, aviation and precise marine applications. During the past few decades many positioning and navigation systems and technologies have been developed to address a variety of user requirements under different application environments. Satellite-based Global Navigation Satellite System (GNSS) technology is able to provide accurate position, velocity and time data, on a 24/7 basis, without any impact of mission length or time since update. However it is most effective in open outdoor environments where there is no (or at least very little) blockage, signal interference or attenuation. On the other hand, inertial navigation system (INS) technology comprises a self-contained single hardware package with sensors that have relatively high short-term stability (i.e. low system drift errors), and are immune to jamming or signal outages because they do not make use of any external transmitted signals. Because of the high degree of complementarity, a combination of GNSS and INS technologies could not only mitigate the weakness of GNSS, but also bound the INS error that otherwise would grow with time when the INS operates without GNSS solutions. This powerful synergy between GNSS and INS makes the integration of the two technologies widespread and indispensable. Although an integrated GNSS/INS system provides augmented solutions its performance is still limited by the quality of GNSS measurements, and the geometric strength of the satellite constellation (Leick 2004; Groves 2008). When GNSS signals are blocked or there is interference, disrupting availability beyond a certain period of time, INS sensor error will grow with time and impact on positioning accuracy, reliability and availability. To address this problem, there have been many investigations into the estimation filtering algorithm. Nonlinear integration techniques such as the Sigma-point Kalman filtering (Wendel et al. 2006), and the Particle Filter (PF) (Donovan 2012) have been recently investigated in order to enhance the performance of GNSS/INS systems (Aggarwal et al. 2008). Some backward smoothing
1
Chapter 1 Introduction techniques have been considered, e.g. the RTS smoother (Gelb 1974). However, all these methods are only valid for scenarios with short GNSS outage period. In the case of longer GNSS outages navigation outputs do not satisfy the performance requirements of many applications.
The development of terrestrial-based positioning technology with “GNSS characteristics” can be traced back to the early days of GPS, where they have been used to validate the GPS concept before the satellites were launched. Certain class of transmitters have become known as “pseudo-satellites” or “pseudolites” because the signals they transmit are almost the same as GPS signals (Cobb 1997). Over the past decades, many kinds of terrestrial ranging technologies have been developed derived from the pseudolite concept. Since 2002, Locata Corporation has been developing a positioning technology called “Locata” as a ground-based alternative positioning technology. Locata uses a “local constellation” to provide continuously time- synchronised ranging signals, and can be used in GNSS challenged environments, e.g. poor satellite geometry, signal blockage in suburban, tunnels, high-rise building canyons (Barnes et al. 2004; Choudhury et al. 2009a; Gauthier et al. 2013; Rizos et al. 2010; Jiang et al. 2013) as it has stronger signals than GNSS.
As Locata is derived from the pseudolite concept, it has good interoperability with GNSS constellations when transmitted signals are synchronised with GNSS signals. The additional Locata signals can significantly enhance the performance of the total system in a number ways, including reducing the dilution of precision (DOP) to improve the accuracy, availability and reliability of the final solutions, and being included into GNSS/INS integration systems as an independent but complementary component to address issues such as GNSS signal blockage or interference, so as to assure the continuity of the accurate navigation solutions (Grejner-Brzezinska et al. 2011). Moreover, in some severe GNSS signal attenuation cases as in indoor positioning, where GNSS cannot be used for precise positioning, Locata could be used to help provide continuous navigation or positioning as a GNSS-alternative technology, as long as it can overcome multipath effects in indoor environments.
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Chapter 1 Introduction
In a multi-sensor navigation strategy, with the addition of more sensors, more information become available. In a GNSS/Locata/INS integration system each subsystem could provide position, velocity and acceleration information to users. The navigation system needs to fuse the navigation solutions from all the sensors, to create a single optimal solution for the user. Hence the fusion algorithm is crucial. However all sensors can suffer failures or generate faulty measurements. Therefore increasing the fault-tolerance of a multi-sensor navigation system is another important issue and is a research challenge.
1.2 Research Motivation and Objective
This thesis deals with the issue of seamless and accurate positioning through the integration of GNSS, Locata, and INS. The objectives of this research are summarised below.
Locata is able to provide centimetre-level accuracy when carrier phase measurements are used. It requires estimation of the carrier phase ambiguity terms in a similar manner to GNSS. In the system’s conventional design ambiguity resolution is carried out through a “known point initialisation” (KPI) procedure on a precisely surveyed point, or using measurements from previous epochs by applying non-linear batch Least Square estimation techniques (Amt 2006; Bertsch et al. 2009). However, both methods are inconvenient when some of the ambiguities need to be recomputed if their signal status changes. Therefore a new Locata ambiguity resolution method is investigated in order to achieve carrier phase ambiguity resolution “on-the-fly” (OTF). Furthermore, by improving the ambiguity resolution method, the navigation process is expected to improve performance.
Most precise GNSS positioning rely on the Network-based Real-Time Kinematic (N- RTK) principle. However the requirement for one or more nearby reference station equipped with a reference GNSS receiver may limit the operational range of the N-RTK system, as well as increasing system cost and complexity (Du and Gao 2012). An alternative to the differential positioning techniques is the Precise Point Positioning (PPP) approach, which is based on the processing of observations from a single user 3
Chapter 1 Introduction
GNSS receiver. For PPP there is no longer a need to use corrections and/or measurements from one or more GNSS reference stations. Moreover PPP has a lower computational burden in comparison with the N-RTK approach (Zumberge et al. 1997). However, the PPP technique typically requires long convergence periods, especially for kinematic positioning, and the resultant accuracy is not as high as in the case of N-RTK solutions. It is of interest to combine Locata and GNSS technologies and build a Locata- augmented PPP-GNSS system. The proposed system is expected to preserve the advantage of PPP-GNSS and at the same time improve the initialisation performance and accuracy of conventional PPP-GNSS positioning.
As a GNSS-augmented technology Locata can be incorporated within GNSS/INS integration systems to address the GNSS disadvantages. In this study, in order to satisfy the requirements of high accuracy and high reliability, the PPP-GNSS and Locata technologies are fused with INS to provide a robust global estimate of the navigation parameters via a loosely-coupled architecture. The fundamental problem of integrated navigation systems is information fusion. The commonly used methods are the Centralised Kalman filtering (CKF) and Decentralised Kalman filtering (DKF) (Caron et al. 2006; Seo and Lee 2005). However, both CKF and DKF have problems in practical applications. For example, CKF can result in a large computational burden and large data memory demands (Gao et al. 2009). DKF may not achieve higher accuracy than the CKF method, though the DKF has low computational load and processing demands (Lo et al. 2013; Li and Zhang 2010). To investigate the optimal fusion algorithm for the proposed PPP-GNSS/Locata/INS multi-sensor navigation system, CKF, Federated Kalman filter (FKF) and the information space based Global Optimal filter (GOF) are considered.
In practical applications, the measurement characteristics of sensors may vary as the environment changes, which may occasionally cause sensor failure. Therefore a capability for robustness and fault tolerance should be taken into consideration during system design. In a normal operational situation, the measurement noise levels are a priori defined as fixed values and remain constant for the recursive process. However, the a priori statistics may not be appropriate for all scenarios, which leads to sub- optimal filter estimation. In the case of measurement failures, the assumption of
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Chapter 1 Introduction constant measurement statistics would further degrade the system performance, or even lead to a divergence of the filter itself (Loebis et al. 2004; Mohamed and Schwarz 1999). Hence, it is desirable to implement an adaptive fault-tolerant navigation filter algorithm that can adapt to changes in the sensor measurement statistical characteristics as well as dealing with sensor failures. In this research, the proposed GNSS/Locata/INS multi- sensor navigation system is implemented via an optimal data fusion algorithm, and further improved with the adaptive fault-tolerant algorithm. The adaptive algorithm is investigated based on the estimated innovation covariance and expected to adapt to the changes in sensor measurement statistical properties so as to mitigate the adverse influence caused by these changes and hence to improve the system fault-tolerance capability.
Locata technology can not only be used outdoor as a GNSS “augmentation”, it can also be used indoors as a GNSS “alternative”. However, the more severe multipath effects in indoor environments suggest that the Locata system’s indoor performance cannot match its outdoor performance. Recently Locata’s new indoor antenna “V-Ray” appears to address the challenges of multipath by forming tight beams that provide line-of-sight range measurements as well as azimuth measurements. Therefore the performance of the V-Ray antenna is analysed and evaluated. Moreover, taking advantage of the two types of multipath-mitigated measurements provided by Locata, a new navigation methodology is investigated which requires the simultaneous processing of carrier phase and azimuth measurements via a common filter, and output improved navigation solutions. In contrast to conventional position and attitude determination using GNSS, which require three or more receivers/antennas mounted on a platform, the proposed technique can determine the position, velocity and platform attitude parameters using a single Locata receiver/antenna.
1.3 Contributions of the Research
The following are the contributions of this research:
Systematic errors introduced by Locata technology have been investigated. The single-differenced Locata carrier phase measurements model has been developed to 5
Chapter 1 Introduction
eliminate the receiver clock error. The OTF ambiguity resolution technique has been developed, which allows the ambiguity terms resolved on an epoch-by-epoch basis along with the navigation parameter estimation via an Extended Kalman filter (EKF), without the requirement for initialisation on a precisely surveyed point.
A Locata/INS integration system has been developed and tested. The results confirm the effectiveness of Locata/INS integration for high accuracy maritime positioning applications, and the superiority of the integration solution to both Locata and INS navigation solutions.
A Locata-augmented PPP-GNSS approach for kinematic applications has been investigated. This method integrates the PPP-GNSS and Locata positioning approaches in order to provide high accuracy point positioning solutions without requirement for a GNSS reference station, with a short initial convergence period. A field test was conducted on Sydney Harbour and the results demonstrate the advantage of the proposed method in terms of accuracy and convergence times compared with the conventional PPP-GNSS method and Locata standalone system.
A multi-sensor navigation system is designed based on the loosely-couple integration of PPP-GNSS, Locata and INS. To achieve the reliable and accurate solution three data fusion algorithms – CKF, FKF and GOF – are analysed from both the theoretical perspective and real world testing. Comparative studies of the CKF, FKF and GOF solutions confirm theoretical analyses – the FKF and CKF solutions have the same accuracy and the GOF solution has a higher accuracy.
The proposed PPP-GNSS/Locata/INS multi-sensor navigation system has been improved with a new adaptive fault-tolerant GOF integration algorithm. To evaluate the accuracy and reliability of the system, GNSS failures were simulated and incorporated into real experiment data files. A comparison between the proposed method and conventional methods verifies the higher reliability and fault-tolerant capability of the proposed system.
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Chapter 1 Introduction
A new indoor navigation methodology – the position and attitude modelling system (PAMS) – has been proposed with the use of the “V-Ray” antenna. The PAMS can output the complete set of navigation parameters position, velocity, acceleration and attitude using an Unscented Kalman filter (UKF). An indoor test was conducted in a metal warehouse to evaluate system performance, and the results confirm accurate solutions in indoor environments.
1.4 Thesis Outline
This thesis consists of eight chapters.
Chapter 1 provides the background to integrated systems for precise navigation, based on the use of GNSS, Locata, and INS subsystems and sensors. The research motivation and objectives are defined, as well as the contributions and outline of the thesis structure.
Chapter 2 reviews the georeferencing technologies, including GNSS, terrestrial ranging systems and INS, as well as describes the integration strategy and filtering method.
Chapter 3 describes the mathematical model for Locata positioning technology. The OTF method is proposed, which takes advantage of geometry change via an EKF. To validate the Locata performance within an integrated system, a loosely-coupled Locata/INS integration system is described, including the system mathematical and stochastic models. A field trial conducted in a port area is described.
Chapter 4 proposes a Locata-augmented PPP-GNSS system which can overcome the shortcomings of conventional PPP-GNSS: long convergence periods and low accuracy compared with N-RTK method for kinematic applications. In the proposed method the Locata and GNSS carrier phase measurements are processed in a tightly-coupled mode, with the ambiguities resolved on an epoch-by-epoch basis in order to avoid the need for cycle slip repair. To evaluate the system performance, the proposed system is compared with a conventional PPP-GNSS system, as well as a Locata standalone system.
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Chapter 1 Introduction
Chapter 5 investigates a robust georeferencing system that could satisfy centimetre- level accuracy requirements for both open and occluded environments. The design is based on the loosely-coupled integrated PPP-GNSS, Locata, and INS system. To satisfy both accuracy and reliability requirements, three integrated algorithms – CKF, FKF, and GOF – are investigated and implemented into a triple-integrated PPP-GNSS/Locata/INS system. An assessment, based on the analysis of real data, is also conducted.
Chapter 6 describes an adaptive fault-tolerant multi-sensor integrated navigation system. The proposed system uses a decentralised filtering architecture to fuse the INS, GNSS and Locata subsystems. Based on the conclusion from Chapter 5, the GOF algorithm is implemented to fuse the subsystems. In order to improve the system robustness and reliability, an adaptive fault-tolerant algorithm based on the innovation covariance discrepancy is proposed and applied, which mainly adapts to changes in sensor measurement statistical properties, and mitigates the adverse influence caused by these changes. In order to evaluate the system fault-tolerance capability, typical GNSS failures are simulated to evaluate the fault-tolerant ability of the proposed system.
Chapter 7 presents the results of a new multipath mitigating Locata antenna for use with terrestrial ranging signals in severe multipath-affected indoor environments. Taking advantage of range and azimuth measurements from the V-Ray antenna a new navigation algorithm – namely the PAMS – is proposed. As the measurement model of PAMS is non-linear, the UKF, instead of the EKF is used. The PAMS mechanisation is described, together with the evolution of the UKF. To evaluate the system performance, a field test was conducted in a metal warehouse which has severe multipath effects. The proposed PAMS system is compared with an EKF-based position/attitude determination system, and conventional position/attitude determination systems.
Chapter 8 summarises the findings of the thesis research. This chapter also presents concluding remarks and makes recommendations for future work.
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Chapter 1 Introduction
1.5 List of Publications
1.5.1 Peer-reviewed Journal Publications
1) Jiang, W., Li, Y., & Rizos, C., 2013. Flight evaluation of a Locata-augmented multisensor navigation system. Journal of Applied Geodesy, 7(4), 281-290. 2) Jiang, W., Li, Y., & Rizos, C., 2013. On-the-fly Locata/inertial navigation system integration for precise maritime application. Measurement Science & Technology, 24(10), 105104. 3) Jiang, W., Li, Y., & Rizos, C., 2014. Locata-based precise point positioning for kinematic maritime applications. GPS Solutions, 19(1), 117-128. 4) Jiang, W., Li, Y., & Rizos, C., 2014. Precise indoor positioning and attitude determination using terrestrial ranging signals. Journal of navigation, 68(2), 274-290. 5) Jiang, W., Li, Y., & Rizos, C., 2015. Optimal data fusion algorithm for robust navigation using triple integration of PPP-GNSS, INS and terrestrial ranging system. IEEE Sensors Journal, in print, DOI 10.1109/JSEN.2015.2447015. 6) Jiang, W., Li, Y., Rizos, C., & Yang, L., 2015. A multi-sensor navigation system based on an adaptive fault-tolerant GOF algorithm. IEEE transactions on Intelligent Transportation Systems, under review. 7) Li, Y., Sun, G., & Jiang, W., 2013. Integrated navigation: GPS/BeiDou/INS performance in two hemispheres. Inside GNSS, November/December issue, 57-63. 8) Yang, L., Li, Y., Jiang, W., & Rizos, C., 2014. Locata network design and reliability analysis for harbour positioning. Journal of Navigation, 68(2), 238-252.
1.5.2 Full Paper Peer-reviewed Conference Publications
9) Jiang, W., Li, Y., & Rizos, C., 2012. Flight evaluation of a Locata-augmented multisensor navigation system. Present at 3th Chinese Satellite Navigation Conference Guangzhou, Guangdong, China, 15-17 May. Win the Outstanding Youth Paper (3rd Award). 10) Jiang, W., Li, Y., Rizos, C., Barnes, J., & Hewitson, S., 2013. Precise maritime navigation based on Locata-augmented multi-sensor system. 4th Chinese Satellite
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Chapter 1 Introduction
Navigation Conference, Wuhan, Hubei, China, 15-17 May, 577-587, Lecture Notes in Electrical Engineering 245, Springer Berlin Heidelberg. 11) Jiang, W., Li, Y., & Rizos, C., 2015. An optimal data fusion algorithm based on the triple integration of PPP-GNSS, INS and terrestrial ranging system. 6th Chinese Satellite Navigation Conference, Xian, Shaanxi, China, 15-17 May, 493-505, Lecture Notes in Electrical Engineering 342, Springer Berlin Heidelberg. Win the Outstanding Youth Paper (3rd Award).
1.5.3 Abstract Reviewed Conference Publications
12) Jiang, W., Li, Y., & Rizos, C., 2012. Using Locata and INS for indoor positioning. 3rd International Conference on Indoor Positioning & Indoor Navigation, Sydney, Australia, 13-15 November, CD-ROM procs. 13) Jiang, W., Li, Y., & Rizos, C., 2014. On-The-Fly indoor positioning and attitude determination using terrestrial ranging signals. 27th International Technical Meeting of The Satellite Division of the Institute of Navigation, Tampa, Florida, USA, 8-12 September, 3222-3230.
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CHAPTER 2 REVIEW THE GEO-REFERENCING TECHNOLOGIES AND NAVIGATION ALGORITHMS
2.1 Overview of GNSS Positioning Technology
2.1.1 GNSS Introduction
A satellite navigation system with global coverage is referred to as a Global Navigation Satellite System (GNSS). In this decade a number of GNSSs are operating or being developed, including the U.S.’s GPS, Russia’s GLONASS, EU’s Galileo and China’s Beidou. GNSS technology can be characterised as precise, continuous, all-weather and near-real-time microwave (L-band) technique based on satellite signals transmitted through the Earth’s atmosphere.
In 1973, the Joint Program Office (JPO) was directed by the U.S. Department of Defense (DOD) to develop and deploy a spaceborne positioning system, which today is known as the NAVigation System with Timing And Ranging Global Positioning System (NAVSTAR-GPS), or simply as GPS. The first NAVSTAR satellite was launched in 1989; the 24th satellite was launched in 1994, with full operational capability being declared in April 1995. Between 1997 and 2009, 20 satellites of different generations, Block IIR and IIR-M, were launched, and constitute a majority of the current GPS constellation. The Block IIR-M satellites made available to civilian users an open ranging signal modulated on the L2 frequency carrier. An additional safety-of-life civilian-use signal (on the L5 carrier frequency) is provided by the Block IIF generation of GPS satellites. Over the last decade, the U.S. has implemented several improvements to the GPS service, including new technology and new signals for civil use, and increased accuracy and integrity for all users, all while maintaining compatibility with existing GPS equipment. “GPS modernization” is an ongoing initiative to upgrade the GPS with new capabilities to meet growing military, civil, and commercial needs. The program is being implemented through a series of satellite acquisitions, including GPS Block III and the Next Generation Operational Control
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System (OCX). The U.S. Government continues to improve the GPS space and ground segments to increase system performance and accuracy.
The Global Navigation Satellite System (GLONASS) is the Russian-operated constellation of GNSS satellites. The abbreviation GLONASS derives from the Russian “Global’naya Navigatsionnaya Sputnikovaya Sistema”, translated to its English equivalent – Global Navigation Satellite System. It reached full operational capability in 1995 with the deployment of 24 satellites. Unfortunately, due to the inability to maintain the system, the size of the constellation slowly reduced, reaching a minimum of eight operational satellites in subsequent years. In August 2001, a Federal Task Program on the Global Navigation System (GNS) was approved, which has the objective of improving both the space, control and user equipment segments of GLONASS system and restoring full capability by the Russian government (Dvorkin and Karutin 2006). By 2010, GLONASS had achieved full coverage of Russia's territory, and in October 2011 the full operational capability (24 satellites) was reached, enabling full global coverage. The GLONASS space segment currently is composed of 24 satellites distributed over three orbital planes (separated by 120 degrees in right ascension) with orbit radius equal to 25500km and 65 degrees inclination. GLONASS satellites broadcast signals in the L1 and L2 bands, using Frequency Division Multiple Access (FDMA) technique as the channel access method technique. Since 2008, new Code Division Multiple Access (CDMA) signals are being researched for use with GLONASS to improve its interoperability with other GNSSs.
The “Galileo” navigation system is the third satellite-based navigation system currently under development. It was started by the European Union and European Space Agency in March 2008, and aims to provide an alternative high-precision positioning system upon which European nations can rely independently from the U.S. GPS and Russian GLONASS systems. Galileo is expected to be fully functional by 2020 and compatible with the modernised GPS system. A multi-GNSS receiver will be able to combine the signals from both Galileo and GPS satellites to increase accuracy significantly. Compared to GPS and GLONASS, Galileo is designed specifically for civilian and commercial purposes. The first four operational satellites designed to validate the Galileo concept in both space and on Earth have been successfully launched on October
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2012. This In-Orbit Validation (IOV) phase is now being followed by additional satellite launches to reach Full Operational Capability (FOC). The fully deployed Galileo system will consist of 30 satellites (27 operational + 3 active spares), positioned in three circular Medium Earth Orbit (MEO) planes at 23222km altitude above the Earth, and at an inclination of the orbital planes of 56 degrees to the equator. The signals will be broadcast in the L1, E5 and E6 bands to provide Open Service (OS), Integrity Monitoring Service (IMS), Commercial (CS) and Public Regulated Service (PRS), and Search and Rescue Service (SAR).
China is also developing its own GNSS – named the Beidou Navigation System (BDS) – to join the GNSS community of technology. The BDS is under construction and will be a global satellite navigation system consisting of 35 satellites, including 5 Geostationary Earth Orbit (GEO) satellites and 30 non-geostationary satellites (27 in Medium Earth orbit – MEO and 3 in inclined geosynchronous orbit – IGSO). As of December 2014, 14 satellites of the constellation, including 6 GEO satellites and 5 IGSO satellites and 4 MEO satellites, were able to provide positioning navigation and timing (PNT) services for the Asia-Pacific region. These satellites transmit signals in three frequency bands – B1, B2 and B3 – and broadcast signals with structures using CDMA techniques. By 2020, the system will evolve to global navigation capability. Similar to Galileo and GPS, different services will be offered – a standard signal for civilian users and a more precise (encrypted) signal for restricted uses.
To compete and augment the existing space-based navigation systems, several regional systems are being developed by various countries, such as the Quasi-Zenith Satellite System (QZSS) by Japan and the Indian Regional Navigation Satellite System (IRNSS) by India.
QZSS is proposed as three-satellite regional time transfer system and Satellite Based Augmentation System (SBAS) for the GPS. Its service area covers East Asia and Oceania region and its platform is multi-constellation GNSS. To date (February 2015) only a single satellite has been launched, however three additional satellites are scheduled to be launched before the end of 2017. The QZSS system is not required to work in a standalone mode, but together with data from other GNSS satellites. There are
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6 transmitted signals: L1-C/A, L1C, L2C, L5, L1-SAIF and LEX, where L1-C/A, L2C, L5 and L1C.
IRNSS was approved to provide an autonomous navigation service for the Indian subcontinent in May 2006. The IRNSS constellation will consist of seven satellites, three of them in IGSO, and the other four in GEO. IRNSS signals will consist of a Special Positioning Service and a Precision Service, both will be carried on L5 (1176.45MHz) and S band (2492.028MHz). To date four satellites have been successfully launched, and India has announced the deadline of 2015-2016 to launch the remaining satellites.
2.1.2 GNSS Measurements
Typically, there are three measurements from a GNSS receiver – code, Doppler, and carrier phase. The code measurement, often also referred to as a “pseudorange”, comprises the actual range corrupted by measurement errors (primarily the receiver clock error). The Doppler measurement describes the frequency shift in the signal due to vehicle and receiver clock dynamics, and the carrier phase can be thought of as integrated Doppler. The term “raw” is used to distinguish these measurements from the navigation processor outputs such as position, velocity, and acceleration.
The pseudorange measurement is the difference between the transmission time at a signal emitting antenna and the reception time at a receiver – the so-called “travel time” – scaled by the speed of electromagnetic radiation (i.e. light). If the receiver and satellite clocks were perfectly synchronised and there were no atmospheric refraction effects, multiplication of the travel time by the speed of light would yield the true range or distance between the satellite transmitter and the signal receiver. However, the satellite and receiver clocks have different accuracy levels and errorless synchronisation cannot be achieved. In addition, there are additional errors and biases affecting the ranging signals as the signals propagate through the Earth’s atmosphere. Considering these error sources, the mathematical expression for the GNSS satellite pseudorange observation is (Hofmann-Wellenhof et al. 2001):
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ii i i i i i i cp dsdTdt iono dd trop dM p p (2.1) where, pi is the pseudorange measurement in units of metres between GNSS
receiver and satellite i ; i is the true or “geometric” range between GNSS receiver and satellite ;
dt i is the satellite clock error; dT is the receiver clock error; dsi is the satellite orbit error;
i diono is the ionosphere delay;
i dtrop is the troposphere delay;
i dM p is the multipath effect on pseudorange;
i p is the pseudorange measurement noise; c is the velocity of light in vacuum.
The carrier phase observation is a measure of the integrated phase difference between the carrier signal generated by a receiver oscillator and the carrier signal from a satellite. The carrier phase observation consists of an integer number of full cycles and an additional fractional part. GNSS receivers cannot distinguish one cycle from another, but only measure the fractional part, but keep track of changes in the carrier phase. Hence when the receiver locks onto a satellite signal, the number of full cycles is initially unknown, or “ambiguous”. This is known as the integer carrier phase ambiguity. The mathematical expression for the GNSS carrier phase observation is (Hofmann- Wellenhof et al. 2001):
ii i ii i i ii c dTdt N ds iono dd trop dM (2.2) where, i is the carrier phase measurement in units of cycles between GNSS
receiver and satellite ;
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is the wavelength of the GNSS carrier phase, a function of the transmitting frequency; i is the true or “geometric” range between GNSS receiver and satellite i ;
dt i is the satellite clock error; dT is the receiver clock error; N i is the carrier phase ambiguity term (non-integer);
dsi is the satellite orbit error;
i diono is the ionosphere delay;
i dtrop is the troposphere delay;
i dM is the multipath effect on the carrier phase;
i is the carrier phase measurement noise. The other terms are the same as Equation (2.1).
The Doppler frequency is the rate-of-change of the carrier phase measurement, and is typically measured in L1 cycles per second (Hz). These measurements, when scaled by the L1 wavelength, provide the range-rate measurement. The range-rate reflects the relative velocity between the receiver and the GNSS satellite, and thus can be used for computing velocities. This quantity can be expressed as (Godha 2006):
iii i i i i i (2.3) iono trop MdddsdTdtdcp p p where, p i is the range-rate measurement derived from Doppler measurements;
i is the relative velocity between the GNSS receiver and the satellite ;
tdi is the satellite clock drift; Td is the receiver clock drift;
sdi is the satellite orbit drift error;
i diono is the ionosphere drift error;
i dtrop is the troposphere drift error;
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i Md p is the multipath drift error;
i p is the range-rate measurement noise.
2.1.3 GNSS Error Sources
As indicated in Equation (2.1) – Equation (2.3), the GNSS measurements are contaminated by several error sources. In order to achieve accurate results these errors must be taken into account in the measurement modelling and subsequent data processing. The errors can be classified as: transmitter-related errors, propagation errors, and receiver-related errors.
2.1.3.1 Transmitter-Related Errors
Satellite Clock Error. The amount of satellite clock “drift” with respect to the nominal “perfect” GNSS reference time is referred to as the satellite clock error. Each satellite controls its own timing via an on-board atomic clock. Although the clock is very accurate, it is still impossible to synchronise all the satellites of the constellation with the master reference clock on the ground. The GNSS Control Segment monitors the clocks of each satellite (against the master clock on the ground) and determines the correction information so as to keep a common time frame across the entire constellation. The correction information in the case of GPS is represented as a quadratic polynomial in time, whose coefficients are transmitted as part of the Navigation Message. However it is impossible to predict these corrections without error, resulting in additional “residual” range errors. The average residual clock error for the GPS constellation has been estimated as being up to 1m (Creel et al. 2006; Olynik et al. 2002). However for the new generation of satellite clocks, this error is typically less.
Satellite Orbit Error. This is also referred to as “ephemeris error”. The satellite orbit error is the difference between the transmitter position information available to a user (e.g. via the information in the Navigation Message) and its true position. The GNSS Control Segment predicts the satellite ephemerides based on satellite tracking at ground monitoring stations, and uploads this information to the satellite for 17
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transmission in the Navigation Message (Zumberge and Bertiger 1996). The broadcast ephemerides are estimated to be accurate at the 1m level or so. Due to improvements in satellite tracking and satellite orbit modelling, the orbit error is decreasing. Currently the combined effects of satellite clock and satellite orbit error in the GPS Navigation Message are at the 0.6-0.7m level. The ephemeris products provided by the International GNSS Service (IGS) on the other hand are as low as 15mm (1 sigma global average) for each daily arc, which brings great benefits to those high precision users (Griffiths and Ray 2009).
2.1.3.2 Propagation Errors
Ionosphere Errors. The ionosphere starts from height of about 50km and extends to beyond 1000km above the Earth’s surface. The free electrons in the ionosphere prohibit the GNSS signals from travelling at the vacuum speed of light. When passing through the ionosphere, the propagation of the modulation on the carrier is delayed, while the propagation of the carrier wave is advanced. This retardation and advance is collectively referred to as the “ionospheric effect” (Leick 2004; Rizos 1996). These effects on the pseudorange and carrier phase are therefore opposite in sign. GNSS signals are delayed as a function of the number of free electrons along the path of the ranging signal and are also proportional to the inverse of the carrier frequency squared (Parkinson 1996). The density of free electrons varies with time, season and geographic location, with the main influence on the signal propagation being the solar activity, the geomagnetic field and the elevation angle of the satellite above the horizon. In general, the magnitude of the ionospheric delay is of the order of 5m to 15m, but can reach over 100m. The simplest correction is an empirical model such as the Klobuchar model broadcast by the GNSS Navigation Message (Klobuchar 1996). As the ionosphere error is frequency-dependent, it can be directly solved for by combining measurements from different frequencies when a dual- frequency GNSS receiver is used.
Troposphere Errors. The troposphere is the lower part of the atmosphere from the Earth’s surface up to approximately 50km, with the majority being in the lowest 10km of the atmosphere. The error is a function of elevation angle and is dependent
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on a number of meteorological parameters, such as humidity, temperature, and pressure. Since the troposphere is a non-dispersive medium all GNSS signals are delayed by an equal amount, and there is no code-carrier divergence as in the case of the ionosphere. The magnitude of the tropospheric delay ranges from approximately 2m for signals at the zenith to about 20m for signals at an elevation angle of 10 degrees above the horizon (Brunner and Welsch 1993). The tropospheric delay consists of a “dry component” and a “wet component”. The dry component constitutes about 90% of the total delay and can be accurately determined using empirical models (Hopfield 1969; Saastamoinen 1973), whereas the wet component is more difficult to model due to the variable water vapour content in the troposphere.
Multipath Effect. Multipath errors are caused by reflected signals entering the receiver’s RF “front end” and disturbing the processing of the direct radio signal. This effect is more pronounced for antennas that are placed near reflective surfaces, like metallic objects, ground or water surfaces. Signals with low elevation angle path are susceptible to the greatest multipath disturbance. Instrumental techniques, such as narrow correlator (Dierendonck et al. 1992), Multipath Estimating Delay Locked Loop (MEDLL) (Townsend et al. 1995), and choke ring antennas (Leick 2004) can be implemented to mitigate signal multipath.
2.1.3.3 Receiver-Related Errors
Receiver Clock Error. Similar to the satellite clock error, the receiver clock error is the offset between the receiver clock time and the GNSS reference time system. Since most GNSS receiver clocks use a quartz crystal oscillator with absolute accuracies in the 1ppm to 10ppm range, which is much lower than that of the satellite clocks, their long term stability is insufficient for positioning purposes. Fortunately, receiver clock error is common for all measurements to all satellites if the measurements are made simultaneously. This error can be included in the estimation as a variable along with the receiver coordinates or eliminated by differencing measurements from two satellites tracked by the one user receiver.
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Receiver Noise. This error is mainly contributed by the active (amplifier, mixers) and passive (filters) components in the receiver’s RF front end, digitisation noise in the A/D (analogue-to-digital) converter, and thermal and dynamic stress noise in the receiver tracking loops. The magnitude of these errors is dependent on the technology incorporated within a particular receiver (Farrell and Barth 2001). Modern GNSS receiver technology can maintain a very low noise level, as low as a few millimetres for carrier phase and several decimetres for pseudorange. This noise is normally assumed to be uncorrelated and can be modelled as white Gaussian noise in subsequent GNSS measurement positioning.
2.1.4 Precise GNSS Positioning Methods
The satellite ranging signals continuously broadcast ephemerides information and the receiver measures the (biased) distance from the satellites to the receiver as pseudorange and carrier phase measurements. Therefore, with distances from three satellites to one receiver, the rover position can be theoretically determined by distance resection or trilateration (Wang 2001). In real applications the unknown receiver clock error needs to be estimated as well, which implies that distance measurements to a minimum of four satellites is necessary for 3D positioning. Given the distance information from satellite to receiver, there are two basic positioning methods that can be applied: relative positioning and absolute positioning.
2.1.4.1 Precise Relative Positioning
Relative positioning employs two (or more) receivers simultaneously tracking the same satellites, determining the position of one receiver (the “rover”) relative to the stationary “base” or “reference” receiver, whose coordinates are assumed to be known. These are the so-called “baseline” components, being the vector between the rover receiver and the base receiver. Both the pseudorange and carrier phase measurements can be used for data processing. Typically precise relative positioning is carried out using the method of measurement “double-differencing”, between two satellites and two receivers, as shown in Figure 2.1. The spatially-correlated range errors, such as residual satellite clock, ionospheric and tropospheric delays, vary slowly with time and rover receiver location,
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Chapter 2 Review the Geo-referencing Technologies and Navigation Algorithms thus double-differencing the measurements made simultaneously by two GNSS receivers can mitigate, or even eliminate, such correlated range errors.
Various techniques of double-differencing for precise relative positioning have been developed, and can be classified into two groups: precise static surveying and precise kinematic positioning. In precise static positioning the rover receiver is set up on a stationary point. If the baseline length between the two receivers is less than 10km, after measurement double-differencing only the baseline components and the integer ambiguities (in the case of carrier phase measurements) remain to be estimated. With “resolved” integer ambiguities, millimetre-level static positioning accuracy can be achieved (Leick 2004; Xu 2007; Grewal et al. 2013). Nowadays, there are many permanent static receiver stations around the world to support geodetic and surveying applications. These include the IGS GNSS tracking stations and many commercial, academic or government Continuously Operating Reference Stations (CORS).
The concept of precise kinematic positioning was first introduced by Remondi (1985). As the word implies, kinematic positioning involves one (or more) rover receivers that are in motion. In order to improve the geometry of precise kinematic positioning, multiple CORS can be used. The kinematic double-differenced measurements can be processed in the post-processed mode after both rover and reference station data are brought together. If it is carried out in real-time mode, known as the Real Time Kinematic (RTK) positioning mode, the reference receiver(s) transmit in real-time their data/measurements to the rover receiver via a radio link. Centimetre-level accuracy instantaneous results can be generated after carrier integer ambiguity resolution has been carried out.
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Figure 2.1 GNSS positioning based on measurement double-differencing.
2.1.4.2 Precise Point Positioning (PPP)
Point positioning differs from relative positioning, as this mode of positioning involves only one user/rover receiver. The most commonly used absolute positioning method is GNSS single point positioning (SPP), which uses only the pseudorange measurements to determine the user receiver’s location and hence, the accuracy of SPP is rarely better than at the few metre-level.
Precise Point Positioning (PPP) employs carrier phase measurements, or both pseudorange and carrier phase measurements, to calculate the receiver position with a single receiver (Zumberge et al. 1997). This technique uses high accuracy satellite ephemeris and satellite clock information, provided by organisations such as the IGS, and accurate error model corrections (Kouba 2009). The position solution accuracy can be at the centimetre to decimetre level after some period of convergence time. Since the PPP technique significantly improves operational flexibility and reduces system cost, due to the non-requirement of nearby CORS as in the case of relative or differential positioning, it increases the number of applications using GNSS technology (Aldel- Salam 2005). 22
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2.2 Overview of the Terrestrial Ranging Technology
The use of terrestrial ranging technology can be traced back much earlier than GPS. Before the U.S. DOD launched the first GPS satellites, it tested the system concept and the initial GPS user equipment with ground-based transmitters which transmit GPS-like ranging signals, referred as “pseudolites” (Harrington and Dolloff 1976). From the early 1980’s this technology began to be considered as a complementary for GPS operations (Beser and Parkinson 1982; Klein and Parkinson 1984). “Locata” has been under development as a terrestrial ranging system since 2002. The fundamentals of the Locata technology, and some results of earlier testing, have been comprehensively reported in the literature (Barnes et al. 2003; Choudhury et al. 2009a; Li and Rizos 2010; Montillet et al. 2009). Such studies have verified that this technology can be used for a wide range of positioning applications, including precise indoor positioning (Barnes et al. 2003; Rizos et al. 2010), slow structural displacement monitoring (Choudhury et al. 2009a) and kinematic navigation (Bertsch et al. 2009; Li and Rizos 2010).
2.2.1 Locata Introduction
Locata is a ground-based positioning system which transmits ranging signals at frequencies in the 2.4GHz Industrial, Scientific, and Medical (ISM) radio band. Such ranging signals, from transmitters known as “LocataLites”, can be tracked by a user receiver. A Locata network – or “LocataNet” – consists of a number of time- synchronised LocataLite transceivers located within or around a defined service area (Barnes et al. 2004, Rizos et al. 2010). The “user segment” includes any number of fixed or moving Locata user receivers (or “rovers”) operating within the service area, deriving position and time using signals transmitted by the LocataNet. Figure 2.2 illustrates how Locata provides a positioning solution even in GNSS-challenged areas.
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Figure 2.2 The Locata technology positioning concept (Barnes et al. 2003).
The LocataLite device consists of an integrated Locata transmitter and receiver, currently based on Field Programmable Gate Array (FPGA) technology, as shown in Figure 2.3. A Locata rover contains only the receiver component board (Li and Rizos 2010). Raw measurement data from the receiver can be either recorded on a compact flash card or streamed serially via an RS232 port at rates of up to 25Hz.
Figure 2.3 LocataLite: receiver (left) and transmitter (right).
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It has been reported that the operating range of a LocataNet can be up to 50 kilometres, when transmitting with adequate signal power (Locata Corporation 2014). Locata has some features that distinguish it from both GNSS technology and conventional pseudolites. These include:
Time synchronisation - All LocataLites in a LocataNet are synchronised to a master station in the network, either in a direct link or in a cascaded mode, using a TimeLoc time synchronisation process. TimeLoc maintains phase difference and compensates the clock difference among all transmitting signals in a LocataNet. By doing this, the time difference can be below a few nanoseconds and the frequency stability is less than one part per billion (ppb) (Gauthier et al. 2013). This implies that there is effectively no transmitter clock error.
Licence-free and frequency diversity - The LocataNet broadcasts signals on two frequencies in the licence-free 2.4GHz ISM band. The two S-band frequencies (S1 – 2.41428GHz and S6 – 2.46543GHz) provide frequency diversity to aid multipath mitigation. For each LocataLite transceiver, two spatially separated antennas are used, hence a cluster of four distinct signals are transmitted by each LocataLite, as shown in Figure 2.4.
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Figure 2.4 LocataLite antenna setup with two transmit antennas and one receive antenna
Time reference – The LocataNet can synchronise to any time source, such as GPS (or other GNSS), providing a 1 pulse-per-second (PPS) time reference. Alternatively the LocataNet can operate completely autonomously by using its own time reference generated by the master LocataLite.
Stronger signals - Typical Locata receiver signal strengths range from -60dBm to - 105dBm, which means that Locata signals can penetrate into buildings and dense forests, and provide positioning service in GNSS-denied areas. Vulnerability to signal jamming is also considerably reduced.
TD/CDMA – The Locata signal ultilises a Time Division Multiple Access (TDMA) scheme for transmissions to supplement the Code Division Multiple Access (CDMA) modulation scheme. The LocataNet pseudo-random spreading codes, derived from the GPS C/A-codes, run at ten times the rate of the GPS C/A-code chip rate but with only a 1/10 transmit duty cycle. The added signal orthogonality introduced by assigning different time slots to different transmitters ensures sufficient signal discrimination to overcome the so-called “near-far” problem.
2.2.2 Locata Measurements and Measurement Equations
Similar to GNSS, the range measurements of Locata are of two types: pseudorange and carrier phase. The carrier phase measurements are more precise than pseudorange measurements. The basic Locata carrier phase observation equation between receiver and LocataLite channel i can be written as:
ii i i cp dT dtrop p (2.4)
ii i i i (2.5) c dT dN trop where 26
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pi and i are the pseudorange measurement and carrier phase measurement
between Locata receiver and LocataLite i , respectively; is the wavelength of the Locata carrier phase, depending on the transmitting frequency; c is the velocity of light in vacuum; i is the true or geometric range between Locata receiver to
LocataLite ; dT is the receiver clock error;
i dtrop is the troposphere delay;
N i is the Locata carrier phase ambiguity;
i i p and are residual errors due to multipath, scattering and any other source on pseudorange and carrier phase, respectively.
Note that there is no transmitter clock error in the observation equations because of the tight time synchronisation of the LocataLites. Nor is there an ionospheric delay term.
i The tropospheric delays in dtrop must be calculated by an appropriate tropospheric model (Choudhury et al. 2009b). The Locata ambiguities are typically estimated as floating-point value which can be resolved using either a known-point-initialisation (KPI) (Mervart et al. 2008) or on-the-fly (OTF) resolution technique (Amt 2006; Bertsch et al. 2009; Jiang et al. 2013).
Locata technology also provides Doppler frequency measurements. The Doppler frequency is measured in both the S1 and S6 frequency bands. When scaled by the corresponding wavelength, the range-rate measurement, which reflects the relative velocity between user rover and LocataLite, can be obtained. The measurement equation is:
ii i i (2.6) dTdcp trop p where, p i is the range-rate measurement derived from Doppler measurements;
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i is the relative velocity between the Locata receiver and the LocataLite
i ; Td is the receiver clock drift; c is the velocity of light in vacuum; i dtrop is the troposphere drift error;
i p is the combined error residual.
The generalised linear observation equation for Locata positioning represented by Equation (2.5) can be simplified as a Gauss-Markov model. The optimal estimation of unknown states can be obtained by Least-squares (LS) estimation applying only the measurement model, or by a Kalman filter (KF) using both dynamic and measurement models.
2.3 Overview of Inertial Navigation Technology
Inertial navigation technology has been used in an increasing number of civil applications for the guidance of aircraft, ships and land vehicles, as well as in other applications like robotic control, vibration detection, etc. The principles of this technology are based on the law of classical mechanics, Newton’s laws, namely that every object in a state of uniform motion will remain in that state of motion unless an external force acts on it.
Inertial navigation is a “dead-reckoning” system in that given an initial velocity and position, the following outputs of velocity and position are derived by performing successive mathematical integrations of the acceleration measurements. Typically an inertial measurement unit (IMU) comprises three accelerometers and three gyroscopes mounted in three orthogonal axes. The three orthogonal acceleration measurements have to be resolved in the appropriate navigation reference frame, and the gravity force has to be extracted before the measurements can be used for positioning. The gyroscope provides angular measurements so as to transform the sensed acceleration to another frame.
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The accelerometers and gyroscopes are commonly mounted perpendicular to each other. The IMU measures linear and angular motion in three dimensions without any external reference signals, and output the incremental angles and velocities. An inertial navigation system (INS), which consists of an IMU and a digital navigation computer, estimates a vehicle’s position, velocity, and attitude as a function of time in a specified navigation frame using the outputs of the IMU (Curey et al. 2004).
Conventional inertial navigation systems use stable platform techniques. Although they are still common in high precision applications like submarine navigation, they are expensive and cumbersome. Modern inertial navigation systems are of the strapdown form, with inertial sensors rigidly attached directly to the host vehicle (Ding 2008).
2.3.1 Coordinate Systems
Navigation calculation in an INS involves conversions among several coordinate systems, such as the inertial frame, the Earth frame, the navigation frame, and the body frame (Titterton and Weston 2004):
The inertial frame has its origin at the centre of the Earth and axes which are non- rotating with respect to the fixed stars. Its z-axis coincides with the Earth’s polar axis (which is assumed to be invariant in direction).
The Earth frame has its origin at the centre of the Earth and axes are fixed with respect to the Earth. Its z-axis coincides with the Earth’s polar axis and the x-axis lies along the intersection of the plane of the Greenwich meridian with the Earth’s equatorial plane. The Earth frame rotates, with respect to the inertial frame, about the z-axis of the inertial frame. The Earth frame can be represented in either Cartesian or geodetic form.
The local navigation frame is a local geographic frame which has its origin at the location of the navigation system and axes aligned with the directions of north, east and the local vertical (down). The turn rate of the navigation frame, with respect to the Earth-fixed frame, is governed by the motion with respect to the Earth.
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The body frame is an orthogonal axis set, which is aligned with the roll, pitch and yaw axes of the vehicle on which the navigation system is installed.
In navigation, the linear and angular motion of one coordinate system must be described with respect to another. Most kinematic quantities, such as position, velocity, acceleration, and angular-rate, involve three coordinate frames (Groves 2008):
The frame whose motion is described, known as the object frame ; The frame with which that motion is respect to, known as the reference frame ; The set of axes in which that motion is respected, known as the resolving frame .
The object frame and the reference frame must be different, otherwise there is no motion. The resolving frame may be the object frame, the reference frame, or another frame. The following notation is used for Cartesian position, velocity, acceleration, and angular-rate:
x where the vector x describes a kinematic property of frame with respect to frame , expressed in the frame axes. For attitude, only object frame and reference frame are involved, and there is no resolving frame.
2.3.2 INS Mechanisation
The navigation equations comprise four steps: attitude update, transformation of the specific force resolving axes, velocity update, and position update. In addition, a gravity or gravitation model is needed to transform specific force into acceleration. In essence the attitude is updated by integrating the angular-rate measurements, the velocity is updated by integrating acceleration, and the position is updated by integrating velocity. The form of the inertial navigation equations depends on which coordinate system the navigation solution is expressed in.
The specific force measurements from the accelerometer are actually expressed in the body frame; while angular-rate measurements from the gyroscope are indications of the
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Chapter 2 Review the Geo-referencing Technologies and Navigation Algorithms angular change rates of the body frame axes with respect to the inertial frame. Since most navigation tasks are being carried out in the vicinity of the Earth’s surface, it is customary to express outputs of an INS in the coordinates of the navigation frame. In the navigation frame implementation of the inertial navigation equations, the Earth frame is used as the reference frame, while the navigation frame comprises the resolving axis. Thus, attitude is expressed as the body-to-navigation-frame coordinate
n transformation matrix Cb , and velocity is Earth-referenced in the navigation frame axes
n veb . Position is expressed in the curvilinear form (geodetic latitude L , longitude and geodetic height h ) and is commonly integrated directly from the velocity rather than converted from its Cartesian form. The discussion below is from Groves (2008).
2.3.2.1 Attitude Update
The attitude update step of the navigation frame navigation equations uses the position
n and velocity solutions as well as the angular-rate measurement to update Cb . This is necessary because the orientation of the north, east, and down axes changes as the navigation system moves with respect to the Earth. The time derivative of the coordinate transformation matrix is:
n n b n b n n n (2.7) b b nb CCC b ib ie en Cb
b b where nb is the skew-symmetric matrix of nb , which means the angular rotation rate of the body frame with respect to the navigation frame, coordinated in the body frame;
b b ib is the skew-symmetric matrix of the angular-rate measurement ib from the gyroscope; n and n are the skew-symmetric matrices of the vectors n and n ie en ie en which are the angular-rate vectors of the Earth frame with respect to the inertial frame and the navigation frame with respect to the Earth frame, respectively, both resolved in the navigation frame.
The latter part of Equation (2.7) can be split into three terms. The first term is due to the inertially referenced angular rate measured by the gyroscope. The second term is due to the rotation of the Earth with respect to an inertial frame. The third term, known as the 31
Chapter 2 Review the Geo-referencing Technologies and Navigation Algorithms transport rate, arises from the rotation of the navigation frame axes as the frame centre moves with respect to the Earth. The angular-rate vectors n and n in the navigation ie en frame can be written as:
n T ie ie cos0 ie sin LL (2.8)
T vn vn n tan Lv n eb,N eb,E eb,E en (2.9) n hR m hR m hR
Where is the Earth’s rotation rate, vn and vn are the north and east components ie eb,N eb,E of the velocity of the body frame with respect to the Earth frame, expressed in the navigation frame. R R n and m are the meridian and transverse radius of curvature, respectively, given by:
2 0 1 eR R0 (2.10) Rn ; R 3 m 22 sin1 22 Le sin1 Le
where R0 is the semi-major axis, and e is the major eccentricity of the ellipsoid.
By integrating Equation (2.7) a reasonable approximation of the new transformation matrix can be obtained:
n n b n n n (2.11) b b ICC ib i ie en Cb i where the descriptor “ ” means the current epoch and “ ” means the previous epoch.
i is the time interval between these two epochs.
2.3.2.2 Velocity and Position Update
b The IMU measures specific force fib along the body frame resolving axes. However, for use in the velocity integration step of the navigation equation, it must be resolved 32
Chapter 2 Review the Geo-referencing Technologies and Navigation Algorithms about the same axes as the velocity, in that case, the navigation frame. The resolving axes are transformed simply by applying the coordinate transformation matrix:
n n b (2.12) ib b fCf ib
Then expressing the acceleration in terms of the specific force, gravity, and centrifugal acceleration gives:
n n n n n n (2.13) eb ib b ,hLgfv en 2 ie veb where the acceleration due to the gravity, as the second term, is modelled as a function of latitude and height, and the third term is the Coriolis and transport-rate acceleration, which are much smaller than the specific force and gravity terms. Thus the velocity can be updated by:
n n n n n n n eb eb ib b ,hLgfvv bb en 2 ie veb i n n n n n n (2.14) eb ib b ,hLgvv bb en 2 ie veb i
Finally, the latitude, longitude, and height can be derived from the integration of the updated velocity. Assuming the velocity varies as a linear function of time over the integration interval, a suitable approximation for the position update is:
i n vvhh n 2 eb,D eb,D vn vn i eb,N eb,N LL (2.15) 2 n hLR n hLR
vn vn i eb,E eb,E 2 m cos LhLR m cos LhLR where vn is the vertical component of the velocity of the body frame with respect to eb,D the Earth frame, expressed in the navigation frame.
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2.3.3 INS Error Characteristics
Due to the dead-reckoning nature of an INS, a very small bias error at the raw sensor output will eventually be integrated into a large positioning error. This places very high demands on sensor manufacturing accuracy, which is so high that often additional sensor calibration is necessary in order to satisfy the performance requirements. Different types of sensors would exhibit different error characteristics due to their operating principles and the methods of manufacture. However, there are some common types of errors in an INS, which are bias, scale factor and cross-coupling errors:
The bias is a constant error exhibited by all accelerometers and gyroscopes. It is independent of the underlying specific force and angular-rate. In most cases the bias is the dominant term in the overall error of an inertial sensor. It is sometimes convenient to split the bias into a static component and a dynamic component. The static component, also known as the fixed bias, comprises the run-to-run variation of each instrument bias plus the residual fixed bias remaining after sensor calibration. It is assumed constant for an IMU operating period, but varies from run to run. The dynamic component, also known as the in-run bias variation, varies over periods of the order of a minute, and also incorporates the residual bias remaining after sensor calibration. The dynamic bias is typically about 10 percent of the static bias.
Scale factor error is the error in the ratio between the change in the output signal and the change in the input, which includes bias, non-linearity, and asymmetry. The accelerometer output error due to the scale factor error is proportional to the true specific force along the sensitive axis, while the gyro output error due to the scale factor error is proportional to the true angular-rate about the sensitive axis.
Cross-coupling errors, also known as misalignment errors, in all types of IMU arise from the misalignment of the sensitive axes of the inertial sensors with respect to the orthogonal axes of the body frame as a result of manufacturing flaws. These make each accelerometer sensitive to the specific force along the axis orthogonal to its sensitive axis and each gyro sensitive to the angular rate about the axis orthogonal to
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its sensitive axis. In vibratory sensors, cross-coupling errors can also arise due to the cross-talk between the individual sensors.
Noise is inherent to any measurement and is an additional signal resulting from the sensor itself or any other electronic equipment that interferes with the output signals being measured. It is generally stochastic and thus cannot be removed from the data using deterministic models. Alternatively it can be modelled as a zero-mean white Gaussian noise.
In a practical application often not all of these errors would be estimated or compensated for on-line due to the limited observability of the parameters. Only those with the largest impact, like the bias and scale factor error, would be modelled. The remaining errors such as the cross-coupling errors normally accounted for using factory calibration data.
2.3.4 INS Error Model
Investigation of the error propagation behaviour in the navigation mechanism of an INS is of great importance since with an accurate error propagation model, the impact of each error source can be investigated.
Two approaches used for deriving INS error propagation models are well known in the literature, namely the perturbation approach and the psi-angle approach (Bar-Itzhack and Berman 1988; Benson 1975; Da et al. 1996). In the perturbation error model, the navigation equations are perturbed in the local-level north-pointing Cartesian coordinate system that corresponds to the true geographic location of the INS; while in the psi- angle error model, the navigation equations are perturbed in the local-level north- pointing coordinate system that corresponds to the geographic location calculated by the INS. Both models are equivalent and should yield identical results. The psi-angle error is the most widely used approach and has been implemented in many INS-related integration systems (Da 1997; Lee et al. 1998; Goshen-Meskin and Bar-Itzhack 1992):
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nn nn en rvr
n n nn nnn ie in gfψvωωv (2.16)
n n in εω where r n ,v n are the position, velocity and attitude error vectors, respectively;
n ωin is the angular-rate vector, strongly depends on the quality and geometry of the navigation frame with respect to the inertial frame, resolved in the navigation frame;
f n is the specific force vector;
n is the accelerometer error vector;
g n is the error in the computed gravity vector;
ε n is the gyro drift vector.
2.4 Integration Overview
Every navigation sensor has its own advantages and disadvantages, and will make a unique (and complementary) contribution to an integrated system. An INS is an autonomous sensor that operates independent of external signal sources, and has high output rate for position, velocity and attitude parameters. However its navigation error grows rapidly without correction. While GNSS can achieve high positioning accuracy in an open sky environment, it becomes unavailable when the satellite signals are blocked. In addition the GNSS solution is sensitive to satellite-receiver geometry, especially in the case of the vertical component. Locata’s flexibility means that when integrated with GNSS the system geometry can be enhanced, improving the positioning accuracy as well as enhancing navigation availability. Therefore by integrating GNSS, Locata and INS technologies a continuous and reliable navigation system would result.
2.4.1 Integration Strategy
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Chapter 2 Review the Geo-referencing Technologies and Navigation Algorithms
An integrated GNSS/Locata/INS system must take into account the complementary nature of the component technologies. The estimated states of the navigation filtering typically include corrections to the position, velocity, attitude and IMU sensor errors. The filtering outputs may be fed forward to the INS navigation outputs to generate integrated outputs, or fed back to the INS sensors to calibrate the sensor errors. In the literature, the integration strategies are often described as belonging to one of three categories, namely loosely-coupled, tightly-coupled, and ultra-tightly coupled (Swarna 2006; Wang 2007).
In a loosely-coupled approach, the GNSS and Locata position and velocity solutions are used as the measurement inputs to the integration algorithm, which uses them to estimate the INS errors. The integrated navigation solution is the INS navigation solution, corrected with the system filter estimates of its errors. The two main advantages of loosely-coupled integration are simplicity and redundancy. The architecture is simple in that it can be used with any INS, and any GNSS and Locata user equipment, making it particularly suited for retrofit applications. In a loosely- coupled architecture, the standalone GNSS and Locata navigation solutions are usually available in addition to the integrated solution. Where open-loop INS correction is implemented, there is also an independent INS solution. This enables basic parallel solution integrity monitoring. The main problem of this approach is that it requires at least four GNSS signals to ensure a navigation solution, as does Locata.
The tightly-coupled approach is more complex. Raw pseudorange, carrier phase, and range-rate measurements from GNSS and Locata are input as measurements to the estimation filter, which uses them to estimate the errors in the INS, GNSS and Locata. As with a loosely-coupled architecture, the corrected inertial navigation solution forms the integrated navigation solution. The benefits of the tightly-coupled architecture is that the system does not need a full GNSS or Locata solution to aid the INS. Measurement data is still input even if only one GNSS satellite and one LocataLite tracked. However, the GNSS, Locata and INS are no longer operated as independent systems. Instead the navigation solution would only be generated at the central data fusion filter, and there is no inherent standalone GNSS or Locata solution. Moreover, since the central filter needs to handle raw pseudorange, carrier phase and range-rate
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Chapter 2 Review the Geo-referencing Technologies and Navigation Algorithms measurement processing and INS navigation computation, the algorithms are much more sophisticated.
The ultra-tightly coupled approach, also referred to as “deep-coupled”, is at an even lower level (refers to early stage of signal acquisition and processing). System dynamics sensed by the INS are fed into GNSS or Locata signal tracking loops to enhance their tracking performance. Its main advantages are robustness and anti-jamming due to the reduced tracking bandwidth (Swarna 2006).
2.4.2 Integration Data Filtering
In an integration system, the central component is an error filtering mechanism which provides estimates of the INS errors based on a comparison of the measurement differences. The most commonly used estimation filtering is based on the KF (Hwang et al. 2005).
The mathematical models of the KF include the system dynamic model and measurement model. The mathematic models in a linear discrete form are given as:
ttGtxtFtx (2.17)
ttxkHtz (2.18) where tx is the estimated state vector at time t ;
tF is the system dynamic matrix at time t ;
tG is the system noise distribution matrix at time t ;
tz is the observation vector at time ;
tH is the observation matrix at time ;
t is the system process noise vector at time ;
t is the measurement noise vector at time .
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t and t are zero-mean white sequences uncorrelated with each other with the mean and covariance:
tEtE 0
T ttE 21 0 (2.19) T 21 tttQttE 122
T 21 tttRttE 122 where E denotes the expectation function;
tQ is the covariance matrix of the system process noise;
tR is the covariance matrix of the observation noise.
The discrete KF mathematical models are:
1 kωkxkkx (2.20)
kkxkHkz (2.21) where kx and kx 1 are the state vector at epochs tk and tk1 , respectively;
k is the state transition matrix from tk1 to tk ;
kω is the process driving noise at epoch tk with covariance kQ ; kz is the measurement vector at epoch ;
kH is the design matrix relating the measurements to the state parameters;
k is the measurement noise vector at epoch with the covariance kR .
The transition matrix k can be obtained from the continuous time dynamic matrix tF :
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tF 2 tF tFIek tFI (2.22) !2 where I is the identify matrix, and t is the transition time interval of the discrete KF.
The process noise covariance matrix kQ represents the uncertainty in the assumed process model and can be obtained from the integral of the continuous time spectral density matrix tQ :
tk tQ (2.23) TT dkGQGkkQ tk 1 t
The KF algorithm is composed of time and measurement updates. The prediction of the state kx , and its covariance matrix kP , are obtained from the time-updating step:
ˆ kxkkx 1 (2.24)
ˆ 1 T kQkkPkkP (2.25) where ˆkx is the KF estimated state vector; kx is the predicted state vector;
ˆkP is the estimated state covariance matrix; kP is the estimated state covariance matrix.
When the measurements are available the state vector is updated as:
1 T T kRkHkPkHkHkPkK (2.26)
ˆ kPkHkKIkP (2.27)
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Chapter 2 Review the Geo-referencing Technologies and Navigation Algorithms
ˆ kxkHkzkKkxkx (2.28)
where kK is the Kalman gain, which defines the updating weight between new measurements and predictions from the system dynamic model.
The linear KF cannot be used when either the state dynamic or measurement model contains nonlinearities. Methods that choose to ignore old data due to cumulative errors, or that decrease the filter’s confidence in the adequacy of the filter model have been used to address the problem of nonlinearities. A better way to deal with nonlinearities is through a linearisaiton of the measurement or dynamic model, the so-called linearised estimation techniques. A linearised KF consists of a first order Taylor series approximation to nonlinear models, linearising about a nominal trajectory in state space that does not depend on the measurement data. The Extended Kalman filter (EKF) differs from the linearised KF in that the nonlinear system model is linearised about a trajectory that is continually updated with the state estimates generated from the KF measurement updates. This enables an EKF to handle larger nonlinearities more adequately (Maybeck 1994).
For a generic multivariable nonlinear discrete system:
,1 kkxfkx (2.29)
, kkxhkz (2.30)
Linearisation of the system models can be expressed as:
f (2.31) k x ˆkxx 1
h (2.32) kH x ˆkxx 1
where f and h denote arbitrary nonlinear functions. 41
Chapter 2 Review the Geo-referencing Technologies and Navigation Algorithms
After linearisation, the time update and measurement update of the EKF are the same as for the linear KF. The EKF is currently widely adopted in the implementation of integration systems in order to handle the nonlinearity of the INS error models.
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CHAPTER 3 LOCATA POSITIONING AND LOCATA/INS INTEGRATION FOR PRECISE MARITIME APPLICATION
3.1 Introduction
World economic output and international trade has kept growing over the last few decades and will likely further increase over the coming decades. Over 90% of global trade is carried by sea. As a consequence ports and coastal area are busier and more crowded than ever before. Furthermore certain applications in port areas (for example automated docking) or in constricted waterways, have very stringent positioning and navigation performance requirements. The Global Navigation Satellite System (GNSS) has very good positioning and navigation performance in open sky environments, hence mariners have access to a more reliable and more accurate positioning capability than in the past. However, it could be argued that high accuracy maritime positioning applications are too reliant on GNSS. GNSS cannot meet all emerging performance requirements of robustness, integrity and availability for critical near-shore and in- harbour applications due to vulnerability to signal jamming, as well as some constraints on positioning geometry if the sky view is blocked. Common to all current requirements and future plans is the need to ensure high positioning accuracy with reduced dependence on GNSS. This chapter describes using “Locata” technology to provide accurate positioning with reduced reliance on GNSS.
Centimetre-level accuracy is possible when Locata carrier phase measurements are used, which requires solving for the carrier phase ambiguity terms in a similar manner as is done in GNSS. In the system’s current design this is done through a “known point initialisation” (KPI) on a precisely surveyed point. However, in practical kinematic applications it would be more convenient to resolve the ambiguities “on-the-fly” (OTF). Amt (2006) and Bertsch et al. (2009) described an OTF ambiguity resolution method based on non-linear batch Least Squares estimation. However this method needs observations of multiple previous epochs to maintain system observability, which is inconvenient when some of the ambiguities need to be recomputed due to their
43 Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application changing signal status. This chapter describes a method based on geometry change. The ambiguities are able to be resolved using an Extended Kalman filter (EKF) on an epoch- by-epoch basis. An introduction is given in section 3.2.
The inertial navigation system (INS) is now standard equipment for navigation systems used by aircraft, ships, missiles and spacecraft (Moore et al. 2008), as it is entirely autonomous. However the INS sensor drifts can result in significant misalignments between the instrument frame and an earth-referenced frame, causing navigator errors to grow with time. Currently most INS applications use the GNSS position to correct these INS errors. In this chapter a method based on Locata position and velocity to control the growth of such errors is presented. The integrated system is described in section 3.3.
This chapter investigates a Locata/INS navigation system, with the emphasis on its potential for use in port environments. Locata carrier phase measurements are processed and combined with INS measurements to implement a loosely-coupled integration system. The trial description and result analysis are presented in section 3.4.
3.2 Locata On-The-Fly Positioning Method
Locata measurements and measurement equations have been discussed in section 2.2.2. To achieve precise positioning, Locata carrier phase measurements are used. The carrier phase measurement function is given in Equation (2.5). The receiver clock error may be estimated as an unknown parameter, or eliminated using measurement differencing. To eliminate the receiver clock the carrier phase measurements of the same frequency are single-differenced (SD). When j is chosen as the reference signal, and i is another signal of the same frequency, the SD ij is:
ij ji ij i ij )( trop Nd (3.1)
Ambiguities can be resolved using either KPI or OTF resolution techniques. KPI is used for LocataLite channel i at epoch k using the following set of equations:
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
ij ijij i N dtrop (3.2)
To calculate precise ij , a survey of the initial position of the Locata rover is required.
Total station or a survey-grade GNSS can be used for obtaining the accurate initial coordinates (Choudhury 2011). Once the float-valued ambiguities are estimated with a certain level of accuracy, they can be treated as “fixed” known parameters in Equation (3.1). Note that using KPI method, most of the unmodelled systematic errors and/or biases (ie. ) are absorbed, which is an advantage as it reduces the impact of these errors on coordinate solutions.
OTF ambiguity resolution is dependent on transmitter-receiver geometry change. Since LocataLites are fixed on the ground, the OTF method can be realised “kinematically”. For a Locata system, the kinematic mode of the rover receiver provides the spatial diversity in the measurements, which makes the Locata OTF algorithm feasible. The proposed method achieves Locata OTF resolution via an EKF using the SD carrier phase and tide height measurements of the current epoch. The SD filter estimates position, velocity, acceleration, and float-valued carrier phase ambiguity estimates for the rover. The EKF first makes a prediction based on the dynamics of the vehicle, and later corrects this prediction using measurements.
3.2.1 Dynamic Model
In the proposed system, since the estimated state consists of nine parameters (three for position, three for velocity, and three for acceleration) and differenced carrier phase ambiguities, the number of measurements at one epoch is less than the number of estimated states. The performance of the EKF is therefore heavily dependent on the dynamic model. Typically the acceleration is modelled as a white noise process – white noise process is “isolated” in time since its value at one time is uncorrelated with that at any other time. However, the acceleration of the host vehicle is dominated by the thrust, which has a strong temporal correlation. In such a case it is appropriate to model the acceleration as a first-order Gauss Markov (GM) process rather than as a white noise process. A GM process is “local” in time as its value at one time depends on values at
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application other time instants only through its nearest neighbours (Li and Jilkov 2010). The acceleration model is given by:
/1 aa a (3.3)
where is the correlation-time constant; and a is zero-mean white noise (Li and Jilkov 2010). The position and velocity states do not include any direct driving noise and their determination relies entirely on other states and measurements.
Because the SD carrier phase ambiguity states are time-invariant, they are modelled as a random walk process:
(3.4) N N
The system state can be represented as:
T 1 j NNrrrtx 2 j Ν nj (3.5) where r , r and r represent the platform position, velocity and acceleration (in three dimensions), respectively.
The dynamic model is represented as:
tωtxtFtx (3.6)
0 I 3333 33 00 3n 00 3333 I 33 03n where tF 1 , 00 I 0 3333 τ 333 n nn 33 n3 0000 nn
T tω 00 3131 aaa N1 j ωωωωω N 2 j ωN nj
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
3.2.2 Measurement Model
The measurement model of Locata is non-linear, and the EKF is therefore used to linearise the (non-linear) function around the current predicted estimates. The measurement model of the Locata filter is:
ttxtHtz (3.7)
where tz is the measurement vector of the EKF, which is formed by SD carrier phase measurements and tide height measurements:
1 j 2 j nj T (3.8) tz htide
In the test, the LocataNet was established in an almost planar configuration (i.e. little height difference between LocataLites), and for that reason the height of the rover antenna relative to the Mean Sea Level (MSL) datum needed to be constrained in order to ensure an accurate 3D navigation solution. To preserve the independence of the Locata navigation solution from GNSS, vertical information from tide gauge records h was provided to overcome the influence of poor vertical geometry. tide
tH is the computed Jacobian matrix, which is evaluated with current predicted states;
R and t ~N 0,R is the measurement noise. The R matrix is R 2 . Since σ htide SD carrier phase measurements are correlated with each other, the covariance is 112 2 σ 121 therefore assumed to be half of the variance, which is R , where 2 1 2111
2 2 and are the noise variance of the tide height and SD carrier phase htide measurements, respectively.
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
3.2.3 Calculation of Approximate Initial State
In principle the initial estimate of the state does not affect the convergence of the system filter. However, the proposed method has a large number of parameters to be estimated and it is difficult to derive a suitable estimate error without any a priori information. A poor initial state could lead to a long convergence period, therefore in the proposed system Locata pseudorange measurements are used to estimate the initial position via a conventional Least Squares method (Jiang et al. 2012). The initial estimated state has metre-level accuracy, which is sufficient for the initialisation of the Locata OTF filtering.
3.3 Locata/INS Integration
In this proposed configuration, the Locata and INS systems are integrated in a loosely- coupled manner. The computed Locata position and velocity (PV) solution derived from the Locata carrier phase is used to correct the INS solution within the integration filter. In addition to reducing PV errors, the PV updates are also used to update the attitude errors, the sensor errors and lever arm between the Locata antenna and inertial measurement unit (IMU) reference point. The estimated sensor errors and lever arm are fed back to the INS, to enable a closed-loop update correction.
The integration filter has 18 states, including position, velocity, angular errors, as well as sensor errors and lever arm errors. The INS errors are described in a navigation frame (Bar-Itzhack 1977). The dynamic model includes the mechanisation of the INS error states of position, velocity and attitude using the psi-angle error approach, augmented with the error states of IMU sensor biases and lever arm corrections. The measurement model, on the other hand, is a linear relationship between Locata PV solution and the error states.
3.3.1 INS Error Dynamic Model
To implement the integration system, the INS error model should be defined. Many INS error models have been described in the literature (see, e.g., Arshal 1987; Goshen- 48
Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Meskin and Bar-Itzhack 1992; Lee et al. 1998). This research utilises the psi-angle error model (Goshen-Meskin and Bar-Itzhack 1992), see Equation (2.16). Therefore the estimated state vector consists of 21 navigation error states, which could be written in three sub-vectors: x , x and x represent the sub-vectors of motion components, rv IMU errors and level arm components, respectively:
xxxtx ηεψrv (3.9)
Specifically:
xrv vvvrrr DENDENDEN
x zyxzyx (3.10)
x zyx where the subscripts N, E, D denote the north, east, and down axis in the navigation frame, respectively; the subscripts x, y, z represent the direction of the roll, pitch, and yaw axis in the body frame, respectively; and the last three symbols represent the unknown lever arm components. The accelerometer and gyroscope errors are modelled as random biases.
The system dynamic model is:
(3.11) xrv 11 FF 12 0 39 xrv 0 19 x 000 366696 x x 000 336393 x 0 13
where is the noise vectors of accelerometer and gyroscope errors, which are modelled as random biases; the sub-matrices F11 and F12 of the system dynamic matrix F are calculated based on the INS error model, and given as:
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
n FFF Cb 0 33 ψvψrψψ F11 0 FF rvrr , F12 00 3333 n (3.12) vψ FFF vvvr 0 33 Cb where
n FFF ψvψrψψ C 0 b 33 F11 0 FF rvrr , F12 00 3333 n vψ FFF vvvr 0 33 Cb
tan Lv v E N 0 ie sin L n hR m hR vE vE Fψψ ie sin L 0 ie cos L , n hR n hR v v N E ie cos L 0 m hR n hR
vE 1 ie sin L 0 0 0 2 n hR n hR vN 1 Fψr 0 0 , Fψv 00 , hR 2 hR m m v tan Lv tan L E 2 E 0 0 ie cos L L 0sec 2 n hR n hR n hR
vN 1 00 2 00 hR hR m m E sectan LLv E sec Lv 1 Frr 0 , F 0 0 , hR hR 2 rv cos LhR n n n 000 0 0 1
0 ff yz Fvψ f z 0 f x , ff xy 0
sec2 Lv 2 tan Lv vv v cos2 L E 0 E DN E ie 2 2 n hR n hR m hR 2 EN sec Lvv N tan vLv D Fvr ie N cos2 D sin LvLv 0 vE , 2 m hR m hR 2 2 vN vE ie E sin2 Lv 0 2 2 m hR n hR
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
v tan Lv v D E N ie sin2 L m hR n hR m hR E tan Lv N tan vLv D vE Fvv ie sin2 L ie cos2 L , n hR m hR m hR v E 0 ie cos2 L 0 n hR in which f x , f y and f z are the accelerometer-sensed specific force in the three directions.
3.3.2 Integration Measurement Model
Due to the lever arm uncertainty, the relationship between the position of the Locata antenna and the IMU reference point is represented as:
n n bn (3.13) Locata INS b ηCrr
n n n n bn bn b (3.14) Locata INS ie en b b ωηCηCωωvv ib
Using the model above, the computed PV at the Locata antenna is given by:
n n bn bn ˆˆˆ bn (3.15) Locata ˆˆ INS b 0 b 0 CψηCηCrr b δη
n n ˆ n bb ˆ n bb ˆ n bb (3.16) Locata ˆˆ INS b ib 0 b ωCηωCvv ib δη b ib ηωC 0 where ηb is the initial estimate of the lever arm. 0
The measurement model therefore can be written as:
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
n n bn Locata δrδr INS b ηC 0 n n n bb Locata δvδv INS b ib ηωC 0 (3.17) ˆ bn IηC 00 Cˆ n b 0 633333 b ttx ˆ n bb ˆ n b b ib ηωC 0 0 I 0 633333 b ωC ib
The covariance of the measurement noise in the integration system is defined by the general accuracy level of the computed Locata stand-alone solution, which is described as:
0 05 2 0 05 2 0 05 2 2 2 ...... diagR 101010 2 (3.18) where the first three terms are the covariance of position in units of m2 , and the last three are the covariance of the velocity in units of / sm 2 .
3.4 Experiment and Result Analysis
The test was conducted on October 2012 on Sydney Harbour, on the fringes of Sydney’s CBD where the multipath effect is quite severe. The LocataNet comprised eight LocataLites, six of them installed along the shore, and the remaining two were located further away, with one on the Harbour Bridge (LL7) and the other at Kirribilli (LL8). LocataNet was time-synchronised in a cascaded mode with the Master LocataLite (LL3) configured for synchronisation with respect to GPS time. The rover trajectory and the location of the LocataLites are shown in Figure 3.1.
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Figure 3.1 LocataNet configuration and rover trajectory for Sydney Harbour test
The rover setup was on a survey vessel provided by the Sydney Ports Authority. A Locata rover unit and a dual-frequency Leica GNSS receiver were installed, with antenna locations as shown in Figure 3.2. A survey-grade Applanix POS-MV INS was also fixed on the vessel. The performance parameters of the inertial sensors are listed in Table 3.1. GNSS integer-fixed differential carrier phase positioning solutions computed by the Leica Geo Office (LGO) software were used to provide the position reference, and the velocity reference was computed using MV-POSView, which has a stated horizontal velocity accuracy of better than 0.03m/s (Applanix Corporation 2009). In order to conduct performance evaluation all the raw data from the Locata rover and the INS were recorded and post-processed. Although the results presented in this research were obtained in the post-processed mode, the proposed method can operate in real-time. Locata data output rate and inertial measurement rate were set to 10Hz and 200Hz, respectively, and are synchronised with GPS time. Tide height data were recorded by the Fort Denison Tide Gauge, updated every 6 minutes (Watson and Lord 2008).
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Table 3.1 Specifications of the Applanix POS-MV (Applanix Corporation 2009)
Gyroscopes Accelerometers Bias 1°/h ~ 5°/h 50 ~ 500 μg Scale factor - 0.01% ~ 0.02% Random noise 0.07°/sqrt(h) -
Figure 3.2 Test vessel and experimental setup
The trajectory consists of continuous circular motion for approximately 15 minutes. The signal availabilities and dilution of precision (DOP) plots are shown in Figure 3.3. During the test, 4-8 LocataLites with 11-32 signals were available to provide continuous navigation. As the vessel was moving in three circles, as shown in Figure 3.1, the DOP and signal availability exhibit a similar pattern. In order to analyse the geometry change, periods with poor horizontal geometry (plotted in bold) are shown in Figure 3.4. The poor geometry occurred during the time periods 210s – 245s, 480s – 534s, and 797s- 828s. It can be seen that those periods were when the vessel moved furthest away from the Master LocataLite.
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Figure 3.3 Signal availabilities and DOP values for the Sydney Harbour test
Figure 3.4 Periods of poor geometry for the Sydney Harbour tests
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Figure 3.5 and Figure 3.6 show the 3D position and velocity differences computed by the tide-augmented Locata OTF method against the reference trajectory. One can see that the errors in the horizontal directions are less than 8 centimetres after filter converges, and horizontal velocity solution errors are less than 0.5m/s. From the horizontal difference plot in Figure 3.5 it can be seen that the magnitude of the error trend is 0.15m. As Locata’s carrier wavelength is approximately 0.12m, one could interpret that the difference is as due to Locata’s float-value ambiguity uncertainty.
Figure 3.5 Position differences between Locata and reference solutions
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Figure 3.6 Velocity differences between Locata and reference solutions
In order to demonstrate the effectiveness of the proposed OTF algorithm, a position comparison with the Locata KPI algorithm is shown in Table 3.2 and Figure 3.7, where the result computed by the OTF algorithm is plotted in blue and the solution computed by the KPI method is indicated in red. The Distance Root Mean Square (DRMS) value of the horizontal error, RMS value, Mean value and Standard Deviation (STD) value of the two algorithms are listed in Table 3.2. Since tide height constraints are applied to both methods, the vertical solutions of the two are very similar, and hence the horizontal numerical comparison is highlighted in Table 3.2. The DRMS computed by the KPI and OTF methods are 0.07m and 0.06m, respectively. OTF shows a 14.3% improvement compared with KPI. Similarly, the RMS values of OTF in the north and east directions are 0.04m, which show improvement from those of the KPI result (0.05m in north and east). These statistical results show that by using OTF method, the position accuracy has improvement of 20% in the north and east directions, respectively.
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Table 3.2 Comparison of Locata stand-alone OTF and KPI solutions
RMS (m) Mean (m) STD (m) DRMS (m) North East North East North East Locata KPI 0.07 0.05 0.05 0.02 -0.02 0.05 0.05 Locata OTF 0.06 0.04 0.04 -0.02 -0.02 0.04 0.03
Figure 3.7 Comparison of Locata stand-alone OTF and KPI solutions
Figure 3.8 shows the difference between INS solutions without external correction and the reference trajectory. Even under conditions of good alignment/initialisation, the navigation solutions (velocity, position and attitude) all have large accumulated errors. In contrast, the performance of the Locata OTF/INS integration system is illustrated in Figure 3.9, Figure 3.10, and Table 3.3. Figure 3.9 and Figure 3.10 show the differences between the integrated position and velocity with the reference, respectively. Comparing Figure 3.9 and Figure 3.10 with Figure 3.8, the position and velocity of integration system are better than those of the INS standalone system. In order to analyse the performance of the integration system and Locata standalone system, position and velocity solution comparisons are given in Table 3.3.
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Figure 3.8 INS stand-alone solutions
Figure 3.9 Position difference between Locata/INS and reference solution
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Figure 3.10 Velocity difference between Locata/INS and reference solution
The lever arm estimates for starboard, bow and down directions (in the body system) are plotted in Figure 3.11, from which one can see that the solution converges after approximately 50 seconds. The numerical results in Table 3.3 exclude the initial 50 seconds of convergence period.
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
Figure 3.11 Lever arm estimation
Similar to the comparison in Table 3.2, the DRMS horizontal error, RMS value, mean value and STD value of the position and velocity differences of the two systems are listed in Table 3.3. The RMS value of the integrated position difference in north, east and vertical directions are 0.04m, 0.04m and 0.06m. Compared with that computed by Locata standalone OTF method (0.04m, 0.04m, and 0.08m respectively), it can be concluded the horizontal positions of the two systems have the similar accuracy, however, the integrated position has an improvement of 25% on the vertical direction. Similarly, a velocity analysis of the two systems is also conducted. The integrated velocity difference has the RMS of 0.01m/s in north, east and vertical directions, while that of Locata standalone OTF system is 0.20m/s, 0.15m/s and 0.09m/s in the three directions. It is interesting to note that the improvement in the integrated velocity, which is 95%, 93.3% and 88.9% in north, east and vertical, is much larger than the position component. There are two reasons caused this situation. The first one is that Locata position is in centimetre level, but the velocity cannot achieve the corresponding centimetre-per-second level. According to Figure 3.6, the accuracy of Locata standalone velocity accuracy is decimetre-per-second level. In that way, if position and velocity estimation during integration process is equivalent, the velocity component should have 61
Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application a more obvious improvement. The second reason is that in integration filtering, the velocity component has a better estimation than the position component, because the velocity states have a larger observability than the position states (Rhee et al. 2004). From the INS navigation mechanisation, the position computation requires one more integration over the angular-rate measurement than velocity does. Therefore although both position and velocity are direct measurements in the integration system filter, the velocity states have the better estimation.
Table 3.3 Comparison of Locata OTF stand-alone and Locata/INS integration solutions Position (m) Velocity (m/s) Locata OTF Locata/ INS Locata OTF Locata/ INS DRMS 0.10 0.08 0.27 0.02 North 0.04 0.04 0.20 0.01 RMS East 0.04 0.04 0.15 0.01 Vertical 0.08 0.06 0.09 0.01 North -0.02 -0.02 0.00 0.00 Mean East -0.02 -0.02 0.00 0.00 Vertical -0.06 0.06 0.00 0.00 North 0.04 0.04 0.20 0.01 STD East 0.03 0.03 0.15 0.01 Vertical 0.05 0.03 0.09 0.01
3.5 Summary
A Locata OTF algorithm is proposed for high accuracy position and velocity estimation, which can be implemented completely independent of GNSS. The trial data solution demonstrates the method, and indicates the improvement obtained compared with a conventional KPI algorithm. The trial was conducted on Sydney Harbour, with the aiding of a tide height model. The Locata standalone solution could achieve centimetre- level accuracy.
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Chapter 3 Locata Positioning and Locata/INS Integration for Precise Maritime Application
In addition, from the results of the trial, the integration of Locata and INS could optimise the solutions of both navigation approaches. Locata, by replacing GNSS, can effectively correct INS sensor errors using its position and velocity output as the measurements. The unknown lever arm between the Locata antenna and the INS reference point can also be estimated accurately. Compared with the position component, the improvement in estimated velocity component is more significant, from decimetre-per-second level to centimetre-per-second level. Such solutions validate the effectiveness of Locata OTF/INS integration for high accuracy maritime positioning applications.
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CHAPTER 4 LOCATA AUGMENTED PRECISE POINT POSITIONING FOR KINEMATIC APPLICATIONS
4.1 Introduction
Global Navigation Satellite System (GNSS) positioning accuracy is affected by measurement errors, especially for the kinematic positioning scenarios. Network-based real-time kinematic (N-RTK) positioning with fixed ambiguity resolution is a widely used technique for RTK carrier phase-based GNSS positioning (Fotopoulos and Cannon 2001; Landau et al. 2007). Many systematic measurement errors are mitigated by double-differencing (DD) the raw GNSS observations made at user “rover” receivers (whose coordinates are to be determined) and at a reference station receiver set up at a point whose coordinate is known. N-RTK, and RTK in general, achieve centimetre- level positioning accuracy in real-time and even when the rover is moving in an erratic and unpredictable fashion. However, the requirements of such RTK approaches are quite stringent. In the case of single reference station RTK, simultaneous GNSS satellite observations by both the rover and the reference station are needed, and the reference receiver observations must be transmitted to the user receiver under certain operational constraints in order to ensure successful carrier phase DD ambiguity resolution. One of these constraints is that inter-receiver distances are less than 30km in mid-latitude regions of the world to support single-reference receiver RTK operations, but may be much less than 20km if ionospheric conditions are so severe that spatial-correlation is significantly reduced. To address such stringent requirements, a network of reference receivers at 50km – 70km spacing is typically needed to ensure reliable N-RTK service. The substantial resources for the physical construction and service maintenance of N- RTK or RTK infrastructure means it is often difficult to provide a centimetre-level accuracy positioning service based on differential GNSS techniques across large regions (Ge et al. 2012).
An alternative to the differential positioning techniques is the Precise Point Positioning (PPP) approach, which is based on the processing of observations from a single GNSS user receiver, and employing precise satellite orbit and clock correction information
64 Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application instead of the ephemeris and clock data encoded within the broadcast navigation message. For PPP there is no longer a need to use corrections and/or measurements from GNSS reference stations. Moreover PPP has a lower computational burden in comparison with the N-RTK approach (Zumberge et al. 1997). PPP-GNSS can be used for orbit determination (Bisnath and Langley 2001), crustal deformation measurement (Hammond and Thatcher 2005; Calais et al. 2006), and precise navigation and positioning (Abdel-Salam 2005; Du and Gao 2012).
Unlike the GNSS differential techniques, the measurement error in PPP can only be reduced by accurate bias modelling or parameter estimation. Important modifications include improved satellite orbit and satellite clock error models, atmospheric delay model/estimation, and application of station effects such as phase centre variation corrections and site displacement due to earth and ocean loading tides. As with differential techniques, in order to achieve centimetre- to decimetre-level positioning accuracy, carrier phase measurements must be used. Hence there is the challenge of ambiguity resolution. Due to the existence of uncalibrated phase delays (UPDs), the ambiguities are no longer integer values. Over the last five or so years many researchers have been investigating the issue of resolving the ambiguities for PPP (e.g. Ge et al. 2008; Collins 2008; Geng et al. 2010). However, the computation process is still complex and it is often difficult to assure a high reliable ambiguity fixing rate. A commonly used approach estimates the ambiguities as floating-point values and does not try to resolve the ambiguities to their correct integer values (Abdel-Salam 2005). This approach is easier to implement and is more reliable, however, such methods typically require long “convergence” periods, especially for kinematic positioning scenarios. Furthermore the resultant accuracy is not as high as in the case of N-RTK solutions, even after a lengthy convergence period.
As discussed in Chapter 2, “Locata” technology has good interoperability with other GNSS constellations when the transmitted signals are synchronised with GNSS signals (Locata Corporation 2014). Furthermore Locata has several unique characteristics vis-à- vis a GNSS system. Firstly, since Locata is a ground-based system and GNSS is space- based, the integration of Locata and GNSS can improve the local geometry, which further improves the system performance. Secondly, Locata is a local navigation system
65
Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application and hence the transmitter-receiver geometry change is faster than in the case of GNSS if the Locata user receiver is in motion. As both the Locata and PPP-GNSS estimated float ambiguities converge to their correct values with geometry change (Shen 2002), the addition of Locata measurements could help shorten the convergence period. The objective of this chapter is to present results from an investigation of a Locata augmented PPP-GNSS solution strategy. In the proposed system the Locata signals are synchronised with GPS time, and the Locata and GNSS carrier phase measurements are processed in a tightly-coupled mode, with the corresponding ambiguities resolved on an epoch-by-epoch basis.
This chapter is organised as follows. A modified PPP-GNSS system, and the related error models are first described in section 4.2. In section 4.3 the detailed system filter settings are discussed. Finally, the evaluated field test is introduced, and the data analysis and results are presented in section 4.4. The chapter summary is given in section 4.5.
4.2 GNSS Precise Point Positioning Technology
GNSS Precise Point Positioning is a positioning methodology that uses “undifferenced” GNSS phase and code measurements from a single- or dual-frequency receiver, and precise satellite orbit and clock information generated by service providers such as the International GNSS Service (IGS – http://igs.org). The use of carrier phase observations as the primary observable can deliver centimetre- to decimetre-level accuracy of point positioning (Kouba 2009).
4.2.1 Error Sources and Mitigation Techniques in PPP
GNSS positioning accuracy is affected by measurement errors. Unlike the GNSS differential techniques, the spatially correlated measurement errors in PPP cannot be eliminated or mitigated by differencing observations between receivers. Thus the errors in PPP must be reduced by accurate bias modelling or parameter estimation. Important modifications include improved satellite orbit and satellite clock error models,
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Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application atmospheric delay model/estimation, and application of station effects such as phase centre variation corrections, and site displacement due to earth and ocean loading tides.
4.2.1.1 Orbit and Clock Error
GNSS algorithms usually employ the broadcast ephemeris, which is of comparatively low accuracy (of the order of a few metres). As an alternative, and where the user does not want to employ the differential positioning mode, more accurate orbit and satellite clock information can be obtained from the IGS – available in various forms, from the Final, Rapid to the Ultra-Rapid, which became officially available on November 5, 2000 (http://www.igs.org/components/prods.html). The various precise IGS satellite orbit and clock products are listed in Table 4.1. Since April 1, 2013 the Real-Time Service has also been available.
Table 4.1 IGS satellite orbit and clock products
Products Parameters Accuracy Latency Orbits ~5 cm Ultra rapid (Predicted half) Real-time Sat. Clocks ~3 ns RMS Orbits ~3 cm Ultra rapid (Observed half) 3~9 hours Sat. Clocks ~1.5 ns RMS Orbits ~2.5 cm Rapid 17~41 hours Sat. Clocks ~75 ps RMS Orbits ~2.5 cm Final 12~18 days Sat. Clocks ~75 ps RMS
In addition to precise satellite orbit and clock information, satellite antenna offset/variations, site displacement corrections, tropospheric and ionospheric delay models need to be considered for a high accuracy solution.
4.2.1.2 Atmosphere Errors
Satellite signals travelling through the earth’s atmosphere experience both distance delay and bending effects. Among all the atmosphere layers, the lower troposphere and 67
Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application upper ionosphere are particularly important for PPP-GNSS solutions. The ionospheric error is the dominant source of error in GNSS positioning, which depends on the electron density of the ionosphere along the signal path. Thus, many studies focus on ionospheric modelling in order to improve accuracy in the case of single-frequency receivers (Gao et al. 2004). However, since the ionosphere is dispersive and the ionospheric delay is frequency dependent, PPP-GNSS users of dual-frequency receivers can employ an ionosphere-free measurement combination to eliminate the first-order ionospheric signal delay, which accounts for more than 99% of that error. Taking the GPS system as an example, the ionosphere-free model equation is:
2 2 (4.1) f1 f2 IF 2 2 L1 2 2 L2 1 ff 2 1 ff 2
where f1 and f2 are the frequencies of the L1 and L2 carrier waves, respectively.
In the case of GNSS positioning, the total tropospheric range delay resulting from propagation of the satellite signals through the neutral atmosphere is expressed as a function of the hydrostatic (dry) and wet zenith path delay with their individual mapping function:
trop hrdro hydro wet MdMdd wet (4.2) where d and d are the hydrostatic and wet zenith path delay, respectively; and hydro wet
M * denotes the related mapping function.
Range delays resulting from the hydrostatic component of the troposphere, which is the major part of the tropospheric error, can be computed using, say, the Saastamionen model (IERS 2010). Surface pressure, height above mean sea level and the latitude of the user location are used as input to the model.
The troposphere zenith hydrostatic delay can be calculated with up to 0.2mm accuracy if precise meteorological data are used (Shi 2012). However, the real measured
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Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application meteorological data are not always available, and one way to overcome this limitation is by adopting an empirical global pressure and temperature model (Boehm et al. 2007), currently recommended as the IGS and International Earth Rotation and Reference Systems Service (IERS) standard. Sample code is available at: ftp://maia.usno.navy.mil/conv2010/convupdt/chapter9/GPT2.F (updated June 10, 2013).
Unlike the case of the troposphere zenith hydrostatic delay, precisely modelling the troposphere zenith wet delay is not possible. Instead, the troposphere zenith wet delay is estimated in PPP solutions as an additional unknown parameter.
Once the troposphere zenith hydrostatic delay is modelled and the troposphere zenith wet delay is estimated, a mapping function is required to project the troposphere zenith delay to the user-satellite slant distance. In this study the Global Mapping Function is used (Boehm et al. 2006). It is an empirical function that requires user latitude, longitude, height and day of year as input. Sample code is available at http://maia.usno.navy.mil/conv2010/chapter9/GMF.F.
4.2.1.3 Other Small Errors
Because PPP-GNSS does not use measurement differencing, those errors that could be eliminated in the differential positioning approach must now be taken into account. Table 4.2 gives an overview of these effects and the related mitigation method.
Table 4.2 PPP-GNSS errors and corresponding mitigation methods
Error effects Mitigation method Official model from GPS ICD (ICD- Relativistic effect GPS-200C, 1993). Absolute phase centre correction model Satellite-related Satellite antenna phase (Kouba 2009) with IGS ANTEX effects centre offset and variation product Phase windup correction model (Kouba Phase windup 2009)
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Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application
Absolute phase centre correction model Receiver antenna phase Receiver-related (Kouba 2009) with IGS ANTEX centre offset and variation effects product Sagnac effect Sagnac effect model (Ashby 2003) Solid earth tides Model recommended by the IERS Site displacement Polar tides (IERS 2010) effects Ocean loading
Earth rotation parameters
4.2.2 PPP-GNSS Mathematical Model
Errors resulting from relativity and phase windup at the satellite antenna, the offset variation of antenna phase centre and site displacement, are assumed to have been corrected by models and are ignored here. The GNSS phase observation equation is given in Equation (2.2). To simplify the measurement model, the multipath effect is considered here as being incorporated within the residual errors.
In order to mitigate the ionospheric effect the ionosphere-free model, Equation (4.1) is used, and the observation equation becomes:
f 2 f 2 i 1 1 i 2 2 i IFIF 2 ff 2 L1 2 ff 2 L2 (4.3) 1 2 1 2 2 i 2 NfNf i i c i dsdTdt i d i 1 211 22 i trop 2 2 IF 1 ff 2
2 i 2 NfNf i The ionosphere-free ambiguity N i 1 21 2 is calculated as a IF 2 ff 2 1 2 “lumped” term and treated as a non-integer value. The receiver clock error dT may be either estimated, or eliminated by differencing the ionosphere-free measurements between satellites. When the signal from satellite k is chosen as the reference, the
ik single differenced (SD) ionosphere-free carrier phase measurement IF can be written as:
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Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application
ik i k ik dsik ik cd dt ik N ikik (4.4) IF IF IF trop IF IF
The unknown variables are the three position component parameters, the SD zenith tropospheric wet delay, and the SD ionosphere-free carrier phase ambiguities. In order to avoid the cycle slip problem, the carrier phase ambiguities are resolved on an epoch- by-epoch basis. The number of estimated states is greater than the number of measurements, hence the EKF is adopted. Similar to the Locata positioning method, an accurate dynamic model with first-order Gauss Markov (GM) modelled acceleration is developed to improve the filter performance, which is given as:
a /1 a a (4.5) where is the correlation time constant; and is zero-mean white noise. a
The carrier phase ambiguities and tropospheric wet delay are modelled as random walks. The system state vector is:
1k 2k mk T (4.6) rrrtx Δd wet IF NN IF ΝIF where d is the SD zenith tropospheric wet delay; and m is the number of wet ionosphere-free carrier phase measurements.
The system dynamic model of EKF describes how the true state of the system evolves over time. The dynamic model, the dynamic matrix and the process noise vector can be written as:
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Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application
tωtxtFtx (4.7)
0 33 I 33 33 00 m 13 (4.8) 33 00 33 I 33 0 m 13 tF 1 00 I 0 33 33 τ m 1333 m 31 m 31 m 31 0000 mm 11
T (4.9) tω 00 3131 daaa 1k ωωωωωω 2k ω mk wet NIF NIF NIF
where d is the process noise of the tropospheric wet delay; and *k is the process wet NIF noise of the SD GNSS ionosphere-free ambiguity.
The measurement model (4.4) is non-linear, thus the EKF must linearise the function around the current predicted estimates. The measurement model is:
ttxtHtz (4.10)
The measurement vector tz , which is formed from the set of error-corrected SD GNSS carrier phase, and the observation matrix H can be written as:
1k 2k mk T (4.11) tz IF IF IF
1 ee k M wet (4.12) ee M H 2 k 0 wet I m6 M mm wet ee km M wet where is the line-of-sight vector between receiver and satellite. e*
t ~N 0,R is the measurement noise vector, and the measurement noise covariance matrix R is defined by the variance of the measurements.
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Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application
4.3 Locata Augmented PPP-GNSS System
In the proposed configuration, Locata and GNSS carrier phase measurements are jointly processed in the tightly-coupled mode, which means that the raw observations of all sensor systems are input to a common navigation filter (Rizos et al. 2008). For the proposed Locata augmented PPP-GNSS system, a common system estimator (EKF is used here) is designed to process the Locata and GNSS carrier phase measurements simultaneously in order to derive the optimal navigation solutions (position, velocity and acceleration). Referring to the principles of Locata point positioning described in section 3.2 and the PPP-GNSS mathematical models presented in section 4.2, the measurement functions of Locata and GNSS are considered independently and the respective carrier phase float-valued Locata and GNSS ambiguities will estimated by the EKF along with the navigation solutions.
Since the Locata and GNSS systems use different antennas, the lever arm correction needs to be applied. Here the Locata antenna position is referred to the GNSS antenna centre, with the lever arm estimated as unknown parameters at each epoch. The length of the lever arm is known beforehand and treated as an additional measurement. The system state vector is:
1 j 2 j nj 1k 2k mk T (4.13) wet Lzyx NNddddrrrtx L L IF ΝΝΝ IF ΝIF where the superscript n is the number of Locata SD carrier phase measurements and j is the Locata signal chosen as the reference for SD processing; the subscript “L” denotes “Locata”; the term represents the unknown lever arm components. The acceleration d * is modelled as a first-order (GM) process, while other terms such as the tropospheric wet delay, lever arm and carrier phase ambiguities are modelled as random biases.
According to the EKF dynamic model, in Equation (4.7), the dynamic matrix F and process noise vector tω in the dynamic model can be written as:
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Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application
0 33 I 33 33 00 mn 43 (4.14) 33 00 33 I 33 0 mn 43 tF 1 00 I 0 33 33 τ 33 mn 43 mn 34 mn 34 mn 34 0000 mnmn 44
T (4.15) tω 00 3131 aaa Δd dηdηdη ωωωωωωωω 1 j nj ωω 1k ω mk wet ΔN L ΔN L ΔN IF ΔN IF
where d is the process noise of the lever arm.
Since the lever arm considered, and the GNSS antenna centre are computed as the user location, the premeasured lever arm distance and the Locata geometric range in Equation (3.1) from Locata antenna centre to the LocataLite can be written as:
2 2 dddl 2 (4.16) LA x y z
2 2 2 (4.17) i i i zdzydyxdx i L x y z where x , y and z represent the user coordinates in the Earth frame.
The measurements used for the Locata augmented PPP-GNSS solutions is the combination of Locata carrier phase and GNSS carrier phase, where the error effects on GNSS carrier phase can be mitigated by the model described in section 4.2. Therefore the measurement vector and the design matrix in Equation (4.10) can be written as:
1 j 2 j nj 1k 2k nk (4.18) tz L L L IF IF IF tide lh LA
(4.19) 11 12 IHH 0 mmnn H H 21 m 31 00 I mmnn 31 HH 32 00 22 mn where 74
Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application
1 j 1 j 1 j L L L L L L 1 j x x y y z dddddd z ee LL 2 j 2 j 2 j 2 j L L L L L L ee LL H11 0n7 , H12 dddddd , x x y y z z n j n j n j n j L ee L L L L L L L x x y y z dddddd z
1 k ee GG M wet 2 k ee M wet sinsincoscoscos LλLλL H GG 0 , H 0 , 21 m6 31 72 M wet 0 00 m k G ee G M wet
0 31 H l . 32 LA η
2 2 The measurement covariance matrix R is diag ( R , R , σ , σ ). Since both L IF htide lLA Locata and GNSS measurements are processed in the SD mode, the SD carrier phase measurements are correlated with each other, and the covariance is therefore assumed to be half of the variance, which can be written as:
112 (4.20) 2 121 * R * 2 1 2111
2 2 2 where , and are the noise variance of the SD carrier phase measurements, * htide lLA tide height and lever arm distance, respectively.
4.4 Experiment and Result Analysis
The experiment data collected in the Sydney Harbour test were used for evaluation and analysis. In this experiment, a Locata user unit and a Leica GNSS dual-frequency receiver were installed on a survey vessel provided by the Sydney Ports Authority, with antenna locations as shown in Figure 4.1. The distance between Locata and GNSS
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Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application antenna centres was measured beforehand as 0.24m. The GNSS antenna centre was considered to be the required user location, and the Locata antenna centre was corrected for the lever arm so that its coordinate referred to the GNSS antenna centre. The Locata configuration is the same as in the experiment described in section 3.4.
Figure 4.1 Test vessel and installed Locata and GNSS antennas used for the Sydney Harbour test
In order to establish a reference trajectory for accuracy assessment, GNSS integer-fixed differential carrier phase positioning solutions computed using the Leica Geo Office (LGO) software served as the ground-truth. A precisely surveyed point was setup as the base station where a dual-frequency GNSS receiver was installed. The distance between the GNSS base station and the rover trajectory was less than 10km. The vessel trajectory and the base station are shown in Figure 4.2, where the red line denotes the trajectory and the green dot is the base station. The raw data from the Locata rover receiver and GNSS receiver were collected and post-processed. Both Locata and GNSS data output rates were set to 10Hz. Tide height data were recorded by the Fort Denison Tide Gauge, updated every 6 minutes.
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Figure 4.2 Sydney Harbour experiment configuration and vessel trajectories
The trajectory solution using the PPP-GNSS approach was first computed. Figure 4.3 shows the GNSS geometry during the experimental period (lasting 2 hours and 45 minutes) – the Horizontal Dilution of Precision (HDOP), Vertical Dilution of Precision (VDOP) and the number of visible satellites are plotted. There were 6–9 available satellites during this period, and by applying the SD approach 5–8 SD observables could be obtained.
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Figure 4.3 Geometric conditions for GNSS positioning for the Sydney Harbour test
Figure 4.4 is a plot comparing the PPP-GNSS solution and the reference (ground-truth) solution. The differences are displayed in the navigation frame (North-East-Down). It can be seen from the plot that the convergence period lasts for approximately 500s, after which the accuracy of the three position components are less than half metre. Table 4.3 summarises the accuracy of the PPP-GNSS solution, with the exclusion of the initial 500s convergence period. The Standard Deviation (STD), the Root Mean Square (RMS) value, Distance Root Mean Square (DRMS) for 2D (horizontal components), and Mean Radial Spherical Error (MRSE) for 3D are listed. The DRMS and MRSE are 0.14m and 0.23m, respectively. The STD values are 0.07m and 0.08m for the north and east components, respectively, and 0.17m for the vertical. The RMS values for the horizontal components are 0.08m (north) and 0.11m (east), and for the vertical direction it is 0.19m. Both STD and RMS values indicate that the vertical accuracy is typically half that of the horizontal component accuracy.
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Figure 4.4 PPP-GNSS solution accuracy with respect to the ground-truth solution
Table 4.3 Error statistics of the PPP-GNSS solution STD (m) RMS (m) Horizontal DRMS (m) MRSE (m) North 0.07 0.08 0.14 East 0.08 0.11 0.23 Vertical 0.17 0.19 -
The yellow line in Figure 4.2 is the trajectory derived by the Locata augmented PPP- GNSS technique. In this session, both Locata and GNSS signals were tracked and the vessel travelled in a continuous circular motion for approximately 15 minutes. Figure 4.5 is a plot of the geometric conditions. During this period 7–8 GNSS satellites and 4– 8 LocataLites (with 11–32 Locata signals) could be tracked (each LocataLite transmits four separate signals). Excluding one satellite and two Locata signals as the reference in the Locata augmented PPP-GNSS system, a total 15–37 SD observables were obtained. The average HDOP and VDOP for GNSS, for the Locata augmented PPP-GNSS system and for the Locata standalone system are compared in Table 4.4. Since the LocataNet was established in an almost planar configuration, the vertical geometry of the Locata standalone system is poor, therefore only the HDOP of the Locata standalone system is compared in Table 4.4. The HDOP of the Locata standalone system is also shown in 79
Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application
Figure 4.5, as the green line. Compared with GNSS, the Locata augmented PPP-GNSS indicates an improvement of 65.3% and 72% for HDOP and VDOP, respectively. Compared with the Locata standalone system, the proposed Locata augmented PPP- GNSS system improves HDOP by 28.8%. It can be seen for both the horizontal and vertical position components, the proposed system would ensure the most optimal geometry.
Figure 4.5 Geometric conditions for Locata augmented PPP-GNSS system and horizontal geometry for the Locata standalone system
Table 4.4 DOP comparison of geometries for different sensor configurations
Ave. Ave. HDOP VDOP GNSS 1.21 2.25 Locata standalone 0.59 - Locata augmented PPP- 0.42 0.63 GNSS
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Figure 4.6 shows the difference between the position solution computed using the Locata augmented PPP-GNSS approach and the reference (ground-truth) solution. With the same initial state value, the convergence time using the Locata augmented PPP- GNSS is very short, at most the first 100 epochs (10s), which is a significant reduction in comparison with the PPP-GNSS approach which has a convergence period of about 500s. The statistics are summarised in Table 4.5, excluding the first 10s convergence period. Similar to Table 4.3, the STD, RMS, Horizontal DRMS and MRSE values are listed. The RMS values are 0.03m, 0.01m and 0.17m for the north, east and vertical directions, respectively. The horizontal DRMS is 0.03m and the MRSE is 0.17m. Compared to the PPP-GNSS solutions, all the error statistics are improved.
Figure 4.6 Locata augmented PPP-GNSS accuracy with respect to the ground-truth solution
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Table 4.5 Error statistics of the Locata augmented PPP-GNSS solution
STD (m) RMS (m) Horizontal DRMS (m) MRSE (m) North 0.03 0.03 0.03 East 0.01 0.01 0.17 Vertical 0.05 0.17 -
Since more than four LocataLites were used during the experiment, the Locata standalone solutions can be computed using the method described in section 3.2. For a comparison, the Locata standalone positioning difference with respect to the reference solution is plotted (as the green line) in Figure 4.7, and the related error analysis is summarised in Table 4.6. Since the rover receiver was installed on a maritime vessel, the horizontal positioning performance is more important than of the vertical. Figure 4.7 and Table 4.6 thus focus on the horizontal (north and east) components. The red line in Figure 4.7 is the PPP-GNSS solution difference with respect to the reference solution, which is extracted from the solution for the whole trajectory in Figure 4.4. Therefore this trajectory is used for comparison purposes, after neglecting the initial convergence period. The zoom-in plots in Figure 4.7 compare the initial convergence period of the Locata standalone and Locata augmented PPP-GNSS solutions, from which one can see that the convergence time for the Locata augmented PPP-GNSS system (about 10s) is shorter than that of the Locata standalone system (approximately 200 epochs, or 20s). The Locata augmented PPP-GNSS system therefore converges about twice as fast as the Locata standalone system. Both of these two systems, however, have shorter convergence periods than the PPP-GNSS approach (500s, as shown in Figure 4.4).
Excluding the initial filter convergence period and considering only the after- convergence system performance, the solution of the Locata augmented PPP-GNSS system is more stable than for the other two techniques. The comparison of the three techniques during the experiment is shown in Table 4.6. One can see that for all three error quantities the Locata augmented PPP-GNSS is the most accurate solution. With respect to the horizontal DRMS, the proposed system shows an improvement of 33.3% against the Locata standalone solution. Comparing with the PPP-GNSS approach, the improvement is more obvious, being 63.6%. All indications are that the proposed Locata augmented PPP-GNSS approach has the best performance, not only providing 82
Chapter 4 Locata Augmented Precise Point Positioning for Kinematic Application the most stable and accurate solution, but also having the fastest filter convergence speed.
Figure 4.7 Horizontal accuracy comparison of PPP-GNSS, Locata standalone, and Locata augmented PPP-GNSS systems
Table 4.6 Error statistics of PPP-GNSS, Locata standalone and Locata augmented PPP- GNSS
STD (m) RMS (m) Horizontal Convergence
North East North East DRMS (m) time (s) PPP-GNSS 0.04 0.03 0.11 0.03 0.11 500 Locata standalone 0.04 0.03 0.04 0.04 0.06 20 Locata augmented 0.03 0.01 0.03 0.01 0.04 10 PPP-GNSS
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4.5 Summary
In this study the potential of using the Locata augmented PPP-GNSS technique for kinematic positioning applications was investigated. The proposed method integrates the PPP-GNSS and the Locata positioning approaches in order to provide high accuracy point positioning solutions without the requirement for a nearby GNSS reference station. The Locata and GNSS carrier phase measurements are processed simultaneously in a tightly-combined mode with the ambiguities estimated as floating-point values on an epoch-by-epoch basis. The unknown lever arm between the Locata antenna and the GNSS antenna is estimated by the system filter.
A field test was conducted on Sydney Harbour to evaluate the system performance. An analysis of the PPP-GNSS, Locata standalone and Locata augmented PPP-GNSS solutions was conducted. The test demonstrated that the Locata augmented PPP-GNSS system can achieve positioning accuracy at the centimetre-level, which is better than either the PPP-GNSS or the Locata standalone techniques. Moreover, the initial filter convergence time of the proposed method is significantly shorter compared to the PPP- GNSS technique. These advantages distinguish the proposed Locata augmented PPP- GNSS system from the conventional PPP-GNSS technique, and confirm this system as an effective navigation approach to providing high accuracy positioning solutions for kinematic maritime applications.
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CHAPTER 5 OPTIMAL DATA FUSION ALGORITHM FOR NAVIGATION USING TRIPLE INTEGRATION OF PPP-GNSS, LOCATA AND INS
5.1 Introduction
Global Navigation Satellite System (GNSS) technology is widely used to satisfy positioning and navigation requirements in many application fields, including geodesy, surveying, mapping, and precise marine and aviation navigation. Most precise GNSS positioning applications rely on the differential GNSS (DGNSS) principle. However the requirement for one or more nearby base station equipped with a reference GNSS receiver may limit the operational range of the DGNSS system, as well as increasing system cost and complexity. An alternative to the differential positioning techniques is the Precise Point Positioning (PPP) approach, which is based on the processing of observations from a single GNSS receiver. As discussed in Chapter 4, for PPP there is no longer a need to use corrections and/or measurements from GNSS reference stations. With improvements of the International GNSS Service (IGS) products, in particular the availability of precise satellite ephemerides and clock error correction information, including in real time, the performance of PPP-GNSS has dramatically improved.
Although DGNSS is widely used and PPP-GNSS is nowadays a viable precise positioning technology option, the major disadvantage of GNSS still remains: signal blockage due to obstructions in urban and built up environments, and extreme power attenuation of the signals when operated in indoor environment. The combination of GNSS with other sensors, such as a self-contained inertial navigation system (INS), provides an ideal position and attitude determination solution which can not only mitigate the weakness of GNSS, but also bound the INS error that otherwise would grow with time when the INS operates alone. However, the navigation accuracy provided by GNSS/INS strongly depends on the quality and geometry of the GNSS observations, the quality of the INS technology used, and the integration model used to fuse the measurements.
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In general, with limited GNSS availability, the navigation accuracy can only be maintained at the metre-level for no more than a few minutes even if a reasonably high quality INS is used. Many fusion algorithms have been investigated to mitigate this problem, however during longer GNSS outages navigation outputs will not meet the requirements for many applications (Han and Wang 2011; Jaradat and Abdel-Hafez 2014). Alternative sensors, integrated with the GNSS/INS system, could assure the accuracy and continuity of the navigation solutions (Grejner-Brzezinska et al. 2011). The terrestrial-based “Locata” technology uses a “local constellation” of ranging signals to address local user positioning requirements, especially in challenging GNSS environments. A number of papers have been published on Locata technology, for both indoor and outdoor applications (Barnes et al. 2003; Barnes et al. 2004; Choudhury et al. 2009a; Gauthier et al. 2013; Li and Rizos 2010; Rizos et al. 2010).
In this study, in order to satisfy the requirements of high accuracy and high reliability, the PPP-GNSS and Locata measurements or data are fused with those of the INS via a loosely-coupled architecture. A loosely-coupled integration system uses solved-for position and velocity as the measurement inputs to the integration algorithm, which uses them to then estimate the INS errors. The integrated navigation solution is the INS navigation solution, corrected with the Kalman filter estimates of its errors. The two main advantages of loosely-coupled integration are simplicity and redundancy. The architecture is simple in that it can be used with any INS and any GNSS/Locata user equipment, making it particularly suited for retrofit applications. Moreover, the standalone GNSS and Locata solutions are usually available, in addition to the integrated solution, which enables basic parallel solution integrity monitoring (Groves 2008). The loosely-coupled architecture is adopted in this research to integrate the PPP- GNSS, Locata and INS.
In addition to the integration navigation architecture, the other part of the multi-sensor navigation system that needs to be defined is the data fusion algorithm. The conventional Centralised Kalman filtering (CKF) algorithm provides global state estimation by directly combining local measurement data. In this method, all sensor measurements support system navigation estimation via one master filter. However the centralised filter can have a large computational burden due to the high dimensional 86
Chapter 5 Optimal Data Fusion Algorithm for Navigation using Triple Integration of PPP-GNSS, Locata and INS problem and large data memory requirements (Gao et al. 2009). From the point of view of fault tolerance, CKF is not convenient for adaptively detecting and isolating sensor faults. Hence CKF-based navigation systems have limited reliability (Lo et al. 2013; Li and Zhang 2010). Decentralised Kalman filtering (DKF) methods have been developed to overcome such limitations (Gao et al. 2009; Lo et al. 2013; Li and Zhang 2010; Li 2014). These differ from CKF because, as the name implies, there is no “central filtering” of the measurements. Instead measurements from local sensors are processed locally to obtain local state estimates, then the local optimal (or sub-optimal) estimates are sent to a fusion centre to yield the global optimal solution according to certain information fusion criteria. Due to the parallel structure, the communications and computational loads are reduced, and fault detection and isolation can be more easily implemented. Currently one of the most commonly used DKF algorithm is Federated Kalman filtering (FKF).
Data fusion techniques can also be applied for target tracking applications, and are classified either as low level “scan” fusion or high level “track-to-track” fusion, which are achieved by combining observations from different sensors and combining estimates from sensor sites, respectively. Similar to the DKF in multi-sensor navigation applications, the advantages of easy fault detection and low computational load make track-to-track fusion architecture popular. The key issue for track-to-track fusion is strong correlation between the tracks because they have a common prediction error resulting from a common process model (Bar-Shalom 1981). Systems that ignore such correlation would be expected to have poor performance. Many methods have been developed to address the correlation problem (Bar-Shalom 1981; Aeberhard et al. 2012), however, such methods still cannot achieve better performance than the low-level “scan” fusion method.
Li (2014) proposed a decentralised data fusion algorithm called Global Optimal filtering (GOF) which is based on the theory of information space. All the information sources – the state predictions, estimations and measurements – can be treated equally as information vectors. Using these information sources, the multi-sensor data fusion is expressed as the sum of the transformations of the information vectors. The utilisation
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Chapter 5 Optimal Data Fusion Algorithm for Navigation using Triple Integration of PPP-GNSS, Locata and INS of all the information resources makes GOF different to conventional data fusion algorithms.
In this study, a PPP-GNSS/Locata/INS multi-sensor navigation system is proposed that overcomes the sensor error accumulation problem of the INS and the signal blockage problem of the GNSS. In the proposed PPP-GNSS/Locata/INS multi-sensor system, the radio navigation systems have their own drawbacks. For example, the Locata signals are range-limited and the GNSS signals can be easily jammed. Neither Locata nor GNSS alone can fully satisfy the fault-tolerant requirement of the system, thus a well-designed integration filter is needed, which could be responsive and reliable when one of the sub- systems becomes unavailable.
This chapter is structured as follows. The three data fusion algorithms – CKF, FKF and GOF – are first reviewed and compared in section 5.2. The design of the proposed PPP- GNSS/Locata/INS system, the system error models and system statistics are further discussed in section 5.3. Finally, the performance assessment based on field data is presented in section 5.4, followed by the chapter summary.
5.2 Multi-sensor Filtering Algorithms
There are a number of ways of combining information from multiple navigation systems. The design of any integration algorithm is typically a trade-off between maximising the accuracy and robustness of the navigation solutions, minimising the complexity, and optimising the processing efficiency. This section describes the different integration algorithms and discusses their advantages and shortcomings.
5.2.1 Centralised Kalman Filtering
The CKF has a typical configuration as shown in Figure 5.1 – estimating the global state vector by constructing a global measurement vector when all of the measurements from the sensors are available. The dynamic system and observation equations of the CKF in a linear discrete form are:
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1 kωkxkkx (5.1)
kkxkHkz (5.2)
n n where k is the system transition matrix; Rkx is the state vector; Rkω is T T T the process noise; 1 2 n kzkzkzkz is the stacked observation vector; kH is the design matrix; and k is the observation noise. It is assumed that kω and k are zero-mean white sequences uncorrelated with each other, and
T T δkQjωkωE kj , δkRjkE k,j . The initial state x0 is a zero-mean
Gaussian random vector; x ~N x ,P 000 and is independent of kω and k .
The computational steps of CKF are same as for a standard Kalman filter, including the measurement update and time update, as given in Equation (2.24) – Equation (2.24). The CKF provides a recursive solution for the estimate ˆkx of the state kx in terms of the estimate kx and the new observation kz .
Figure 5.1 System configuration of CKF
In centralised integration architecture, the systematic errors and noise sources of all of the navigation sensors are modelled in the same Kalman filter. This ensures that all error correlations are accounted for and all measurements optimally weighted. Thus, the centralised integration architecture provides the optimal navigation solutions, in terms of accuracy, compared with the decentralised architecture. However, this is contingent on having the necessary information to model all sensors correctly. With all of the error 89
Chapter 5 Optimal Data Fusion Algorithm for Navigation using Triple Integration of PPP-GNSS, Locata and INS sources modelled in one place, the principal disadvantage of centralised integration is the high processor load, as well as not being able to fulfill the integrity requirements (fault detection and isolation) of applications that have high reliability demands.
5.2.2 Federated Kalman Filtering
Decentralised integration architecture was developed to overcome the limitations of the centralised filtering approach. The most commonly used decentralised filtering algorithm is the FKF (Calson and Berarducci 1994; Calson 1996). It is usually regarded as a two-stage data processing algorithm, composed of a set of local filters and one master filter, as illustrated in Figure 5.2. The local filters work in parallel and independent of each other, and their solutions are periodically fused by the master filter to yield a global solution. This decentralisation characteristic of FKF ensures a low computation load and a good fault detection and isolation ability. However the accuracy decreases compared with CKF. In order to achieve the same level of accuracy as CKF, the information sharing approach is applied in FKF. The basic concept of the information distribution approach is to divide the global state prediction and its covariance across the local filters, implement the parallel local processing with the sensor measurements, and then fuse the updated local information in the master filter to generate a global estimation.
Figure 5.2 System configuration of FKF
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Assume the state equation and observation equation of the local system are:
i ii 1 i kωkxkkx ,i 21 n, (5.3)
i iii kkxkHkz ,i 21 n, (5.4)
where both i kω and i k are assumed to be zero-mean white Gaussian noises whose covariance matrix are i kQ and i kR respectively.
If the local filters and master filter are uncorrelated, then the global estimation is given by:
n 1 1 1 (5.5) f i PPP m i1
n 1 1 1 (5.6) ff ii xPxPxP ˆˆˆ mm i1 where the subscript “ f ”, “i ”, and “ m ” represent the full filter, local filter and master filter, respectively. The inverse covariance is the “information matrix”.
If the local filters and the master filter are statistically independent, the global solution could be optimally achieved, otherwise only a sub-optimal solution can be output after the feedback correction. However for the typical FKF, the local filters and the master filter share the same system model, thus the estimates of the local filters and the master filter are correlated (Calson and Berarducci 1994; Calson 1996). In order to eliminate this correlation the state error covariance and process noise are set to their upper bounds:
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ˆˆ kxkx (5.7) i f 21 n,m,i i kk
1 ˆˆ 1βPkP (5.8) i if 21 n,m,i 1 1 i βQkQ if
,mn where i 0 is the information-sharing factors which satisfy the condition i 1. i1
Time propagation process is executed for each local filter and master filter:
ˆ T (5.9) i ii 1 i i 21 n,m,ikQkkPkkP
i ˆii ,2,11 mnikxkkx (5.10)
Measurement update processes of the local filters and master filter are different:
T T 1 (5.11) i ii iii i 2,1 nikRkHkPkHkHkPkK
ˆ (5.12) i iii 2,1 nikPkHkKIkP
ˆi i ii ii 2,1 nikxkHkzkKkxkx (5.13)
ˆ (5.14) m m kPkP
ˆm m kxkx (5.15)
The above results are combined by the fusion algorithm to yield the global solution:
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n (5.16) 1 1 ˆˆˆ 1 f m i kPkPkP i1
n (5.17) ˆˆ 1 ˆ 1 ˆ ˆmmf ˆii kxkPkxkPkPkx i1
5.2.3 Global Optimal Filtering
The multi-sensor optimal estimation is resolved in two approaches: in terms of the random vector space (RVS) approach and the information space approach (Li 2014). In the RVS framework, the sources of information have been identified and used as the bases of the space. The estimation is mathematically described as the procedure for finding the projection of the state vector on the bases of the space. The fusion algorithm therefore describes how the global state estimate is combined by the projections and associated bases.
Differing from the RVS approach, from the point of view of the information space, optimal fusion is implemented by a series of transformations between the information spaces. The transformations map the source information vectors from the measurement information spaces to the estimate information space to produce the fused information vector. The information space approach provides a means by which the accuracies of different algorithms can be compared on a theoretical basis.
As the RVS approach is similar to the widely applied Kalman filtering forms, it is used below to illuminate the nature of GOF.
Suppose for a linear discrete system ˆi ,,2,1 nix is the vector of unbiased estimators of the stochastic vector x . If xˆi are orthogonal vectors, the estimate of x can be xˆ expressed as the sum of the projections of i in a random vector space :
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n (5.18) ˆ | xCxx ˆˆ ii i1
According to the optimal state estimation and its covariance can be written as (Li 2014; Gao et al. 2009):
n (5.19) T ˆˆ 1 ˆ i xPSPx ˆii i1
1 n (5.20) T ˆˆ 1 i SPSP ii i1
where Si is the mapping matrix between xˆ and xˆi , and ii xSx ˆˆ . It can be seen that the ˆ more information used, represented here as xˆi , the smaller the trace of P , and therefore the system should have better performance.
For a better understanding, recall the Kalman filter’s measurement updating equation. This prediction equation indicates that the state prediction is corrected when the measurement is made available. It can be rewritten in the following fusion form:
ˆ kzkKkxkHkKIkx (5.21)
It also can be regarded as the random vector space below (Li 2014):
ˆ| ˆ 1 2 kzkCkxkCkxkx (5.22)
ˆ 1 ˆ T 1 where 1 PPC , and 2 RHPC .
The estimation xˆ can be seen as a point or vector in the space , which is expanded by the bases of state prediction kx and measurement kz ; and C1 and C2 are the projections of ˆkx on kx and kz in space .
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Similarly, the RVS of CKF can be expanded by the measurements 1 kz , 2 kz and the global prediction kx :
(5.23) CKF ˆ| ˆ 11 22 kzkCkzkCkxkCkxkx
ˆ 1 ˆ T 1 ˆ T 1 where PPC , 1 RHPC 11 , 2 RHPC 22 .
The concept can be generalised to the multi-sensor optimal estimation problem such that:
n (5.24) ˆ | ˆ ˆii kxkCkxkx i1 where xˆ are the bases of RVS. An optimal multi-sensor estimation requires the i selection of the information on the bases and the determination of the associated projections. The following random vectors in a multi-sensor system can be used as the bases (Li 2014):
Measurements: i 2,1, nikz Local predictions: i 2,1, nikx Global predictions: kx
Utilising different sources as the bases of RVS leads to different fusion algorithms. For example, both CKF and FKF optimally fuse the global prediction and all local measurements, which means they have the same accuracy, although FKF utilises the decentralised structure. The estimation of CKF and FKF can be represented as the random vector space (Li 2014):
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n (5.25) ˆˆ ii kzkbkxkakx|kx i1 where a and b are the projections of the global estimate vector on the information bases. Differing from CKF and FKF, the GOF uses all the information sources including the measurements, the local and global predictions, to achieve the global optimality, which can be represented as:
n n (5.26) GOF ˆˆ ii ii kxkekzkdkxkckx|kx i1 i1
The measurements and the local predictions comprise the local Kalman filtering fusion, thus they can be replaced by the local state estimates. The GOF configuration is shown in Figure 5.3. The random vector space of GOF, Equation (5.26) can be rewritten as:
n (5.27) GOF ˆˆ ˆii kxkekxkfkx|kx i1
Figure 5.3 System configuration of GOF
The current global state prediction is obtained from the previous state estimate:
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n (5.28) ˆ 1 i 1 ˆi kxkakxkbkkxkkx 111 i1
Since the global prediction kx is correlated with the previous local state estimate
ˆi kx 1 , and the current local state estimate ˆi kx is also correlated with the previous local state estimate ˆi kx 1 , the global prediction and local estimates are oblique to each other, not orthogonal. Therefore these three vectors need to be orthogonalised. The reconstructed orthogonal global prediction and local estimates are represented as ~kx ~ and i kx :
~ i ˆi kxkx
n (5.29) ~ ˆii kxkxkx i1
The corresponding covariance of reconstructed global prediction is:
n n n ~ T ˆ T ~ T ~T T (5.30) kPkP ii kP i i kP i ii kP i1 i1 i1 where
~ ~ ˆ TT 1 ˆ (5.31) i ,cov i 1 i ii 2,1 nikPkPkkSkPkxxkP
ˆ kx As global prediction kx and local estimates i are all unbiased estimates, the ~ ~ orthogonalised global prediction kx is also unbiased, hence kxkxE =0, from which one can derive:
n (5.32) i I i1
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~ ~ Since the reconstructed global prediction kx and local estimation i kx are orthogonal ~ ~ to each other. Thus cov , i kxkx 0, from which one can obtain:
n 1 (5.33) ~ ˆ 1 ii kPkPI i1
~ ˆ 1 (5.34) i ii 2,1 niPP
According to the optimal state estimation equation, Equation (5.19) and its covariance Equation (5.20), the optimal fused global estimation is:
n (5.35) ˆ ~1 ~ T ˆ 1 ˆ k|kxkPkPkx 1 i ˆii kxkPS i1
1 n (5.36) ˆ ~1 T ˆ 1 i SkPSkPkP ii i1
5.3 PPP-GNSS/Locata/INS Integration System
Similar to the conventional GNSS/INS integration system and the Locata/INS integration system described in section 3.3, the INS error model needs to be defined so as to drive the system dynamic model. In this research the psi-angle error model is applied, which has been discussed in section 2.3.4.
Since the Locata and GNSS systems use different antennas, the lever arm correction needs to be applied. Here the positions of the Locata antenna and GNSS antenna are both referred to the inertial measurement unit (IMU) reference point, with the lever arm estimated as unknown parameters at each epoch. Therefore the estimated state vector consists of 21 navigation error states, which could be written in three sub-vectors: xψrv ,
xε and xη represent the sub-vectors of motion component, gyro and accelerometer errors and level arm components, respectively: 98
Chapter 5 Optimal Data Fusion Algorithm for Navigation using Triple Integration of PPP-GNSS, Locata and INS
xxxtx ηεψrv (5.37) specifically
ψrv ψψψx δvδvδvδrδrδr DENDENDEN
εεεx zyxzyxε
xη Lx Ly Lz Gx Gy δηδηδηδηδηδη Gz where the subscripts “N”, “E”, “D” denote the north, east, and down axes in the n-frame, respectively; the subscripts “x”, “y”, “z” represent the direction of the roll, pitch, and yaw axes in the body frame, respectively; and the last six symbols represent the unknown Locata and GNSS lever arm components.
The system dynamic model is:
xψrv 11 FF 12 0 69 xψrv 0 19 xε 000 666696 xε ωε (5.38) xη 000 666696 xη 0 16 where ω is the noise vector of the accelerometer and gyro errors, which is modelled ε as a random bias; the sub-matrices F11 and F12 of the system matrix F are calculated based on the INS error model, given as Equation (3.12).
In the proposed PPP-GNSS/Locata/INS integration system the local filters and global filter share the same system model. Thus for the local filters the state vectors are also represented by Equation (5.37). As for the measurement updates, both Locata and PPP- GNSS can provide the carrier phase-based position and velocity solutions to correct the INS errors. Due to the lever arm uncertainty, the positions of both Locata antenna and GNSS antenna need to be corrected to the IMU reference point:
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n n n b (5.39) * INS b ηCrr *
n n n n n b n b b (5.40) * INS ie en b * b * ωηCηCωωvv ib where the subscript * denotes the Locata and GNSS antennas. Using the above model the computed position and velocity at the Locata antenna is given by:
n n n b ˆˆ n b ˆ n b (5.41) * ˆˆ INS b *0 b *0 CψηCηCrr b δη*
n n ˆ n b b ˆ n b b ˆ n b b (5.42) * ˆˆ INS b ib 0* b ωCηωCvv ib δη* b ib ηωC 0* where ηb is the initial estimate of the lever arm of Locata and GNSS. 0*
The linearised measurement models of the Locata local filter and GNSS local filter can now be written as:
n n n b (5.43) L δrδr INS b ηC L0 n n n b b L δvδv INS b ib ηωC L0
ˆ n ηC b I 00 Cˆ n 0 b L0 633333 b 33 ttx ˆ n b b ˆ n b b ib ηωC L0 0 I 0 633333 b ωC ib 0 33
n n n b (5.44) G δrδr INS b ηC G0 n n n b b G δvδv INS b ib ηωC G0
ˆ n ηC b I 000 Cˆ n b G0 33633333 b ttx ˆ n b b ˆ n b b ib ηωC G0 0 I 00 33633333 b ωC ib
The covariance of the measurement noise in the local filter is defined by the general accuracy of the local Locata and PPP-GNSS solutions, which is described as:
2 2 2 2 2 2 L 0 05 0 05 0 05 ...... diagR 101010
2 2 2 2 2 2 G 015 015 0 05 ...... diagR 202020 100
Chapter 5 Optimal Data Fusion Algorithm for Navigation using Triple Integration of PPP-GNSS, Locata and INS where the first three are the covariance of position in units of m2 , and the last three are the covariance of the velocity in units of / sm 2 .
5.4 System Evaluation and Result Analysis
The system was evaluated using the experiment data collected in October 2012 on Sydney Harbour. The experiment configuration was described in section 3.4 and section 4.4.
In order to evaluate the performance of the CKF, FKF and GOF algorithms, position and velocity solutions calculated by the three data fusion algorithms were analysed, and are summarised in Figure 5.4 – Figure 5.6. As the LocataNet was almost planar, the vertical component observability by Locata is not as good as for the horizontal components. The tide height data, measured and recorded by the Fort Denison Tide Gauge, was used to constrain the height in the processing, and the experiment analysis below focuses on the horizontal direction components. From the position plots in the three figures it can be seen that all three algorithms can achieve accurate and stable positioning solutions for the horizontal direction components.
By comparing the three plots one can see that the performance of CKF and FKF are similar, while the solution using GOF is more accurate and stable. The Root Mean Square (RMS) and Distance Root Mean Square (DRMS) values for the horizontal direction components are listed in Table 5.1. It can be seen that the accuracy of all three solutions are better than 0.08m. CKF and FKF have similar accuracy with a DRMS of about 0.08m. However GOF achieves a slightly higher accuracy with the DRMS of 0.07m, which is an improvement of 12.5% in comparison with CKF and FKF.
For the velocity solution there is a similar conclusion to that of the position solution. The velocity from GOF has a higher accuracy than the CKF and FKF derived velocities. The FKF solution is slightly worse than CKF. The GOF improves the horizontal velocity DRMS by 33.3% in comparison with CKF and FKF velocities.
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Table 5.1 Position and velocity analysis of the three filtering systems
CKF FKF GOF North 0.06 0.06 0.05 Position RMS East 0.06 0.06 0.05 (m) DRMS 0.08 0.08 0.07 North 0.02 0.03 0.02 Velocity RMS East 0.02 0.02 0.01 (m/s) DRMS 0.03 0.03 0.02
Figure 5.4 Position and velocity error of the CKF system
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Figure 5.5 Position and velocity error of the FKF system
Figure 5.6 Position and velocity error of the GOF system
In order to investigate the precision performance of the data fusion algorithms, the corresponding a posteriori estimate error covariance ˆkP of every calculation epoch 103
Chapter 5 Optimal Data Fusion Algorithm for Navigation using Triple Integration of PPP-GNSS, Locata and INS was also computed. Figure 5.7 – Figure 5.9 show the square root of error covariance
ˆkP (w.r.t sqrtP) of the position and velocity, for the CKF, FKF, and GOF solutions. In each figure, (a) is the sqrtP of position at all epochs and, (b) shows the sqrtP of position during the last 1000 epochs. Similarly, (c) is the sqrtP of velocity at all epochs and (d) is the sqrtP of velocity during the last 1000 epochs. The blue colour and green colour represent the north and east directions, respectively.
For the position components, the CKF’s and FKF’s sqrtP are close and both finally converge to less than 0.02m for north and east. The GOF solution converges to a similar value, but better than those produced by CKF or FKF. For the velocity component, the GOF solution has an obvious improvement, i.e. from 5103 m/s to 4103 m/s for both north and east direction components. It can therefore be concluded that the GOF estimate of position and velocity error covariance have obvious improvements in comparison with the conventional CKF and FKF algorithms.
Figure 5.7 Position and velocity precision evaluation of the CKF system
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Figure 5.8 Position and velocity precision evaluation of the FKF system
Figure 5.9 Position and velocity precision evaluation of the GOF system
To evaluate the fault-tolerance capability of the GOF-based triple-integration system, GNSS outlier failures were simulated. The performance of the GOF-based system under
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Chapter 5 Optimal Data Fusion Algorithm for Navigation using Triple Integration of PPP-GNSS, Locata and INS a GNSS outlier failure scenario is shown in Figure 5.10. In particular, at 250s, 260s, 270s, 280s, 290s, and 300s, the 1m and 0.5m/s additive errors were introduced to the GNSS position and velocity outputs, respectively. The plots (a) and (c) in Figure 5.10 are the horizontal position and velocity results for all epochs, (b) and (d) are the plots zoomed-in for the period from 240s to 310s (to show the six outliers more clearly). It can be seen that the proposed system has stable performance and is not affected by such failures. This demonstrates that the GOF-based triple-integration system is able to provide an (admittedly) small outlier-tolerant navigation solution.
Figure 5.10 Fault-tolerance evaluation of GOF-based triple integration system
5.5 Summary
This chapter described a triple-integration system based on PPP-GNSS/Locata/INS, which can be used for kinematic navigation. In order to address the limitations of the system and make it more convenient for implementation, the GNSS observations have been processed using the Precise Point Positioning (PPP) algorithm instead of the conventional differential approach. As GNSS signals are not always reliable and can be easily jammed, a standard GNSS/INS solution will suffer. The Locata system has thus 106
Chapter 5 Optimal Data Fusion Algorithm for Navigation using Triple Integration of PPP-GNSS, Locata and INS been incorporated in order to have a more robust system. The triple-integration algorithm has been implemented in the form of a loosely-coupled Kalman filter. To satisfy both accuracy and reliability requirements, three integration algorithms – CKF, FKF and GOF – have been investigated. From the concept of information sources, CKF utilises the local measurements and global prediction, and FKF also utilises local measurements and local prediction. The GOF utilises the full information sources of the local measurements, local prediction and global prediction which, in principle, is superior to CKF and FKF. In order to implement the optimal triple-integration system, the three data fusion algorithms have been evaluated using data from a field test conducted on Sydney Harbour. An analysis of the results has demonstrated that the integrated system is able to provide centimetre-level accuracy. The comparison of the CKF, FKF and GOF solutions verifies the theoretical analysis result, that is, that the FKF and CKF solutions have the same accuracy, and the GOF solution has a higher accuracy. Moreover, to evaluate the reliability of the GOF algorithm, a series of outliers were simulated. The results confirm the small outlier fault-tolerant capability of the GOF-based triple-integration system.
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CHAPTER 6 MULTI-SENSOR NAVIGATION SYSTEM BASED ON AN ADAPTIVE FAULT-TOLERANT GOF ALGORITHM
6.1 Introduction
It is well recognised that the accuracy of the navigation system of moving vehicles is critical, but also the reliability. For this reason, a variety of navigation modes and technologies have been developed, e.g., machine vision, the Global Navigation Satellite System (GNSS), initial technology, terrestrial ranging system, and others. However, every navigation system has its own advantages and disadvantages. Furthermore they can even fail in some cases, hence no single navigation mode or technology can ensure complete reliability and availability to satisfy the stringent demands of vehicles.
In last chapter, a GNSS/Locata/INS multi-sensor navigation system was described that utilises an information fusion strategy to overcome individual sensor limitations. It has been demonstrated that the proposed triple-integration system is able to support precise positioning. However, this system still has weaknesses that need to be addressed.
In practical applications the measurement characteristics of navigation sensors may vary as the environment changes, which may cause sensor failure. Therefore ensuring a certain capability for robustness and fault tolerance should be taken into consideration in the system design. In operational situations the measurement noise levels are a priori defined as fixed values, and assumed constant for the whole navigation process. Such a priori statistical information can be determined from in-house experiments and/or sensor manufacturers’ specifications. However, the a priori statistics may not be appropriate for all scenarios, which leads to sub-optimal Kalman filter estimation. In the case of measurement failures, such fixed measurement statistics would further degrade system performance, or even lead to a divergence of the filter itself (Loebis et al. 2004, Mohamed and Schwarz 1999). Hence, for reliable navigation of automated vehicles, it is desirable to implement a fault-tolerant navigation filter algorithm that can adapt to changes in sensor statistical characteristics as well as deal with sensor failures.
108 Chapter 6 Multi-sensor Navigation System based on an Adaptive Fault-tolerant GOF Algorithm
This chapter describes a novel adaptive fault-tolerant multi-sensor integrated navigation system. The multi-sensor-aided INS filter model is developed using the Global Optimal filtering (GOF) architecture, which fuses the outputs of multiple navigation sensors. A decentralised estimation is established for individual integrations of GNSS/INS and Locata/INS to independently obtain the local prediction and local estimation of the systems. In the local estimation, the measurement noise covariance is adaptively adjusting to improve the system’s fault tolerance. The GOF algorithm is then applied to fuse the local and global information to generate the optimal state estimation of the GNSS/Locata/INS integrated navigation system. To highlight the advantages of the proposed method over traditional methods, real-world test data were collected and post- processed. To evaluate the reliability of the proposed system, GNSS failures were simulated. A series of fault-tolerant analyses were then conducted.
6.2 Adaptive Fault-tolerant Filtering Algorithm
6.2.1 Adaptive Sensor Fusion Strategy
The sensor measurement statistics may vary from their a priori values, e.g. due to variations in measurement noise or bias drift caused by the environment, or a system level error caused by signal obstruction. To tolerant such variance and to improve system performance, the innovation-based Kalman filter scheme is widely used to adjust the system statistics (Geng and Wang 2008; Hu et al. 2003; Ding et al. 2007).
As discussed in section 2.4.2, the Kalman filtering process consists of the time-updating from step k-1 to k, and the measurement-updating steps. From the incoming measurement kz and the optimal prediction kx obtained at the previous step, the innovation sequence is defined as:
kzkzkr (6.1)
The innovation reflects the discrepancy between the predicted measurement kxkH and the actual measurement kz . The weighted innovation kxkHkzkK acts 109
Chapter 6 Multi-sensor Navigation System based on an Adaptive Fault-tolerant GOF Algorithm as a correction to the prediction kx to generate the estimate ˆkx . The innovation sequence is regarded as the most relevant source of information to adaptively adjust online (i.e. in real time) the measurement covariance matrix kR .
Substituting the measurement model equation, Equation (2.18) into Equation (6.1), the innovation sequence can be rewritten as:
kkxkxkHkr (6.2) which is a zero-mean Gaussian white noise sequence. An innovation of zero means that the two are in complete agreement.
By taking the variances on both sides, one obtains the theoretical covariance, and the covariance matrix of the innovation sequence is given by:
T T (6.3) r kRkHkPkHkrkrEkC
ˆ Defining r kC as the actual variance covariance of kr , it can be approximated by the statistical sample variance estimation, e.g. by averaging over a moving window of length N:
k (6.4) ˆ 1 T r kC jrjr N Nkj 1 where N is the number of samples (or window size), and is chosen empirically to give the appropriate level of statistical smoothing.
To assure filter estimation performance it is desirable to adaptively tune the covariance to be consistent with the innovation value. If a discrepancy between the innovation covariance of kr and its pre-defined theoretical value is found, then measures should be taken to adjust the diagonal elements of kR .
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To enhance the tracking capability, the time-varying vector variable k is defined to describe the discrepancy between the theoretical covariance and its actual value. The discrepancy factor k has the same dimension as the innovation vector kr . Each element (denoted as m ) of k is calculated as:
,mmkC (6.5) mk r ˆ r ,mmkC
where ,mmC is the m th diagonal element of the covariance matrix. As mk is a relative quantity that denotes the deviation of the theoretical covariance of mkr from its actual value, the mk should be equal to 1 if the selected statistics correctly reflect the actual modelling. To realise covariance matching, if mk is less than 1 then the theoretical estimated covariance is less than the actual value, and hence the measurement noise covariance ,mmkR should be increased, and vice versa.
The adaptive adjustment of ˆkR can be written as:
,mmkR (6.6) ˆ ,mmkR mk
, ˆ ,1 mmkRmmkR (6.7)
In this way the time-varying kR leads to a time-varying r kC , and the converged adaptive adjustment discrepancy factor k should be equal to 1.
As the decentralised estimation fusion method is established by obtaining the local predictions and the local estimates independently in the local filters, the fault-tolerant adaptive Kalman filter could be applied for both the Locata/INS sub-system and the GNSS/INS sub-system. The adaptive local filter based on the innovation covariance discrepancy is shown in the flowchart in Figure 6.1. As the local measurement noise
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covariance matrix i kR is time-varying, the statistics of the initial covariance Ri 0 would not be as significant as in the conventional estimation approach.
Figure 6.1 Adaptive fault-tolerant filtering algorithm in the local filter. The ˆ measurement noise covariance i kR is adjusted in each epoch by matching the ˆ innovation covariance r kC and its pre-defined value r kC
6.2.2 Adaptive Fault-tolerant Multi-sensor Navigation System
The proposed adaptive fault-tolerant multi-sensor navigation system is shown in Figure 6.2. The implementation is a decentralised filtering architecture of the GOF algorithm that utilises measurement statistics adaption in the local filters. As shown in Figure 6.2, the system consists of two adaptive local filters, a global predictor, and a global fusion filter. The two adaptive local filters implement the fusion of Locata/INS, and GNSS/INS. In each local filter the adaptive technique based on the innovation covariance discrepancy is applied, which mainly adapts to changes in sensor statistical properties and mitigates the adverse influence caused by these changes. The local estimate and its covariance from the adaptive local filters and the global prediction and its covariance from the global predictor, are all sent to the GOF fusion algorithm. As the local estimates and global predictions are oblique to each other, an orthogonisation process must be applied before fusion. 112
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Figure 6.2 Adaptive fault-tolerant multi-sensor navigation system based on GOF
decentralised estimation filtering. The measurements 1kz and 2 kz of Locata/INS and GNSS/INS subsystems are input to the local adaptive filters to achieve the local ˆ estimation, the GOF algorithm is then applied to fuse the local estimation ˆi kx , i kP , and global prediction kx , kP
The aforementioned adaptive fault-tolerant filter navigation system is summarised below:
Step 1 For each local filter, the time-updating step is executed as:
i ˆi kxkkx 1 (6.8)
ˆ T (6.9) i i 1 i kQkkPkkP
where i kQ is the i th local filter process noise covariance matrix at sample time k, and here i 2,1 . For the global predictor, the global prediction is also a time-updating process:
m ˆm kxkkx 1 (6.10)
ˆ T (6.11) m m 1 m kQkkPkkP
Step 2 In the local filters, the innovation covariance discrepancy-based adaptive 113
Chapter 6 Multi-sensor Navigation System based on an Adaptive Fault-tolerant GOF Algorithm algorithm is applied to adjust the measurement statistics using Equation (6.2) – Equation (6.7), then the measurement-updating is executed as:
T T 1 (6.12) i ii iii i kRkHkPkHkHkPkK
ˆ (6.13) i iii kPkHkKIkP
ˆi i ii ii kxkHkzkKkxkx (6.14)
Step 3 The calculated local estimates and global predictions are oblique, thus the three vectors are reconstructed to obtain orthogonal local estimations and global ~ ~ ~ predictions via the orthogonisation process, represented as x1 , x2 and x :
~ ~ (6.15) 1 ˆ1 kxkx ， 2 ˆ2 kxkx ~ 11 ˆˆ 22 kxkxkxkx
2 2 2 ~ T ˆ T ~ T ~T T (6.16) kPkP ii kP i i kP i ii kP i1 i1 i1
~ ~ ˆ T 1 ˆ (6.17) i ,cov i 1 ii kPkPkkPkxxP
~ ˆ 1 ~ ˆ 1 (6.18) 1 PP 11 ， 2 PP 22 1 ~ ˆ 1 ~ ˆ 1 11 PPPPI 22
Step 4 The orthogonalised local estimations and global predictions are fused to achieve the optimal global estimation:
ˆ ~1 ~ ˆ 1 ˆ 1 (6.19) ˆ 1 ˆ1 2 ˆ2 kxkPkxkPkxkPkPkx
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ˆ ~1 1 ˆˆ 1 1 (6.20) 1 2 kPkPkPkP
6.3 Experiment and Simulation Analysis
A test was conducted at the Locata Corporation Numerella Test Facility, located in rural NSW, Australia. A number of LocataNet configurations were used. The devices that were used in the test included two Leica dual-frequency GNSS receivers (one used as the rover receiver, and the other as the base station), one Honeywell H764 IMU, and one Locata rover unit. The GNSS antenna and Locata antenna were mounted with the inertial measurement unit (IMU) on top of a truck. The GNSS data rates and Locata data rates were both set to 10Hz, while the IMU’s data rate was 256Hz. Both the Locata and IMU were time-synchronised with GPS. The performance parameters of the inertial sensors are listed in Table 6.1.
Table 6.1 Specifications of the Honeywell H764 IMU
Gyros Accelerometers Bias 0.0035°/h 25μg Scale factor 0.0005% 0.01% Random noise 0.0035°/sqrt(h) 8.3μg (100Hz bw)
The GNSS and Locata solutions were processed independently. (Note the Locata hardware used in this experiment is the older version, thus the accuracy of the Locata solutions is not as high as for the latest version.) The RTK-GNSS solution, which was post-processed using the Leica Geo Office software, was used as the navigation system reference as it was estimated to have an accuracy of a few centimetres. No changes were made to the ground configuration during the trial. The trajectory of the field test is shown in Figure 6.3.
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Figure 6.3 Trajectory of the triple-integration system at the Locata Numerella Test Facility
6.3.1 System Performance of GOF based Triple Integration System
As the Centralised Kalman filter (CKF) and Federated Kalman filter (FKF) generate solutions of similar accuracy, and both FKF and GOF are examples of decentralised filtering strategies, Figure 6.4 shows a comparison between GOF and FKF position solutions. Since the experiment was conducted in a relatively flat area, a vertical constraint was applied. It can be seen that the vertical solutions of the two systems are almost the same, however in the horizontal north and east directions the GOF provides a more accurate and smoother solution. In particular during the circular motions from 250s to 600s, the shake error in the FKF solution is obviously improved in the GOF solution. The Mean Radial Spherical Error (MRSE) was also computed to evaluate the 3D positioning performance and the results are displayed in Table 6.2. The MRSE of the GOF-based triple-integrated solution is 0.13m, which is slightly lower than that of the CKF and FKF, namely 0.14m. The GOF shows a minor improvement of 7.1%.
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Figure 6.4 Position solution comparison between the FKF and the GOF-based triple- integrated solutions
In order to evaluate the precision performance of the data fusion algorithms, the corresponding a posteriori estimate error covariance ˆkP was also computed. Figure 6.5 shows the square root of the converged position and velocity error covariance
ˆkP of the FKF and GOF during the last 100 seconds of the test. The blue colour and red colour represent the precision of FKF and GOF solutions, respectively. The left three plots compare the position error covariance in the three direction components, and the right three plots are the velocity error covariance. It can be seen that the GOF estimate of the position and velocity error covariance for all three direction components is improved in comparison with the conventional decentralised FKF.
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Figure 6.5 Position and velocity precision comparison ( ˆkP ) between the FKF (blue line) and the GOF (red line) results during the last 100 seconds
An analysis was also made of the local systems GNSS/INS and Locata/INS, compared with the triple-integrated system. Figure 6.6 shows the position comparison. It can be seen that the triple-integration solution can provide the best positioning solution for the horizontal (north and east) components. From 650s to 1050s, the rover has three consecutive east-west runs. During this period, the geometry changes more obvious than other period. Locata, as a terrestrial ranging system, is more sensitive to the geometry change than GNSS when positioning. The oscillations of Locata/INS integration solution are just caused by the geometry change. From the results of the numerical analyses in Table 6.2, the MRSE of the GNSS/INS and Locata/INS are 0.14m and 0.19m respectively, while the MRSE of the GOF-based triple-integrated system is 0.13m, lower than either the GNSS/INS or Locata/INS solution. This can be confirmed that the GOF-based multi-sensor navigation system is able to provide higher accurate navigation solution compared with the conventional GNSS/INS and Locata/INS integration systems.
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Figure 6.6 Position solution difference comparison between the GOF-based triple- integration system, local GNSS/INS system and local Locata/INS system
As before, a position and velocity precision investigation was conducted. The square root of the corresponding a posteriori estimate error covariance was computed. Figure 6.7 shows the comparison of the converged estimated covariance square root between the GOF-based triple-integrated system and the local systems during the last 100 seconds of the test. The triple-integrated solution is plotted in red, and those of the local systems GNSS/INS and Locata/INS are plotted in blue and green, respectively. The left three plots show the comparison of the positioning error covariance in the three directions, and the right three plots show the velocity error covariance. It can be seen that the GOF-based triple-integration system has the smallest estimated position and velocity error covariance in all three direction components.
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Figure 6.7 Position and velocity precision comparison between the GOF-based triple- integration (red line), local GNSS/INS system (blue line) and local Locata/INS system (green line) during the last 100 seconds
Table 6.2 MRSE of triple-integrated system and local systems
Triple-integrated system Local system GOF FKF CKF GNSS/INS Locata/INS MRSE (m) 0.13 0.14 0.14 0.14 0.19
6.3.2 Evaluation of Adaptive GOF Method
The above results indicate that the GOF-based approach is superior to the alternative approaches, however the test was conducted under a good GNSS signal conditions. In real applications, the GNSS signals may be interfered with, especially in GNSS challenging environments such as urban areas. Typical GNSS failures can be categorised as follows (Heredia et al. 2008).
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Outlier failure. This is a temporal failure, where a single solution with a large error is output by the GNSS system, but the subsequent observations are correct.
Constant bias. The sensor output has a constant bias or drift term noise. For example, in an urban area severe multipath or poor GNSS satellite geometry may cause a solution to have a bias.
“Stuck with bias” sensor failure. In this failure type, the sensor gets “stuck with a bias”, and the output remains constant for a short period, then returns to normal. This situation may occur when a vehicle passes through a GNSS-obstructed area, like a tunnel or high rise building canyon. The GNSS satellite signals are unavailable for a short time, and the output is “frozen” during this period.
Sensor hardware failure. This is a catastrophic failure, such as when the sensor stops working and gives a constant zero output.
To evaluate the performance of the proposed adaptive fault-tolerant multi-sensor integrated navigation system, a series of failure simulations were performed. Figure 6.8 to Figure 6.11 show the results of the standard GOF and proposed adaptive GOF (AGOF) for several simulated GNSS failure scenarios. The failure types and the times in the data series are listed in Table 6.3.
Table 6.3 Simulated GNSS failures and periods
Time Slot Simulated Failure Description 600s, 610s, Outlier failure is simulated with adding a 10m error to GNSS position 620s, 630s outputs in three direction components for four time points Constant bias of 0.5m is added to GNSS position outputs in three 730s ~ 760s direction components during 30 seconds period The GNSS output is “frozen” at its 900s value and then returns to 900s ~ 920s normal operation after 920s 1010s ~ The GNSS output is switched to zero for a 20 seconds period 1030s
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Figure 6.8 shows the result of the two systems with the outlier failure scenario (failure type 1 in Table 6.3). The left three plots show the trajectory solutions for the north, east and vertical direction components. The right three are the enlarged plots to show the four outlier points more clearly. It can be seen that in the GOF system, the points with outlier failure indicate an obvious jump in all three direction components, whereas for the AGOF system the solutions are stable.
Figure 6.8 Comparison of the GOF and the AGOF with outlier failure simulation
Figure 6.9 shows results of the two systems with the constant bias simulation (failure type 2 in Table 6.3). As with Figure 6.8, the left three plots show the whole trajectory with simulated error, and the right three plots are the enlarged plots including the time period of failure simulation. It can be seen that the AGOF system does provide reliable positioning solutions, whilst the GOF system has large errors.
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Figure 6.9 Comparison of the GOF and the AGOF with constant bias simulation
Figure 6.10 shows the influence of “stuck bias” for the two systems (failure type 3 in Table 6.3). The position solutions with simulated error for all three direction components are shown in the left three plots, while the enlarged plots of the failure simulation time period are displayed in the right plots. The results for the GOF-based system are worse than for the failure scenario in Figure 6.9, whereas the AGOF system still maintains good performance during this period.
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Figure 6.10 Comparison of the GOF and the AGOF with “stuck bias” simulation
Figure 6.11 shows the results of two systems with error simulation of sensor hardware failure (failure type 4 in Table 6.3). It can be seen that the solution from the GOF system diverges when the failure occurs, while the AGOF system maintains the performance of the fault-free period.
To further evaluate the performance of the AGOF method, the proposed adaptive technique is also applied to the FKF (AFKF) as a comparator. Figure 6.12 and Figure 6.13 compare the AFKF and AGOF-based systems in the cases of all four simulated failure types, and in the case of no failure. The RMS values are listed in Table 6.4.
The results indicate that both the AGOF system and the AFKF system can overcome GNSS failures and generate converged solutions. However, in the case of the AFKF the results still have an obvious jump during the failure periods. In the case of the AGOF there is only a slight difference between the results of the AGOF systems with and without simulated failures. From Table 6.4 it can be seen that the accuracy of the AGOF with-failure system is at the same level as the no-failure system. Hence it can be concluded that the proposed AGOF method has better capability for providing accurate and fault-tolerant navigation solutions.
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Figure 6.11 Comparison of the GOF and the AGOF with GNSS stop working simulation
Figure 6.12 Comparison of the AFKF-based system with and without failure simulation
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Figure 6.13 Comparison of the AGOF-based system with and without failure simulation
Table 6.4 RMS of the AFKF and the AGOF solutions with and without failure simulation
North East Vertical Without failure (m) 0.09 0.11 0.01 AFKF With failure (m) 0.10 0.12 0.01 Without failure (m) 0.08 0.11 0.01 AGOF With failure (m) 0.08 0.11 0.01
6.4 Summary
In this chapter, a novel adaptive fault-tolerant multi-sensor integrated navigation system is described. An improved multi-sensor navigation model is presented which fuses multiple redundant navigation sensors, including INS, GNSS, and Locata. In order to maintain the reliability characteristics of conventional decentralised filtering, but to improve the system accuracy, the GOF data fusion algorithm based on the information space concept is implemented. The GNSS and Locata are individually integrated with the INS to independently obtain the local predictions and local estimates of the local 126
Chapter 6 Multi-sensor Navigation System based on an Adaptive Fault-tolerant GOF Algorithm
GNSS/INS and Locata/INS systems. In each local filter, the adaptive technique based on the innovation covariance discrepancy is applied to improve the system reliability. The GOF algorithm is then applied to fuse the local and global information to generate the global optimal state estimate of the GNSS/Locata/INS integrated navigation system.
In order to evaluate the performance of the proposed method, real-world test data were conducted. A comparison between GOF and conventional multi-sensor data fusion algorithms indicates that the GOF approach does indeed generate improved positioning solutions. Further comparison of the GOF-based triple integration solution with the local GNSS/INS and Locata/INS solutions shows that the GOF-based approach is superior to alternative approaches. To evaluate the fault-tolerant ability of the proposed system, a series of GNSS failure scenarios were simulated. The results show that the proposed system is not affected by these failures, confirming the higher reliability and fault-tolerant capability of the proposed system.
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7.1 Introduction
Global Navigation Satellite System (GNSS) can provide 24/7 high accuracy positioning, navigation and timing (PNT) services to outdoor applications such as surveying and geodesy, car and personal navigation, airborne mapping and sensor geo-referencing, and many others. In addition to the conventional outdoor location based service (LBS), there are many needs for indoor positioning, for example, warehouse logistics management, fire fighting, rescue and emergency services, underground construction, etc. Many of these applications require comparatively high accuracy but are beyond current positioning capability because GNSS signals are unavailable in many indoor environments. Alternatives to GNSS are the many radio-frequency approaches that have been developed over the past decades, including Bluetooth (Altini et al. 2010; Fischer et al. 2004), Radio Frequency Identification (RFID) (Chumkamon et al. 2008), Ultra Wideband (UWB) (Gigl et al. 2007), Wireless Local Area Net (WLAN) and terrestrial ranging techniques. In addition, self-contained inertial navigation technology is widely used for indoor pedestrian navigation. Table 7.1 compares some key indoor technologies with respect to their typical accuracy and coverage (Mautz 2012). It can be seen that, of all techniques considered, terrestrial ranging approach can, in principle, achieve accuracy at the centimetre to decimetre level.
Table 7.1 Overview of indoor positioning technology Indoor sensors Typical accuracy Typical coverage Bluetooth m 5m-10m WLAN/WiFi m 20m-50m RFID dm-m 1m-50m UWB cm-m 1m-50m Terrestrial ranging technique cm-dm 10m-1000m INS 1% 10m-100m
128 Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals
“Locata”, as a terrestrial ranging technology, has been shown to be able to deliver accurate positioning solutions in outdoor environments. However, the system’s indoor performance still cannot compete with its outdoor performance because of the more severe multipath effect in indoor environments. A transmitted signal may reach the receiver by more than one path, and cause deep fading and pulse spreading of the signal (Tam and Tran 1995), and the multipath disturbance for a terrestrial-based PNT system is very challenging to overcome. The typically used multipath-mitigating approach of “elevation masking” is not suitable here since there are more reflective surfaces, and many of them tend to be perpendicular to the signal path. Several techniques have been implemented in radio systems to minimise multipath, including correlation techniques and radio frequency techniques (LaMance and Small 2011). However these are primarily used for anti-jam applications and are not effective against multipath because of the relatively wide signal beamwidth. A new multi-beam antenna – the Locata “V- Ray” – designed to mitigate multipath effects by use of tight beams is described in section 7.2.
The receiver sweeps the beams and searches for the optimal beam settings that point directly to the Locata transmitters. Direct line-of-sight pseudorange and carrier phase measurements can then be obtained. In addition to the standard range measurements, the V-Ray antenna can be used to determine the body frame attitude using angle-of-arrival measurements (LaMance and Small 2011). The V-Ray antenna has a spherical shape, and hence the formed beams can be pointed in any direction and used to determine 3D attitude with a single antenna. Attitude determination based on these unique Locata angle-of-arrival measurements is described in section 7.3.
The conventional method for attitude determination using GNSS is to set up three (or more) receivers/antennas on the platform and to determine the relative positions of each from differenced carrier phase measurements (Cohen 1996). In this study, a position and attitude modelling system (PAMS) is proposed for the determination of position, velocity and platform attitude using a single Locata receiver/antenna.
The range and angle measurements are processed simultaneously by one system filter. Unlike conventional attitude determination using gyroscopes, the PAMS does not need 129
Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals to deal with time-dependent drift errors. Since both the range measurement model and the angle measurement model are non-linear, the Unscented Kalman filter (UKF) is adopted. A short description of the UKF and details of the PAMS are presented in section 7.4.
The PAMS is evaluated in a field test conducted in a metal warehouse, and the analyses are discussed in section 7.5.
7.2 Locata Multipath-mitigation Technology
Locata uses signals chipped at 10.23MHz, which reduces the chip distance to about 30 metres and makes it easier to eliminate the long-wave multipath that causes more than two chips delay. However, in indoor environments, the challenging problem for Locata receivers is short-wave multipath causing delays of less than one chip.
An effective way to reduce the multipath disturbance of the transmitted signal is by “pointing” a narrow beam antenna in the known signal direction, which inhibits the reception of signals from all but the desired direction. With a sufficiently narrow beam, the multipath-corrupted signals can be removed at the user receiver. However, narrow beams are hard to generate, and would ordinarily require a large number of antenna elements. The typical beam-forming antennas use multiple RF front-ends to form tight beams, however the cost and phase-based positioning precision degradation limits the usefulness of such beam-forming antennas.
Locata’s new beam-forming method is known as Correlator Beam-Forming (CBF). This technique creates beams by sequentially switching through each element of an antenna array, and forming the beam with phase and gain corrections in the receiver’s individual channel correlators using only one RF front-end. The CBF gives each receiver channel the capability to independently “point” beams. The V-Ray antenna is capable of generating multiple beams, simultaneously, in different directions. The elements are sequentially switched, and the elements are sequenced completely during a signal integration interval. During each switch interval the gain and phase of the incoming
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Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals signal is adjusted within the correlator by modifying the phase and amplitude of the carrier DCO to form the desired beam. The process is illustrated in Figure 7.1 (LaMance and Small 2011).
Figure 7.1 Locata V-Ray principle (LaMance and Small 2011)
To mitigate multipath the beams must be pointed in the directions of the LocataLites. The position of each LocataLite is known, thus each beam’s direction is dependent on the location of the rover and the orientation of the antenna. Approximate position and orientation are estimated from angle-of-arrival measurements by analysing the signals obtained from different beam settings. The receiver sweeps the beams searching for beam settings that maximise the signal from each LocataLite.
The current “V-Ray” antenna is a basketball-sized spherical array consisting of 20 panels with 80 elements. Each panel comprises four elements arranged with one central element and the three other elements forming a triangle. The element spacing between each panel is half the signal wavelength (LaMance and Small 2011). The V-Ray beam- forming antenna is shown in Figure 7.2.
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Figure 7.2 Locata beam-forming V-Ray antenna
V-Ray needs only one RF front-end for all elements, resulting in a simpler and less expensive antenna design. Every beam is controlled individually, hence as the platform on which the antenna is mounted moves, each beam adjusts dynamically. The elements are switched through at a rate of 80 elements every 100 microseconds, and more than 2.5 million individual steered beams per second can be produced. The switches are implemented by a simple Programmable Logic Device (PLD), and the timing for the PLD switch control is provided by the digital section of the receiver.
With its spherical shape the V-Ray antenna has the ability to point in any direction (i.e. 3D). The new generation Locata receiver is designed to deal with hundreds of simultaneous unique beams, and hence can make measurements from many directions at the same time. However, the Locata receiver used in this experiment had experimental firmware that only enabled it to process thousands of beams per second, hence only the azimuth measurements could be decoded to generate one-axial orientation solutions.
7.3 Locata Position and Attitude Computation Model
7.3.1 Locata Indoor Position Computation Model
The Locata range measurement models have been discussed in section 3.2. For indoor precise positioning, the carrier phase measurements are used. Unlike outdoor 132
Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals positioning, Locata signals have severe problems due to cycle slips and loss-of-lock. The presence of cycle slips would cause a change of the ambiguity value, which would create inconsistencies in the solutions, resulting in biased coordinate solutions.
Low signal-noise-ratio (SNR) values can be a useful indicator of an increased risk of cycle slips in the associated measurement, however the SNR indicator is not always reliable because cycle slips can also occur during periods of good SNR (Shockley 2006). Another detection strategy makes use of the typical Locata signal set-up, where a group of four signals are transmitted from the same LocataLite. This method uses the double- differenced (DD) carrier phase measurements to detect cycle slips. The first difference is made on the raw carrier phase measurements from Locata signal i between two subsequent epochs t1 and t2 to eliminate the ambiguities and any unchanged error:
ii i 1 tt 2 )()( (7.1)
Each LocataLite transmits four signals from the same location, or a very close location (since two transmit antennas and each antenna transmit two signals), thus the second difference is made between the four signals from the same LocataLite, see Equation (7.2). If there are no cycle slips, the DD carrier phase measurements would only have the receiver clock drift and other unmodelled errors, which can be assumed to have very small value (Bertsch 2009):
ij i j 1 tt 2 )()( (7.2)
Then by comparing the six DD carrier phase measurements from each LocataLite the channel that contains the cycle slip(s) will exceed the threshold of 0.32 cycles. If all the DD carrier phase measurements that are larger than the threshold contain a specific signal, then this specific signal is assumed to be responsible for the cycle slip.
After the cycle slip is detected there are two ways to proceed: either to repair the cycle slip in the raw carrier phase measurement(s), or to re-fix the ambiguities. Since Locata’s cycle slips may be multiples of half cycles, which makes them harder to repair, the
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Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals second approach is adopted. The navigation algorithm first calculates the rover’s location from the (assumed correct) carrier phase measurements (without cycle slips), then re-fixes the ambiguities with the calculated position, and finally uses the re-fixed ambiguities as known parameters in the subsequent positioning solutions.
7.3.2 Locata Attitude Computation Model
V-Ray is a 3D antenna which can, in principle, measure attitude angles in three orthogonal directions. However, the firmware version that was available for these tests only allowed for the measurement of azimuth. The azimuth angle measurement is the angle between the signal source (the LocataLite) and the reference direction on the receiver’s body frame, see Figure 7.3, where is the orientation angle of the platform and is the measured azimuth angle.
Figure 7.3 Geometry of Locata azimuth angle measurement
The angle measurement function can be written as:
xx (7.3) arctan LL R LL yy R
where xLL and yLL are the horizontal coordinates of the LocataLites in the local reference frame, and xR and yR are the horizontal coordinates of the receiver in the same frame.
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7.4 Locata Position and Attitude Modelling System (PAMS) Mechanisation
7.4.1 UKF Introduction
The EKF is a commonly used estimator for navigation systems, however it has several drawbacks due to the linearisation scheme that is employed. In the EKF the state distribution is propagated through the first-order linearisation of the non-linear system (using the Jacobian matrix). This process will introduce large errors in the true a posteriori mean and covariance of the transformed variables which leads to sub-optimal performance, and sometimes filter divergence (Wan and Van 2000). To overcome this shortcoming, the Unscented Kalman filter (UKF) has been developed using a deterministic sampling approach (Julier et al. 1995). The basic premise of the UKF is that it is easier to approximate a probability distribution than an arbitrary non-linear function. The state distribution is represented by a set of selected sample points which capture the mean and covariance information. The sample points are directly propagated through the true non-linear function, and hence the linearisation of the model is not necessary (Zhang et al. 2005). The a posteriori mean and covariance can be represented accurately to the third-order of Taylor series expansion of the non-linear function, which has obvious advantages over the EKF.
7.4.1.1 Unscented Transformation
The unscented transformation (UT) is the first step of the UKF, and used to generate the sample points. Consider an n-dimensional random variable x having mean xˆ and covariance P . Suppose that it propagates through an arbitrary non-linear function f . The UT creates the n 12 sigma vector X . The sigma points in the state space and associate weights W are given by:
0 ˆ k|kxk|kX (7.4)
(7.5) i ˆ i ,,2,1 nik|kPκnk|kxk|kX
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(7.6) ni ˆ i 21 ,,ik|kPκnk|kxk|kX ,n
κ (7.7) W m 0 κn
mc 2 (7.8) 00 1 baWW
1 (7.9) m WW c ,,2,1 ni i i 2 κn
where k|kPκn i is the i th row or column of the matrix square root
k|kPκn . k|kPκn which can be obtained from the lower-triangular matrix of Cholesky factorisation; 2 nna is a scaling parameter; a determines the spread of the sigma points around xˆ and is usually set to a small positive value
( e 141 ); is a second scaling parameter which is usually set as 0; b is a parameter used to incorporate any a priori knowledge about the distribution of xˆ (when
m c x is normally distributed, b 2 is an optimal value); and Wi and Wi are the weight for the mean and covariance associated with the i th point, respectively.
The sigma vectors are propagated through the non-linear function to yield a set of transformed sigma points:
i i 2,,2,1 niXfy (7.10)
The mean and covariance of yi are approximated using a weighted sample mean and covariance of the a posteriori sigma points:
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2n m (7.11) ˆ i yWy i i0
2n c (7.12) yy i i yyWP ˆ i0
7.4.1.2 The Unscented Kalman filter
First the set of sigma points are created using Equation (7.5) and Equation (7.6). After the sigma points have been generated, the UKF approach can be represented as time update and measurement update processes.
Time update:
The transformed set is given by substituting each point into the dynamic model:
i kX 1|k i k|kXf ,k ,,2,1 ni (7.13)
The predicted mean and the predicted covariance can be formed:
2n m (7.14) ˆkx 1|k i i kXW 1|k i0
2n c T (7.15) kP 1|k i i kXW 1|k ˆ kx 1|k i kX 1|k ˆ kx 1|k kQ i0
Measurement update:
The prediction point is propagated by the measurement model:
i kZ 1|k i kXh |k ,k 11 (7.16)
Predicted observation is: 137
Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals
2n m (7.17) ˆkz 1|k i i kZW 1|k i0
Innovation covariance and cross-covariance can be computed as:
2n c T (7.18) zz kP 1|k i i kZW 1|k ˆ kz 1|k i kZ 1|k ˆ kz 1|k kR 1 i0
2n c T (7.19) xz kP 1|k i i kXW 1|k ˆ kx 1|k i kZ 1|k ˆ kz 1|k i0
Performing an update using the nominal Kalman filter (KF) gives:
1 (7.20) xz kPkK |k zz kP 111 |k
ˆkx |k 11 (7.21)
ˆkx 1|k 11 ˆ kzkzkΚ 1|k
kP |k 11 (7.22) Τ kP 1|k zz kPkK |k kK 111
7.4.2 PAMS Estimation Process
The PAMS system is designed with a common filter to process range and azimuth measurements simultaneously, and output the full set of navigation parameters (position, velocity, acceleration and attitude).
7.4.2.1 Dynamic Model
A benefit of a KF approach compared with the conventional least–squares method is the KF’s utilisation of a dynamic model for the moving platform. The state vector of the system consists of ten parameters (three for position, three for velocity, three for acceleration and one orientation angle) and n-differenced carrier phase ambiguities: 138
Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals
T ψrrrtx ΔN 1 j ΔΝ nj (7.23)
The acceleration and the single-differenced (SD) ambiguities states are modelled as first-order Gauss Markov process and random walk process, respectively – Equation (3.3) and Equation (3.4). The orientation angle is also modelled as a random walk process:
(7.24)
The dynamic model is:
tωtxtFtx (7.25) where 0 I 0 0 3333 33 n 13 0 0 I 0 33 3333 n 13 tF 1 , 0 0 I 0 33 33 33 n 13 τ 0 0 0 0 n 31 n 31 n 31 nn 11
T tω 00 3131 ψaaa ωωωωω ΔN1 j ωΔN nj
7.4.2.2 Measurement Model
The carrier phase and azimuth measurement functions – Equation (3.1) and Equation (7.3) – are both non-linear, thus the PAMS measurement model is non-linear. The measurement model of the Locata filter is:
ttxhtz (7.26) where tz is the measurement vector of the filter, which is formed by the SD carrier phase measurements and azimuth measurements:
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T (7.27) m αΔtz m 211
T 1 j ΔΔ 2 j mj 21 αααΔ m2 where m represents the number of SD carrier phase measurements. Since the Locata signals are transmitted on two frequencies and the azimuth measurements are not single- differenced, the number of azimuth measurements is m 2 .
txh is the non-linear transformation function, which can be represented as:
T (7.28) α txhtxhtxh
where φ txh and α txh are derived from the carrier phase and azimuth measurement functions in Equation (3.1) and Equation (7.3). t ~N 0,R is the measurement noise. The R matrix consists of SD carrier phase and azimuth components, given by:
(7.29) RΔ R Rα
The azimuth measurement covariance sub-matrix can be written as:
2 IσR mmαα 22 (7.30)
2 where is the noise variance of the azimuth measurements.
7.5 Experiment and Analyses
The indoor experiment was conducted in a metal building at Locata Corporation’s Numerella Test Facility (NTF), located in rural NSW, Australia. The warehouse was mostly empty with the exception of some furniture and tools placed near the walls. Five
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LocataLites were installed in the corners of the warehouse. Table 7.2 lists the coordinates of the five LocataLites in latitude (degree), longitude (degree) and height (metre). A Locata rover receiver was placed on a trolley with a V-Ray antenna and conventional omni-directional antenna mounted on it. Figure 7.4 shows the testing environment. The benchmark system was an auto-tracking Total Station (TS), which could provide position and orientation information. The orientation of the antenna from the TS was determined by measuring the two prisms on the bar as can be seen in Figure 7.4.
Figure 7.4 Indoor testing environment at the NTF
Table 7.2 Configuration of LocataLites for indoor testing
Latitude (degree) Longitude (degree) Height (metre) LocataLite 1 -36.157310 149.255936 858.764 LocataLite 2 -36.157309 149.255774 858.770 LocataLite 3 -36.157045 149.255775 858.766 LocataLite 4 -36.157047 149.255938 858.764 LocataLite 5 -26.157148 149.255775 857.749
It can be seen from Table 7.2 that the LocataNet was setup in an almost planar configuration and that the line-of-sight between the rover and the LocataLites is also mainly horizontal. Thus the vertical geometry is not good enough for height 141
Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals determination. For that reason a pre-measured distance between the antenna and the ground is used to constrain the height solutions.
In order to evaluate the multipath mitigation ability of the V-Ray, the carrier phase errors of the V-Ray antenna and the conventional omni-directional antenna are compared in Figure 7.5. The carrier phase errors are calculated at a precise surveyed point. It can be seen that calculated carrier phase errors of the V-Ray antenna for all 18 channels are less than 0.2 cycle (the wavelength of Locata signal is approximate 0.12m), while the carrier phase received by the conventional omni-directional antenna cannot be used because they are of such poor quality.
Figure 7.5 Comparison of calculated carrier phase error between V-Ray antenna (top) and conventional omni-directional antenna (bottom)
Using the range and azimuth measurements from the V-Ray antenna, the PAMS is used to estimate the position and orientation of the host platform. As the Locata indoor geometry change is not as great as for an outdoor environment, the system first takes a short period of time to converge. The float-valued ambiguities are computed using the on-the-fly (OTF) method. The trajectory is shown as the blue line in Figure 7.6, while the red dots represent the static points, and the blue dots are the locations of the
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LocataLites. The Locata rover receiver commenced at the start point and then moved sequentially to other points, stopping at each point for several minutes. The trajectory includes 10 static check points.
Figure 7.6 Locata trajectory and LocataLite installations for indoor testing
Figure 7.7 shows the DD carrier phase measurements and cycle slip detection. The cycle slip affected measurements are detected using a threshold of 0.32 cycles, as illustrated by the red line in the plot. It can be seen that most of the DD observables are less than 0.2 cycles, though some are larger than the threshold.
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Figure 7.7 DD carrier phase measurements and cycle slip detection
Figure 7.8 – Figure 7.10 show the Mean and Standard Deviation (STD) values of the north and east position components and the orientation solution. The 10 bar charts in each plot represent the solutions at the 10 static points. It can be seen that in all cases the positioning accuracy in the north and east components is less than 5cm, and the orientation accuracy is better than 0.7 degrees. The STD value indicates that the solution is stable.
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Figure 7.8 Mean and STD of the position difference in the north component
Figure 7.9 Mean and STD of the position difference in the east component
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Figure 7.10 Mean and STD of orientation differences
As discussed in section 7.3, both Locata range and azimuth measurement functions are non-linear, thus the UKF was implemented in the PAMS instead of the commonly used EKF. A comparison of the horizontal positioning performance, including the convergence process of UKF and EKF, is shown in Figure 7.11, where the blue and the red bars denote the Distance Root Mean Square (DRMS) values of the EKF and UKF position solutions, respectively. It can be seen that the UKF system has better performance during the initialisation, as reflected in a smaller initial error and a faster convergence speed. After the filter has converged, the two solutions have the same positioning error trends, although the UKF solution has a higher horizontal positioning accuracy. The Root Mean Square (RMS) comparison of the converged solutions is given in Table 7.3. The UKF has a lower RMS for both horizontal directions: 0.02m for the north component and 0.03m for the east component. Compared with the EKF solution, the UKF solution has an improvement of 50% and 25% for the north and east components, respectively.
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Table 7.3 RMS comparison of positioning differences
RMS (m)
North East EKF 0.04 0.04 UKF 0.02 0.03
Figure 7.11 Comparison of horizontal position differences calculated using the EKF and UKF
Due to the azimuth measurements available from the V-Ray antenna, the azimuth measurements can be used to estimate the orientation, as well as contribute to horizontal position determination. Figure 7.12 shows horizontal positioning performance of the integrated range-azimuth system compared to the standard range-only system configuration. The range-based system was also estimated using the UKF with OTF on an epoch-by-epoch basis. The bar charts in the plot are the DRMS calculated at the 10 static check points. The red and blue bars represent the range-azimuth integrated system and the range-only system, respectively. The DRMS of the 10 points computed via the range-based system is 0.07m, and that computed using the PAMS is 0.04m, an improvement of 42.9%. 147
Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals
Similarly, the orientation RMS of the integrated PAMS system compared to the typical azimuth-only system configuration is shown in Figure 7.13, where the PAMS solution is shown in red bars and the blue bars denote the azimuth-only solution. From Figure 7.13 it can be seen that the orientation solution computed using the PAMS is of higher quality than the azimuth-only solution at all 10 check points. The RMS of orientation computed by the PAMS is 0.32 degrees compared to that of the azimuth-only solution which has 0.39 degree RMS, an improvement of 18%.
Figure 7.12 DRMS comparison between typical range-based system and the integrated range-azimuth system
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Figure 7.13 Orientation RMS comparison between azimuth-based system and the integrated range-azimuth system
7.6 Summary
This chapter presents the results of a new position and attitude modelling system based on an innovative correlator beam-forming antenna that can provide accurate navigation information in indoor environments even in the presence of severe multipath. The PAMS algorithm was developed to process the carrier phase and azimuth measurements simultaneously via an UKF, so as to obtain the complete set of navigation parameters – position, velocity, acceleration and orientation. The indoor test was conducted in a metal warehouse subjected to considerable signal multipath disturbance. A beam- forming antenna connected to a Locata rover receiver was moved slowly around the room, stopping at 10 static check points. Comparing trajectory solutions confirmed that the horizontal position accuracy was about 5cm and the orientation has an accuracy of better than 0.7 degrees. A comparison of system models based on the UKF and EKF was conducted, indicating that: 1) the UKF has a better performance with respect to system convergence; and 2) the accuracy of the UKF-based PAMS is better than the EKF. A comparison of the PAMS and conventional algorithms that compute range- 149
Chapter 7 Precise Indoor Positioning and Attitude Determination Using Terrestrial Ranging Signals based position and azimuth-based orientation solutions was also conducted. The results indicate that both the positioning and orientation accuracies computed using the PAMS are higher than using the conventional algorithms.
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8.1 Concluding Remarks
Precise positioning and navigation plays an important role in surveying and mapping applications, precise navigation and vehicle guidance systems, and many other applications. GNSS has been widely used to provide accurate position, velocity and time on a 24/7 basis. However, due to limitations on its availability in urban areas, as well as its vulnerability to signal interference, attention is focused on augmenting GNSS for critical applications. Integrated GNSS/INS systems have been developed during the past few decades to overcome the inherent drawbacks of each component system, and such integrated systems are increasingly used in many kinematic surveying, mapping and navigation applications that require precise and continuous position, velocity and attitude information. Although significant progress development in GNSS/INS direct geo-referencing technology has taken place in the last decades, its performance in terms of accuracy and vulnerability when used in challenging GNSS environments still needs to be improved. GNSS measurements calibrate the inertial sensor errors and subsequently feedback to the INS in order to correct the raw inertial sensor measurements. Therefore the system performance relies heavily on the quality of GNSS measurements. Under some circumstances there may be an insufficient number of visible satellites, and/or the satellite geometry is poor. Moreover, if GNSS signal blockage occurs, the system navigation errors rapidly increase with time as the system operation mode is switched to an INS standalone mode. Such a scenario is unfortunately a common occurrence for kinematic applications. It is therefore necessary to strengthen the availability, accuracy and integrity of the integrated system navigation solutions, by improving the GNSS/INS integration technology and/or combining it with other measurements. This study has focused on an integration of GNSS, INS and terrestrial ranging technologies for high precision kinematic positioning and navigation. The objectives of this thesis can be summarised as:
To develop a more accurate and robust Locata positioning and navigation system, including investigating the carrier phase measurement model with initialisation 151 Chapter 8 Conclusions and Recommendations
process resolved on-the-fly (OTF), and improving the system dynamic model estimate position, velocity and acceleration navigation parameters; and extending the current Locata positioning for Locata/INS integration when GNSS is not available.
To investigate the GNSS precise point positioning (PPP-GNSS) methodology, and combine PPP-GNSS and Locata positioning methods so as to build a Locata augmented PPP-GNSS system, which can take advantage of both technologies, in order to improve the system performance in terms of convergence and navigation accuracy.
To develop a multi-sensor navigation system that implements GNSS, Locata and INS technologies. In order to make the system more accurate and reliable data fusion algorithms are analysed and compared, an adaptive fault-tolerant multi-sensor navigation method which can decrease the adverse influences caused by changes in the sensor measurement stochastic characteristics has been proposed.
To evaluate Locata’s indoor positioning ability when using the new multipath- resistant “V-Ray” antenna. By taking advantage of the available range measurements and azimuth measurements, an indoor positioning and attitude determination algorithm has been tested. The algorithm can output the full suite of navigation parameters (including position, velocity, acceleration and attitude) simultaneously from a single Locata user receiver with better navigation accuracy.
The research work addressing these objectives, as reported in this thesis, is summarised below.
8.1.1 Locata Positioning and Integration of Locata and INS Technology
Although centimetre-level accuracy is possible for Locata positioning using carrier phase, the current Locata ambiguity resolution is carried out via the so-called “known point initialisation” (KPI) or batch least squares method. In this study, Locata ambiguity can be resolved OTF without the need for any pre-initialisation. This method takes
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Chapter 8 Conclusions and Recommendations advantage of the rapid geometry change of the Locata transmitters (the LocataNet) with respect to a user receiver to estimate the ambiguities as floating or real-valued quantities on an epoch-by-epoch basis. Within a short convergence period, the ambiguities can be resolved to a converged “fixed” value.
To improve the precision of the estimation and to simplify the measurement model, the carrier phase measurements are processed in the single-differenced mode, thus the unknown parameters are reduced to only the user’s location and the carrier phase ambiguities. The Extended Kalman filter is applied to estimate the unknown parameters. In the system dynamic model, the acceleration is modelled as a first-order Gauss Markov (GM) process so that the position, velocity and acceleration can be estimated at every measurement epoch. A maritime field experiment was performed to evaluate the performance of this Locata positioning system.
The positioning geometry was analysed. The average horizontal dilution of precision (HDOP) was 0.6, and the horizontal geometry is dependent on the signal availability and the relative position between the maritime vessel and the LocataNet. When the vessel moved far away from the Master LocataLite, the geometry would be rather poor. A comparison between the OTF-based Locata positioning system and the KPI-based Locata positioning system was conducted. Both can achieve centimetre accurate horizontal position solutions. However, OTF approach seems to generate higher accurate solutions, with an improvement of 14.3% in Distance Root Mean Square (DRMS) compared to the KPI approach.
Locata/INS integration can be used as an alternative to the conventional GNSS/INS integration system when GNSS measurements are not available. The Locata position and velocity solutions are used to correct the INS solutions within an integration Kalman filter. The Locata phase centre is corrected to the Inertial Measurement Unit (IMU) centre by estimating the lever arm between Locata antenna and the IMU reference point. The estimated sensor errors and lever arm are fed back to the INS, to enable a closed-loop update correction. The Locata/INS integration system was evaluated using the maritime dataset. The integrated solution demonstrated a better position solution compared with Locata-only technology, with an improvement of 20%
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Chapter 8 Conclusions and Recommendations in terms of DRMS. The velocity comparison between the integrated system and Locata standalone system showed a more obvious improvement – 92.6% of DRMS. The main reason is that the velocity component has better observability compared with the position component from the view of INS navigation mechanisation.
This part of the research work demonstrated that: (1) Locata-only OTF-based positioning does not need any pre-initialisation, and at the same time can provide more accurate navigation solutions than the conventional KPI-based Locata method; (2) the Locata/INS integration mechanisation is able to provide optimal navigation solutions, better than both the INS standalone solution and the Locata-only solution; and (3) Locata can be treated as a GNSS alternative navigation technology, which can be used when GNSS measurements are not available.
8.1.2 Locata-augmented GNSS Precise Point Positioning
Because network-based real-time kinematic (N-RTK) precise carrier phase-based GNSS positioning has limited operational range and considerable system cost and complexity, GNSS precise point positioning (PPP) is becoming an increasingly attractive alternative. However, PPP techniques typically require long convergence periods, especially for kinematic positioning, and the resultant accuracy is not as high as in the case of N-RTK solutions. It is possible to augment GNSS with both Locata and GNSS technology. The local geometry can be improved because of Locata’s ground-based design, and the initial convergence period should be shorter as user’s kinematic motion results in faster transmitter-receiver geometry change and hence better conditions for reliable estimation of the ambiguities.
In the proposed Locata-augmented PPP-GNSS system, the Locata measurement model described in chapter 3 was adopted. The PPP-GNSS measurement model is processed in single-differenced mode to eliminate the receiver clock error, and other GNSS measurement errors are dealt with either by modelling or estimation, wherever possible using International GNSS Service (IGS) products. Locata and GNSS carrier phase measurements are processed in a tightly-coupled mode, where both Locata and GNSS carrier phase ambiguities are estimated as float-valued quantities. For the system
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Chapter 8 Conclusions and Recommendations dynamic model for estimation filtering the acceleration is modelled as a first-order GM process.
The navigation performance of the proposed Locata-augmented PPP-GNSS was evaluated using the maritime kinematic dataset, and compared with PPP-GNSS and Locata standalone solutions. From the geometry point of view, the HDOP and VDOP of the Locata-augmented PPP-GNSS solution were 0.42 and 0.63 respectively, which is an obvious improvement from Locata standalone geometry and PPP-GNSS geometry. The Locata-augmented PPP-GNSS also produced better positioning solutions than for the other two approaches, with the DRMS improvement being 33.3% against the Locata standalone solution, and 63.6% against the PPP-GNSS solution. In this maritime test, the proposed system converged in 10 seconds, which was much faster than the 500 seconds convergence period for the PPP-GNSS approach, or the 20 seconds convergence period for Locata in the standalone mode.
This part of the research work demonstrated that: (1) Locata technology can augment the current widely used PPP-GNSS method, and compensate for the lower accuracy and longer convergence time of PPP-GNSS on its own; (2) the proposed Locata-augmented PPP-GNSS system is able to provide optimal performance in terms of navigation accuracy and initialisation time, better than either the Locata standalone system or PPP- GNSS mode; and (3) the advantages of the proposed system distinguish it from the conventional PPP-GNSS system and confirm it as an effective navigation approach which could be used for some kinematic applications.
8.1.3 GNSS/Locata/INS Multi-sensor Navigation System
It has been proved that both GNSS/INS and Locata/INS integration approaches are valid navigation strategies for kinematic positioning and navigation. As GNSS is not always available, an integrated system based on combining GNSS, Locata and INS could be the basis of a robust system. In this study, GNSS and Locata are fused with the INS in a loosely-coupled architecture. In the multi-sensor navigation system, the core element is the data fusion algorithm. The most commonly used fusion algorithms – Centralised Kalman filtering (CKF) and Decentralised Kalman filtering (DKF) – were
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Chapter 8 Conclusions and Recommendations analysed in terms of system reliability and computational burden. In the case of decentralised architecture, the Federated Kalman filtering (FKF) and the Global Optimal filtering (GOF) algorithms were the focus of investigation. In contrast to the CKF and FKF, the GOF algorithm is based on the information space concept which utilises the full information sources of local measurements, local predictions and global prediction. The GNSS/Locata/INS multi-sensor navigation system with implemented CKF, FKF, and GOF have been developed and evaluated.
The system evaluation was conducted using the maritime kinematic dataset referred to earlier. By analysing the position and velocity solutions generated by the three algorithms it was found that all three data fusion algorithms could provide centimetre- level positioning and centimetre-per-second-level velocity accuracy. Compared to the CKF and FKF, the GOF-based approach indicated a higher accuracy and better stability, with the improvement in the velocity parameter more obvious than for the position component. The CKF and FKF-based approaches had similar system performance. Further analysis was conducted in order to evaluate the system precision by calculating the a posteriori estimated error covariance. It can be concluded that the GOF estimated position and velocity error covariance have obvious improvements in comparison with those generated by the CKF and FKF algorithms.
Although a GOF-based multi-sensor navigation system has been shown to be capable of providing accurate and stable navigation solutions, in practical applications environmental changes may cause the sensor measurement characteristics to change, and failure may even result in severe conditions. Therefore, besides accuracy and stability, system robustness and fault tolerance is also a fundamental factor to be considered in navigation system design. In this study, an adaptive fault-tolerant filtering algorithm based on innovation covariance discrepancy has been proposed to adaptively adjust the measurement statistics. When used in the GNSS/Locata/INS multi-sensor navigation system, adaptive fault-tolerant filtering was first implemented in the local GNSS/INS and Locata/INS local systems, then the solutions from the two systems were optimally fused together by the GOF algorithm.
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A vehicle experiment dataset was processed to evaluate the performance of the proposed multi-sensor navigation system. The results demonstrated that for vehicular navigation, the GOF-based GNSS/Locata/INS system was optimal, better than those multi-sensor navigation systems implemented with other data fusion algorithms and other available GNSS/INS and Locata/INS systems. To evaluate the system robustness and its fault-tolerant capability, typical GNSS failures such as outlier failure, constant bias, ‘stuck with bias’ sensor failure, and sensor hardware failure, were simulated. The proposed GOF-based adaptive navigation system, the standard GOF-based system, and the FKF algorithm-based adaptive multi-sensor navigation system were evaluated. The results indicate that only the GOF-based adaptive system and the FKF-based adaptive system could provide continuous navigation solutions for all the four failure scenarios. The GOF-based adaptive system had higher accuracy than the FKF-based adaptive system during failure periods.
This part of work demonstrated that: (1) the theoretical foundation of the GOF data fusion algorithm was proved to be valid and capable of providing more optimal solutions compared with conventional CKF and FKF algorithms; (2) the proposed GNSS/Locata/INS multi-sensor navigation system was able to output accurate navigation solutions, and was superior to the alternative navigation strategies, including the common GNSS/INS and Locata/INS strategies; and (3) by applying the adaptive filtering algorithm, the robustness and fault-tolerant capability of the system was considerably improved.
8.1.4 Locata Indoor Navigation
GNSS technology cannot provide precise positioning in indoor environments because of the severe signal power attenuation and multipath. On the other hand, Locata can be implemented indoors. The Locata “V-Ray” antenna was designed to mitigate multipath effects by creating “tight” beams and searching only for the direct line-of-sight signals as transmitted by the LocataLites. Comparing the system performance of the V-Ray antenna against that of a conventional omni-directional antenna, the measured carrier phase error indicates a big difference between the two systems. The carrier phase measurements from the omni-directional antenna were very distorted, whereas the V-
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Ray antenna was responsible for accurate measurements, at a similar level to outdoor measurements.
Because the V-Ray antenna searches for direct line-of-sight beams the measured angle- of-arrival could be output and used in the navigation filter along with the range measurements. A position and attitude determination system (PAMS) was proposed to provide all navigation parameters simultaneously, including position, velocity, acceleration and attitude. As both the Locata range measurement model and the attitude determination model are non-linear, the Unscented Kalman filter (UKF) rather than a conventional Extended Kalman filter (EKF) is used in the PAMS system.
The PAMS performance for indoor applications was evaluated and the general results have demonstrated that the overall solution was stable, with the positioning accuracy for horizontal components being better than 5cm, and the orientation accuracy was better than 0.7 degrees. To investigate the performance of the UKF and EKF, PAMS was compared with the same system strategy but estimated by the EKF algorithm. The results indicate that the PAMS solution had a lower RMS for the horizontal direction components than the EKF solution. In addition, the initialisation of PAMS had a better performance than the EKF-based system in terms of smaller initial error and a faster convergence speed. Further analysis was conducted by comparing PAMS and a standard range-only system and an angle-only system, and the results indicate that both the positioning and attitude solutions computed by PAMS were better than those of the conventional algorithms.
This part of work demonstrated that: (1) the Locata V-Ray antenna can provide multipath mitigated range and angle measurements for indoor environments; (2) for the proposed non-linear position and attitude determination system, the UKF performed better than the EKF algorithm in terms of both navigation accuracy and initialisation; and (3) the Locata PAMS is a suitable indoor navigation system that is superior to the range-only and angle-only systems.
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8.2 Recommendations for Future Work
Based on both the theoretical and experimental results obtained in this study, the following recommendations are made for future research:
The GNSS/Locata/INS integration approach discussed in this research has shown to be successful in providing precise geo-referencing and navigation information. However, the proposed system is operated in the post-processing mode only. In order to meet the growing demands for real-time positioning and navigation, a true real-time system should be developed to better study the various integration issues associated with building such complex systems and integrating them into upcoming applications. Moreover, in real-time systems, the issues of system integrity monitoring and quality control would need to be further investigated.
The current PPP-GNSS solution in this research could achieve decimetre-level accuracy for kinematic positioning applications. This PPP-GNSS solution uses the conventional ionosphere-free GNSS observable to eliminate (to first-order) the ionosphere signal delay. However, the ionosphere-free observable requires a dual-frequency GNSS receiver, and furthermore the observable has a higher level of noise compared with the raw measurements. Hence further research could be undertaken into improving the ionospheric delay mitigation so that single-frequency GNSS receivers could be used.
Both Locata and PPP-GNSS positioning in this research involve the use of carrier phase measurements. The carrier phase ambiguities are estimated along with the navigation solutions as real-valued quantities on an epoch-by-epoch basis. This method is simple and reliable to implement, and the process converges in several seconds. However, as the ambiguities are not fixed to their integer values, the navigation solutions could be improved if they were resolved to integer values. Integer ambiguity resolution and validation for precise GNSS and Locata positioning is still a topic for future research.
The study of data fusion algorithms is one of the core topics of this thesis. The data fusion algorithm is not only important for multi-sensor navigation systems, but can be extended and used for other applications such as target tracking. The data fusion
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Chapter 8 Conclusions and Recommendations algorithm investigation reported on in this thesis could be modified to accommodate the requirements of other applications.
Locata-augmented outdoor navigation and Locata-only indoor navigation have been investigated in a number of trials reported here. Locata-enabled indoor-outdoor seamless navigation is still under investigation. Further tests will be conducted in the near future. For these tests GNSS positioning would be implemented in outdoor environments, and Locata and INS technologies would be used to provide the seamless link from outdoor to indoor environments.
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