ICAS 2002 CONGRESS ROBUST INTEGRATED INS/RADAR ALTIMETER ACCOUNTING FAULTS AT THE MEASUREMENT CHANNELS Ch. Hajiyev, R.Saltoglu (Istanbul Technical University) Keywords: Integrated Navigation, INS/Radar Altimeter, Robust Kalman Fillter, Error Model, Abstract was a milestone, and we were witnesses to these improvements in the near past. A great amount of In this study, the integrated navigation system, study has already been made about this issue. consisting of radio and INS altimeters, is Many more seem to be observed in the future. As presented. INS and the radio altimeter have many of these studies were examined, and some different benefits and drawbacks. The reason for useful information was reached. integrating these two navigators is mainly to Integrated navigation systems combine the combine the best features, and eliminate the best features of both autonomous and stand-alone shortcomings, briefly described above. systems and are not only capable of good short- The integration is achieved by using an term performance in the autonomous or stand- indirect Kalman filter. Hereby, the error models alone mode of operation, but also provide of the navigators are used by the Kalman filter to exceptional performance over extended periods estimate vertical channel parameters of the of time when in the aided mode. Integration thus navigation system. In the open loop system, INS brings increased performance, improved is the main source of information, and radio reliability and system integrity, and of course altimeter provides discrete aiding data to support increased complexity and cost [1,2]. Moreover, the estimations. outputs of an integrated navigation system are At the next step of the study, in case of digital, thus they are capable of being used by abnormal measurements, the performance of the other resources of being transmitted without loss integrated system is examined. The optimal or distortion. Kalman filter reacts with abnormal estimates to In the paper [3] integrated navigation this situation as expected. To recover such a system issue has been discussed. In the paper it is possible malfunctioning, the Robust Kalman stated that, with the demand from the aviation Filter (RKF) algorithm is suggested. industry, Instrumental Landing Systems (ILS) tend to be improved. This could not only be 1 Introduction through replacement with the Microwave Landing System (MLS), but also by integrating The new century’s improvements in computer Global Positioning System to the ILS that is technology, and increased data processing rates practically in service. brought the ability to improve the navigation Due to the paper, the majority of current systems of air vehicles in precision, correctness precision landing research has exploited stand- and reliability.The integrated navigation systems alone GPS receiver techniques. This paper, as an concept with the application of the Kalman filter improvement, exploits the possibilities of using 684.1 Ch.Hajiyev & R.Saltoglu and Extended Kalman Filter (EKF) that group named ‘High Precision Navigation’ integrates an Inertial Navigation System (INS), showed some experimental effort to prove the GPS, Barometric Altimeter, and Radar Altimeter improvement of navigation parameters in an for precision aircraft approaches. As a result, it is integrated navigation system. The main tool was seen that Federal Aviation Authority (FAA) the Kalman filter as usual, but this time the requirements for Category I and II approaches attitude of the vehicle was monitored as shown in could be met through this new approach. their paper dated 1994 [5]. The work in the paper is conducted through a NASA was also interested in the application computer simulation. The simulation program is of Kalman filter in the navigation systems. The basically developed on Kalman filter algorithms. need for the precision altitude determination at The plotted outputs are generated by the low altitude flight phases was the main issue. On commercial software package MATLAB. In this a multi-sensor navigation suite, again using manner, regarding the subject and the tools, this Kalman filter as the main tool for integrating paper is very close to the issue discussed in this navigation data from different origins, radar study(3) . altimeter and INS data was used for selecting the In the paper [4] development of a Kalman most similar digital map profile in obtaining filter for optimal combination of GPS, INS and horizontal position. Radar Altimeter data is presented. Due to the A close subject was discussed by a working paper, being two independent navigation systems, group of NASA and U.S. Army in 1993. The GPS and INS have their own shortcomings when improvement of a terrain-referenced guidance used in a stand-alone mode. The ever-growing system with the implementation of radar drift in position accuracy of the INS, and the altimeter into the traditional navigation system by possible unavailability of the GPS signals are the help of the Kalman filter was exploited. discussed. The author suggests that, these Starting from mathematical models, this group shortcomings would be eliminated, and each was able to accomplish some flight tests and system’s best performances combined through experiments on a Blackhawk Helicopter, as a the Kalman filter. navigation test bed [6]. The benefits of integrating GPS with a The integrated systems designed in the past strapdown INS are significant. However, altitude studies do not have robust character towards accuracy can further be improved by integrating abnormal measurements. Generally, more than the GPS, baro-inertial loop aided strapdown INS, 10% of the radio measurements, and 5% of the and radar altimeter data. An error model of the whole navigation measurements are expected to strapdown INS plays an important role in the be abnormal in the navigation systems [7]. In development of a Kalman filter for optimal some measurement periods, the abnormal rate of combination of navigation data provided by GPS, the radio measurements might exceed %10. This strapdown INS and radar altimeter. Integrating fact certainly decreases the efficiency of most of the error models of each system with the use of the standard statistical processing methods.Thus, the Kalman filter simulates this. The simulation these abnormal measurements resulting from results show an undeniable improvement in the some possible failures at the measurement demanded properties. The approach, tools and the channels significantly decrease the effectiveness data are identical to the ones in this study and the of the integrated navigation systems. In this results are somehow in the same manner [4]. study, to overcome such a problem, design of an Another work on the integration of INS and integrated system, which is robust to the GPS was done in [5] by a group of scientists at abnormal measurements, is intended as an the Technical University of Darmstadt. The improvement. 684 .2 ROBUST INTEGRATED INS/RADAR ALTIMETER ACCOUNTING FAULTS AT THE MEASUREMENT CHANNELS 2.1 INS Error Model, The Altimeter ∆g() k −1 : Measurement error of the gravitational acceleration Having numerous output parameters out of U∆ () k −1 : White Gauss noise with different channels, the INS has a complex error az model. This model is nevertheless useless in this zero mean ()− study, because the issue covers the INS altimeter. U∆g k 1 : White Gauss noise with For this reason, only the vertical channel of the zero mean INS is considered. α β , g : The terms for the Although the subject is about the INS altimeter, correlation period not only the vertical position (altitude), but also ∆t : Discrete time the other vertical channel parameters will be RRH= + (H - the flight altitude, R - the discussed, and included in the calculations. The I 0 0 INS vertical channel parameters are, radius of earth) 1. Vertical position (altitude). H I 2. Vertical speed. Wz 3.2 Error Model, The Radio Altimeter 3. Vertical acceleration. a z The error model of the radio altimeter, which 4. Gravitational acceleration. g will be used in our calculations, is as follows(14). The system design in the following sections will be in discrete form, so the Kalman filter. The ∆H()() k = ∆ H k −1 − ∆ tβ ∆ H () k − 1 + linear and discrete error model of the INS RRR (5) + ∆tU∆ () k −1 altimeter is given as follows [8] H R ∆() = ∆ ( − ) + ∆ ∆ ( − ) HI k H I k1 t W z k 1 (1) In the error model expressions, the following are the explanations for the terms. 2g∆ t ∆ () ∆() = ∆ ( − ) + ∆() − + HR k : Measurement error of the Wz k W z k 1 HI k 1 RI (2) radio altitude + ∆ ∆() − + ∆ ∆ () − U∆ () k −1 : White Gauss noise with t az k1 t g k 1 H R zero mean ∆()() = ∆ − − ∆α ∆ () − + β az k a z k1 t a z k 1 : The term for the + ∆() − (3) correlation period tU∆a k 1 z ∆t : Discrete time ∆() = ∆ ( − ) − ∆β ∆ ( − ) + g k g k1 tg g k 1 (4) + ∆() − 4 Radio-INS Integration tU∆g k 1 The core task of this study is to combine two In the error model expressions, the following are different navigation sources with the use of the explanations for the terms. Kalman filter. In fact, the main task for any kind ∆() − Wz k 1 : Measurement error of the of navigation study is to fight with the vertical speed disadvantages of a navigation equipment, thus to ∆ () increase correctness and reliability. By HI k : Measurement error of the altitude integrating Radio and INS altimeters, the ∆() − objective is to benefit from the advantages of az k 1 : Measurement error of the vertical acceleration 684 .3 Ch.Hajiyev & R.Saltoglu both of the systems, while eliminating the 1. INS altimeter shortcomings. 2. Radio altimeter There are two possible Kalman filter designs for 3. Data (central) processing unit integrating such systems. 4. Control block (Kalman filter) 1. Total state space Kalman filter (direct 5. Display (avionics users) method). 2. Error state space Kalman filter (indirect method). In the direct method, all of the states of the system are used by the Kalman filter, where the INS accelerometer and the aiding navigator signals are the sources.