I HYBRID GPS /LORAN-C : ,. -- " A NEXT-GENERATION OF SOLE MEANS AIR NAVIGATION
A Dissertation Presented to
The Faculty of the College of Engineering and Technology
Ohio University
In Partial Fulfillment
of the Requirements for the Degree
Docror of Philosophy
Frank van Graas - ?. I November, 1988 This dissertation has been approved
for the Department of Electrical
and Computer Engineering and the
College of Engineering and Technology
/'-'\ /'-'\ /
/
Prdiessor of Elec~rice; a1' h Computer ingineering 1'
Dean of the College of Engineering and Technology ACKNOWLEDGEMENTS
The work presented in this dissertation was funded in part by the
Federal Aviation Administration and NASA Langley Research Center under the Joint University Program in Air Transportation Systems under Grant
NGR-009-017. Additional funding was obtained from the Federal
Aviation Administration under Contract DTRS-57-87-C-00006, TTD-13, and
NASA Ames Research Center under Contract NAS2-11969.
The author is indebted to Dr. Richard H. McFarland, Director of the Avionics Engineering Center at Ohio University and Director of this dissertation, and Dr. Robert W. Lilley, Deputy Director of the
Avionics Engineering Center, for their valuable suggestions and remarks.
The author also wishes to acknowledge the following individuals for their assistance and contributions to this work:
Dr. Jerrel R. Mitchell, Chairman of Electrical and Computer
Engineering, Dr. Herman W. Hill, Associate Professor of Electrical and
Computer Engineering, Dr. John. A. Tague, Assistant Professor of
Electrical and Computer Engineering, and Dr. Donald 0. Norris,
Professor of Mathematics, for reviewing this document and serving as members of the Dissertation Committee.
Mr. William L. Polhemus, Polhemus Associates, Inc. , for many helpful conversations and his active support for hybrid GPS/LORAN-C.
Dr. Per K. Enge, Assistant Professor of Electrical Engineering at
Worcester Polytechnic Institute, for his enthusiasm and valuable remarks.
Mr. Richard L. Zoulek, Chief Avionics Airborne Facilities, for his assistance with the airborne equipment installation. Mr. James
D. Waid and Mr. Paul A. Kline, undergraduate students at Ohio
University have assisted me with the data collection and the simula- tion models. TABLE OF CONTENTS
PAGE
ACKNOWLEDGEMENTS i
List of Figures vi
List of Tables ix
1. INTRODUCTION 1
2. OVERVIEW OF GPS AND LORAN-C 5
2.1 Historical Perspective 5
2.2 The Long Range Navigation System LORAN-C G
2.3 The NAVSTAR Global Positioning System (GPS) 13
3. AIR NAVIGATION SYSTEM REQUIREMENTS 17
4. THE CONCEPT OF MULTISENSOR AND HYBRID AIR NAVIGATION 2 4 SYSTEMS
4.1 Hybrid Navigation Systems
4.2 Hybrid Systems Based on Long-Term and Short-Term Stability Sensors
4.3 Hybrid Systems Based on Sensors with Similar Performance
5. GPSILORAN-C INTEROPERABILITY
5.1 GPS/LORAN-C System Integration
5.1.1 GPS Timing
5.1.2 LORAN-C Timing
5.1.2.1 Current LORAN-C Timing
5.1.2.2 Master Station Time of Transmission Control
5.1.2.3 Time of Transmission Control for all LORAN-C Stations
5.1.2.4 Determination of LORAN-C Transmitter Offset with Respect to GPS Time TABLE OF CONTENTS (Continued)
5.2 Airborne Equipment
5.2.1 Hybrid GPS/LORAN-C Receiver Concepts
5.2.2 Hardware Implementation Concepts
GPSILORAN-C PERFORMANCE CAPABILITIES
6.1 LORAN-C Coverage, Reliability, and Availability
6.1.1 LORAN-C Pseudorange Coverage Prediction Model
6.1.2 Signal-to-Noise Ratio Calculation
6.1.3 Horizontal Dilution of Precision Calculation
6.1.4 Predicted LORAN-C Pseudorange Coverage Results
6.1.5 LORAN-C Reliability and Availability
6.1.5.1 LORAN-C Failure Data
6.1.5.2 LORAN-C Markov Model for Four- Transmitter Availability
6.2 GPS Coverage, Reliability, and Availability
6.2.1 GPS Coverage
6.2.2 GPS Coverage Prediction Computer Model
6.2.3 Predicted GPS Coverage Results
6.2.4 GPS Reliability and Availability
6.3 Hybrid GPSILORAN-C Coverage, Reliability, and Availability
6.3.1 Hybrid GPS/LORAN-C Coverage
6.3.2 Predicted Hybrid GPSILORAN-C Coverage
6.3.3 Hybrid GPS/LORAN-C Reliability and Availability TABLE OF CONTENTS (Continued)
7. HYBRID GPSILORAN-C NAVIGATION SOLUTION 101
7.1 Consolidated Statement of Navigation Solution 101 Philosophy
7.2 Hybrid GPSILORAN-C Measurement Equations and 104 Error L4odels
7.3 Hybrid GPSILORAN-C Navigation Equations 107
7.4 Range Domain Filtering 114
7.5 Receiver Autonomous Integrity Monitoring (RAIM) 117
7.5.1 GPS and LORAN-C System Integrity 118
7.5.2 RAIM for Hybrid GPS/LORAN-C
7.6 Computer Simulation Results
8. GPSILORAN-C STATIC EXPERIMENT 132
8.1 Description of the Static GPS/LORAN-C Experiment 132
8.2 Static Test Results 135
9. DIFFERENTIAL GPS TRUTH REFERENCE SYSTEM 139
9.1 Description of the Differential GPS Reference System 140
9.2 Differential Test Results (Static)
10. GPS/LORAN-C FLIGHT EXPERIMENT
10.1 Data Processing for the Dynamic GPS/LORAN-C Experiment
10.2 Dynamic Test Results
11. CONCLUSIONS
12. RECOtTMENDATIONS
13. REFERENCES
ABSTRACT LIST OF FIGURES
Figure 2.1 LORAN-C pulse shape and chain transmissions 7 (from reference [14]).
Figure 2.2 LORAN-C hyperbolic and pseudorange positioning. 10
Figure 5.1 Separated (a) and hybridized (b) GPSILORAN-C 40 functional block diagrams.
Figure 5.2 Functional block diagram of a generic, hybrid 43 navigation receiver.
Figure 6.1 LORAN-C ranging geometry for a receiver at 50 sea-level.
Figure 6.2 LORAN-C transmitter locations with the "mid-continent gap" filled.
Figure 6.3 Predicted LORAN-C pseudorange coverage with 56 the "mid-continent gap" filled for three or more stations (0.25 nm).
Figure 6.4 Predicted LORAN-C pseudorange coverage with 5 7 the "mid-continent gap" filled for three or more stations (0.125 nm).
Figure 6.5 Predicted LORAN-C pseudorange coverage with the "mid-continent gap" filled for four or more stations (0.25 nm).
Figure 6.6 Predicted LORAN-C pseudorange coverage with the "mid-continent gap" filled, simulated Baudette failure (top) and Middletown (bottom).
Figure 6.7 Markov model for the determination of the 64 time-dependent availability of four LORAN-C transmitters.
Figure 6.8 The stochastic transitional probability matrix P 66 for the four-transmitter Markov model.
Figure 6.9 GPS phasing diagrams for the symmetrical 7 1 21-satellite baseline constellation (top) and the Optimal 21-satellite constellation (bottom).
Figure 6.10 GPS phasing diagram for the Primary 21-satellite 74 constellation (24 satellites, reference [89]). LIST OF FIGURES (Continued)
Figure 6.11 Degraded GPS coverage for the symmetrical 7 7 21-satellite baseline constellation accumulated over one day.
Figure 6.12 Degraded GPS coverage for the symmetrical 79 21-satellite baseline constellation with one simulated satellite failure, accumulated over one day.
Figure 6.13 Degraded GFS coverage for the Primary 21-satellite constellation with two simulated satellite failures, accumulated over one day.
Figure 6.14 Markov model for the determination of the 83 time-dependent availability of the 21 and 24-satellite GPS constellations.
Figure 6.15 GPS time-dependent state probabilities for a 87 21-satellite constellation, parameterized with respect to short-term and long-term MTTFs and MTTRs .
Figure 6.16 Horizontal Dilution of Precision (HDOP) for 92 hybrid GPSILORAN-C.
Figure 6.17 Markov model for the determination of the time- 96 dependent availability of hybrid GPSILORAN-C.
Figure 7.1 GPS ranging geometry. 105
Figure 7.2 Example of Receiver Autonomous Integrity 121 Monitoring (R4IM) in the position domain (from reference [127].
Figure 7.3 Block diagram of the computer simulation for 125 the evaluation of the hybrid GPSILORAN-C navigation algorithms.
Figure 7.4 Number of iterations required by the navigation 127 solution as a function of the radial distance between the true and estimated positions.
Figure 7.5 Frequency distribution of the integrity parameter.
Figure 7.6 Radial position error and the integrity 130 parameter for the hybrid solution with a bias of 1000 meters added to one of the GFS pseudoranges. LIST OF FIGURES (Continued)
Figure 8.1 Block diagram of the GPS/LORAN-C hardware used 133 for the static experiment.
Figure 8.2 GPSILORAN-C equipment used for the static test. 134
Figure 8.3 Static GPS/LORAN-C data processing block 136 diagram.
Figure 8.4 Static, two-dimensional position errors for GPS, 135 LORAN-C, and hybrid GPS/LORAN-C.
Figure 9.1 Differential GPS reference station equipment. 142
Figure 9.2 Unfiltered differential range corrections from 143 the sequential GPS receiver (ST1 TTS-502B) with a high-quality reference oscillator.
Figure 9.3 Unfiltered and filtered differential correc- 144 tions for each satellite (SV) tracked by the sequential GPS receiver.
Figure 9.4 Static Differential GPS validation processing. 146
Figure 9.5 Differential range corrections for the reference 145 and user GPS receivers (top), and two- dimensional GPS and DGPS position errors for the user receiver (middle and bottom).
Figure 9.6 DGPS reference station antenna and nearby roof 150 structure, which causes multipath errors.
Figure 10.1 Overview of the hybrid GPS/LORAN-C flight 152 experiment equipment with a Differential GPS truth reference system.
Figure 10.2 Piper Saratoga aircraft, N8238C, used for the 153 in-fligh~evaluation of hybrid GPS/LORAN-C.
Figure 10.3 Hybrid GPS/LORAN-C data processing with a 154 Differential GPS truth reference system.
Figure 10.4 Differential GPS ground track for a 70 minutes 15 7 hybrid GPS/LORAN-C test flight in the vicinity of Ohio University airport.
Figure 10.5 'RJo-dimensionalposition errors for the hybrid 159 GPS/LORAN-C receiver. LIST OF TABLES
Table 3.1 Current and future navigation system accuracy 18 requirements for specific phases of flight in the conterminous United States.
Table 3.2 Goals for integrity criteria as developed by 22 the integrity working group of RTCA Special Committee 159.
Table 5.1 A comparison of anticipated error budgets for 33 LORAN-C pseudorange measurements with respect to current and proposed system timing.
Table 6.1 LORAN-C state probabilities after one month 69 for four-transmitter coverage, parameterized with respect to MTTF and MTTR.
Table 6.2 Elements of the stochastic transitional 84 probability matrix P corresponding to the GPS failure transition diagram (Figure 6.14).
Table 6.3 GPS state probabilities after two years for a 21-satellite constellation, parameterized with respect to MTTF and MTTR.
Table 6.4 GPS state probabilities after two years for a 24-satellite constellation, parameterized with respect to MTTF and MTTR.
Table 6.5 Worst case failure scenarios for the hybrid 94 GPS/LORAN-C system for four representative locations in the United States.
Table 6.6 Hybrid GPSILORAN-C state probabilities after 98 two years for 21 GPS satellites and 23 LORAN-C transmitters. 1. INTRODUCTION
Air navigation in controlled airspace within the National
Airspace System (NAS) requires a sole means of navigation [l].
Current civil sole means of navigation for the conterminous United
States (CONUS) are based on the Very High Frequency Omnidirectional
Range (VOR) system and Distance Measuring Equipment (DME). Navigation systems that do not qualify for sole means but may be used in combination with a sole means of navigation are supplemental type systems. Examples of supplemental type systems are Omega, Non-Direc- tional Beacons (NDB), and the Long Range Navigation system, LORAN-C.
At the present time, the VOR/DME system provides sufficient accuracy and coverage to support air traffic within the CONUS. Increasing traffic during the next decade may necessitate the establishment of additional low-altitude routes which are not covered by the VOR/DME system [2]. This will likely occur in combination with integrated
Communication, Navigation, and Surveillance (ICNS), and an Automatic
Dependent Surveillance (ADS) system to eliminate "blunders" and to improve the knowledge about the location of aircraft at any altitude within the NAS [3].
The NAVSTAR Global Positioning System (GPS) is a radionavigation system currently under development by the Department of Defense (DoD).
Idhen GPS becomes operational in 1991, it will only be certified as a supplemental type navigation system [4]. GPS lacks sufficient integrity, and the planned 21.-satellite constellation will only 2 provide an availability of 98% for an operational constellation of eighteen satellites. Since GPS is considered to be the replacement
for VOR and DME, several techniques have been proposed that improve the GPS performance in the areas of availability and integrity with
the intent to meet sole-means requirements [5]. These techniques
include the addition of GPS satellites, ground-based monitoring stations and geostationary satellite repeaters for integrity broad- cast, and Differential GPS.
Ground monitors will be able to determine satellite failures and
therefore can generate an integrity message, however, the availability problem will not be solved. The Differential GPS approach is capable of correcting so-called "soft" GPS errors such as those which might result from satellite clock degradation. This will improve system availability somewhat, but will still not correct for total satellite failures. Additional GPS satellites could satisfy the requirements.
The main dtsadvantage of this approach is the combined manufacturing and launch cost of a GPS satellite, which totals approximately one hundred million dollars [6]. The expected lifetime of a satellite is estimated to be 7.5 years [7]. Even though some of the additional satellites might be necessary to satisfy the DoD operational require- ments, it is expected that the civil availability requirements will dictate more satellites than the number required by the DoD. In addition, civil requirements indicate a need for dissimilar redundancy
~~hichca~l orlly be attained by a navigation system mix. 3
Another way to fulfill the integrity and availability require- ments and also achieve dissimilar redundancy is to combine navigation systems. This dissertation identifies a scheme for meeting sole-means navigation requirements. Two inherently different implementations exist for the combination of navigation sensors for an airborne system:
- Multi-Sensor Systems
- Hybrid or Integrated Systems
In the case of a multi-sensor navigation system, either the system operator or an automatic sensor selection scheme selects the naviga- tion sensors to be used for the positioning of the aircraft. A multi- sensor system may be approved for enroute and terminal navigation, however, a sole means of navigation must be installed and operable at the same time [8].
Hybrid or integrated navigation systems employ a navigation solution that is based on all data available from the position sensors. The introduction of hybrid systems into air navigation is difficult as hybrid systems are currently not approved for sole means navigation and many different mechanisms can be developed for integrating different sensors. On the other hand, tremendous benefits can result from hybrid radionavigation systems. These benefits include improved safety, cost reduction, and airspace capacity expansion. This paper is concerned with a new technique that hybridizes GPS and LORAN-C used in the ranging mode of operation. The hybrid system has the potential to meet all requirements for a sole means of navigation for the CONUS and could lead to a new generation of air radionavigation systems. The concept, theoretical analysis, and justification of a hybrid GPS/LORAN-C system are presented. Following the design and modeling phase, a prototype hybrid GPS/I,ORAN-C receiver has been developed and implemented. The hybrid GPS/LORAM-C receiver concept has been proven through an actual flight test, which was referenced to a Differential GPS truth trajectory. The data are presented in Section 10. 2. OVERVIEW OF GPS AND LORAN-C
2.1 Historical Perspective
Air navigation in the United States using radio frequency signih started as early as 1920 with the operation of aeronautical radio stations by the air mail service [9]. These radio stations were used
2s non-directional beacons (NDB), which, in combinat-ion with Automatic
Direction Finding (ADF) equipment, provide the pilot with the bearing of the beacon with respect to the aircraft. Because of their low cost and simplicity, NDB's will remain part of the National Airspace System
(NAS) into the next century [lo].
In 1927 the first directional beacons were introduced, better known as the four-course radio ranges [11,12]. Directional beacons made it possible for the pilot to fly one of 4 fixed courses.
Shortly after World War 11, the Very High Frequency Omnidirec- tional Ranges (VOR) in combination with Distance Pleasurement Equipment
(DME) were introduced as the basis for the NAS 1131. VOR/DME is a rho-theta system, providing both bearing and distance with respect to tho VOR/DNE station at any point in de coverage ared.
About 20 years layer, in 1974, the Long Range Navigation system
LORATT-C xias selected as the federally-provided radionavigation syste~i:
For civil rnarinc use in tlie U.S. coastal areas. Just-. n few years later, the aviation community became interested in the system and consequently, the Federal Aviation Administration (FAA) responded by sponsoring four additional LORAN-C stations. These stations, now under construction, will cover the mid-continent, expanding the
LORAN-C coverage to include all of the conterminous United States.
In the same time period, the DoD initiated the design of a world- wide, high-performance satellite navigation system. This resulted in the NAVSTAR Global Positioning System. At the time of this writing, ten experimental satellites have been launched successfully, and the launch of the operational satellites will start in December 1988.
Full, three-dimensional coverage provided by 21 satellites is expected by late 1991.
Both GPS and LORAN-C can, in general, provide better accuracies than the VOR/DME system, but they lack performance in the areas of system availability and integrity. On the other hand, these systems are earth referenced, allowing the user to obtain a position fix at any altitude anywhere in the CONUS.
2.2 The Long Range Navigation System LORAN-C
LORAN-C is a 1-and-based radionavigation system operating in the
90 to 110 kHz frequency band. Each LORAN-C transmitter generates a series of pulses as depicted in Figure 2.1 [14]. Each pulse consists of a 100 kHz carrier that rapidly increases in amplitude consistent Time (ps)
GROUP REPETITION INTERVAL b
MASTER SECONDARY SECOhDARY SECONDARY hL4STER PULSES X PULSES Y PULSES Z PULSES PLTSES r-7 A r"7
Figure 2.1 LORAN-C pulse shape and chain transmissions (from reference [14]). with the spectrum requirements, and slowly decays depending on transmitter characteristics.
LORAN-C measurements are made with respect to the third positive- going zero-crossing of a pulse. This point is selected for maximum signal strength occurring before the arrival of the skywave, which could degrade significantly the accuracy of the measurement.
LORAN-C transmitters are grouped into chains. Each chain consists ofi one master station and two to four secondary stations. It should bc noted that the South Central United States (SOCUS) chain, which is currently under construction, will have five secondary stations [15]. Master stations initiate the transmissions of a chain with nine pulses followed by secondary transmissions of eight pulses each, in a predetermined order (Figure 2.1). The time period between successive master station transmissions is determined by the Group
Repetition Interval (GRI). The GRI is different for each chain allowing for chain identification. GRIs may range from 40 milli- seconds to 99.99 milliseconds, in increments of 10 microseconds.
Secondary transmissions are timed relative to the master station transmissions, under control of System Area Monitors (SM1). A SAP1 deter:nincs the time difference (TD) between the signal receptions of the master snd a particular secondary station. This TD is then compared ro a Control ling Standard Time Difference (CSTD) and corrections are made to tl~e secondary transmissions, if necessary. 9
LORAN-C was initially designed to be used in the hyperbolic mode of operation. In this mode, each master-secondary pair defines a hyperbolic line-of-position (LOP) based on the time difference between the reception of master and secondary pulses, as illustrated in Figure
2.2. The receiver is located at the crossing of two or more lines-of- position, requiring a minimum of three transmitters.
Instead of measuring TDs, the LORAN-C receiver could also measure the time of arrivals (TOA) of the LORAN-C signals. If the receiver clock is synchronized with the LORAN-C transmitters, the range between a certain transmitter and the receiver can be found by taking the difference between the signal time of arrival and the known signal time of transmission, multiplied by the velocity of the radio wave.
Each transmitter then defines a circular LOP on which the receiver is located. Normally two measurements are needed to find the receiver position. A third measurement would be needed if the receiver clock is not synchronized with the LORAN-C transmitters to solve for the clock offset between LORAN-C time and the receiver clock. This clock offset appears as an added bias in the observation of the true range.
A measurement which contains both the true range and a clock offset is called a pseudorange.
The accuracy of the LORAN-C measurements is affected by the following three error sources: LORAN-C HYPERBO1,IC POSITIONING
LORAN-C PSEUDORANGE POSITIONING
SECONDARY X
Figure 2.2 LORAN-C hyperbolic and pseudorange positioning. - Transmitter synchronization errors.
- Receiver measurement errors.
- Propagation errors of the 100 kHz ground wave.
Transmitter synchronization errors depend on the timing control of the LORAN-C transmitters as explained in detail in Section 5.1.
Receiver measurement errors are a function of receiver architecture, signal strength, and vehicle dynamics. State-of-the-art (1985) LORAM-
C receiver measurement errors are typically less than 25 nanoseconds
(95%) [16].
Propagation errors are caused by geophysical (spatial) variations and by meteorological (temporal) variations. Geophysical errors consist of surface impedance inhomogeneities and terrain variations.
Since these errors are time stable, they can be determined and corrections can be applied to the measurements as a function of he signal path. Meteorological errors can be diurnal or seasonal and affect several propagation properties of the ground wave [17]:
- Surf ace impedance.
- The index of refraction of air at the surface of the ground.
- The gradient of the index of refraction with respect to
altitude (vertical lapse rate of the index of refraction).
- Terrain roughness, soil consistency, geologic underlayment, and
atmosphere. At the receiver, the phase of the LORAN-C ground wave is given by
where : 7 is the frequency of the ground wave (2n * lo5 rad/s). c isthespeedof lightinvacuum (299792458 m/s). is the index of refraction of air at the " a surface of the ground (typically 1.000338). d is the distance between transmitter and receiver (m). is the secondary wave correction containing Qc geophysical and meteorological propagation delays (rad) .
The current LORAN-C system accuracy is defined for hyperbolic positioning only. The root-sum-squared of the three error sources
(after propagation modeling) is assigned a standard deviation of 100 nanoseconds for each TD [19]. The TD errors propagate into the position domain as a function of geometry, also referred to as the
Horizontal Dilution of Precision (HDOP).
Based on the maximum allowable HDOP of 7.8 and the TD standard deviation of 100 nanoseconds, 957; of all measurements will fall wi~21in a circle with a radius given by [20]:
here : IIDOP is the Horizon~alDilution of Precision (dimensionless). is the standard deviation of the O'TD Time Difference neasurements (m). 2.3 The NAVSTAR Global Positioning System (GPS)
The NAVSTAR Global Positioning System is a satellite-based radionavigation system currently under development by the DoD [21].
When fully operational in 1991, GPS will provide worldwide navigation and timing information through a 21-satellite space segment under control of the ground segment. The ground segment will consist of one master control station and several monitor stations that continuously track the GPS satellites and determine the satellites' orbital and clock parameters. These parameters are transmitted to the satellites for retransmission to the users. Each satellite continuously transmits a composite spread spectrum signal at center frequencies of
1.2276 (L2) and 1.57542 (Ll) GHz.
The L1 and L2 signals are modulated by either or both a 10.23 MHz precision (P-code) signal and/or by a 1.023 MHz coarse/acquisition
(CIA-code) signal. Each of these two binary signals is formed by a P- code or a CIA-code which is modulo-2 added to 50 bits per second navigation data (D), to form P @ D and CIA @ D. The P @ D and CIA @ D signals are modulo-2 added to L1 and L2 in phase quadrature [22].
Both the P-code and the CIA-code are pseudorandom noise sequen- ces. The CIA-code has a period of one millisecond, and the P-code has a period of one week. The receiver correlates the incorning code with the same code generated by the receiver. A correlation peak will occur when both signals are synchronized. This allows the receiver to 14 track the incoming signal very accurately. A pseudorange measurement is made by taking the difference between the measured signal time of arrival and the corresponding known signal time of transmission.
The satellite navigation data contains the orbital parameters
(ephemeris), clock data, ionospheric correction data, and constella- tion health information. These data, in combination with four pseudorange measurements allow the user to solve for three-dimensional position and clock offset with respect to GPS system time.
GPS offers two navigation services, the Precise Positioning
Service (PPS or P-code) and the Standard Positioning Service (SPS or
CIA-code). The PPS is intended for military users and for qualified civil users [23]. The PPS will provide a predictable positioning accuracy of 17.8 meters (2 drms), horizontally and 27.7 meters (2 sigma) vertically, and timing accuracy within 90 nanoseconds. The SPS will be available to any user. Although the SPS accuracy is typically better than 40 meters (2 drms), DoD will degrade the accuracy consistent with U.S. national security interests under a program called Selective Availability (SA). Present DoD policy indicates a horizontal positioning accuracy of 100 meters (2 drms), vertical accuracies of 156 meters (2 sigma), and timing accuracy within 175 nanoseconds.
The accuracy of tile GPS measurement is affected by the following error sources: - Satellite ephemeris and clock errors.
- Propagation errors, including ionospheric and tropospheric
propagation delays, and multipath errors.
- Receiver measurement errors.
- Selective Availability errors.
Satellite ephemeris errors are the geometric differences between the actual satelli-te locations, and those predicted by the satellite ephemeris data. These errors are slowly varying and usually result in rangi-ng errors of less than 5 meters [24]. Similarly, satellite clock errors are differences between the actual satellite clock offset from
GPS system time and that predicted by the satellite clock data. These errors are also slowly varying and are generally less than 5 meters.
Ionospheric delays are mostly a function of the elec~roncontent of the ionosphere. These delays can be as much as 20-30 meters
(typically) during the day to as small as one meter at night for the single frequency SPS user [25]. The data transmitted by the satel- lites contain parameters for an ionospheric correction model that can remove up to 50% of the error [26]. PPS users can employ a two- frequency measurement to remove as much as 98-99% of the ionospheric delay. !6
Tropospheric delays can also be as large as 30 meters, but can be modeled quite well: up to 80-90% of the error can be removed [27]. blultipath errors can change very rapidly but are generally less than three meters, depending upon antenna type and environment. Receiver measurement errors are very small, typically less than one meter.
Finally, the Selective Availability errors are on the order of 30 meters (1 sigma), along the line-of-sight to the satellite and change in an unpredictable manner. These artificial errors cannot be corrected for using modeling and can therefore always degrade the stand-alone SPS GPS accuracy to 100 meters (2 drms).
At this point, it should be noted that the GPS accuracies can be improved upon tremendously by using a differential technique. The
Differential GPS approach is based on a GPS receiver at a known location. This receiver compares the GPS derived ranges to the actual ranges calculated from the known receiver and satellite positions.
The differsnces, or differential corrections, are then transmitted to suitably equipped users to allow them to improve their own solutions.
Differential GPS is discussed in detail in Section 9. Because of dynamic Differential GPS accuracies of better than 10 meters (2 drms), it is very well suited as a truth reference system for the evaluation of navigstiou system results where the highest accuracy requirement is
100 meters (2 drms), as given in Section 3. 3. AIR NAVIGATION SYSTEM REQUIREMENTS
Air navigation in controlled airspace requires the presence of a sole means of navigation. Although many descriptions and even a definition exist for a sole means of navigation, not all requirements that constitute such a system are specified. The definition of a sole means of navigation is given by [28]: An approved navigation system that can be used for specific phases of air navigation in controlled airspace without the need for any other navigation system.
Looking at currently accepted sole means of navigation such as
VOR/DME, and considering five major performance characteristics, accuracy, availability, reliability, coverage, and integrity, both the known requirements and deficiencies of the definition for a sole means of navigation can be derived as follows. (formal definitions for some of the requirements can be found in references [29,30].)
Accuracy: Both current accuracy requirements and future goals exist.
Table 3.1 summarizes these accuracies for specific phases of flight in the CONUS [31]. Accuracies are defined in terms of the "2 drms" measure which means "twice the distance root-mean-squared radial error" and is calculated from [32]:
-- - 2 2 2 drms = 2 x 4 c ( n + yn) / N whe r e : x are the x and y error components of a rneasurerncnt n' with respect to a set of orthogonal axes (m). N is the total l~umberof measurements. Current system Future System (1) Accuracy Requirements Phases of Flight AC 90-45A [ s i I Accuracy Requirements FRP-84 r21 95% conf. for cross track and along track 2 drms
Enroute Domestic 1.5 nmi 1000 m
Terminal 1.1 nmi 500 m
Non-Precision Approach 0.3 nrni 100 m
(1) System accuracy requirements do not include Flight Technical Errors. (2) Does not include radiated signal accuracy. It is not clear from AC 90-45A how to account for these errors.
Table 3.1 Current and future navigation system accuracy requirements for specific phases of flight in the Conterminous United States. 13
If the errors are normally distributed, the 2 drms measure can be thought of as the radius of a circle that contains 95% of the measure- ment s.
Coverage: Navigation signals must be adequate to determine position accurately within the coverage area.
Availability: This is the percentage of time that the navigation system can be used at a certain location. Availability should be close to 100 percent (VOR); the exact percentage is not specified.
Generally, the requirement states that a system outage should not overload the air traffic controller. Whether an availability of 99.9%
(526 minutes of outage during a year) or 99.9999% (32 seconds of outage during a year) would satisfy this requirement is not known.
Also, it is important to make a distinction between the maximum allowable outage period at one particular time and the cumulated ourage time during a whole year. A single outage of one hour is unacceprable, but 60 outages each lasting one minute might be acceptable. If the navigation system is to be used as part of an
Automatic Dependent Surveillance (ADS) system, availability is even more important, especially for areas without radar coverage.
Availability must be defined as a function of location as indicated by the defirlition. It should be recognized that the formulation of the availability requirement will differ from current
VOR/DME performance. For instance, a VOR outage only affects a 2 0 relatively small area (radius less than 30 nm at ground level); a failing GPS satellite affects a large service area (radius approxi- mately 4000 nm). In the latter case, course deviation would not necessarily solve the outaee problem.
Reliability: Reliability is the probability that a system will be operational continuously over a specified period of time at a certain location. Reliability indicates how likely the system will experience a failure during the specified period of rime. A low reliability means that the system is likely to fail., a high reliability means that the system is likely not to fail during the specified period of time.
It is useful to note that the reliability of a system is not very important if the repair time is on the order of a few seconds. In that case, the failing system would soon be back in service, hardly affecting the user. On the other hand, if a system has a long repair time, the system should be very reliable as a failure will result in a long down time.
Solid-state VOR or DME stations have a specified Mean Time To
Failure (MTTF) of 10,000 hours [33]. For area navigation, two signals are needed at the same time. Redundant VOR/DME then results in a reliability of 95% over a period of approximately 120 days.
Tnte:ri~y: This is the capability of the system to provide timely warnings to users when the system performance is outside some preset 2 1 accuracy bound. An adequate definition of integrity used for the
Institute of Navigation workshop on GPS integrity is given by [34]:
Guaranteeing to the user (with probability p) that he will be
promptly notified (within time T) when GPS system induced errors
are greater than a prespecified level.
Other definitions of integrity exist, they all have the same three ingredients: a warning time T, an error limit, and a probability p.
The integrity working group of RTCA Special Committee 159 has developed goals for warning times and error limits, these goals are summarized in Table 3.2 for navigation in the CONUS [35]. A figure for probability has not been specified. This probability deals with the integrity of the integrity technique used. For example, this figure would indicate how many redundant measurements are needed to keep the missed detection rate below the required detection proba- bility for a receiver autonomous detection scheme. It would also specify the requirement for the probability of correct operation of ground monitors and their data link to the users. Note that the integrity of a data link servicing many users is more critical than the integrity of a receiver autonomous detection scheme. A problem with the data link would affect many users at the same time, a missed detection in the receiver only affects one user.
In summary, the following requirements for a sole means of navigation for the NAS must be established: Phases of Flight Radial Alarm Limit Time to Alarm
Enroute Domestic 1000 m 30 s
Terrnj~~al 500 m 10 s
Non-Precision Approach 100 m 6 s
Table 3.2 Goals for integrity criteria as developed by the integrity working group of RTCA Special Committee 159. 2 3
- Availability and Reliability: These requirements should be
developed by analyzing the current sole means of navigation
VORIDME and by analyzing the impact of navigation outages on Air
Traffic Control and users that rely heavily on navigation and
timing data. These requirements should also be extrapolated to
future air navigation demand in combination with an evaluation of
realistic navigation performance requirements for future systems.
- Integrity: The allowable probability of an un-annunciated
failure or out of tolerance condition has not been established.
This probability is essential for the development and certifica-
tion of integrity techniques.
Sole means of navigation system requirements will be addressed by the
Federal Aviation Administration (FAA) as a result of an amendment to
the Airport and Airway Improvement Bill [36]. This bill was passed by
the United States Congress in December, 1987, and calls for a complete definition of a sole means of navigation by September 1989. 2 4
4. THE CONCEPT OF MULTISENSOR AND HYBRID AIR NAVIGATION SYSTEMS
Navigation systems can be combined either at the system level or ac the user level. This section will discuss the combination of navigation sensors for airborne navigation at the user level, in general. The next section will provide combination options at the system level as well as at the user level focused on GPS and LORAN-C.
Two inherently different implementations exist for the combina- tion of navigation sensors for an airborne system:
- Multi-Sensor Systems
- Hybrid or Integrated Systems
In the case of a multi-sensor navigation syscem, either the system operator or an automatic sensor selection scheme selects the navigation sensors to be used for the positioning of the aircraft. A multi-sensor system may be approved for enroute and terminal naviga- tion, however, a sole means of navigation must be installed and operable at the same time. For instrument approaches, the selection of the sensors is limited to those sensors that are approved for use during an approach operation [37]. Therefore, a multi-sensor system based on GPS and LORAN-C, two supplemental type navigation systems, cannot be used as a sole means of navigation under the current multi- sensor system specification since neither system is approved as a sole means of navigation. 25
Hybrid or integrated navigation systems, by definition, employ a navigation solution that is based on all data available from the posi- tion sensors. For instance, a hybrid GPSILORAN-C system could use three satellites and two LORAN-C transmitters to determine aircraft position. Four measurements would then be needed to solve the navigation equations, and the fifth measurement would be used to verify the integrity of the solution (see Section 7).
A hybrid GPS/LORAN-C system for air navigation is currently non- existent. In order to determine the most effective mechanization of a hybrid system, a literature search was performed to determine the state-of-the-art techniques used for hybrid navigation systems.
4.1 Hybrid Navigation Systems
The hybrid navigation systems literature search revealed two classes of hybrid systems. The first class contains hybrid systems where sensors with different characteristics are used to create a system that performs substantially better than each of the navigation sensors. This class of hybrid systems typically integrates high- precision short-term stabili~ysensors such as Inertial Navigation
Systems (INS) with high-precision long-term stabil-ity sensors such a;
GPS to calibrate the drift of the short-term sensor.
The second class of hybrid systems contains sensors with similar characterjs~ics. T'r.c intcnt is to provide a navigatton solution using 26 all sensor inputs, allowing the system to function under conditions where one or more sensors alone would not provide a position. In addition, during normal operation, the redundant measurements can be used to autonomously verify the integrity of the navigation solution.
This class of hybrid systems is of specific interest for the GPS/
LORAN-C system, as GPS and LORAN-C have similar performance charac- teristics.
Both classes of hybrid systems sometimes also include a dead- reckoning capability. This allows the system to coast through naviga- tion sensor outages and can also be used for integrity checking and velocity aiding.
4.2 Hybrid Systems Based on Long-Term and Short-Term Stability
Sensors
A large number of hybrid systems have been identified that incorporate both long-term and short-term stability sensors. Most of the older system implementations primarily use an Inertial Measurement
Unit (IMU) to keep track of the current position. The drift of the inertial system is then periodically bounded by an input from a radionavigation sensor such as Omega, LORAN-C, the Navy Satellite
Plax~igation System, Transit (NNSS), or GPS. More recent designs fully integrate the inertial system and the instantaneous navigation sensor
[38-/t2]. For exaIT,ple, reference [43] describes a seventeen-variable
K~lm,infilter imple~centationof a hybrid GPS/IMU system. The filter 2 7 models for position, velocity, attitude, gyro drift bias, accelerome- ter bias, clock bias, and clock drift.
Although a Kalman filter with a large number of state-variables promises to generate an elegant and optimal solution for the in- tegrated navigation processing, two important problems associated with such a filter become significant for the next generation of navigation systems. These problems are the computational burden and complexity inherent to large filters, and a series of problems related to filter stability and sensitivity to error sources [44,45]. To avoid these complications, the filter is partitioned into several smaller filters.
Each of these smaller filters is then optimized in a relatively straightforward manner. Information about the correlation between the state-variables that are in different filters will be lost, but for most applications it is possible to find state-variables that are hardly correlated. In addition to filter partitioning, it is also important to minimize feedback loops within the filter, as any feedback loop is a source for instability.
4.3 Hybrid Systems Based on Sensors with Similar Performance
Three hybrid systems have been identified that incorporate sensors with similar performance characteristics and that are of interest to the development of a hybrid GPS/LORAN-C system for a sole means of air navigation: - LORAN-C and Omega
- VOR, Omega, and Dead-Reckoning
-- GPS and LORAN-C
Some of the design techniques found in the literature with respect to these three systems are directly applicable to a hybrid
GPS/LORAN-C system. These techniques have been evaluated and the results are summarized below [46-511:
- LORAN-C should be used in the ranging mode of operation. This
~~ouldallow the hybrid system to process the LORAN-C signals in a
manner very similar to GPS and will also take advantage of the
LORAN-C clock information. Uniform processing of the measurement
data is very important. For instance, reference [52] describes a
hybrid GPS/LORAN-C receiver that combines GPS ranges with LORAN-C
time differences. As a result, the system cannot be completely
tested because of the large number of possible combinations with
geometric effects that are hard to characterize.
- The hardware configuration of the hybrid system should allow
for all-in-view tracking of navigation signals. The redundant
inputs can then be used for user-autonomous integrity checking of
the aircraft position and the individual sensor inputs. 2 9
- The hybrid navigation solution should be implemented using a partitioned filter to avoid numerical instabilities and unpredictable failure modes. 5. GPSILORAN-C INTEROPERABILITY
Two areas must be addressed for the interoperability of GPS and
LORAN-C: the airborne equipment and the groundlspace facilities. The first part of this section is mainly concerned with the timing of GPS and LORAN-C, timing being the basis for the accuracy of these types of radionavigation systems. Improved system timing could also result in increased system availability (see Section 6.). The second part of this section discusses receiver concepts for a hybrid GPS/LOR4N-C navigation receiver.
5.1 GPS/LORAN-C System Integration
Ldithout a complete redesign of either system, LOR4N-C and GPS would be most effectively integrated by synchronizing their time references. Time synchronization would not only improve the naviga- tion capabilities, but would also greatly enhance the dissemination of time .
GPS maintains all timing relations between the space segment and the ground segment. However, for navigation users, LORAN-C timing is established for each chain only. Current developments in LORAN-C include proposed system timing changes. These will result in improve- ments of navigational accuracies and system robustness. LORAN-C rnastpr stations will be synchronized to within 100 nanoseconds of lJ:iive-r;nl Ti~e,Coordinated (UTC) by September 1989 [53]. At the ~ivc 3 1 of this writing, the synchronization of all stations is being studied by the United States Coast Guard. This option will affect the performance of current LORAN-C receivers, and is therefore not expected to be considered for implementation by the Coast Guard.
5.1.1 GPS Timing
The timing of the GPS system is very well defined [54]. The
Plaster Control Station at Falcon AFS maintains GPS system time. Each satellite operates on its own reference time (space vehicle time) which is closely monitored by the GPS Ground Control Segment.
Information about space vehicle clock phase offset with respect to GPS time can be calculated continuously from the navigation data trans- mitted by the satellites with a typical accuracy of 15 nanoseconds f5-51.
Currently, GPS system time is monitored to within 100 nanoseconds with respect to Universal Time, Coordinated (UTC). Offset between GPS time and UTC is also transmitted by the satellites and can be determined continuously by the user with a resolution of one nano- second [56]. With the installation of three hydrogen masers at the
Plaster Control Station, the capability exists to determine time offset between UTC and GPS time to within 30 nanoseconds [57]. 5.1.2 LORAN-C Timing
In order to consider the effect of LORAN-C system timing on the user navigation and timing accuracies, four LORAN-C system timing options are described below. Table 5.1 summarizes the anticipated error budgets for pseudorange measurements to LORAN-C transmitters for the four timing options based on references [58-631.
Navigation system error sources are usually combined on a root- sum-square (RSS) basis [64]. From a statistical point of view, the
RSS approach is only valid if the ensemble statistics of the error sources are uncorrelated and the ensemble average of each error source is zero [65]. The LORAN-C error sources given in Table 5.1 are not necessarily zero mean processes, however, the ensemble averages can be set to zero by subtracting the known, nonzero averages. Receiver measurement errors change rapidly, and are uncorrelated with the propagation and timing error sources. Propagation and timing errors, on the other hand, can be correlated. For example, if the timing of a transmitter is monitored and controlled at a location 300 miles from the transmitter, propagation effects over the 300 miles distance will affect the timing of the transmitter.
Another ccmplication in using the RSS approach is due ~o the slow variations of the timing and propagation errors. These errors could add up during particular flight missions. As a result, the range LORAN-C TIMING OPTIONS ERROR SOURCES I I1 I11 IV
MASTER TRANSMTTER - UTC SYNCHRONIZATIONERROR (ns) (95%) + 2500" 100" 100" 60"
SECOhDARY - MASTER SYNCHRONIZATION ERRORS (ns) (95%)
CHAIN TMNG 5- 50 + 50 - - TEMPORAL PROPAGATION EFFECTS 0 - 50 0 - 50 PROPAGATION ERRORS (ns) (95%) (TRANSMITTER TO USER, 50 - 100 50 - 100 50 - 100 50 - 100 AFER MODELING)
RECEIVER MEASUREMENT (ns) (95%) 25 25 25 25 ERROR
I = CURRENT LORAN-C TIMING H = MASTER STATION TIME OF TRANSMISSION CONTROL 111 = TIME OF TRANSMISSION CONTROL FOR ALL LORAN-C STATIONS IV = DETERhIINATION OF LORAN-C TRANSMITIER OFFSETS WITH RESPECT TO GPS TIIvlE
" NOTE THAT THE TRANSMITTER OFFSET WITH RESPECT TO UTC ONLY AFFECTS TKE ESTIMATE OF UTC AT THE USER; THE POSITION SOLUTION BASED ON TRAhTSMITTERSFROM THE SAhE CHAIN IS HARDLY AFFECTED. CROSS-CHAINING ON THE OTHER HAND IS AFFECTED SIGNIFICANTLY, UNLESS AN EXTRA TRANSMITTER IS TRACKED TO DETERMINE TIE OFFSET BETWEEN DIFFERENT CHAINS.
Table 5.1 A comparison of anticipated error budgets for LORAN-C pseudorange measurements with respect to current and proposed systern timing. 3 ii error will lie somewhere between the RSS and the direct addition of the individual error sources. For enroute navigation, the RSS approach is adequate, since occasional large deviations from the desired trajectory will most likely be detected by Air Traffic
Control, based on radar measurements. The RSS approach is not acceptable for approach and Automatic Dependent Surveillance (ADS) applications. For these reasons, both the RSS and the direct addition of the timing and propagation errors are used for the different timing options in the following sections.
Pseudorange measurements are considered to be made with respect to a known time reference (UTC or GPS)'at the user. In general, the knowledge of UTC or GPS time at the user is not only a function of geometry, but also depends on the magnitude of common bias errors in the pseudoranges (e.g. unmodeled propagation delays). These errors hardly affect the position solution, but will appear as an additional bias in the estimate of the system time reference (UTCIGPS). Note also that receiver hardware delays from the antenna phase center to the measurement point in the receiver are considered to be calibrated and known.
5.1.2.1 Current LORAN-C Timing
LORAN-C nlaster station transmissioils are synchronized to UTC within 2 2.5 microseconds. Whenever a master drifts too far away fro3
UTC, two nethods can bc used to adjust the offset: a frequency 3 5 adjustment or a phase offset adjustment. Intentional phase changes and frequency adjustments are always announced in advance [66].
Frequency adjustments are on the same order as the drift rates of the
LORAN-C Cesium frequency references, typically 50 - 300 nanoseconds per day.
Secondary stations are held to within ? 50 nanoseconds of the
Controlling Standard Time Difference (CSTD), a reference TD es- tablished for each master-secondary pair, measured by a System Area blonitor (SM?) . The SAP1 initiates Local Phase Adjustments (LPA) at the secondary station to maintain the CSTD. This results in an extremely stable TD for users close to the line-of-position (LOP) on which the
SAM is located.
The main disadvantage of the current LORAN-C timing procedure is that the time of transmission of the secondary station varies when propagation delays to the monitor (SAM) vary. This results in an uneven error distribution with relatively large errors in areas not close to the line-of-position defined by the CSTD [67,68]. Also, propagation delay models cannot be applied easily; besides the signal path delay from secondary transmitter to user, the variations caused by he SAI? would need to be predictad as well.
5.1.2.2 Ifaster Station Tine of Transmission Control
C~.:nt-rollin,: tlic LORAIJ-C master stations to an accuracy of better- 3 6 than 100 nanoseconds with respect to UTC will reduce the uncertainty of the LORAN-C clock phase offset relative to GPS. Including propagation uncertainties, pseudorange measurements to master stations could be within 202 nanoseconds (143.6 ns RSS). Ranging to secon- daries will introduce approximately another 100 nanoseconds due to chain timing and temporal propagation effects. The resulting pseudorange measurements to secondary stations could be within 301 nanoseconds (175 ns RSS). Users of LORAN-C only will see no net change. In fact, LORAN-C users can benefit from the increased coverage and accuracy offered by cross-chaining; approximately a factor of 2 in position accuracy with respect to current LORAN-C, mainly caused by improved geometry (see Section 6.).
5.1.2.3 Time of Transmission Control for all LORAN-C Stations
This option proposes a radical change in the timing control of the LORAN-C system. Each transmitter would be synchronized with respect to UTC. This approach is similar to the French direct ranging
LORAN-C chain where GPS is used to monitor the timing control [69].
Time of transmission control will result in improved navigation accuracies for areas not close to line-of-positions maintained by
SAMs. The main disadvantage of this option is the upward cornpatibil- ity of existing LORAN-C receivers. The very high TD repeatability around the SAPlwould be lost, and tables for propagation corrections will have to be changed, or replaced by propagation delay models.
Single chain LORAN-C users will not necessarily see an improvement in navigation accuracy when compared with master time of transmission control. Chain timing errors and temporal propagation effects will be replaced by timing uncertainties with respect to UTC. Cross-chaining users, on the other hand, will benefit tremendously; all transmitters are equal, opening up a larger coverage area with good geometry. This will also increase the LORAN-C system availability: a failing master station does not result in an unusable chain.
For the interoperability of GPS and LORAN-C, this option is very effective: all LORAN-C transmitters could provide ranging with accuracies better than 202 nanoseconds (143.6 ns RSS).
5.1.2.4 Determination of LORAN-C Transmitter Offset with respect to
GPS Time
All of the timing options discussed above should also be considered in combination with GPS receivers at each transmitter site.
Data collected from GPS can be used to determine the transmitter clock offset from GPS time with an accuracy better than 30 nanoseconds [70].
The clock offset with respect to either UTC or GPS time can then be transmitted to the user. This approach will establish, in essence, time of transmission control without affecting existing user equip- ment. Ranging accuracies to the transmitters will only be limited by the combination of GPS time transfer accuracy, remaining uncertainties after propagation models are applied, and user receiver errors.
State-of-the-art LORAN-C receivers would typically achieve ranging accuracies better than 162 nanoseconds (119 ns RSS).
The use of LORAN-C pulse modulation for the transmission of the clock offset data can be justified by the significant improvement of the timing and navigation capabilities created by this approach.
5.2 Airborne Equipment
The airborne implementation of a combined GPS/LOFAN-C receiver can be divided into two approaches:
1. Two Separate Systems. This approach requires a third system
that combines the two receivers in one of the following ways:
a. A (processor) system that obtains navigation data from
the GPS and LORAN-C receivers, executes the integrity
checking algorithms, and provides the "best" navigation
solution to the pilot (this solution may be based on data
from both systems).
b. An interface that converts the data from one system in
such a way that it can be used as an excra input to the
other system (e.g. LORAN-C as a pseudolite input to the GPS
receiver). This approach might require minor codifications
to the data receiving system. 3 9
2. Hybrid GPS/LORAN-C. Several grades of hybridization can be
implemented. Since this system is currently non-existent, it is
necessary to investigate the most effective method of hybridiza-
tion.
5.2.1 Hybrid GPSILORAN-C Receiver Concepts
A hybrid GPS/LORAN-C system design will have a substantially better performance than the sum of the two separate systems, and the hybrid system will require less hardware than two separate systems as illustrated in Figure 5.1. Except for the Radio Frequency (RF) circuitry, both systems can share all functional sub-systems including the frequency reference source, the receiver processor, the Random
Navigation (RNAV) calculations, and the user interface.
Some of the practical advantages of a hybrid implementation are:
- Ambiguity resolution for the LORAN-C signals, cycle
identification errors can be detected and corrected for.
- Extended coverage, for instance three GPS satellites and one
LORAN-C station, could be used for navigation.
- Increased availability, the hybrid system can provide a
navigation solution under certain conditions where each system
alone would not provide a solution. RECEIVER PROCESSOR kH+lPROCESSOR ~FI
RYAV + b USER USER b7ERFACE CrTERFACE
Figure 5.1 Separated (a) and hybridized (b) GPSILORAN-C functional block diagrams. - Propagation anomaly estimation and/or calibration could be
implemented. Signals from GPS and LORAN-C can be used to
estimate the Additional Secondary Phase Factor (ASF) for the
LORAN-C signals.
- Greater robustness against intentional or unintentional
sources of interference such as thunderstorms, jammers, and
ionospheric anomalies could be obtained. The two systems operate
at different frequencies each affected by completely different
propagation anomalies.
- Position errors due to jamming sources can be detected and
corrected for.
- Common oscillator calibration could be achieved. Both systems
will rely on the same, possibly redundantly implemented,
frequency reference facilitating the exchange of clock phase and
frequency information.
- The hybrid system is expected to satisfy the requirements for
a sole means of air navigation for the CONUS. The two separate
systems would not be able to satisfy these requirements (as
discussed in Section 2.).
In summary, the hybrid system will provide much needed dissimilar redundancy and will be a good candidate for a next generation of sole means air navi-gation for the CONUS. 5.2.2 Hardware Implementation Concepts
It is desirable for the hybrid receiver hardware to be structured in a generic way to allow for addition of other sensor inputs, for example those obtained from an altimeter, DME, Omega, or other satellite navigation systems. A proposed functional block diagram of a generic hybrid navigation receiver is given in Figure 5.2. The radio frequency (RF) sub-system will likely be different for each of the navigation sensors due to their different frequencies and principles of operation. The outputs of the RF sub-systems are connected to a common data-bus. Also connected to this bus is the receiver/processor, which automatically recognizes which sensors are connected and operational. Data provided by the sensors are in a generic format to facilitate effective and transparent processing.
Actual data contents are discussed in detail in Section 7. The receiver frequency reference source is common to all functional sub- systems and must therefore be very reliable. The quality of the oscillator can be similar to those currently used in GPS receivers
(short-term stability between one and ten nanoseconds per second).
The user interface allows for input of waypoints and provides position and guidance information to the pilot. All course calcula- tions are performed by the random navigation (RNAV) processor. It is recommended that test inputs are used by the receiver processor for hardware delay calibration and functional integrity checking. By generating a known signal in the receiver processor, and transmitting PROCESSOR
IXTERFACE
Figure 5.2 Functional. block diagram of a generic, hybrid navigation receiver. 4 4 this test signal (with very low power) inco the antenna, the receiver is able to determine the hardware propagation delays as often as necessary. In addition, this test signal can be used to confirm the hardware integrity of the overall receiver system.
Detailed hardware concepts such as measurement update rate and the communicatio~~requirements between the sub-systems depend on the integrity requirements for a sole means of air navigation. Higher measurement rates can be used to improve the reaction time to detect a signal anomaly and reduce the variance of the position estimate. 6. GPS/LORAN-C PERFORMANCE CAPABILITIES
Data provided in this section will support the hypotheses that hybrid GPSILORAN-C has better performance capabilities in the areas of coverage, reliability, and availability, than the combined performance of each system alone. The advantages of a hybrid implementation are derived quantitatively in this section. First, the performance capabilities of stand-alone GPS and LORAN-C are determined with respect to coverage, reliability, and availability. Results from this part also illustrate the dissimilar redundancy capabilities of a
GPS/LORAN-C navigation service. Next, the performance capabilities of hybrid GPSILORAN-C are determined.
6.1 LORAN-C Coverage, Reliability, and Availability
The hybrid GPSILORAN-C system requires that LORAN-C will be used in the pseudorange mode. In addition, the performance of LORAN-C using pseudoranging significantly increases the system's performance capabilities as discussed in Section 5.1.2.
To predict LORAN-C pseudorange coverage for synchronized transmitters, a computer program has been written based on a hyper- bolic coverage prediction model developed for the FAA [71]. The current program predicts pseudorange coverage accounting for geometry and signal-to-noise ratio at the receiver. Coverage is declared -i.~ilen the geometry (Horizontal Dilution of Precision, KDOP), number of 4 6 stations, and the signal-to-noise ratio conditions are satisfied.
Both the pseudorange coverage and the redundancy of the coverage are addressed. The quality of the redundant coverage is examined:
Given a transmitter failure, do the remaining stations satisfy the coverage requirements? LORAN-C outage data were obtained from the
U.S. Naval Observatory and literature [72,73]. These data are used in a Markov model that determines the time-dependent availability of the
LORAN-C system.
6.1.1 LORAN-C Pseudorange Coverage Prediction Computer Model
The computer program used to predict LORAN-C pseudorange coverage is written in FORTRAN 77 and has been implemented on an IBM mainframe computer system running the VM/CMS operating system. A listing of the source code of the simulation model can be found in reference [74].
The coverage prediction is based on a point-by-point search of a certain geographical area. For each point in the search area, the program predicts the LORAN-C pseudorange coverage as follows:
- For each transmitter that is within a certain distance to the
search point (typically 800 nm) the program will predict the
signal-to-noise ratio at the search point.
- The program calculates the Horizontal Dilution of Precision
(HDOP), based on all stations that have an adequate signsl-to-
noise ratio at the search point. 4 7
- The results of the calculations for each search point are
stored for later use in combination with graphical representation
programs.
6.1.2 Signal-to-Noise Ratio Calculation
The determination of the signal-to-noise ratio (SNR) is almost
identical to the algorithm given in reference [75]. The only
difference is the number of conductivity cells that are used to
calculate the attenuation level of a LORAN-C transmitter at the
receiver. An overview of the SNR calculation is included in this
section.
The SNR at the search point is calculated by taking the dif-
ference between the transmitted signal level and the atmospheric noise level:
SNR = SIG - ANOISE (dB/(lpV/m) ) (6.1) where : SNR is the signal-to-noise ratio at the search point (dB/(lpV/m)). SIG is the transmitted signal level at the search point (dB/(lpV/m)). ANOISE is the mean atmospheric noise level at the search point for a specific season (dB).
The mean atmospheric noise level is calculated based on C.C.I.R. report No. 322 [76]. The values used in the program are the average values for the sumrner season which will not be exceeded more than five percent of the time (95 percent values). It should be noted that the
95 percent ncise values are rather conservative. The transmitted signal level at the search point is obtained using the following formula:
SIG = PDB - OBSIG + PC - SC (dB/(lpV/rn)) (6.2) where : PDB is the signal strength of a certain transmitter at 1 nm distance (dB/lpV/m)). For instance, a 400 kW transmitter results in a PDB of 131.4 dB/(lpV/m). OBSIG is the attenuation level of a certain transmitter at the search point (dB). PC is the power correction for transmitters other than 400 kW (dB). An 800 kW transmitter has a PC of 3.01 dB. SC is a correction factor for measurements other than the pulse peak (dB). SC is 4.08 dB if the signal is measured at the point 30 ps after the start of the pulse.
The attenuation of a LORAN-C signal depends on the ground or sea conductivity of the propagation path. The model described in reference [77] uses two conductivity cells, one for the eastern half and one for the western half of the search area. Currently, the program divides the area containing the conterminous Uni~edStates into 40 cells. The Millington method is used to calculate the attenuation level for a propagation path through one or more conduc- tivity cells [78].
6.1.3 Horizontal Dilution of Precision Calculation
The propagation of range errors into the position domain depends on the gecxnetujr of t:he transmitter location with respect to the sesrch point. For aircraft navigation using LORAN-C, only the two-
dimensional position fix accuracy is used for navigation. The
1.Iorizontal Dilution of Precision (HDOP) determines the error propaga-
tion into this horizontal plane.
The relation between the range measurement errors and the
resulting two-dimensional position errors is derived from the measurement equations. A range measurement to a LORAN-C transmitter
is made with respect to the receiver frequency reference source, the
phase of which is usually not the same as the phase of the LOMN-C
transmitter clock. The phase difference, or clock offset, between the
transmitter and the receiver becomes part of the range measurement to
the transmitter. A receiver range measurement that contains both this
clock offset and the true range to the transmitter is called a
pseudorange.
Within the coverage area, LORAN-C ground waves basically travel
great-circle distances. A receiver at sea-level will interpret the
signals as if they came from transmitters located in the locally level
plane at distances equal to great-circle distances to the transmit-
ters, as depicted in Figure 6.1. Adding measurement errors and a
possible LORAN-C transmitter clock offset with respect to LORAN-C
system time, the LORAN-C pseudorange measurement equation is given by: +' Lti position vector LORAN-C transmitter corrected for earth curvature -3 L , 1 position vector LORAN-C transmitter
3 user position vector +' e i line-of-sight vector for transmitter i
Figure 6.1 LORAN-C ranging geometry for a receiver at sea-level. where: L ' is the position vector of the LORAN-C transmitter i corrected for earth curvature (m). is the user position vector (m). is the speed of light in vacuum (m/s). is the user clock offset from LORAN-C time (s). is the clock offset for transmitter i from LORAN-C time (s). is the delay for measurement i caused by LORAN-C error sources (s). The delay is both a function of time and receiver location.
Next, the following assumptions and simplifications are introduced:
- The receiver is at sea-level. A receiver at altitude will
produce larger pseudorange values than a receiver at sea-level,
which results in a slightly different geometry. For aircraft
navigation, accuracy is more important at low altitudes,
justifying the choice to use a zero altitude.
- The LORAN-C error sources and the transmitter clock offsets
with respect to LORAN-C system time can be neglected for the
geometry calculations, since these values are small with respect
to the range to the transmitters and the receiver clock offset.
Applying these assumptions to the pseudorange measurement equation, it follows that three or more measurements are needed to solve for receiver latitude, longitude, and clock offset with respec: t to LORAN-C time. Using matrix notation, the pseudorange equations can be written as follows:
where e is the line-of-sight unit vector from the user to : i the transmitter. e e are the components of the line-of-sight unit vector il' i2 for measurement i (m). X, Y, B are the receiver coordinates in the horizontal plane (X, Y), and the clock offset (B) from LORAN-C time (m). is the LORAN-C transmitter location corrected for L ; earth curvature (m). P. is the pseudorange measurement to transmitter i I. (m).
Simplifying the matrix notation results in the following equation:
H-S=R or S=H-'OR (6.5) where: H- is the generalized inverse of the H-matrix.
The propagation of the pseudorange errors into the user state vector S (North, East, clock offset) can then be found by taking the covariance of both sides of the matrix equation:
where : E { ) designates the expected value of the quantity inside the parenthesis. 53
The covariance matrix of S is then obtained by setting the cov(R) equal to the identity matrix, which effectively assumes the measure- ment errors to be uncorrelated, and normally distributed with a zero mean and unity variance.
The Horizontal Dilution of Precision is then obtained by using the diagonal elements (variances) of the covariance matrix of S that affect the receiver position:
HDOP = 4 sll + s 22 (6.8) where : s s are the first two diagonal elements of the 11' 22 matrix S.
The relationship between the pseudorange errors and the position error is a function of the matrix H, which is a function of the line- of-sight vectors to the LORAN-C transmitters only. Also, HDOP can now be calculated using three, or more than three transmitters.
6.1.4 Predicted LORAN-C Pseudorange Coverage Results
Predicted LORAN-C pseudorange coverage results have been determined using the computer program described in the previous section. Coverage was computed for the conterminous United States
(CONUS) under the assumption that all transmitters were synchronized.
Although the LORAN-C transmitters are not currently syncilror!ized, 5 4 master synchronization will be completed by the end of 1989 and studies are initiated to investigate time of transmission control for all LORAN-C transmitters as discussed in Section 5.1.
Figure 6.2 shows a map of CONUS with the locations of the LORAN-C transmitters used for the coverage predictions. Note that the four mid-continent transmitters, indicated by triangles, are included in the calculations. These transmitters are scheduled to be operational by 1990.
Predicted LORAN-C pseudorange coverage using three or more stations is shown in Figure 6.3. Coverage is declared when SNR is greater than -10 dB and HDOP is less than 7.8. These coverage conditions result in a positioning accuracy of better then 463 meters
(2 drms). The 463 meters are based on current hyperbolic LORAN-C accuracy, 0.25 nm for a HDOP less than 7.8. This number will most likely improve if all LORAN-C stations are synchronized (see Section
5.1.2). Coverage was also calculated for HDOP less than 4, which provides a positioning accuracy of better than 237 meters (2 drms).
Figure 6.4 shows the resulting coverage.
Figure 6.5 illustrates the redundancy of the pseudorange coverage. Four stations are required with SNR greater than -10 dB and
NDOP of less than 7.8. Again, these numbers would result in navig:?- tional accuracies of better than 0.25 nm (95%). Figure 6.5 shotis that at least one redundant signal is available.
LONGITUDE
-- All stations are synchronized - All-in-view solution using 3 or more stations - SNR greater than -10 dB - HDOP less than 7.8 - Receiver bandwidth = 20 kHz - Atmospheric noise values used are for the summer season, based on C.C.I.R. Report No. 322 - Search increment = 0.5O
Fif~me6.3 Predicted LORAN-C pseudorange coverage with the "mid-continent gap'' filled for three or more stations (0.25 nm). - All stations are synchronized - All-in-view solution using 3 or more stations - SNR greater than -10 dB - HDOP less than 4 - Receiver bandwidth = 20 kHz - Atmospheric noise values used are for the summer season, based on C.C.I.R. Report No. 322 - Search increment = 0.5"
Figure 6.4 Predicted LORAN-C pseudorange coverage with the "mid-continent gap" filled for three or more stations (0.125 nm). 50' H
40' N
25
30. N
20' H 128' W 108' W 68' W LONGITUDE
- All stations are synchronized - All-in-view solution using 4 or more stations - SNR greater than -10 dB - HDOP less than 7.8 - Receiver bandwidth = 20 kHz - Atmospheric noise values used are for the summer season, based on C.C.I.R. Report No. 322 - Search increment = 0.5"
Figure 6.5 Predicted LOR4N-C pseudorange coverage with the "mid-continent gap" filled for four or more stations (0.25 nm). 59
The approach used to determine the quality of the redundant coverage consisted of simulating a failure of one of the LORAN-C
stations and examining the resulting coverage for the CONUS. This was
repeated for each of the LORAN-C stations. Figure 6.6 shows the results for the cases in which the stations Baudette and Middletown were failed, respectively. These results represent worst cases since both Baudette and Middletown cover a relatively large area compared to
other stations. In fact, the simulated Middletown failure would not create an outage area if the coverage requirements are lowered to -16 dB SNR and HDOP less than 10. The SNR requirement of -16 dB would be consistent with the tracking performance of current LORAN-C receivers
[79]. The HDOP requirement of 10 instead of 7.8 would increase the navigation error by at most 20% in a small area just south of the
Fallon, NV, transmitter. Similarly, the simulated Baudette failure would not affect any part of the CONUS if the SNR limit is set to -16
dB.
6.1.5 LORAN-C Reliability and Availability
Numbers for reliability and availability are both necessary to
characterize the possible loss of the navigation service. Availabil-
ity indicates the expected percentage of time that the signal can be used for navigation. Reliability tells how likely the system, or a
specific transmitter, will fail during a specified period of time. 50. N
40' N
30' N
20. N 128' W 108' W 88' W 68. W LONGITUDE
LONGITUDE
Figure 6.6 Predicted LORAN-C pseudorange coverage with the "mid-continent gap1' filled, simulated Baudette failure (top) and Middletown (bottom). 6 1
Assuming exponential failure and repair probability density functions, reliability can be expressed as:
- -t MTTF R(t) = e where: MTTF is the mean time to failure (s) . t is the time (s). and availability is given by:
where : MTTF is the mean time to failure (s). MTTR is the mean time to repair (s).
6.1.5.1 LORAN-C Failure Data
LORAN-C outage data is published by the U.S. Naval Observatory in
"Daily Time Differences and Relative Phase Values, Series 4" [80].
From these data, LORAN-C mean time to failure (MTTF) and mean time to repair (MTTR) statistics can be calculated [81].
A distinction should be made between two types of transmitter outages, scheduled off-air periods and unscheduled off-air periods or periods of unstable transmissions. Scheduled off-air periods result from maintenance operations and typically last from a few minutes up to several hours [82]. Since these periods are known in advance, they can be scheduled such that the impact on the user is minimal. For instance, scheduled maintenance should never allow for the simul-
+,caneo~~s unavailability of two transmitters servicing overlapping areas.
Unscheduled outages result from hardware failures such as transmitter equipment failures, clock degradation, and signal transmission anomalies. These outages are generally shorter ~hanthe scheduled outages. Typical repair times for unscheduled outages are between a few seconds and one hour.
Unscheduled transmitter outage data are given in reference [83].
For the year 1981, these data result in the following MTTF, MTTR, and percent unavailability:
LORAN-C transmitter unscheduled failure statistics for 1981
MTTF - 1500 hours MTTR - 35 minutes percent unavailability = .04%
The Federal Radionavigation Plan (FRP) provides the following numbers for LORAN-C unavailability [84]:
LORAN-C Unavailability
transmitter percent unavailability < .1% triad percent unavailability < .3%
IJote that he FRP numbers include both scheduled and unscheduled outages. For example, areas covered by only one triad will suffer approximztely a total of 1.1 days of outage during a year. This 6 3 example could be improved upon significantly if pseudoranging is used in combination with synchronized LORAN-C transmitters. Almost all of the CONUS is covered by at least four transmitters with good geometry for all sub-sets of three transmitters. Because of this, the availability of LORAN-C for four synchronized transmitters is the topic of the next section.
6.1.5.2 LORAN-C Markov Model for Four-Transmitter Availability
To determine the time dependent availability of four transmit- ters, a Markov model has been implemented. The model is shown in
Figure 6.7. Five states are identified, the left-most state (1) represents the case of four working transmitters, the right-most state
(5) represents the case of four failed transmitters. Each discrete time-step, the system can either remain in a state or transition to a neighboring state. For instance, starting with four operational transmitters (state I), a small amount of time later the four transmitters can still be operational (state l), or one of the transmitters could have been failed (transition to state 2). During a time-step, only one transmitter is allowed to fail or repair. This can be justified by choosing small time-steps [85].
The Markov analysis requires the definition of a state probabil- ity vector s, which elements indicate the probability that the system brill be in a certain state at a specific time. Next, the stochastic transitional probability matrix P is defined. The elements of the
6 5
P-matrix represent the probabilities that the system will remain in a certain state (diagonal elements) and the probabilities that the system will transition to another state (off-diagonal elements). The
P-matrix for the LORAN-C model is given in Figure 6.8.
For each time-step, the state probability vector s is multiplied by the stochastic transitional probability matrix P resulting in the state probabilities corresponding to the new time.
Starting with the initial state probability vector so, the calculation proceeds as follows:
after 1 time-step S = s P 1 0
after 2 time-steps s = (s0P)P = s p2 2 0
after n time-steps s = s pn (6.11) n 0
The number of time-steps is calculated from the mission time and the time-step:
mission time n = (6.12) Ot
The size of the time-step is determined experimentally by decreasing the time-step until the change in the results is below the desired accuracy.
After n time-steps, the elements of the state probability vector sn contain the time-dependent availability numbers for each of the states. The time-limiting state availnbilities are obtained by TO STATE ---+
FROM 1 1-4h 4h 0 0 0 STATE 2 1-3h-p 3h 0
4 2i 1-~~pl~~-3p 5 [ 4P 1-4~1
h is the transmitter failure rate (failuresls)
CL is the transmitter repair rate (repairsts)
~t is thetime-step
Figure 6.8 The stochastic transitional probability matrix P for the four-transmitter Markov model. 6 7
increasing the mission time until the change in the state probability
vector is small with respect to the desired accuracy. These time-
limiting availabilities can be interpreted as the availabilities for
each state after the system has been operational for a period of time
a few times longer than the MTTF.
A complication in the evaluation of the state probability vector
becomes apparent for long mission times with short time-steps. For
instance, a mission time of two years and a time-step of 10 minutes would require the 105,120tli power of the matrix P.
The problem of raising the transition matrix P to the power n,
where n is large, is addressed by decomposing the P-matrix as follows
[86]:
where : D is a diagonal matrix containing the eigenvalues of the matrix P. S is the eigenvector matrix containing columns of eigen- vectors corresponding to the eigenvalues of P.
The matrix multiplication can then be written as follows:
The problem is now reduced to finding the eigenvalues and eigerlvectors
of the transition matrix, inverting the eigenvector matrix, raising
the eigenvalues to the po~~ern, and multiplying tlie matrices. Results
The Markov model as described above has been run for a mission time of two years with an one-minute time-step. The numbers for MTTR and LITTF were parameterized based on the numbers given in Section
6.1.5.1. Starting with four operational transmitters, the state availabilities stabilized after one month. Table 6.1 provides the time-limiting availabilities for each of the five states. These numbers are representative for the expected availability of four, three, two, one, and zero transmitters.
Based on the 1981 LORAN-C MTTF and MTTR data, it can be concluded that LORAN-C pseudoranging results in an availability of at least
99.9995%. It should be noted that large areas of the CONUS are covered by more than four transmitters, and transmitter outages will likely decrease in the future. Results for the latter case can also be read from Table 6.1, where availabilities are given for a MTTF of
2000 hours and repair times of 10, 35, and 60 minutes. Table 6.1 indicates that the expected unavailability of LORAN-C is less than three minutes during a year. This level of unavailability is a good estimate, but does not include major catastrophes such as those caused by hurricanes and mechanical antenna failures [87]. Also, a high intensity thunderstorm could cause the LORAN-C receiver to loose track on the signal. For these reasons, it is desirable to have another system available, which is not affected by the same error sources. MTTF MTlR (11ours) (minutes) P4 P3 P2 PI Po
1500 10 0.999556 0.000444 1.48~-07 3.29e-11 3.66e-15
1500 35 0.998445 0.001553 1.81e-06 1.4 1e-09 5.48e-13
------1500 60 0.997335 0.002660 5.32e-06 7.09~-09 4.73e-12
2000 10 0.999667 0.000333 8.33e-08 1.39e- 11 1.16e-15
2000 35 0.998834 0.001 165 1.02e-06 5.95e-10 1.73e-13
2000 60 0.998001 0.001996 2.99e-06 2.99e-09 1.50e-12
Table 6.1 LORAN-C state probabilities after one month for four-transmitter coverage, parameterized with respect to MTTF and MTTR. 6.2 GPS Coverage, Reliability, and Availability
GPS coverage is not only a function of location, but also a
function of time which complicates the coverage calculations. For-
tunately, GPS coverage repeats after approximately one day as a result
of the satellites' orbital period of 11 hours and 58 minutes.
Coverage for the 21 and 24-satellite constellations is provided
together with anticipated constellation changes. GPS availability and
reliability are addressed and a Markov model has been developed to
analyze possible improvements with respect to GPS system availability.
6.2.1 GPS Coverage
The currently DoD-approved GPS baseline constellation consists of
21 satellites. Eighteen satellites are symmetrically spaced in six
orbital planes inclined at 55 degrees, as depicted in Figure 6.9.
Three active spares are added to every other plane to obtain a 98%
availability of the 18-satellite constellation [88]. A computer program has been developed that calculates the GPS coverage based on
requirements for satellite visibility and geometry. BASELINE
ARGUbIENT OF LATITUDE
OPTIMAL
ARGUMENT OF LATITUDE
OF TI*, NODE
Figure 6.9 GPS phasing diagrams for the symmetrical 21-satellite baseline constellation (top) and the Optimal 21-satellite constellation (bottom). Two major GPS constellation changes are expected [89]:
1. The Optimal 21-satellite constellation in which the three
active spares are better integrated into the constellation. The
satellites will be non-symmetrically spaced in the six orbital
planes. This constellation is expected to be operational by
1991.
2. The addition of three more satellites resulting in the
Primary 21-satellite constellation. This 24-satellite constel-
lation will be non-uniform also. Funding will be requested in
the fiscal year 1990 budget to expand the 21-satellite constella-
tion with three more satellites by 1995 [go].
The Optimal 21-satellite constellation phasing diagram is depicted in
Figure 6.9. This constellation has the following advantages when compared with the symmetrical constellation [91]:
- Improved Position Dilution of Precision (PDOP), the satellite
geometry is bounded by a value of 11 for the PDOP. The PDOP for
the symmetrical constellation is not bounded for short periods of
time at certain locations.
- Improved coverage, the Optimal constellation provides 5-fold
coverage everywhere. 7 3
- Higher availability, the maintenance of the Optimal constella-
tion is based on local optimization. This results in shorter
satellite moves without degraded performance during transition.
The Primary 21-satellite constellation is optimized to provide
he best possible coverage in the event of any single satellite failure. The maintenance of this constellation will be based on a launch-on-schedule policy. A new satellite will be launched once every three months. The phasing diagram for the Primary 21-satellite constellation is given in Figure 6.10.
In addition, the orbital altitude of the GPS satellites will be increased by about 50 kilometers [92]. This will increase the orbital period from 11 hours and 58 minutes to exactly 12 hours. A
12-hour orbit requires less constellation maintenance. The current orbital period requires orbital adjustments about once a year. These adjustments last for two or three days during which time the satellite is unavailable for navigationttiming purposes.
6.2.2 GPS Coverage Prediction Computer Model
The structure of the GPS coverage prediction model is similar to the program for LORAN-C (see Section 6.1.1). The coverage prediction is based on a point-by-point search of a geographical area. Coverage is calculated for one whole day in time-increments of 1-10 minutes, based on a predetermined set of GPS orbital parameters as follovs: PRIMARY
Figure 6.10 GPS phasing diagram for the Primary 21-satellite constella~ion (24 satellites, from reference [89]). 7 5
- The elevation angle of each satellite measured upwards with
respect to the locally level plane is determined. A satellite is
labeled visible if the elevation angle is greater than the mask
angle (typically 7.5 degrees).
- The horizontal dilution of precision (HDOP) is calculated
based on the visible satellites.
- Calculation results for each search point are stored for later
use, in combination with graphical representation programs.
The HDOP is calculated from (see also Section 6.1.3):
HDOP = dTl + s 22
where : s s are the first two diagonal elements of the 11' 22 matrix S. H is the direction cosine matrix. e e e are the components of the line-of-sight uni-t il' i2' i3 vector from the user to the satellite.
6.2.3 Predicted GPS Coverage Results
Predicted GPS coverage results for the CONUS have been determined using the compucer model for two cases: 7 6
Case 1. The symmetrical 21-satellite baseline constellation.
Case 2. The Primary 21-satellite constellation (24 satellites).
The Optimal 21-satellite constellation was not simulated, as the coverage is very similar to the uniform baseline constellation. The model has been run for a period of one day in lo-minute time-incre- ments, using a satellite elevation mask angle of 7.5 degrees and HDOP less than 6. These coverage conditions would result in a positioning accuracy of 100 meters (2 drms) [93]. Initially, the position search increment was taken to be five degrees in the latitude and longitude directions, which provides good coverage information. To improve the resolution of the coverage contours, a search increment of one degree was selected for the graphical results presented in this section.
The results for Case 1 show degraded coverage for parts of
California, as depicted in Figure 6.11. These results are consistent with previously published GPS coverage for the 21-satellite baseline constellation [94,95]. The outage area was further investigated by computing the coverage for a one-degree position increment and a one- minute time increment. It was found that the HDOP does not exceed
110. The corresponding positioning accuracy would then be 110 divided by six and multiplied by 100, or 1833 meters (2 drms). This accuracy meets the current requirements for domestic enroute and terminal navigation (Section 3.), however, none of the future accuracy goals would be met. Note that the outage area would not occur for the fully operational Optimal 21-satellite constellation. Case 2, the Primary 'W 108' W 88'W 68' W LONGITUDE
l2?zzzl 1 - 14 minutes
NO FAILURES
Figure 6.11 Degraded GPS coverage for the symmetrical 21-satellite baseline constellation accumulated over one day. 7 8
21-satellite constellation experiences small outage areas for periods of approximately 5 minutes during a day, see also reference [96].
The redundancy of each of the constellations has been inves- tigated by failing one GPS satellite at the time and examining the resulting coverage for CONUS. The 21-satellite constellation shows significant periods of time with degraded coverage, as illustrated in
Figure 6.12 for one particular satellite failure.
The coverage of the Primary 21-satellite constellation is also affected by single satellite failures. Outage areas are relatively small compared to the symmetrical 21-satellite constellation, but can last up to 20 minutes. To further determine the robustness of the
Primary constellation, combinations of two satellites were failed.
Figure 6.13 shows a typical result for two failed satellites that are close to one another in the constellation. The coverage was computed using an elevation mask angle of 5 degrees and HDOP less than 10.
Major parts of the United States experience degraded coverage for periods of up to 40 minutes. These outage areas will move in the
West-direction at a rate of one degree per day, as a result of the 12- hour orbital period. Outage areas for the symmetrical 21-satellite constellation are stationary. 1 - 19 minutes
20 - 59 minutes
SV 2 FAILED Longitude of the ascending node = 0"
Argument of latitude = 137"
Figure 6.12 Degraded GPS coverage for the symmetrical 21-satellite baseline constellation with one simulated satellite failure, accumulated over o11c day. 1 - 19 minutes
20 - 39 minutes
SV 2 and SV 5 FAILED
Longitudes of the ascending node: O", 60"
Arguments of latitude: 190.9", 25.3"
Figure 6.13 Degraded GPS coverage for the Primary 21-satellite constellation with two simulated satellite failures, accumulated over one day. 6.2.4 GPS Reliability and Availability
The reliability of GPS satellites is affected by two failure modes, short-term failures and long-term failures [97]. A long-term failure occurs when the satellite is "unrepairable" and a new satellite must be launched to replace the failed one. Short-term failures are mainly caused by satellite clock degradation and orbital repositioning procedures.
Based on over five years of operational experience with the ten
Block I satellites and the current production design, the expected satellite life-time for the Block I1 satellites is 7.5 years.
Although Block I satellites experience short-term outages once or twice a year, each lasting between a few hours and a few days, short- term failures for the Block I1 satellites are expected to be less frequent and of shorter durations [98]:
- Four clocks will be onboard each satellite. Malfunctioning
clocks will be taken off-line prior to loss of lock.
- An altitude increase of approximately 50 kilometers, eliminat-
ing the need for yearly orbital adjustments which cause satellite
unavailability of 2-3 days.
The maintenance of the symmetrical 21-satellite cor~stellation is designed to result in a 98% availability of at least 18 satellites.
Rased on this, a space-shuttle launch schedule exists that would 8 2 satisfy the 98% availability. Unfortunately, the shuttle access to space has been a problem during recent years and consequently, the current satellite launch schedule hardly depends on the space shuttle.
Instead, stretched Delta-I1 rockets are expected to launch most of the
Block I1 satellites starting December 1988 [99].
To predict the availability of the 21 and 24-satellite constella- tions, a Markov model has been implemented. The model is shown in
Figure 6.14, both short-term and long-term failure and repair rates are considered for a total of sixteen states. The corresponding stochastic transitional probability matrix P is given in Table 6.2.
Truncation of the model to sixteen states has been determined experimentally by starting with eleven states and expanding until no significant change in the state probabilities was found.
Results
The Markov model as described above has been run for a mission time of two years. The numbers for short-term and long-term MTTFs and
MTTRs were parameterized as given in Tables 6.3 and 6.4. Figure 6.15 shows the availability results for the 21-satellite constellation wit11 both long-term and short-term failures. The time-dependent availabil- ity curves for the 24-satellite constellation are similar to those for the 21-satellite constellation. Overall availability of the 24- satellite constellation is improved as more satellite failures can be tolerated before the coverage is degraded. The time-limiting State 1 : all operational State 2 : one short-term failure State 3 : one long-term failure State 4 : two short-term failures State 5 : one long-term and one short-term failure
Figure 6.14 Markov model for the de~erminatio11of the time-dependent availability of the 21 and 24-satellite GPS constellations. 8 5 2Ps 16 13 3ps+3pl 8 12 (n-311, 16 14 2ps+4p, 8 13 (II-~)?~~ 16 15 ps+.5p1 1 S diagonal elements: = I - l? j=l 'I jzi
all other elements are zero
Table 6.2 Elements of the stochastic transitional probability matrix P corresponding to the GPS failure transition diagram (Figure 6.14). 1 LONG TERM SHORT TERM
MlTF MTTR MTTF M'ITR p2 1 80 PI 9 PIS (years) (months) (years) (hours)
7.5 1 - - 0.770 0.180 0.040 0.008
7.5 2 - - 0.555 0.25 8 0.113 0.047
7.5 3 - - 0.387 0.264 0.166 0.095
7.5 1 1 6 0.762 0.188 0.041 0.008
7.5 1 1 36 0.71 1 0.227 0.052 0.010
7.5 2 1 6 0.574 0.272 0.113 0.037
7.5 2 1 3 6 0.540 0.293 0.122 0.039
A
Table 6.3 GPS state probabilities after two years for a 21-satellite constellation, parameterized with respect to MTTF and MTTR.
5 8 availabilities for the 24-satellite constellation are given in Table
6.4.
Based on these results, the conclusion is that:
- The availability of the 21-satellite constellation is not
sufficient; more than 23% of the time less than 21-satellites
will be available resulting in significant outage areas (based on
a long-term MTTF of 7.5 years and a (optimistic) long-term MTTR
of one month).
- Short-term failures have a relatively small affect on the GPS
availability, especially for repair times less than six hours.
- The availability of the 24-satellite constellation is, as
expected, much improved with respect to the 21-satellite
constellation. However, more than 6% of the time, two or more
satellites are unavailable, which could result in significant
outage areas, based on a long-term MTTF of 7.5 years and a
long-term MTTR of one month. If the repair time increases to two
months, three satellites would be unavailable for more than 6% of
the time.
The actual percentage of time of degraded coverage at a par- ticular location would be less than 6% for the 24-satellite constella- tion with a repair time of one month. For example, consider the C~SC 8 3 in which only one combination of two failed satellites out of 24 satellites would affect a certain location. For that location, a rota1 of 276 combinations of two failed satellites are possible, resulting in an expected unavailability of 0.022% (11276 * 6%). This corresponds to an unavailability of approximately two hours during a year. The availability of the GPS system would significantly improve if HDOP values of larger than 6 are tolerated. On the other hand, less frequent satellite launches would have a major negative effect on the availability.
6.3 Hybrid GPS/LORAN-C Coverage, Reliability, and Availability
The hybrid GPS/LORAN-C receiver can utilize pseudorange measure- ments from both systems, thus improving tremendously on coverage, reliability, and availability when compared to each system alone. The performance of the hybrid system is analyzed under the following assumptions:
- LORAN-C master station transmitters are synchronized to UTC to
within 100 nanoseconds and the mid-continent transmitters are
operational. The first item will be implemented by September
1989, and the mid-continent transmitters are expected to be
operational by 1990.
- The GPS space segment consists of a symmetrical 21-satellite
constellation which is expected to be operational by 1991. - The hybrid receiver transmits a test pulse to determine the
receiver hardware bias. Without this capability, one extra
measurement would be needed to determine this offset.
The focus will be on enroute domestic and terminal navigation.
With respect to the current and future accuracy requirements for these
phases of flight (see Section 3), both GPS and LORAN-C signals can be
used.
6.3.1 Hybrid GPSILORAN-C Coverage
The coverage of the hybrid GPSILORAN-C system has been determined using the computer models which are described in Section 6.1.1 (LORAN-
C) and Section 6.2.1 (GPS). The models for GPS and LORAN-C have been
integrated into one program that calculates the coverage based on all measurements for each point in a search area for a period of one day, with a 10-minute time-increment. LORAN-C signals are declared
receivable for SNR greater than -10 dB, and GPS satellites are
declared visible for elevation angles greater than 7.5 degrees, measured upwards with respect to the surface.
In order to evaluate the system accuracy under different condi-
tions, it was decided not to limit the IIDOP value. The importance of determining the HDOP value is explained as follows. The future
requirement for nonprecision approach accuracy is 100 meters (2 drrns). GPS will provide this accuracy for HDOP less than six. If HDOP becomes larger than six, nonprecision approaches are no longer acceptable using GPS. However, the future requirement for enroute navigation is only 1000 meters (2 drms). This would allow for a much larger value of HDOP, as the horizontal position error for the minimum number of measurements is determined by the product of HDOP and twice the one-sigma range error (or):
position error (2 drms) = 2 * HDOP * or (6.16)
Different LORAN-C timing options result in different one-sigma range errors for LORAN-C. Again, the evaluation of the system accuracy would be more effective by looking at the largest value of
HDOP in combination with the range errors for different timing opt ions.
6.3.2 Predicted Hybrid GPSILORAN-C Coverage
The first step of the hybrid GPSILORAN-C coverage prediction consists of the calculation of the HDOP values with all GPS satellites and LORAN-C transmitters operational. The HDOP has been calculated for the CONUS in five-degree position increments and 10-minute time- increments. The highest values for the HDOP, based on four measure- ments, at a search point have been obtained. Figure 6.16 shows the results for 72 locations in and around the CONUS: HDOP is never larger than 2.3. Even with a LORAN-C pseudorange error of 50 meters (one sigma), horizontal positioning accuracy would be 230 meters (2 drms).
9 3
The next step consists of simulating one signal failure at the time. The resulting coverage for each of the 44 cases (21 GPS satellites and 23 LORAN-C transmitters) is then examined. For one particular location and time, the lowest HDOP-combination is selected from all possible combinations of four measurements, not including the failed signal. This procedure is repeated for a whole day in 10- minute time-increments, and coverage information is stored for the time with the largest HDOP.
One signal failure does not affect the navigation service as either GPS or LORAN-C would still be available. Simulated failures of all combinations of two or more signals rapidly increases the computational requirements. Therefore, the analysis was continued for four representative locations in the United States. The worst case performance has been obtained by failing all combinations of up to 6 signals and by using the best HDOP value for the combination with the worst results. This process has been simplified by only failing those signals that are part of the measurement set at a certain location.
For instance, failing 5-out-of-44 signals results in a total of
1,086,008 combinations of failed signals. Typically, 10 signals are available for navigation, reducing the number of combinations to 252
(5-out-of-10).
Different failure scenarios and the corresponding results are shown in Table 6.5. Denver, CO, Athens, OH, and Washington, DC, can tolerate four failures without loss of an accurate navigati-on service BEST VALUE OF HDOP FOR THE WORST CASE FAILURE NUhlBER PERCENTAGE OF TIME WITH HDOP > 10 IS GIVEN BETWEEN PARENTHESIS. OF FAILURES SAN FRANCISCO DENVER ATHENS WASHINGTON C A CO OH DC
0 1.8 1.2 1.2 1.2
1 2.6 1.3 1.4 1.4
2 8.3 1.5 1.7 1.9
3 16.6 1.9 (4.2%) 2.5 2.5
4 1296.1 2.5 3.9 4.1 (26.4%) 10.4 5 - 3.5 7.5 (0.7%)
11.2 79.2 6 144.4 - (0.7%) (2 1.5%) (27.8%)
Table 6.5 Worst case failure scenarios for the hybrid GPSILORAN-C system for four representative locations in the United States. 9 5
The results for San Francisco, CA, are less favorable as the San
Francisco area experiences degraded GPS coverage for the symmetrical
21-satellite constellation and does not have redundant coverage to compensate for a Middletown-station failure. It should be noted that
San Francisco could tolerate four failures if the SNR-limit for LORAN-
C is set to -16 dB, and the Optimal 21-satellite constellation is used. Also shown in Table 6.5 are the percentages of time for which the HDOP exceeds a value of 10, based on the worst case failures.
The above results are not conclusive for all of the CONUS, although they do indicate the capabilities of a hybrid GPSILORAN-C navigation service. The next section will analyze the probabilities
for the different failure scenarios, in combination with coverage results.
6.3.3 Hybrid GPS/LORAN-C Reliability and Availability
The reliability of the LORAN-C transmitters and the GPS satel- lites is discussed in detail in the previous sections. To predict the availability of the hybrid system, a Markov model has been imple- mented. The model is shown in Figure 6.17. The assumptions for the model are similar to those used in the models for stand-alone GPS and
LORAN-C. For GPS, only long-term failures with a MTTF of 7.5 years and a MTTR of two months are implemented. The effect of short-term
failures with relatively small repair times do not affect the availability significantly (see Section 6.2.2, Figure 6.15). The MTTF
9 7
of 7.5 years is based on the design life-time of the Block I1
satellites. In order to keep a 21-satellite constellation operational
over a longer period of time, approximately three launches are
required each year. Therefore, the mean time to a launch would be two months, justifying a MTTR of two months. LORAN-C reliability numbers
are based on the 1981 statistics for unscheduled failures, a MTTF of
1500 hours and a MTTR of 35 minutes.
Results
The Markov model as described above has been run for a mission
time of two years with an one-minute time-step. Table 6.6 shows the
time-limiting availabilities for the 29 states of the Markov model.
The state-probabilities for multiple failures are very small. To
investigate the effect of calculation round-off errors on the results,
the Markov model was also implemented with a straightforward matrix multiplication method instead of the decomposition method (Section
6.1.5.2). It was found that the differences between the two methods was less than 10%. Although calculation round-off errors do affect
the accuracy of the results, a disagreement of less than 10% between
two different implementations is acceptable.
The state probabilities can be combined with the coverage
information to derive availabilities as a function of location. First
of all, all states with GPS satellite failures only can be discarded,
since (redundant) LORAN-C is still available. Next, all combinations S'I'iiTIS I'I 4 0.065 19 23 5 0.003 20 22 6 0.00002 2 1 21 1 22 0.0000005 15 23 23 0.0000006 16 22 24 0.00000003 17 2 1 - 25 0.000000002 I5 20 26 0.0000000006 19 19 27 0.0000000005 20 1 S 28 0.0000000005 21 17 29 0.0000000GOj < 14 < 16 I Table 6.6 Hybrid GPSILORAN-C state probabilities after two years for 21 GPS satellites and 23 LORAN-C transmitters. 99 of 6 or more failures can be neglected, since the corresponding state- probabilities result in outage periods of less than 19 seconds during a year. Fairly straightforward dead-reckoning can be used by the pilot or the navigation computer to coast through outage periods of up to several minutes. Similarly, 5 failures are only significant for state number 17 (4 GPS failures and 1 LORAN-C failure) with a corresponding unavailabil- ity of 4.2 minutes during a year. In this state, LORAN-C navigation is still available and most of the time sufficient satellite coverage will be available for integrity checking. This is also illustrated in Table 6.5 for four representative locations. Note that the numbers in Table 6.5 are based on the worst case failures for each of the locations. On the average, these numbers are much better. Combinations of four failures are only significant for state number 12 (3 GPS failures and 1 LORAN-C failure). Again, LORAN-C navigation is still available. The same arguments can be used for combinations of less than four failures. States 3, 5, and 8 have LORAN-C available, and states 6 and 10 have GPS available. State number 9 (1 GPS failure and 2 LORAN-C failures) has an unavailability of 5 minutes during a year. This number would be more realistic if only those fsilures are considered which result in a navigation outage. For example, consider the worst case with only four LORAN-C signals available. Two-out-of-four transmitters can fail in 6 different ways. A total of 23 transmitters is available, resulting in 100 253 (2-out-of-23) possible failure combinations. Because of this, the expected unavailability is reduced by a factor of 42 (25316) to less than 10 seconds during a year. Similarly, if 6 GPS satellites are available, the unavailability is further reduced by a factor of 3.5 (2116) to less than 3 seconds during a year. Based on these results, the conclusion is that hybrid GPS/LORAN-c has un unavailability of less than one minute during a year, which corresponds to an availability of better than 99.9998% 7. HYBRID GPS/LORAN-C NAVIGATION SOLUTION Several schemes can be implemented to combine the navigation data from LORAN-C and GPS. For example, a large Kalman filter could be developed that processes all available GPS pseudorange measurements and LORAN-C time differences. Even though such an approach promises to be optimal, certification procedures are most likely to be hindered by the physically impossible task of ensuring the performance of the navigation filter under all input conditions for reasons given in Section 4.2. Another concern is the complexity of modifications caused by the addition or deletion of navigation sensors or upgrades of existing sensors. These modifications should not necessitate a new system design with related certification and training procedures. Instead, the system should recognize the change and take appropriate actions. Therefore, the navigation solution should be based on a generic design that emphasizes effective, modular, and transparent rather than optimal processing. 7.1 Consolidated Statement of Navigation Solution Philosophy A system design philosophy that satisfies the above requirements could be based on the conversion of all sensor inputs into comparable quantities. Differences in sensor performance could be accounted for by assigning weights to the individual sensor measurements. These weights, for instance, would be determined by the magnitude and variance of measurement residuals (differences between actual measurements and predicted measurements based on previous data). The process of assigning weights could also be aided by measurement heuristics. Pseudorange measurements are in common to both GPS and LORAN-C. Although LORAN-C is normally operated in the hyperbolic mode, the range mode of operation will make LORAN-C a better system (see Section 6.1). This will especially be true when all LORAN-C transmitters are synchronized. Other advantages of LORAN-C ranging are the additional clock phase offset and drift information and the option to use single transmitters instead of pairs. Knowledge about the receiver clock phase offset and drift can be used to aid the tracking of the navigation signals and also allow the receiver to coast for several minutes on the receiver clock as a replacement for one of the measurements. One of the problems related to LORAN-C pseudoranging is that the receiver hardware delay is a function of temperature and of the number and location of the notch filters [100,101]. The receiver hardware delay is the time the LORAN-C signal needs to travel from the antenna phase center to the measurement point in the receiver. Temperature changes affect the propagation time of the signal through the antenna coupler, notch filters, and RF circuitry. Variations in temperature of about 10 degrees Celsius can cause up to a 50 nanoseconds change in 103 range, depending on the receiver design. The location of the notch filters and the number of filters used can cause up to 500 nanoseconds delay time. When only LORAN-C signals are used these errors hardly affect the position solution since the delays are in common between the measurements and therefore appear as an additional bias in the estimate of the LORAN-C system time. For the hybrid GPS/LORAN-C system, these delays need to be calibrated using hardware, as described in Section 5.2.2, or an extra measurement is needed to determine the LORAN-C receiver hardware bias. GPS is less sensitive to these errors because of the higher frequency, 1575 MHz versus LOO kHz for LORAN-C. Noise on the pseudorange measurements can be effectively reduced by range domain filtering tzechniques [102,103]. This eliminates the possibility of navigation domain filtering divergence and allows for straightforward filter tuning. Although process noise cross-correla- tion terms are discarded in the range filters, it was shown for stand-alone GPS that the overall system performance is essentially that of navigation domain filters [104]. Similar results may be expected for a solution based on both GPS and LORAN-C pseudorange measurements. Integrity is an essential part of the navigation solution. As indicated in Section l., integrity can be obtained from an external source, or through utilization of redundant measurements from GPS ant1 LORAN-C. For both solutions, the main parameter of i~lteres~is the 104 probability of a missed detection. If all aircraft rely on the same integrity broadcasting system, a missed detection would be very undesirable. Missed detections in a receiver autonomous integrity monitoring (RAIM) approach would only affect one aircraft. Therefore, RAIM will be addressed in detail in this section. 7.2 Hybrid GPSILORAN-C Measurement Equations and Error Models Pseudorange measurements to GPS satellites are made by taking the difference between the measured time of signal arrival and the cor- responding known time of signal transmission, corrected for known and estimated error sources. Figure 7.1 illustrates the ranging geometry. The equation for the measured pseudorange is given by [105]: P.(t) = I Si(t - Pi(t)) - U(t) I + 1 where : S is the position vector for satellite i (m). i is the line-of-sight travel time for signals from Pi satellite i (s). U is the user position vector (m). c is the GPS speed of light (299792458 m/s). is the user clock offset from GPS system time (s). T~~~ is the clock offset for satellite i from GPS time (s). s i is the delay for measurement i caused by GPS error i sources (s). Satellite positions and satellite clock offsets from GPS time are calculated from the navigation data transmitted by the satellites [106]. Positions are expressed in the ECEF coordinate system at the tine of signal reception. Therefore, the satellite positions are -+ S position vector satellite i -+ u user position vector -+ e. 1 line-of-sight vector for satellite i Figure 7.1 GPS ranging geometry. 106 corrected for the rotation of the earth during the signal travel time (PI. Tropospheric propagation delays are modeled using the following equation [lo71 : where: E is the satellite elevation angle (rad). h is the altitude of the receiver (km). The model for the ionospheric propagation delays is based on parameters transmitted by the satellites and is given in reference [lo81 . LOR4N-C pseudorange measurements are discussed in Section 6.1.3. The equation for the pseudorange is given by: LORAN-C transmitter locations are known. Transmitter synchro- nization is currently established for each chain only. Synchroniza- tion of all master stations to within 100 nanoseconds with respect to UTC will remove a large part of the LORAN-C timing uncertainty. Propagation models for LORAN-C are more complicated than those for GPS. For this study, the LORAN-C errors are assumed to be calibrated using a known location. The navigation results are then evaluated using the expected modeling accuracies as described in Section 5.1.2. 107 A review of the literature on LORAN-C propagation has been conducted. Based on this review, the following recommendations are made with respect to the LORAN-C propagation models for the hybrid GPS/LORAN-C receiver. - Geophysical variations should be calibrated as a function of location. Remote areas would only require a few calibration points. In the vicinity of airports, a denser calibration grid is recommended to reduce interpolation errors. - Meteorological variations should be modeled as a function of surface impedance, distance to the transmitter, user altitude, and the vertical lapse factor for the index of refraction of air at the surface [log]. Some of these parameters could be determined by long-term monitoring of the LORAN-C signals. It should be noted that current LORAN-C receivers mostly utilize empirical models for the propagation corrections. In essence, these models include the propagation path from the transmitters to the user as well as the effects of the SAM control (see Section 5.1.2). Based on these empirical models, positioning accuracies are within 470 meters (2 drms), which can only be obtained if the modeling errors are 1~7ellwithin 100 meters (see Section 6.1.4 and Equation 6.16). 7.3 Hybrid GPS/LORAN-C Navigation Equations The pseudorange equations for GPS and LORAN-C given in the previous section can be rewritten as follows: where : Pi is the ith pseudorange measurement, corrected for known and estimated error sources (m). Xi' yi, Zi are the coordinates of the ith GPS satellite or LORAN-C transmitter (corrected for earth curvature (m). u u , u are the user coordinates (m). X' y z is the receiver clock offset with respect to UTC (m) . This equation is non-linear, therefore a variation of Newton's method for nonlinear systems has been developed to solve for the three-dimensional user coordinates and clock offset [110]. Newton's method is generally expected to give quadratic convergence, especially if the estimate if close to the solution. Define an user state vector x containing the user position coordinates and clock offset, and a measurement vector z, containing the corrected pseudorange measurements: Next, the pseudorange equations are linearized using the partial deri-vative, or Jacobian, matrix H which relates a change in the user state vecror x to a change in the measurement vector z. where each row of the H-matrix is given by: The first element of a row of the H-matrix is calculated from: Similarly: Equation 7.6 can be rewritten as follows: If weighting is added to the pseudorange processing, the last equation can be written as [Ill]: ~~11er e : W is a positive definite weighting matrix. 110 The navigation solution algorithm contains two iteration loops. One iteration loop is used to update the LORAN-C transmitter and GPS satellite coordinates in the locally level plane with respect to the user estimate. The second iteration loop is used to update the user state vector in the locally level plane based on the difference between predicted and actual pseudorange measurements. The algorithm proceeds as follows: 1. Obtain the user state estimate f and the pseudorange measurement vector z. 2. Convert the LORAN-C transmitter coordinates to the locally level plane (East-North-Up coordinates) with f as the origin. 3. Convert the GPS satellite ECEF-coordinates to the ENU-coordinates with f as the origin. 4. Calculate the estima~edpseudorange vector Z using f, GPS satellite positions, and LORAN-C transmitter positions. 5. Calculate the partial derivative matrix II, the rows of H are obtained from: 6. Calculate the user state update as follows: -1 HT sx = (H~H) (2 - Z) 7. Update the user state with 6x: j7 = X + 6x 8. If the update is too large ( 16x1 > E ), go to step 4. 9. Use the new user state estimate 2 in the locally level plane (ENU) to update the user position in latitude, longitude, and height. 10. If the update is too large 12 go to step 2. ( ENU I > p ), 11. Repeat steps one through ten for the next set of measurements. The second step of the algorithm is relatively straightforward for a receiver at sea-level. The azimuth (@) between user and transmitter along with the great-circle distance (s) are calculated based on the modified Rainsford's Method with Helmert's Elliptical Terms as given in reference [112]. The transmitter coordinates in the locally level plane are then given by: X (east) = s * sin(9) Y (north) = s * cos(Q) z (up) = 0 The signal propagation for a receiver at altitude is not any Ioiigcr described by a pure groundvrave. For instance, an aircraft 112 flying directly above a LORAN-C transmitter would receive a direct wave. It was shown in reference [I131 that for receiver altitudes of less than ten times the distance to the transmitter, the phase error for a receiver at 1.3 km is about 30 meters. Models can be applied to limit the phase error to 30 meters for all altitudes [114]. Further studies are required to determine the direction of arrival of the 100 kHz wave for a receiver at altitude. For this study, the ratio of receiver altitude to distance from the transmitter is limited to 0.05 and the receiver altitude is limited to 3 km, thus reducing the geometry error to less than 75 meters (4(602 + 32) - 60). The third step of the algorithm consists of a coordinate transformarion given by: -sin(+) cos(0) 8 [ i ] = [ -sin(Q)cos(+) -sin)sin() cos(0) ] [ ] (7.15) cos(e)cos(@) cos(e)sin($) sin(@) ENU ECEF where : ENU is the locally level plane coordinate system (East, North, Up) (m). ECEF is the earth-centered-earth-fixed coordinate system (m). @ is the latitude of the receiver location (rad). 8 is the longitude of the receiver location (rad). The elements of the estimated pseudorange vector Z, in step 4, are calculated as the sum of the estimated clock offset and the distance between the estimated user position and satellites or transmitters. 113 Finally, the user state update in latitude and longitude (step 9) is approximated by: lat = lat YENU(north) C new old + * (7.16) lon = lon (east) * C * cos(1at ) new old + 'ENU new where : C is the conversion factor from meters to degrees in latitude ( 1 / (1852 * 60 ) ). Altitude can be updated directly: alt - new - altold + ZENU(up) The clock estimate is replaced (not updated), since a coordinate transformation does not change the time-axis: bias = bias new ENU (7.18) If the clock offset between GPS and LORAN-C is not known, the user state vector (equation 7.5) is replaced by: equations 7.6 and 7.7 are replaced by: 62 = H dx where each row of the H-matrix is given by: 6P' -i - 0, for LORAN-C pseudoranges 1, for GPS pseudoranges 6b~~~ 6P' -i - 1, for LORAN-C pseudoranges 0, for GPS pseudoranges 6b~~ 7.4 Range Domain Filtering The derivation of the discrete Kalman filter is very well docu- mented [115-1171, therefore, in this section only the filter equations and the necessary definitions are presented. Consider a system with state and measurement equations given by: : is the system state vector at time t Xk k ' is the measurement vector at time t Zk k ' is the state transition matrix, representing the 'k 'k known system dynamics at time t k - is the measurement matrix, representing the relation- Hk ship between the measurements z and the state vector k xk in the absence of noise. W is the system noise vector (normally distributed) with k covariance matrix Q. v,_ is the measurement noise vector (normally distributed) K with covariance matrix R. rn v1 ) = 0, for all k and i. E ( w k i The best estimate xk of the system state vector and its covariance matrix Pk can be updated with the measurements using the equations: where : Kk = P-kk HT ( Hk Pk HE + R.)-' are estimates of xk and P k just before and just after time t k ' The updated state vector and covariance matrix are projected to the time of the next measurement as follows: A two-variable discrete Kalman filter with a random walk acceleration (RWA) model was selected for the pseudorange measure- ments. The state vector is given by: where : r is the range from the user to the GPS satellite or LORAN-C transmitter. v is the relative line-of-sight velocity between the user and satellite or transmitter. The continuous state transition matrix F is then constant. Therefore, the discrete state transition matrix #k can be written as an exponen- tial series [118]: where : T=tk+l- 'k In the continuous time domain, the system equation is given by: therefore, Additive (normally distributed) acceleration noise to the discrete system equation can be represented by the noise vector: with corresponding covariance matrix Qk: For pseudorange measurements only, the measurement equation reduces to: The measurement noise scalar vk is assumed normally distributed with variance or.2 The two-variable RWA filter described above is capable of reducing the RMS navigation error by a factor of two [119,120]. If highly accurate delta range (Doppler shift) measurements are available to the filter, the resulting improvement in the RMS position error can be an order of magnitude or more [121]. If Doppler shift measurements are available, it is suggested to use a three-variable filter to model for acceleration also. 7.5 Receiver Autonomous Integrity Monitoring (RAIN) Integrity is the ability of a system to detect operational malfunctions and to promptly warn the user that the system is not operating within the specified performance limits. Malfunctions such 118 as signal outages and large changes in the received signal do not present a problem as these are easily detected by the receiver. Malfunctions that are important and difficult to detect are slowly increasing bias errors such as those which might result from clock degradation. 7.5.1 GPS and LORAN-C System Integrity Although the GPS Ground Segment monitors the performance of the satellites, it can take up to one hour before this information is available to the user [122,123]. LORAN-C signals are monitored by the System Area Monitors (SAM). Signal abnormalities which would render the system unusable for navigation cause the secondary stations to "blink" [124]. Blink is a repetitive on-off pattern of the first two pulses of the secondary signal which indicates that the master-secondary pair is unusable. A master station failure causes all stations in a chain to "blink", This is unfortunate, as it greatly reduces the availability of the LOMN-C transmitters. It is therefore recommended not to blink transmitters that are still operating properly. Currently, blink is initiated for outage ~eriodslarger than one minute. Because of aviation requirements for warning times of less than one minute, the USCG and the FAA are considering to implement shorter warning times for the LORAN-C transmitters. Another concern is that the SAM monitors the signals from a master-secondary pair at only one location. Due to local meteorologi- cal conditions, the signal could be out of tolerance in certain areas even though the SAM determines the signal to be in tolerance. These errors are bounded, but are currently not very well characterized. With the implementation of the FAA-sponsored LORAN-C monicor network [125], data will be available to further address the issue of meteorological effects on the propagation of the LORAN-C signals. 7.5.2 RAIM for Hybrid GPSILORAN-C The important parameters of interest for receiver autonomous integrity monitoring (RAIM) are: - The protection limit - Probability of missed detection - False alarm rate The consistency of the measurements can either be examined at one particular time (snapshot approach) or a time-history of measurements can be used. The time-history approach would be useful for measure- ments with a high noise level, allowing for some averaging of the data. The measurements can either be processed in the range domain or in the position domain as these two approaches were shown to be mathematically equivalent [ 1261 . 120 Figure 7.2 shows an example of RAIM processing in the position domain [127]. The center of the circles represent the (unknown) true position, the radius of the circle is the desired protection limit. The left case shows the solutions for all sub-sets of four out of five measurements. If the geometry of the sub-sets (HDOP) is sufficient, all sub-solutions should be close to one another. The right case shows the solutions with measurement five failed. Note that the sub- solution without measurement five does not change, all other solutions are scattered. A detection parameter for the inconsistency of the positions could consist of the maximum separation distance (MSD) between two sub-solutions. Detection occurs if the MSD exceeds a certain value (see also reference [128]). If more than five measurements are available, the calculation of all sub-solutions becomes computationally rather extensive. Integrity monitoring in the range domain somewhat reduces the amount of calcula- tions required. The range domain RAIM could proceed as follows (this procedure is similar to the technique described in reference [129]. 1. Calculate a (weighted) least squares solution (LSS) based on M measurements as described in Section 7.3. 2. Take the difference between the ranges based on the LSS and the (corrected) measured ranges to form the range residuals Ei. 5 MEASUREMENTS (SNAPSHOT) 5 GOOD SIGNALS SIGNAL 5 FAILED Figure 7.2 Example of Receiver Autonomous Integrity Monitoring (RAIM) in the position domain (from reference [127]. 122 3. Calculate the integrity parameter r as the square root of the sum of squares of the range residuals: 4. If the integrity parameter r exceeds a predetermined detection limit rdet, a failure is declared. The integrity parameter I? indicates how well the measurements agree. Closely clustered measurements will result in a relatively small value for r. On the other hand, one faulty measurement will increase r significantly. Under normal conditions, the hybrid GPSILORAN-C receiver has at least 4 more measurements available than the number of measurements that are required for the navigation solution. It would be very inefficient to fail the receiver as soon as one or more of the measurements are out of tolerance. Until positive failure identifica- tion is received from the GPS or LORAN-C system it is useful to try to identify and isolate the failed measurement to allow for continued navigation with the remaining measurements. The steps of the detection algorithm as given above are continued as follows (steps 5 and 6 are similar to the technique described in reference [130]): 5. Assume that a single un-announced signal failure occurred. Calculate N least squares position solutions based on sub-sets of N-1 measurements, and the corresponding integrity parameters ri (i = 1, N). 6. If only one of the integrity parameters ri is below the isolation threshold, rise, isolation is achieved. The sub-solution with the low ri does not contain the faulty measurement. 7. If more than one integrity parameter ri is below the isolation threshold, isolation is not possible, or multiple failures occurred. 8. One likely source for multiple failures is that the time referen- ces of GPS and LORAN-C could be drifting apart. This can be verified by calculating two sub-solutions, one based on GPS only, and one based on LORAN-C only. If the two positions agree to within a certain value, the assumption is made that the time references are no longer synchronized. The navigation solution is then repeated using a solution algorithm that solves for position, clock offset from GPS time, and clock offset from LORAN-C time (Section 7.3). 9. To investigate the possibility of two simultaneous failures, all sub-solutions with two measurements omitted are calculated together with their integrity parameters rij (i = 1, N; j = 1, N; rij = rji) . Again, if only one of the integrity parameters rij is below the i.;olation threshold, rise, isolation of two faulty measurements is 124 achieved. If more than one rij is below the isolation threshold, three simultaneous failures could be assumed and the procedure could continue with the calculation of all sub-sets with three measurements omitted. The selection of the parameters for the detection threshold, rdet, and the isolation threshold, ri,,, are based on the requirements for the protection limit, the false alarm rate, and the probability of missed detections. Values for the detection parameters are determined empirically in the next section based on a computer simulation. 7.6 Computer Simulation Results The navigation solution and the integrity monitoring algorithm have been implemented in FORTRAN 77. The GPS/LORAN-C simulation model as described in Section 6 has been used to evaluate the navigation software. Figure 7.3 shows the block diagram of the computer simulation software. The GPSILORAN-C truth model determines which GPS satellites and LORAN-C transmitters can be used for navigation at a certain time, based on the user position. Pseudorange errors are determined and added to the true pseudoranges, which are calculated from the GPS satellite positions, the LORAN-C transmitter positions, and the true user state. The filtered pseudoranges in combination wit11 the satellite and transmitter coordinates, and an estimate of the user state are employed by the navigation solution to solve for user position and clock off set. INITIALIZATION DATA RUN TIME I PSEUDORANGE ERRORS I GPS MASK ANGLE LORAN-C SNR USER STATE ESTIMATE x L-, GPSILORAN-C NAVIGATION PSEUDORANGE b 4 b INTEGRITY TRUTH MODEL FILTER SOLUTION MONITORING MRAN-C TRANSMllTER PSEUDORANGES LOCATIONS t INTEGRITY CALCULATED f FLAG USER STATE TRUE USER STATE ) USER STATE ERROR x = (x,y,z,b) Figure 7.3 Block diagram of the computer simulation for the evaluation of the hybrid GPSILORAN-C navigation algorithms. The convergence of the navigation solution algorithm has been examined for navigation in CONUS. The truth model was executed without error sources added to the pseudoranges. The model was run for one day in increments of ten minutes for the CONUS with position increments of one degree. Random noise was added to the true position to provide an user estimate for the navigation solution. The noise represented a horizontal position error with a magnitude of 100 kilometers (one sigma). Convergence was found for all cases. Next, the robustness of the convergence was addressed by choosing an arbitrary position and moving the estimated position away from the true position. Figure 7.4 shows the total number of iterations required as a function of the radial error between the true and estimated positions. For this case, the user estimate was moved in the east and west directions by a distance of up to 2000 km. The true position was at 39 degrees latitude and -82 degrees longitude, and a combination of three LORAN-C transmitters and four GPS satellites were employed. The solution converged for all cases. With increasing distance, more iterations are needed, as the partial derivatives used to update the user state are less representative for the true update. The integrity algorithm was examined separately. Errors were added to the pseudoranges consisting of 80 meters (one sigma) normally distributed noise with a mean of zero. The simulation has been run to determine the position error and the frequency distribution of the inregrity parameter r. A total of 144,000 data points were generated. Radial Displacement (km) Figure 7.4 Number of iterations required by the navigation solution as a function of the radial distance between the true and estimated positions. 128 The position error was found to be 101.4 meters (2 drms), a surpris- ingly low number, which is explained by the fact that at least 8 measurements are employed by the least-squares-solution. The frequency distribution of the integrity parameter is given in Figure 7.5. No occurrences of the integrity parameter above 523 meters were found. Based on Figure 7.5, the following values for the integrity detection parameter as a function of the probability of a false alarm can be approximated. Probability of False Alarm Detection Parameter 0.01 3 7 0 0.001 420 < 7 * 10-6 52 4 The simulation was rerun with a bias error of 1000 meters added to one of the GPS measurements, in addition to the noise. Figure 7.6 shows the time-histories of both the radial position error and the integrity parameter. The radial position error is limited to 253 meters, and the resulting horizontal position error is 334 meters (2 drms). The integrity parameter for this run is always larger than 649 meters. Next, the integrity detection parameter and the integrity isolation parameter were both assigned the value 500, and the simulation was repeated. No missed detections were found, and the faulty measurement was isolated correctly for all cases. Although the above does not constitute a rigorous verification of the integrity algorithm, the results do illustrate the potential of a receiver 0. 200. 400. 600. 800. 1000. 1200. Integrity Parameter (m) Figure 7.5 Frequency distribution of the integrity parameter. 1NrfEGRl'TY PAIIAhlETER MEAN = 862.3 (m) STD = 80.2 (m) RADIAL POSITION ERROR MEAN = 164.0 (m) STD = 31.3 (m) I I I I I I 200. 400. 600. 800. 1000. 1200. Run time (s) Figure 7.6 Radial position error and the integrity parameter for the hybrid solution with a bias of 1000 meters added to one of the GPS pseudoranges. 131 autonomous integrity monitoring scheme. Further research is required, once the integrity requirements for a sole means of navigation are developed. 8. GPS/LORAN-C STATIC EXPERIMENT The static GPSILORAN-C experiment is designed as the first step in the development of a hybrid GPS/LORAN-C receiver. The goal is to test the hybrid GPSILORAN-C navigation solution with "real" measure- ment data. The test results will then be used to identify possible problem areas and to improve on the data processing. 8.1 Description of the Static GPS/LORAN-C Experiment The block diagram of the hardware configuration for the static experiment is shown in Figure 8.1. A four-channel GPS receiver (Motorola, Model Eagle) and an eight-channel LORAN-C ranging receiver (Advanced Navigation, Inc., Model 5300), both with continuous tracking, are used to collect GPS and LORAN-C data. The two receivers are interfaced with a microcomputer (IBM PC) through two serial communication ports. Figure 8.2 shows the equipment used for the static GPSILORAN-C experiment. After receiver initialization, the microcomputer collects the measurement data from the receivers through interrupt service routines. Each incoming byte of data generates an interrupt, causing the microprocessor to store the data in a circular buffer. Selected data from the circular buffers are written to a magnetic storage device at a rate of approximately once per 4 seconds. The off-line data analysis uses the GPS and LORAN-C pseudoranges, the satellite ephemerides data, and the known antenna locations. The pseudoranges are converted into the position domain as described in PRE- GPS RECEIVER L * AMPLIFIER w 4-CHANNEL I MICRO- DATA COMPUTER * STORAGE A PRE- LORAN-C AMPLIFIER + RANGING RECEIVER 8-CHANNEL v 1 OPERATOR WERFACE Figure 8.1 Block diagram of the GPSILORAN-C hardware used for the static experiment. Section 7. Currently, the GPS and LORAN-C time references are not synchro- nized. Therefore, the navigation solution solves for both the clock offset from GPS time and from LORAN-C time. A block diagram of the data processing is given in Figure 8.3. Propagation corrections for GPS are described in Section 7.2. The propagation model for LORAN-C is a first order approximation which is proportional to the distance to the transmitter: where: a is a constant. r is the great-circle distance to the transmitter (m). The proportionality constant, a, is initialized using the LORAN-C derived hyperbolic position during the first few minutes of a data collection session. The hyperbolic solution is obtained from the LORAN-C receiver, which employs an advanced propagation correction model. 8.2 Static Test Results Data have been collected at Ohio University on September 8, 1988, for a period of 30 minutes from four GPS satellites and three LORAN-C stations using the hardware configuration as described in the previous section (Figures 8.1 and 8.2). Pseudorange filtering was not enabled to facilitate the interpretation of the system capabilities. Surveyed antenna locn~ionswere used to determine the position errors. Figure 137 8.4 shows the two-dimensional position errors for GPS only, LORAN-C only, and for a least-squares hybrid solution based on all seven measurements. The GPS errors are relatively small with an accuracy of 18.4 meters (2 drms). The LORAN-C pseudorange processing results of 257.1 meters (2 drms) are representative for master station synchro- nization. Time of transmission control for all stations would allow for propagation models that could decrease the modeling error by a factor of two (Section 5.1). The hybrid solution provides a position accuracy of 138.1 meters (2 drms), this level of accuracy was expected as the hybrid solution processes measurements from GPS and LORAN-C with equal weights. The one-sigma standard deviation for the hybrid solution is reduced with respect to the GPS and LORAN-C solutions, also a result of the least-squares-solution. Note that the GPS accuracy for the operational satellites will be reduced to 100 meters (2 drms) under the Selective Availability program (see Section 2.3). Also, the accuracy of the hybrid solution could be similar to the GPS accuracy if proper weighting is applied to the GPS and LORAN-C signals. The process of assigning weights is not always feasible, as a priori information is required with respect to the accuracy of the individual signals. LORAN-C ONLY - 257.1 m (2 drms) IIYBRID GPS/L,ORAN-C - 138.1 m (2 drms) I GPS ONLY - 18.4 m (2 drms) I I I I I I 10. 41 21 00. 41 2300. 41 2500. 41 2700. 41 2900. 41 31 00. GPS Time of Week (s) Figure 8.4 S~atic,two-dimensional position errors for GPS, LORAN-C, and hybrid GPSILORAN-C. The hybrid position errors are based on a least squares solution with equal weighting for GPS and LORAN-C pseudoranges. 9. DIFFERENTIAL GPS TRUTH REFERENCE SYSTEM To establish a reference trajectory for a dynamic hybrid GPS/LORAN-C receiver test, a Differential GPS (DGPS) system has been developed. The DGPS approach is based on a GPS receiver at a known location. This receiver compares the measured GPS ranges to the actual ranges calculated from the known receiver and satellite positions. The differences, or differential corrections, are then transmitted to suitably equipped users to allow them to improve their own solutions to an accuracy of better than 10 meters (2 drms) [131,132]. This level of accuracy qualifies DGPS very well for a truth reference system for the evaluation of navigation results where the highest accuracy requirement is 100 m (2 drms). Ideally, the differential correction contains only those error sources that are both unobservable to the user and common to the user and the reference station. Fortunately, the majority of GPS errors meet this requirement. Furthermore, biases that are common to all measurements do not affect the navigation solution as they appear as a clock bias in the solution for the clock offset. The differential correction is obtained by taking the difference between the measured pseudorange and the calculated pseudorange corrected for known error sources such as space vehicle clock offset. The resulting correction can be written as follows: OP = d + UERE + 6 + 6 r tropo + diono bias noise where: d is the tropospheric propagation delay (m). tropo d is the ionospheric propagation delay (m). ion0 UERE is the user-equivalent ranging error due to satellite ephemeris and clock errors (m). 6 are biases caused by receiver measurement circuitry, bias antenna location uncertainty, and biases that are common to all measurements (clock and hardware) (m). 6 is receiver measurement noise, clock noise, and noise multipath noise (m). The biases that are different for all measurements are relatively small, generally less than one meter [133]. Noise can most effective- ly be reduced by taking multiple measurements and by filtering. The combination of tropospheric, ionospheric, and UERE is typically around 20-40 meters, and are a function of location. The UERE is not much affected by the separation distance between the user and the reference station. Ionospheric and tropospheric delays do decorrelate with increasing separation distances. Horizontal decorrelation is generally less than 0.2 meter over distances up to 100 km [134]. Vertical decorrelation does not affect the ionospheric delays (up to ionospheric altitudes), but greatly affects the tropospheric delay. Most of the tropospheric vertical decorrelation can be corrected usine a relatively simple model as described in Section 7.2. 9.1 Description of the Differential GPS Reference System The Differential GPS reference station for the evaluation of the hybrid GPSILORAN-C flight data consists of a single-channel GPS receiver (S~anfordTelecommunications, Inc. Model TTS-502B). During the flight test, the receiver is programmed to track different satellites for five minutes each. Satellite and measurement data are collected by an external microcomputer (IBM PC) for off-line data analysis. Figure 9.1 shows the equipment used for the Differential GPS reference station. After receiver initialization, the first satellite is acquired. Since only one satellite is being tracked, it is not possible to distinguish between the receiver clock offset and the differential correction. This complication can be resolved as soon as a second satellite is being tracked. Assuming a stable reference oscillator, the change in the differential correction between the two satellites is all that is needed, as the clock offset will be a common bias error. Each time the receiver switches from one satellite to the next, an accurate estimate of the relative difference between the differential corrections is available to correct to flight data. Note that the flight data does not need to be corrected for ionospheric delays as these are contained in the differential corrections. Tropospheric delays must be corrected for the difference in altitude between the user and the reference station. The above process is documented in detail in reference [135]. Figure 9.2 show the unfiltered differential corrections with an arbitrary bias value obtained from the sequential GPS receiver for a period of two hours. From this figure, the differential corrections for each satellite are extracted as shown in Figure 9.3. Also shown -20. 1 I I I I I 1 64800. 66000. 67200. 68400. 69600. 70800. 72000. GPS Time of Week (s) Figure 9.2 Unfiltered differential range corrections from the sequential GPS receiver (ST1 TTS-502B) with a high-quality reference oscillator. 145 in this figure are the results of a second order polynomial curve-fit on the differential correction data for each satellite. The coeffi- cients that describe the polynomials are used to calculate the differential corrections corresponding to the flight test data. 9.2 Differential Test Results (Static) Static validation of a Differential GPS system can be very tedious and time-consuming (see also ref [136]). A block diagram of the static DGPS validation processing is shown in Figure 9.4. First, the user GPS software must be compatible with the reference station software. This includes the proper decoding of the satellite navigation data and timing parameters, the calculation of the satellite positions and clock offsets for a particular time, and the correct determination and processing of the differential corrections. One of the complications encountered during the static validation is the difference between the earth reference frames used by the two GPS receivers. The ground reference station receiver uses the World Geodetic System 1972 (WGS-72) and the user receiver uses the WGS-84 earth model. This results in a difference in position of typically five meters [137]. This discrepancy was corrected for by recomputing the satellite positions for the user receiver based on the WGS-72 earth model. 147 The next test involved the verification of the differential range corrections. Differential range corrections are compatible for the two systems if the relative differences are the same for each system. This means that the numerical difference between the differential corrections for any pair of satellites is equivalent for the reference station and the user receiver. This process assumes that both receivers track the same four or more satellites. Note that only the relative differences are important; the different absolute level of the differential corrections is only an indication of different residual-receiver clock offset and hardware delay. Therefore, depending on the magnitude and sign of the residual-receiver clock offset, differential corrections can be positive or negative. Figure 9.5 shows the results for a one hour data collection session during which the antennas of both receivers were located at almost the same location (within 0.1 meter). The upper portion of the figure shows the filtered differential corrections for both the reference and the user receiver for satellites 6, 11, 12, and 13. The user receiver applies the same clock offset to the pseudorange measurements at each measurement time, this process results in similar variations for each of the differential corrections. The relative differences between the differential corrections for each moment in time agree very well, except for some deviations experienced by the user receiver. The frequency of these deviations is too high for proper representation by a second-order polynomial curve fit in the reference station. The bottom portion shows the final results when GPS Time of Week (s) rllifferentially Corrected GPS (mean = 0.4 m, std = 1.4 m) L Stand-Alone GPS (mean = -12.4 m, std = 1.5 m) 2 h I------II: -I--' L 0 Z -20. I I I I I I 238000. 238400. 238800. 239200. 239600. 240000. 240400. GPS Time of Week (s) -Differentially Corrected GPS (mean = -0.5 rn, std = 7.3 m) 00. GPS Time of Week (s) Figure 9.5 Differential range corrections for the reference and user GPS receivers (top), and two-dimensional GPS and DGPS position errors for the user receiver (middle and bottom). the differential range corrections from the reference receiver are incorporated into the differential navigation solution. The horizon- tal position error for stand-alone GPS was 25 meters (2 drms). After the differential corrections were applied the horizontal position error decreased to 8 meters (2 drms). The deviations in the East-West direction are assumed to be caused by multipath reflections originat- ing from a nearby roof-structure. The roof structure and antenna location are depicted in Figure 9.6. The multipath effects are also present in the reference receiver, but are mostly masked by the polynomial curve-fit. The average residual position errors in each axis during the one hour run have mean values less than 0.5 meter with one-sigma deviations of 7 meters. These results represent good, static, Differential GPS performance using a sequential receiver without carrier tracking for the ground reference station. 10. GPSILORAN-C FLIGHT EXPERIMENT The GPS/LORAN-C flight experiment is designed to evaluate the hybrid GPS/LORAN-C navigation solution with actual measurement data. Figure 10.1 provides an overview of the airborne and ground equipment for the dynamic experiment. GPS and LORAN-C data are collected during the flight and stored on magnetic devices for off-line analysis in combination with simultaneously collected GPS data on the ground. The airborne GPS receiver serves both as part of the hybrid GPS/LORAN-C system and as the airborne Differential GPS component. All software implemented on the microcomputers requires a minimum of operator interaction. The GPS!LORAN-C equipment is installed in a Piper Saratoga PA-32- 301, N8238C, which is owned by Ohio University and shown in Figure 10.2. The N8238C is a 1980 model aircraft with a fixed landing-gear, and a useful load capacity of 1,537 pounds. The aircraft is equipped as a flying laboratory. 10.1 Data Processing for the Dynamic GPSILORAN-C Experiment The data processing for the hybrid GPS/LORAN-C receiver is similar to the processing used for the static experiment as described in Section 8.1. The GPS/LORAN-C navigation solution is compared to he truth trajectory generated by the Differential GPS system. Fisure 10.3 provides an overview of the data processing. Pseudorange da~a Figure 10.2 Piper Saratoga aircraft, N8238C, used for the in-flight evaluation of hybrid GPSILORAN-C. LORAN-C I'RANSbl~fI'ER LOCATIONS I IDRAN-C PROPAGATION C RANGiSG RECEIVER CORRECTIONS 8-CIIANNEL HYBRID CALCULATED GPSILORAN-C WSITIONS AIRBORNE NAVIGATION SoLLrnoN SAI'ELLW DATA I G PS I RECEIVER 4-CHANNEL PROPAGATION CORREmIONS SATELLITE POSITIONS TROPOSPHERIC I CORRECTION ' POSITION ERROR GROUND REFERENCE REFERENCE GPS G PS A p, DIFFERENTIAL POSITION RECEIVER CORRECTION C NAVIGATION 1-CHANNEL - FILTER CORRECTED AIRBORNE SOLUTION 4 PSEUDORANGES I Figure 10.3 Hybrid GPS/LORAN-C data processing with a Differential GPS truth reference system. 155 from the LORAN-C receiver are filtered by a two-variable Kalman filter and corrected for propagation delays. For this study, the LORAN-C propagation delays are modeled by a first order approximation as a function of the distance to the transmitter. Initial values for these delays are determined using validated LORAN-C positions from the beginning of the data collection. GPS pseudoranges are also filtered by a two-variable Kalman filter. Ionospheric and tropospheric propagation corrections are applied before the pseudoranges are entered into the navigation solution. Satellite positions and clock offsets are calculated from the satellite navigation data. The hybrid navigation solution solves for three-dimensional position, clock offset from GPS time, and clock offset from LORAN-C time. Filtered GPS pseudoranges are also corrected for the tropospheric delay difference between the ground reference receiver and the airplane. The resulting pseudoranges are then corrected for remaining error sources by the filtered differential corrections from the reference GPS receiver. Ideally, the corrected pseudoranges only contain errors on the order of less than one meter. After conversion into the position domain, a reference trajectory is established for the flight test. The two-dimensional navigation error of the hybrid GPSILORAN-C receiver is then determined by taking the difference between the hybrid position and the DGPS position. 10.2 Dynamic Test Results The hybrid GPSILORAN-C system was flown on September 16, 1988 for a period of 70 minutes in the vicinity of the Ohio University Airport (Albany, OH). At the same time, GPS data were also collected by the ground reference system to establish a reference trajectory. Six GPS satellites were used, SV3, SV6, SV9, SV11, SV12, and SV13, in combination with three LORAN-C transmitters from the Northeast U.S. Chain, Dana, Nantucket, and Carolina Beach (Figure 6.2). Figure 10.4 shows the ground track based on the Differential GPS reference trajectory. The Differential GPS station is located at Ohio University. Two relatively large discontinuities in the reference trajectory are caused by the exchange of flexible disks and by a system restart. The system was restarted to evaluate the re-acquisi- tion of the navigation signals during operational conditions. A few smaller discontinuities are the result of satellite switching by the airborne GPS receiver. During satellite switching, the receiver temporarily enters an altitude-hold mode. The accuracy of the resulting Differential reference trajectory is then no longer determined, and consequently, the trajectory cannot be used for the evaluation of the hybrid GPSILORAN-C receiver. Note that the hybrid receiver could still continue to provide a solution based on the three remaining satellites and one or more LORAN-C transmitters. Differential GPS Reference Trajectory 39.40 -( 01-110 UNIVERSITY AIRPORT Satcllite Switching Satellite Switching System Restart 38.60 1 I I I I I I -83.1 0 -82.90 -82.70 -82.50 -82.30 -82.1 0 -81.90 Longitude (degrees) Figure 10.4 Differential GPS ground track for a 70 minutes hybrid GPSILORAN-C test flight in the vicinity of Ohio University airport. 15 8 The ground track for the hybrid receiver is almost identical to the reference trajectory. Differences between the ground tracks as a function of time are shown in Figure 10.5. The largest position errors occur during the middle of the flight. These deviations are caused by a relatively bad GPS geometry. Also, all sudden changes in the magnitude of the two-dimensional error are caused by transitions ro different sets of four GPS satellites. The horizontal position accuracy for the hybrid system, based on all measurements (785 data points), is 210 meters (2 drms), with respect to the Differential GPS trajectory. The mean position errors in the North and East directions were found to be -52 meters and 30 meters, respectively. (u)JOJJI a-z 11. CONCLUSIONS A sole means of navigation not only requires integrity, but also coverage, reliability, availability, and accuracy. Even though ground monitored GPS could provide integrity, availability is still not sufficient. Satellite outages could affect a large service area for several hours per day. The same holds for Differential GPS, since a total satellite outage cannot be accommodated. To obtain sufficient coverage, additional measurements are needed, either in the form of extra GPS satellites or through redundant measurements from other systems. GPS use with a different system has the advantage that the much needed dissimilar redundancy will be achieved. LORAN-C is available and when hybridized with GPS, will result in a system that has the potential to satisfy the requirements for a next generation of sole means air navigation for the conterminous United States. Based on the research described in this paper, the following conclusions are given with respect to the interoperability of GPS and LORAN-C : 1. The current LORAN-C navigation and timing system can be greatly enhanced by upgrading the synchronization between stations. Dissemi- nation of LORAN-C transmitter clock offset with respect to GPS time can result in navigational accuracies better than 250 meters (2 drms) throughout the CONUS. 161 2. Generic pseudorange measurement processing is an effective and modular approach to combine measurement data from GPS and LORAN-C. The navigation solution presented in this paper is a variation on Newton's method for nonlinear systems and is shown to be numerically stable over a large range of initial estimates. The navigation solution implementation can be easily extended to include pseudorange data from other sensors, such as Omega, Distance Measurement Equip- ment, altimeter, and other satellite navigation systems. 3. A hybrid GPS/LORAN-C receiver should employ all-in-view tracking to facilitate receiver autonomous integrity monitoring, and test inputs should be implemented for the purposes of hardware delay calibration and receiver functional integrity. 4. A GPSILORAN-C simulation model has provided predicted coverage and availability for LORAN-C, GPS, and hybrid GPS/LORAN-C. LORAN-C pseudoranging will result in an unavailability of less than 3 minutes during a year of operation. GPS availability strongly depends on the maintenance strategy of the constellation. The expected unavailabil- ity of hybrid GPS/LORAN-C is less than one minute during a year of operation. A navigation outage with a duration of one minute can be tolerated if the navigation computer or the pilot utilizes Dead- Reckoning. 5. The hybrid GPSILORAN-C navigation system as described in this paper provides horizontal position accuracies consistent with current 162 and future requirements for domestic enroute and terminal navigation. Static results show a horizontal position accuracy of 138 meters (2 drms). Flight data show a horizontal position accuracy of 210 meters (2 drms), based on equally weighted GPS and LORAN-C measurements, with respect to a Differential GPS reference trajectory (accuracy better than 10 meters, 2 drms). 12. RECOMMENDATIONS The GPS/LORAN-C experiments presented in this paper suggest that a hybrid receiver qualifies for a next generation of sole means air navigation for the CONUS. It is recommended that efforts be continued to develop certification criteria for a sole-means hybrid GPSILORAN-C system. For oceanic navigation, the recommendation is that pseudo- range measurements to Omega stations be added to the hybrid system. Based on the anticipated unavailability of hybrid GPSILORAN-C of less than one minute during a year, the recommendation is that hybrid GPSILORAN-C, in combination with Dead-Reckoning inputs, be evaluated as the position sensor source for Integrated Communication, Naviga- tion, and Surveillance (ICNS), and Automatic Dependent Surveillance (ADS). The United States Coast Guard is currently implementing time of transmission control (TOT) for LORAN-C master stations. In addition to master TOT, it is recommended that GPS receivers be installed at each LORAN-C station to determine the station clock offset with respect to GPS time. These offsets should be transmitted to the users using blink codes or additional LORAN-C pulses. 164 At the same time, efforts should continue to develop a propaga- tion model that takes full advantage of the improved LORAN-C system timing. 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Pealer, "Special Committee 105 Recommendations for Differential NAVSTARIGPS Service," RTCM Paper 200-85/SC 104-58, Final Draft-Report, November 1985. [132] Op. Cit., Edwards, et al. [I331 Op. Cit., Edwards, et al. [134] Sharma, S. "Error Sources Affecting Differential or Ground Monitoring Operation of the NAVSTAR GPS," Master's Thesis, Ohio University, Department of Electrical and Computer Engineering, June 1987. [135] Op. Cit., Edwards, et al. [136] Op. Cit., Edwards, et al. [137] Hoech, R. W., "Impact upon GPS User Segment of GPS Conversion to WGS-84 Earth Model," Proceedings of the Forty-Third Annual Meeting of the ION, Dayton, Ohio, June 23-25, 1987. ABSTRACT Van Graas, Frank. Ph.D. November, 1988 Electrical and Computer Engineering Hybrid GPSILORAN-C: A Next Generation of Sole Means Air Navigation. (173 PP.) Director of Dissertation: Dr. Richard H. McFarland This paper describes a new technique that hybridizes the NAVSTAR Global Positioning System (GPS) and the Long Range Navigation System, LORAN-C, based on a generic pseudorange processing technique. The concept, theoretical analysis, and justification of a hybrid GPS/LO- RAN-C system are presented, along with a scheme for meeting sole means of navigation requirements. Following the design and modeling phase, a prototype hybrid GPSILORAN-C receiver was developed and implemented. The hybrid GPS/LORAN-C receiver concept was proven through an actual flight test, which was referenced to a Differential GPS truth trajectory. The hybrid system has the potential to meet all require- ments for a next generation of sole means of air navigation for the conterminous United States.