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.