1. December,2001 1 Simulation of Tightly Coupled INS/GPS Navigator Ade Mulyana, Takayuki Hoshizaki December, 2001 Purdue University

2. December,2001 2 Model and Parameters to Drive Simulation Aircraft Motion Aircraft Model Trajectory Input Time Input Turbulence Input Errors GPS Satellite Constellation Processing Mode Antennas Number, Location Errors INS Position, Attitude, Rates Filter Aircraft Position & Attitude Estimate and Uncertainty Transformation to Sensor Position, Attitude, and Uncertainty Errors Sensor Parameters Image Acquisition Parameters Site Model Imaging System Target Coordinates Uncertainty, CE90 Graphic Animation Multi-Image Intersection Synthetic Image Generation Errors Target Tracking Covariance data passing

3. December,2001 3 Outline 1.Overview 2. Structure of Simulation 3. Simulation Models 4. Kalman Filter 5. Initial Conditions Error Source Specifications 6. Results 7. Conclusions

4. December,2001 4 Overview (1)UAV Dynamics Nominal Trajectory (2) Navigation Equation INS Output (3) Tightly Coupled INS/GPS INS/GPS Output Covariance Data (4) Covariance data is passed to Imagery Analysis

5. December,2001 5 GPS Receiver IMUNav Structure of Simulation Tightly Coupled INS/GPS Position Velocity Orientation Covariance UAV Kalman Filter + - INS Bias Correction Position, Velocity, Orientation and Covariance correction

6. December,2001 6 Simplified IMU Model where = Bias + White Noise : Sensor Output : Sensor Input Bias: Markov Process, tc=60s for all Accelerometer Outputs Rate Gyro Outputs

7. December,2001 7 GPS Receiver Model : Platform Position : Satellite Position : Pseudorange equvalent Clock Bias (Random Walk) : Pseudorange rate equivalent Clock Drift (Random Walk) : Normally Distributed Random Number Pseudorange Pseudorange Rate

8. December,2001 8 Kalman Filter: Error Dynamics Orientation Angle Errors 17 States Kalman Filter Velocity Errors Position Errors Gyro Biases Accelerometer Biases Clock Bias and Drift

9. December,2001 9 Kalman Filter: Output Equation Measurement:Random Noise: Output Equation: where

10. December,2001 10 Initial Error Condition Initial Errors Initial Covariance Values

11. December,2001 11 Error Source Specifications INS Accelerometers Bias White Noise (sqrt(PSD)) Bias White Noise (sqrt(PSD)) Notation LN-100GLN-200IMUUnits Rate Gyros (good) (worse) 2 levels of INS are used for Simulation (deg/hr/sqrt(Hz))

12. December,2001 12 Error Source Specifications GPS GPS Receiver Notation Receiver 1 Receiver 2 Units Pseudorange 6.6 33.3 m Pseudorange Rate 0.05 0.5 m/s ClockBias White Noise(PSD) 0.009 0.009 ClockDrift White Noise(PSD) 0.0355 0.0355 (good)(worse) 2 levels of GPS Receivers are used for Simulation

13. December,2001 13 Satellite Geometry during the Simulation

14. December,2001 14 Local Frame: x, y, z Xecef Yecef Zecef x y z x=Zecef y=-Yecef z=Xecef-6378137m Nominal Trajectory

15. December,2001 15 Result 1:Comparisons between INS/GPS and Unaided INS;(Good INS,Good GPS) Local Frame Position Errors: (true) – (estimated) dx (m) dy (m) dz (m) 0 400 (sec) INS/GPS works very well

16. December,2001 16 Local Frame Velocity Errors: (true) – (estimated) 400 (sec) 0 INS/GPS works very well Result 1:Comparisons between INS/GPS and Unaided INS;(Good INS,Good GPS)

17. December,2001 17 Local Frame Euler Angle Errors: (true) – (estimated) droll (rad) dpitch (rad) dyaw (rad) Roll and Pitch errors are quickly corrected Yaw error correction takes time 400 (sec) 0 Effect on Geo Positioning? Result 1:Comparisons between INS/GPS and Unaided INS;(Good INS,Good GPS)

18. December,2001 18 Result 2:Ensembles (Good INS,Good GPS) Local Frame Position Errors: (true) – (estimated) dx (m) dy (m) dz (m) 0 400 (sec) Position error is less than 3m Error value is not 0 mean locally LN-100G:10mCEP

19. December,2001 19 Result 2:Ensembles (Good INS,Good GPS) 0 400 (sec) Local Frame Velocity Errors: (true) – (estimated) Velocity error is less than 0.05m/s LN-100G:0.015m/s(rms)

20. December,2001 20 Result 2:Ensembles (Good INS,Good GPS) 0 400 (sec) Local Frame Euler Angle Errors: (true) – (estimated) droll (rad) dpitch (rad) dyaw (rad) Angle error is about 0.003 deg for roll and pitch, 0.06 deg for yaw, LN-100G:0.002deg (rms) for all pitch, roll and yaw

21. December,2001 21 Result 3: Comparisons between 4patterns 0 400 (sec) dx (m) dy (m) dz (m) Local Frame Position Errors: (true) – (estimated) GPS performance directly affects position errors 200~300s covariance and nominal trajectory data are passed to imagery analysis

22. December,2001 22 0 400 (sec) Result 3: Comparisons between 4 patterns Local Frame Velocity Errors: (true) – (estimated) GPS performance directly affects velocity errors

23. December,2001 23 0 400 (sec) droll (rad) dpitch (rad) dyaw (rad) Result 3: Comparisons between 4patterns Local Frame Euler Angle Errors: (true) – (estimated) INS accuracy helps orientation accuracy

24. December,2001 24 Conclusions We have successfully built a realistic integrated INS/GPS which will be used to study the effects of navigation accuracy on target positioning accuracy. The INS/GPS is good at correcting roll and pitch angles, but not yaw angle. Improving GPS accuracy improves aircraft position accuracy. Improving INS accuracy improves aircraft attitude accuracy. Both aircraft position and attitude are needed to locate the target.

25. December,2001 25 Future Work GPS Use of carrier phase observations Use of dual frequencies Differential carrier phase GPS INS Estimate Scale Factor and Nonlinearity as well as Bias:

26. December,2001 26 References (INS) [1]Titterton, D. H. and Weston, J. L. (1997). “Strapdown Inertial Navigation Technology”. Peter Peregrinus Ltd. [2] Rogers, R. M. (2000). “Applied Mathematics In Integrated Navigation Systems”. AIAA Education Series. [3]Chatfield, A. B. (1997). “Fundamentals of High Accuracy Inertial Navigation”. Volume 174, Progress in Astronautics and Aeronautics. AIAA. [4]Britting, K. R. (1971). “Inertial Navigation Systems Analysis”. Wiley Interscience. (Kalman Filter) [5] Brown, R. G. and Hwang, P. Y. C. (1985). “Introduction to Random Signals and Applied Kalman Filtering”. John Wiley & Sons. [6] Gelb, A. (1974). “Applied Optimal Estimation”. M.I.T. Press.

27. December,2001 27 References (Cont.) (Navigation Sensors) [7] B. Stieler and H. Winter (1982). “Gyroscopic Instruments and Their Application to Flight Testing”. AGARDograph No.160 Vol.15. [8] Lawrence, A. (1992). “Modern Inertial Technology”. Springer- Verlag. [9] “IEEE Standard Specification Format Guide and Test Procedure for Single-Axis Laser Gyros”. IEEE Std. 647-1995. (GPS) [10] Kaplan. E. D. (1996). “Understanding GPS Principles and Applications”. Artech House. (Others) [11] Military Standard for Flying Qualities of Piloted Aircraft 1797A. [12] Department of Defense World Geodetic System 1984, “Its Definition and Relationships with Local Geodetic Systems”, National Imagery And Mapping Agency Technical Report

28. December,2001 28 Kalman Filter:Output Equation

29. December,2001 29 Kalman Filter:Output Equation

30. December,2001 30 Simplified IMU Error Model 0

31. December,2001 31 Clock Error Model Updating & Propagation in the Kalman Filter