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Simulation of Tightly Coupled INS/GPS Navigator

Simulation of Tightly Coupled INS/GPS Navigator

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Simulation of Tightly Coupled INS/GPS Navigator

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

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

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

  4. Overview 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. Structure of Simulation Tightly Coupled INS/GPS Position Velocity Orientation Covariance INS UAV IMU Nav Position, Velocity, Orientation and Covariance correction - Kalman Filter Bias Correction + GPS Receiver

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

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

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

  9. Kalman Filter: Output Equation Measurement: Random Noise: Output Equation: where

  10. Initial Errors Initial Covariance Values Initial Error Condition

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

  12. 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 Error Source Specifications GPS (good) (worse) 2 levels of GPS Receivers are used for Simulation

  13. Satellite Geometry during the Simulation

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

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

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

  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 LN-100G:10mCEP Error value is not 0 mean locally

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

  20. Result 2:Ensembles (Good INS,Good GPS) Local Frame Euler Angle Errors: (true) – (estimated) droll (rad) dpitch (rad) dyaw (rad) 0 400 (sec) 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. Result 3: Comparisons between 4patterns Local Frame Position Errors: (true) – (estimated) dx (m) dy (m) dz (m) 0 400 (sec) 200~300s covariance and nominal trajectory data are passed to imagery analysis GPS performance directly affects position errors

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

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

  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. 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. 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. 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. Kalman Filter:Output Equation

  29. Kalman Filter:Output Equation

  30. Simplified IMU Error Model 0

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