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

December, 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

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

December, 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

December, 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

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

December, 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

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

December, Kalman Filter: Output Equation Measurement:Random Noise: Output Equation: where

December, Initial Error Condition Initial Errors Initial Covariance Values

December, 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))

December, Error Source Specifications GPS GPS Receiver Notation Receiver 1 Receiver 2 Units Pseudorange m Pseudorange Rate m/s ClockBias White Noise(PSD) ClockDrift White Noise(PSD) (good)(worse) 2 levels of GPS Receivers are used for Simulation

December, Satellite Geometry during the Simulation

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

December, 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) (sec) INS/GPS works very well

December, 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)

December, 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)

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

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

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

December, Result 3: Comparisons between 4patterns (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

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

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

December, 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.

December, 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:

December, 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.

December, 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 (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

December, Kalman Filter:Output Equation

December, Kalman Filter:Output Equation

December, Simplified IMU Error Model 0

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