10/31/ Simulation of Tightly Coupled INS/GPS Navigator Ade Mulyana, Takayuki Hoshizaki October 31, 2001 Purdue University

10/31/ 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

10/31/ Outline 1.Overview 2. Structure of Simulation 3. Simulation Models 4. Kalman Filter 5. Initial Conditions Error Source Specifications 6. Results 7. Conclusions

10/31/ 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

10/31/ 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

10/31/ Simplified IMU Model where = Bias + White Noise : Sensor Output : Sensor Input Bias: Markov Process, tc=60s for all Accelerometer Outputs Rate Gyro Outputs

10/31/ 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

10/31/ Kalman Filter: Error Dynamics Orientation Angle Errors 17 States Kalman Filter Velocity Errors Position Errors Gyro Biases Accelerometer Biases Clock Bias and Drift

10/31/ Kalman Filter: Output Equation Measurement:Random Noise: Output Equation: where

10/31/ Initial Error Condition Initial Errors Initial Covariance Values

10/31/ 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))

10/31/ 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

10/31/ Satellite Geometry during the Simulation

10/31/ Local Frame: x, y, z Xecef Yecef Zecef x y z x=Zecef y=-Yecef z=Xecef m Nominal Trajectory

10/31/ 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

10/31/ 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)

10/31/ 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)

10/31/ 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

10/31/ 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)

10/31/ 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

10/31/ 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

10/31/ (sec) Result 3: Comparisons between 4 patterns Local Frame Velocity Errors: (true) – (estimated) GPS performance directly affects velocity errors

10/31/ (sec) droll (rad) dpitch (rad) dyaw (rad) Result 3: Comparisons between 4patterns Local Frame Euler Angle Errors: (true) – (estimated) GPS accuracy also helps better orientation correction

10/31/ 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. As long as there is GPS measurement, the two levels of INS accuracy produce about the same overall navigation accuracy.

10/31/ 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:

10/31/ Kalman Filter:Output Equation

10/31/ Kalman Filter:Output Equation

10/31/ Simplified IMU Error Model 0

10/31/ Clock Error Model Updating & Propagation in the Kalman Filter