Simulation of Tightly Coupled INS/GPS Navigator

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Simulation of Tightly Coupled INS/GPS Navigator. Ade Mulyana, Takayuki Hoshizaki. December, 2001. Purdue University. Model and Parameters to Drive Simulation. Trajectory Input. Aircraft. Turbulence Input. Model. Time Input. Aircraft Motion. Satellite Constellation. Errors.
Simulation of Tightly Coupled INS/GPS NavigatorAde Mulyana,Takayuki HoshizakiDecember, 2001Purdue UniversityModel and Parameters to Drive SimulationTrajectory InputAircraft Turbulence InputModel Time InputAircraft MotionSatellite ConstellationErrorsProcessing ModeINSGPS AntennasNumber, LocationErrorsPosition, Attitude, RatesPosition, Attitude, RatesFilter Aircraft Position & Attitude Covariance data passingEstimate and Uncertainty ErrorsTransformation to Sensor Position, Attitude, and Uncertainty ErrorsSynthetic Image GenerationErrorsSensor ParametersTarget TrackingImage AcquisitionImaging ParametersSystem Multi-ImageSite ModelIntersectionTarget CoordinatesGraphic AnimationUncertainty, CE90OutlineOverview2. Structure of Simulation 3. Simulation Models4. Kalman Filter5. Initial Conditions Error Source Specifications6. Results7. ConclusionsOverviewUAV 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 AnalysisStructure of SimulationTightly Coupled INS/GPSPosition VelocityOrientationCovarianceINSUAVIMUNavPosition, Velocity, Orientation and Covariance correction-Kalman FilterBias Correction+GPS Receiver= Bias + White NoiseSimplified IMU Modelwhere : Sensor Output : Sensor InputBias : Markov Process, tc=60sfor allAccelerometer OutputsRate Gyro OutputsGPS Receiver ModelPseudorange 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 NumberKalman Filter: Error Dynamics Orientation Angle ErrorsVelocity ErrorsPosition ErrorsGyro BiasesAccelerometer BiasesClock Bias and Drift17 States Kalman FilterKalman Filter: Output EquationMeasurement: Random Noise: Output Equation: where Initial ErrorsInitial Covariance ValuesInitial Error ConditionError Source SpecificationsINSLN-100GLN-200IMUUnitsAccelerometersNotationBias White Noise (sqrt(PSD))Rate GyrosBias White Noise (sqrt(PSD))(deg/hr/sqrt(Hz))(worse) (good) 2 levels of INS are used for SimulationGPS Receiver Notation Receiver 1 Receiver 2 UnitsPseudorange 6.6 33.3 mPseudorange Rate 0.05 0.5 m/sClockBias White Noise(PSD) 0.009 0.009 ClockDrift White Noise(PSD) 0.0355 0.0355Error Source SpecificationsGPS(good) (worse) 2 levels of GPS Receivers are used for SimulationSatellite Geometry during the Simulationx=Zecefy=-Yecefz=Xecef-6378137mLocal Frame: x, y, zZecefNominal TrajectoryxyYecefzXecefResult 1:Comparisons between INS/GPS and Unaided INS;(Good INS,Good GPS)Local Frame Position Errors: (true) – (estimated)dx (m)dy (m)dz (m)0400 (sec)INS/GPS works very wellResult 1:Comparisons between INS/GPS and Unaided INS;(Good INS,Good GPS)Local Frame Velocity Errors: (true) – (estimated)0400 (sec)INS/GPS works very wellResult 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)0400 (sec)Roll and Pitch errors are quickly correctedYaw error correction takes time Effect on Geo Positioning? Result 2:Ensembles (Good INS,Good GPS)Local Frame Position Errors: (true) – (estimated)dx (m)dy (m)dz (m)0400 (sec)Position error is less than 3mLN-100G:10mCEPError value is not 0 mean locallyVelocity error is less than 0.05m/sResult 2:Ensembles (Good INS,Good GPS)Local Frame Velocity Errors: (true) – (estimated)0400 (sec)LN-100G:0.015m/s(rms)Result 2:Ensembles (Good INS,Good GPS)Local Frame Euler Angle Errors: (true) – (estimated)droll (rad)dpitch (rad)dyaw (rad)0400 (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 yawResult 3: Comparisons between 4patternsLocal Frame Position Errors: (true) – (estimated)dx (m)dy (m)dz (m)0400 (sec)200~300s covariance and nominal trajectory data are passed to imagery analysis GPS performance directly affects position errors Result 3: Comparisons between 4 patternsLocal Frame Velocity Errors: (true) – (estimated)0400 (sec)GPS performance directly affects velocity errors Result 3: Comparisons between 4patternsLocal Frame Euler Angle Errors: (true) – (estimated)droll (rad)dpitch (rad)dyaw (rad)0400 (sec) INS accuracy helps orientation accuracyConclusionsWe 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.Future WorkGPS
  • Use of carrier phase observations
  • Use of dual frequencies
  • Differential carrier phase GPS
  • INS
  • Estimate Scale Factor and Nonlinearity as well as Bias:
  • 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.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 ReportKalman Filter:Output EquationKalman Filter:Output EquationSimplified IMU Error Model0Clock Error ModelUpdating & Propagation in the Kalman Filter
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