Introduction to Inertial Navigation Kenneth Gade Navigation Navigation Estimate the position - PDF document

Introduction to Inertial Navigation (INS tutorial short)Tutorial for:GeodesiHydrografidageneHoenefoss, NorwayKenneth Gade, FFI (Norwegian DefenceResearch Establishment) Note 1:This is a short (20 pages) tutorial. An extended (57 pages) tutorial that also includes Kalman filtering is available at http://www.navlab.net/Publications/Introduction_to _Inertial_Navigation_and_Kalman_Filtering.pdf To cite this tutorial, use:Gade, K. (2005): Introduction to Inertial Navigation. Tutorial for GeodesiHydrografidagene2005, Hoenefoss, Norway Navigation Navigation: Estimate the position, orientation and velocity of a vehicle Inertial navigation: Inertial sensorsare utilized for the navigation Inertial Sensors Based on inertial principles, •Always relative to •Most common inertial sensors: –Accelerometers –Gyros Accelerometers By attaching a massto a spring, measuring its deflection, we get a simple accelerometer. Figure: Gade (2004) Accelerometers (continued) is also measured (Einstein's principle of equivalence)•Total measurement called •Using 3 (or more) accelerometers we can form a 3D specific force Gyros Gyros measure angular velocity relative inertial space: Measurement principles include: B IB Spinning wheel •Mechanicalgyro Sagnac-effect •Ring laser gyro (RLG)•Fiberoptic gyro (FOG)Coriolis-effect •MEMS•“Tuning fork”•“Wine glass”Figure: Caplex(2000)Figure: Titterton& Weston (1997) IMU Three gyros and three accelerometers are normally combined in aninertial measurement unit (IMU) Honeywell HG1700 ("medium quality"):•3 accelerometers, accuracy: 1 mg •3 ring laser gyros, accuracy: 1 deg/h •Rate of all 6 measurements: 100 Hz Inertial Navigation An IMU (giving and given initial values of position–Integrating the sensed acceleration will give velocity.–A second integration gives position.–To integrate in the correct direction, is needed. This is obtained by integrating the sensed angular velocity. I BBf I BB Inertial Navigation System (INS) The combination of an IMU and a computer running navigation equations is called an Inertial Navigation System (INS). Due to errors in the gyros and accelerometers, an INS will have Equations Equations Gyros meters Velocity,Angular velocity,Specific force,INSIMU Attitude, or roll/pitch/yawposition, B I Bf B I B EnL E BvLB R or longitude/ latitude Categorization: IMU technology and IMU performance ClassPositionGyro biasAccbiasNACoriolisMEMS10 -1000°/h10 mg1 nmi/ 24 hESG, RLG, °µ1 nmi/ hRLG, FOGServoVibratingbeam0.01°/h50 µg&#x 30 ;&#xg000; 10 nmi/ hRLG, FOGServoVibratingbeam, AHRSNAMEMS, RLG, 1 -10°/h Aided inertial navigation system example position and The different measurements are Kalman filter. Navigation Equations Gyros A ccelero- Kalman filter Velocit y Angular velocity Specific force INS Compass Position measurement Attitude p th _ V elocity measurementSmoothed Estimate s Reset Horizontal p osition Optimal Smoothing KF Estimate s measurement -300 -290 -280 -270 -260 -250 -240 255 260 265 270 275 280 285 290 295 300 2D trajectory in meters, East [m]North [m]–Improved accuracy–Improved robustness–Improved integrity–Estimate in accordance Figure: NavLab Optimal Smoothing Optimal estimate when also Typical position estimate example (simulation) 200 300 400 500 600 700 -4 -3 -2 -1 0 1 2 3 4 5 6 Position in meters () vs timeTime [s]x [m] Position measurement total error: 5 m (1 )Navigation equation reset ca each 107 sec True trajectoryMeasurementCalculated value from navi g ation e q uationsEstimate from real-time Kalman filterSmoothed estimate Figure: NavLab Gyrocompassing –The concept of finding North by –Earth rotation is measured by means of gyros•An optimally designed AINS I E -gyro axis ro axis (vehicle heading)-gyro axis-gyro measurement-gyro measurementEarth's axis of rotationro measurement x-gyx-gy LatitudeStatic conditions, x-and yin the horizontal plane: What is NavLab? NavLab (Navigation Laboratory) is one common tool for solving a variety of navigation tasks. Estimator (can interface with simulated or real measurements)Trajectory Simulator Trajectory Simulator IMU Simulator Position measurement Simulator measurement Simulator Velocity measurement Simulator Compass Simulator Navigation Navigation Make Kalman filter measure-ments(differences) Error state Kalman filter Error state Kalman filter Optimal Optimal estimates covariance matricesSmoothed estimates covariance matrices–Solid theoretical Simulator •Trajectory simulator –Can simulate any trajectory –No singularities •Sensor simulators –Most common sensors with –All parameters can change –Rate can change with time Figure: NavLab -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Relative East position [m]Relative North position [m]Mapped object positions Std North = 1.17 mStd East = 1.71 mVerified by mapping the HUGIN 3000 @ 1300 m depth: Navigating aircraft with NavLab •Cessna 172, 650 m height, much turbulence •Simple GPS and IMU (no IMU spec. available) Line imager data Positioned with NavLab (abs. accuracy: ca 1 m verified) NavLab Usage Main usage: •Navigation system research and development •Analysis of navigation system •Decision basis for sensor purchase and mission planning •Post-processing of real navigation data •Sensor evaluation •Tuning of navigation system and sensor calibration Users: •Research groups (e.g. FFI (several groups), NATO Undersea Research Centre, QinetiQ, Kongsberg Maritime, NorskElektroOptikk) •Universities (e.g. NTNU, UniK) •Commercial companies (e.g. C&C Technologies, Geoconsult, FUGRO, ThalesGeosolutions, ArtecSubsea, Century Subsea) •Norwegian Navy Vehicles navigated with NavLab:AUVs, ROVs, ships and aircraft For more details, see www.navlab.net Conclusions •An gives: –optimal solution based on all available sensors –all the relevant data with high rate that typically gives sub-optimal so •If real-time data not required,