Introduction To Inertial Navigation And Kalman Filtering.pdf .

Note 1: This is a short (20 pages)tutorial. An extended (57 pages)tutorial that also includes Kalmanfiltering is available athttp://www.navlab.net/Publications/Introduction toInertial Navigation and Kalman Filtering.pdfIntroduction to Inertial Navigation(INS tutorial – short)Tutorial for:Geodesi- ogHydrografidagene 2005,Hoenefoss, NorwayKenneth Gade, FFI(Norwegian DefenceResearch Establishment)To cite this tutorial, use: Gade, K. (2005): Introduction to Inertial Navigation. Tutorial for Geodesi- og Hydrografidagene 2005, Hoenefoss, Norway

NavigationNavigation:Estimate the position, orientation and velocity of a vehicleInertial navigation:Inertial sensors are utilized for the navigation

Inertial SensorsBased on inertial principles, acceleration and angular velocity aremeasured. Always relative to inertial spaceMost common inertial sensors:– Accelerometers– Gyros

AccelerometersBy attaching a mass to a spring, measuring its deflection, we get asimple accelerometer.Figure: Gade (2004)

Accelerometers (continued) Gravitation is also measured (Einstein's principle of equivalence)Total measurement called specific forceUsing 3 (or more) accelerometers we can form a 3D specific forceBmeasurement:IBfThis means: Specific force of the body system (B) relative inertial space (I),decomposed in the body system.

GyrosGyros measure angular velocity relative inertial space:ωBIBMeasurement principles include:Spinning wheel Mechanical gyroFigure: Caplex (2000)Sagnac-effect Ring laser gyro (RLG) Fiber optic gyro (FOG)Figure: Bose (1998)Coriolis-effect MEMS “Tuning fork” “Wine glass”Figure: Titterton & Weston (1997)

IMUThree gyros and three accelerometers are normally combined in aninertial measurement unit (IMU)Example:Honeywell HG1700 ("medium quality"): 3 accelerometers, accuracy: 1 mg3 ring laser gyros, accuracy: 1 deg/hRate of all 6 measurements: 100 HzFoto: FFI

Inertial NavigationBBfAn IMU (giving IB and ω IB) is sufficient to navigate relative to inertialspace (no gravitation present), given initial values of velocity, positionand attitude:– Integrating the sensed acceleration will give velocity.– A second integration gives position.– To integrate in the correct direction, attitude is needed. This isobtained by integrating the sensed angular velocity.In terrestrial navigation (close to the Earth) we compensate forgravitation, and rotation of the EarthEquations integrating the gyro and accelerometer measurements intovelocity, position and orientation are called navigation equations

Inertial Navigation System (INS)The combination of an IMU and a computer running navigation equations iscalled an Inertial Navigation System e, RLB or roll/pitch/yawBIBVelocity,Specificforce,IMUf ontal E or longitude/position, nlatitudeDepth,zINSDue to errors in the gyros and accelerometers, an INS will have unlimited drift invelocity, position and attitude.

Categorization:IMU technology and IMU ccelerometertechnology”Militarygrade”1 nmi / 24 hESG, RLG,FOGServoaccelerometer 0.005 /h 30 µgNavigationgrade1 nmi / hRLG, FOGServoaccelerometer,Vibrating beam0.01 /h50 µgTacticalgrade 10 nmi / hRLG, FOGServoaccelerometer,Vibrating beam,MEMS1 /h1 mgAHRSNAMEMS, RLG, MEMSFOG, Coriolis1 - 10 /h1 mgControlsystemNACoriolis10 - 1000 /h10 mgMEMSGyro biasAcc bias

Aided inertial navigation systemResetTo limit the drift, an INSis usually aided byother sensors thatprovide directmeasurements of forexample position andvelocity.The differentmeasurements areblended in an optimalmanner by means ofa Kalman filter.GyrosAccelerometersAngularvelocitySpecific talpositionError imalSmoothingSmoothedEstimatesThe INS and aiding sensors havecomplementary characteristics.

Optimal SmoothingOptimal estimate when also using future measurements2D trajectory in meters, p MMB300295290285North [m]Smoothing gives:– Improved accuracy– Improved robustness– Improved integrity– Estimate in accordancewith process model280275270265260Example from HUGIN 1000:255-300-290Figure: NavLab-280-270-260East [m]-250-240

Typical position estimate example(simulation)Position in meters (pM) vs timeMB6True trajectoryMeasurementCalculated value from navigation equationsEstimate from real-time Kalman filterSmoothed estimate543x [m]210-1-2-3-4200300400Time [s]Position measurement total error: 5 m (1 σ)Navigation equation reset ca each 107 sec500600Figure: NavLab700

GyrocompassingGyrocompassing– The concept of finding North bymeasuring the direction ofEarth's axis of rotationrelativerto inertial space ω IEStatic conditions, x- and y-gyrosin the horizontal plane:z-gyro axis– Earth rotation is measured bymeans of gyrosz-gyro measurementEarth's axis of rotation An optimally designed AINSBx-gyro measurementinherently gyrocompassesoptimally when getting position orvelocity measurements (better thanyawa dedicated gyrocompass/motionsensor).x-gyro axis (vehicleheading)Latitudey-gyro measurementy-gyro axisNorth

What is NavLab?NavLab (Navigation Laboratory) is one common tool for solving a varietyof navigation tasks.Structure:Development started in1998Main focus duringdevelopment:– Solid theoreticalfoundation(competitive edge)IMU or stateError stateKalman filterKalman iancematricesMake esandcovariancematricesSimulator (can be replaced byreal measurements)Estimator (can interface withsimulated or real measurements)

Simulator Trajectory simulator– Can simulate any trajectoryin the vicinity of Earth– No singularities Sensor simulators– Most common sensors withtheir characteristic errors aresimulated– All parameters can changewith time– Rate can change with timeFigure: NavLab

Verification of Estimator PerformanceVerified using varioussimulationsHUGIN 3000 @1300 m depth:Mapped object positions5Verified by mapping thesame object repeatedlyStd North 1.17 mStd East 1.71 m4Relative North position [m]3210-1-2-3-4-5-5-4-3-2-1012Relative East position [m]345

Navigating aircraft with NavLab Cessna 172, 650 m height, much turbulenceSimple GPS and IMU (no IMU spec. available)Line imager dataPositioned with NavLab (abs. accuracy: ca 1 m verified)

NavLab UsageMain 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 calibrationUsers: Research groups (e.g. FFI (several groups), NATO Undersea ResearchCentre, QinetiQ, Kongsberg Maritime, Norsk Elektro Optikk) Universities (e.g. NTNU, UniK) Commercial companies (e.g. C&C Technologies, Geoconsult, FUGRO,Thales Geosolutions, Artec Subsea, Century Subsea) Norwegian NavyVehicles navigated with NavLab: AUVs, ROVs, ships and aircraft) For more details, see www.navlab.net

Conclusions An aided inertial navigation system gives:– optimal solution based on all available sensors– all the relevant data with high rateCompare this with dedicated gyrocompasses, motion sensors etcthat typically gives sub-optimal solutions, often with a subset ofdataIf real-time data not required, smoothing should always be used toget maximum accuracy, robustness and integrity

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 .