GPS, Inertial Navigation GPS, Inertial Navigation and LIDAR Sensorsand LIDAR Sensors
Brian ClippBrian Clipp
Urban 3D ModelingUrban 3D Modeling
9/26/069/26/06
IntroductionIntroduction
GPS- The Global Positioning SystemGPS- The Global Positioning System Inertial NavigationInertial Navigation
• AccelerometersAccelerometers• GyroscopesGyroscopes
LIDAR- Laser Detection and RangingLIDAR- Laser Detection and Ranging Example SystemsExample Systems
The Global Positioning SystemThe Global Positioning System
Constellation of 24 satellites operated Constellation of 24 satellites operated by the U.S. Department of Defenseby the U.S. Department of Defense
Originally intended for military Originally intended for military applications but extended to civilian useapplications but extended to civilian use
Each satellite’s orbital Each satellite’s orbital period is 12 hoursperiod is 12 hours
6 satellites visible in each 6 satellites visible in each hemispherehemisphere
GPS Operating PrinciplesGPS Operating Principles
Position is determined by the travel Position is determined by the travel time of a signal from four or more time of a signal from four or more satellites to the receiving antennasatellites to the receiving antenna
Image Source: NASA
Three satellites for Three satellites for X,Y,Z position, one X,Y,Z position, one satellite to cancel out satellite to cancel out clock biases in the clock biases in the receiverreceiver
Time of Signal Travel Time of Signal Travel DeterminationDetermination
Code is a pseudorandom sequenceCode is a pseudorandom sequence Use correlation with receiver’s code Use correlation with receiver’s code
sequence at time shift dt to sequence at time shift dt to determine time of signal traveldetermine time of signal travel
GPS Signal FormulationGPS Signal Formulation
Signal CharcteristicsSignal Charcteristics
Code and Carrier Phase ProcessingCode and Carrier Phase Processing• Code used to determine user’s gross Code used to determine user’s gross
positionposition• Carrier phase difference can be used to Carrier phase difference can be used to
gain more accurate positiongain more accurate position Timing of signals must be known to within Timing of signals must be known to within
one carrier cycleone carrier cycle
Triangulation Equations Triangulation Equations Without ErrorWithout Error
Sources Of ErrorSources Of Error Geometric Degree of Geometric Degree of
Precision (GDOP) Precision (GDOP) Selective AvailabilitySelective Availability
• Discontinued in 5/1/2000Discontinued in 5/1/2000 Atmospheric EffectsAtmospheric Effects
• IonosphericIonospheric• TroposphericTropospheric
MultipathMultipath Ephemeris Error Ephemeris Error
(satellite position data)(satellite position data) Satellite Clock ErrorSatellite Clock Error Receiver Clock ErrorReceiver Clock Error
Geometric Degree of Precision Geometric Degree of Precision (GDOP)(GDOP)
Relative geometry of satellite Relative geometry of satellite constellation to receiverconstellation to receiver
With four satellites best GDOP occurs With four satellites best GDOP occurs when when • Three satellites just above the horizon Three satellites just above the horizon
spaced evenly around the compassspaced evenly around the compass• One satellite directly overheadOne satellite directly overhead
Satellite selection minimizes GDOP Satellite selection minimizes GDOP errorerror
Good Geometric Degree Good Geometric Degree of Precisionof Precision
Horizon
Receiver
Bad Geometric Degree of PrecisionBad Geometric Degree of Precision
Horizon
Receiver
Pseudorange MeasurementPseudorange Measurement
Single satellite pseudorange Single satellite pseudorange measurementmeasurement
Error Mitigation TechniquesError Mitigation Techniques
Carriers at L1 and L2 frequenciesCarriers at L1 and L2 frequencies• Ionospheric error is frequency dependent so using two Ionospheric error is frequency dependent so using two
frequencies helps to limit errorfrequencies helps to limit error Differential GPSDifferential GPS
• Post-Process user measurements using measured error Post-Process user measurements using measured error valuesvalues
Space Based Augmentation Systems(SBAS)Space Based Augmentation Systems(SBAS)• Examples are U.S. Wide Area Augmentation System Examples are U.S. Wide Area Augmentation System
(WAAS), European Geostationary Navigational Overlay (WAAS), European Geostationary Navigational Overlay Service (EGNOS)Service (EGNOS)
• SBAS provides atmospheric, ephemeris and satellite SBAS provides atmospheric, ephemeris and satellite clock error correction values in real timeclock error correction values in real time
Differential GPSDifferential GPS
Uses a GPS receiver at a fixed, Uses a GPS receiver at a fixed, surveyed location to measure error in surveyed location to measure error in pseudorange signals from satellitespseudorange signals from satellites
Pseudorange error for each satellite Pseudorange error for each satellite is subtracted from mobile receiver is subtracted from mobile receiver before calculating position (typically before calculating position (typically post processed)post processed)
Differential GPSDifferential GPS
WAAS/EGNOSWAAS/EGNOS
Provide Provide corrections corrections based on user based on user positionposition
Assumes Assumes atmospheric atmospheric error is locally error is locally correlatedcorrelated
Inertial NavigationInertial Navigation
Accelerometers measure linear Accelerometers measure linear accelerationacceleration
Gyroscopes measure angular velocityGyroscopes measure angular velocity
Accelerometer Principles of Accelerometer Principles of OperationOperation
Newton’s Second Newton’s Second LawLaw• F = mAF = mA
Measure force on Measure force on object of known object of known mass (proof mass) mass (proof mass) to determine to determine accelerationacceleration
ProofMass (m)
Direction of Acceleration w.r.t. Inertial Space
Displacement Pickup
Case
a
Spring
Example AccelerometersExample Accelerometers
Force Feedback Pendulous AccelerometerForce Feedback Pendulous Accelerometer
Hinge
Pendulous Arm
Restoring Coil
Permanent Magnet
Case
Excitation Coil
Pick-Off
Sensitive Input Axis
Example AccelerometersExample Accelerometers
Micro electromechanical device Micro electromechanical device (MEMS) solid state silicon (MEMS) solid state silicon accelerometeraccelerometer
Accelerometer Error SourcesAccelerometer Error Sources Fixed BiasFixed Bias
• Non-zero acceleration measurement when zer0 Non-zero acceleration measurement when zer0 acceleration integratedacceleration integrated
Scale Factor ErrorsScale Factor Errors• Deviation of actual output from mathematical model of Deviation of actual output from mathematical model of
output (typically non-linear output)output (typically non-linear output) Cross-CouplingCross-Coupling
• Acceleration in direction orthogonal to sensor Acceleration in direction orthogonal to sensor measurement direction passed into sensor measurement direction passed into sensor measurement (manufacturing imperfections, non-measurement (manufacturing imperfections, non-orthogonal sensor axes)orthogonal sensor axes)
Vibro-Pendulous ErrorVibro-Pendulous Error• Vibration in phase with pendulum displacementVibration in phase with pendulum displacement
(Think of a child on a swing set)(Think of a child on a swing set) Clock ErrorClock Error
• Integration period incorrectly measuredIntegration period incorrectly measured
Gyroscope Principles of OperationGyroscope Principles of Operation
Two primary typesTwo primary types• MechanicalMechanical• OpticalOptical
Measure rotation w.r.t. an inertial Measure rotation w.r.t. an inertial frame which is fixed to the stars (not frame which is fixed to the stars (not fixed w.r.t. the Earth).fixed w.r.t. the Earth).
Mechanical GyroscopesMechanical Gyroscopes
A rotating mass A rotating mass generates angular generates angular momentum which is momentum which is resistive to change or resistive to change or has angular inertia.has angular inertia.
Angular Inertia causes Angular Inertia causes precession which is precession which is rotation of the gimbal rotation of the gimbal in the inertial in the inertial coordinate frame.coordinate frame.
Equations of PrecessionEquations of Precession Angular Momentum vector HAngular Momentum vector H Torque vector TTorque vector T
Torque is proportional to Torque is proportional to • Angular Rate omega cross H plusAngular Rate omega cross H plus• A change in angular momentumA change in angular momentum
δH = Change in angular momentum
SPIN AXIS (At time t = t + δt)
SPIN AXIS (at time t)
DISC
Precession (rate ω)H
H
O
A
B
Problems with Mechanical Problems with Mechanical GyroscopesGyroscopes
Large spinning masses have long Large spinning masses have long start up timesstart up times
Output dependent on environmental Output dependent on environmental conditions (acceleration, vibration, conditions (acceleration, vibration, sock, temperature )sock, temperature )
Mechanical wear degrades gyro Mechanical wear degrades gyro performanceperformance
Gimbal LockGimbal Lock
Gimbal LockGimbal Lock
Occurs in two or more degree of Occurs in two or more degree of freedom (DOF) gyrosfreedom (DOF) gyros
Planes of two gimbals align and once Planes of two gimbals align and once in alignment will never come out of in alignment will never come out of alignment until separated manuallyalignment until separated manually
Reduces DOF of gyroscope by oneReduces DOF of gyroscope by one Alleviated by putting mechanical Alleviated by putting mechanical
limiters on travel of gimbals or using limiters on travel of gimbals or using 1DOF gyroscopes in combination1DOF gyroscopes in combination
Gimbal LockGimbal Lock
Optical GyroscopeOptical Gyroscope
Measure difference in travel time of light Measure difference in travel time of light traveling in opposite directions around a circular traveling in opposite directions around a circular pathpath
Y
X
Ω
Beam Splitter Position at time t = t + δt
Beam Splitter Position at time t = t
Light Input
Light Output
TypesTypes Ring Laser Ring Laser
GyroscopeGyroscope
Fiber OpticFiber Optic
Ring Laser GyroRing Laser Gyro
Change in traveled distance results Change in traveled distance results in different frequency in opposing in different frequency in opposing beamsbeams• Red shift for longer pathRed shift for longer path• Blue shift for shorter pathBlue shift for shorter path
For laser operation peaks must For laser operation peaks must reinforce each other leading to reinforce each other leading to frequency change.frequency change.
Lock In and DitheringLock In and Dithering
Lasers tend to resist having two Lasers tend to resist having two different frequencies at low angular different frequencies at low angular ratesrates• Analogous to mutual oscillation in Analogous to mutual oscillation in
electronic oscillatorselectronic oscillators Dithering or adding some small Dithering or adding some small
random angular accelerations random angular accelerations minimizes time gyro is in locked in minimizes time gyro is in locked in state reducing errorstate reducing error
Fiber Optic GyroscopeFiber Optic Gyroscope
Measure phase Measure phase difference of light difference of light traveling through fiber traveling through fiber optic path around axis optic path around axis of rotationof rotation
Ω
Coupling Lens
Beam Splitter
Light Source Detector
Fiber Optic Coil
Example Complete GPS/INS Example Complete GPS/INS SystemSystem
Applanix POS LV-V4Applanix POS LV-V4 Used in Urbanscape ProjectUsed in Urbanscape Project Also includes wheel rate sensorAlso includes wheel rate sensor
Pulse LIDARPulse LIDAR
Measures time of flight Measures time of flight of a light pulse from of a light pulse from an emitter to an object an emitter to an object and back to determine and back to determine position.position.
Sensitive to Sensitive to atmospheric effects atmospheric effects such as dust and such as dust and aerosolsaerosols
Conceptual DrawingConceptual Drawing
Photo Detector
Laser SourceHalf Silvered
Mirror
Rotating Mirror
Rotation
Sensor Case
Target
Sensor Window
Laser Beam
The MathThe Math
d = Distance from emitter/receiver to d = Distance from emitter/receiver to targettarget
C = speed of light (299,792,458 m/s C = speed of light (299,792,458 m/s in a vacuum)in a vacuum)
ΔΔt = time of flightt = time of flight
Determining Time of FlightDetermining Time of Flight
t
Calculate Cross-Correlation of Measurement and Generated Signal
Pulse generated by emitter
Pulse detected at receiver
time
Sig
nal
Ma
gnitu
de
From Depth to 3DFrom Depth to 3D
Use angle of reflecting mirror to Use angle of reflecting mirror to determine ray directiondetermine ray direction
Measurement is 3D relative to LIDAR Measurement is 3D relative to LIDAR sensor frame of referencesensor frame of reference
Transform into world frame using Transform into world frame using GPS/INS system or known fixed GPS/INS system or known fixed locationlocation
Error SourcesError Sources Aerosols and DustAerosols and Dust
• Scatter Laser reducing signal strength of Laser Scatter Laser reducing signal strength of Laser reaching targetreaching target
• Laser reflected to receiver off of dust Laser reflected to receiver off of dust introduces noiseintroduces noise
Minimally sensitive to temperature Minimally sensitive to temperature variation (changes path length inside of variation (changes path length inside of receiver and clock oscillator rate)receiver and clock oscillator rate)
Error in measurement of rotating mirror Error in measurement of rotating mirror angleangle
Specular SurfacesSpecular Surfaces Clock ErrorClock Error
Example Pulse LIDAR Example Pulse LIDAR CharacteristicsCharacteristics
Sample specification from SICKSample specification from SICK
Doppler LIDARDoppler LIDAR
Uses a continuous beam to measure Uses a continuous beam to measure speed differential of target and speed differential of target and emitter/receiveremitter/receiver• Measure frequency change of reflected Measure frequency change of reflected
lightlight Blue shift- target and LIDAR device moving Blue shift- target and LIDAR device moving
closer togethercloser together Red shift- target and LIDAR device moving Red shift- target and LIDAR device moving
apartapart
Application of Doppler LIDARApplication of Doppler LIDAR
Speed TrapsSpeed Traps
Combined Sensor SystemsCombined Sensor Systems
Questions?Questions?
ReferencesReferences
Grewal, M. Weil, L, Andrews, P. Grewal, M. Weil, L, Andrews, P. Global Positioning Systems, Inertial Global Positioning Systems, Inertial Navigation and Integration, Navigation and Integration, Wiley,New York, 2001. York, 2001.
Titterton, D.H. Weston, J.L. Titterton, D.H. Weston, J.L. Strapdown Inertial Navigation Strapdown Inertial Navigation TechnologyTechnology. Institution of Electrical . Institution of Electrical Engineers, London 1997Engineers, London 1997