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