GPS,%20Inertial%20Navigation%20and%20LIDAR%20Sensors

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GPS, Inertial Navigation and LIDAR Sensors

• Brian Clipp
• Urban 3D Modeling
• 9/26/06

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Introduction

• GPS- The Global Positioning System
• Inertial Navigation
• Accelerometers
• Gyroscopes
• LIDAR- Laser Detection and Ranging
• Example Systems

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The Global Positioning System

• Constellation of 24 satellites operated by the
  U.S. Department of Defense
• Originally intended for military applications but
  extended to civilian use

• Each satellites orbital period is 12 hours
• 6 satellites visible in each hemisphere

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GPS Operating Principles

• Position is determined by the travel time of a
  signal from four or more satellites to the
  receiving antenna

• Three satellites for X,Y,Z position, one
  satellite to cancel out clock biases in the
  receiver

Image Source NASA
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Time of Signal Travel Determination

• Code is a pseudorandom sequence
• Use correlation with receivers code sequence at
  time shift dt to determine time of signal travel

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GPS Signal Formulation
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Signal Charcteristics

• Code and Carrier Phase Processing
• Code used to determine users gross position
• Carrier phase difference can be used to gain more
  accurate position
• Timing of signals must be known to within one
  carrier cycle

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Triangulation Equations Without Error
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Sources Of Error

• Geometric Degree of Precision (GDOP)
• Selective Availability
• Discontinued in 5/1/2000
• Atmospheric Effects
• Ionospheric
• Tropospheric
• Multipath
• Ephemeris Error
• (satellite position data)
• Satellite Clock Error
• Receiver Clock Error

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Geometric Degree of Precision (GDOP)

• Relative geometry of satellite constellation to
  receiver
• With four satellites best GDOP occurs when
• Three satellites just above the horizon spaced
  evenly around the compass
• One satellite directly overhead
• Satellite selection minimizes GDOP error

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Good Geometric Degree of Precision
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Bad Geometric Degree of Precision
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Pseudorange Measurement

• Single satellite pseudorange measurement

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Error Mitigation Techniques

• Carriers at L1 and L2 frequencies
• Ionospheric error is frequency dependent so using
  two frequencies helps to limit error
• Differential GPS
• Post-Process user measurements using measured
  error values
• Space Based Augmentation Systems(SBAS)
• Examples are U.S. Wide Area Augmentation System
  (WAAS), European Geostationary Navigational
  Overlay Service (EGNOS)
• SBAS provides atmospheric, ephemeris and
  satellite clock error correction values in real
  time

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Differential GPS

• Uses a GPS receiver at a fixed, surveyed location
  to measure error in pseudorange signals from
  satellites
• Pseudorange error for each satellite is
  subtracted from mobile receiver before
  calculating position (typically post processed)

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Differential GPS
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WAAS/EGNOS

• Provide corrections based on user position
• Assumes atmospheric error is locally correlated

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Inertial Navigation

• Accelerometers measure linear acceleration
• Gyroscopes measure angular velocity

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Accelerometer Principles of Operation

• Newtons Second Law
• F mA
• Measure force on object of known mass (proof
  mass) to determine acceleration

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Example Accelerometers

• Force Feedback Pendulous Accelerometer

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Example Accelerometers

• Micro electromechanical device (MEMS) solid state
  silicon accelerometer

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Accelerometer Error Sources

• Fixed Bias
• Non-zero acceleration measurement when zer0
  acceleration integrated
• Scale Factor Errors
• Deviation of actual output from mathematical
  model of output (typically non-linear output)
• Cross-Coupling
• Acceleration in direction orthogonal to sensor
  measurement direction passed into sensor
  measurement (manufacturing imperfections,
  non-orthogonal sensor axes)
• Vibro-Pendulous Error
• Vibration in phase with pendulum displacement
• (Think of a child on a swing set)
• Clock Error
• Integration period incorrectly measured

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Gyroscope Principles of Operation

• Two primary types
• Mechanical
• Optical
• Measure rotation w.r.t. an inertial frame which
  is fixed to the stars (not fixed w.r.t. the
  Earth).

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Mechanical Gyroscopes

• A rotating mass generates angular momentum which
  is resistive to change or has angular inertia.
• Angular Inertia causes precession which is
  rotation of the gimbal in the inertial coordinate
  frame.

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Equations of Precession

• Angular Momentum vector H
• Torque vector T

• Torque is proportional to
• Angular Rate omega cross H plus
• A change in angular momentum

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Problems with Mechanical Gyroscopes

• Large spinning masses have long start up times
• Output dependent on environmental conditions
  (acceleration, vibration, sock, temperature )
• Mechanical wear degrades gyro performance
• Gimbal Lock

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Gimbal Lock

• Occurs in two or more degree of freedom (DOF)
  gyros
• Planes of two gimbals align and once in alignment
  will never come out of alignment until separated
  manually
• Reduces DOF of gyroscope by one
• Alleviated by putting mechanical limiters on
  travel of gimbals or using 1DOF gyroscopes in
  combination

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Gimbal Lock
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Optical Gyroscope

• Measure difference in travel time of light
  traveling in opposite directions around a
  circular path

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Types

• Ring Laser Gyroscope
• Fiber Optic

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Ring Laser Gyro

• Change in traveled distance results in different
  frequency in opposing beams
• Red shift for longer path
• Blue shift for shorter path
• For laser operation peaks must reinforce each
  other leading to frequency change.

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Lock In and Dithering

• Lasers tend to resist having two different
  frequencies at low angular rates
• Analogous to mutual oscillation in electronic
  oscillators
• Dithering or adding some small random angular
  accelerations minimizes time gyro is in locked in
  state reducing error

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Fiber Optic Gyroscope

• Measure phase difference of light traveling
  through fiber optic path around axis of rotation

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Example Complete GPS/INS System

• Applanix POS LV-V4
• Used in Urbanscape Project
• Also includes wheel rate sensor

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Pulse LIDAR

• Measures time of flight of a light pulse from an
  emitter to an object and back to determine
  position.
• Sensitive to atmospheric effects such as dust and
  aerosols

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Conceptual Drawing
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The Math

• d Distance from emitter/receiver to target
• C speed of light (299,792,458 m/s in a vacuum)
• ?t time of flight

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Determining Time of Flight
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From Depth to 3D

• Use angle of reflecting mirror to determine ray
  direction
• Measurement is 3D relative to LIDAR sensor frame
  of reference
• Transform into world frame using GPS/INS system
  or known fixed location

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Error Sources

• Aerosols and Dust
• Scatter Laser reducing signal strength of Laser
  reaching target
• Laser reflected to receiver off of dust
  introduces noise
• Minimally sensitive to temperature variation
  (changes path length inside of receiver and clock
  oscillator rate)
• Error in measurement of rotating mirror angle
• Specular Surfaces
• Clock Error

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Example Pulse LIDAR Characteristics

• Sample specification from SICK

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Doppler LIDAR

• Uses a continuous beam to measure speed
  differential of target and emitter/receiver
• Measure frequency change of reflected light
• Blue shift- target and LIDAR device moving closer
  together
• Red shift- target and LIDAR device moving apart

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Application of Doppler LIDAR

• Speed Traps

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Combined Sensor Systems
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Questions?
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References

• Grewal, M. Weil, L, Andrews, P. Global
  Positioning Systems, Inertial Navigation and
  Integration, Wiley,New York, 2001.
• Titterton, D.H. Weston, J.L. Strapdown Inertial
  Navigation Technology. Institution of Electrical
  Engineers, London 1997