Title: GPS,%20Inertial%20Navigation%20and%20LIDAR%20Sensors
1GPS, Inertial Navigation and LIDAR Sensors
- Brian Clipp
- Urban 3D Modeling
- 9/26/06
2Introduction
- GPS- The Global Positioning System
- Inertial Navigation
- Accelerometers
- Gyroscopes
- LIDAR- Laser Detection and Ranging
- Example Systems
3The 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
4GPS 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
5Time 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
6GPS Signal Formulation
7Signal 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
8Triangulation Equations Without Error
9Sources 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
10Geometric 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
11Good Geometric Degree of Precision
12Bad Geometric Degree of Precision
13Pseudorange Measurement
- Single satellite pseudorange measurement
14Error 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
15Differential 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)
16Differential GPS
17WAAS/EGNOS
- Provide corrections based on user position
- Assumes atmospheric error is locally correlated
18Inertial Navigation
- Accelerometers measure linear acceleration
- Gyroscopes measure angular velocity
19Accelerometer Principles of Operation
- Newtons Second Law
- F mA
- Measure force on object of known mass (proof
mass) to determine acceleration
20Example Accelerometers
- Force Feedback Pendulous Accelerometer
21Example Accelerometers
- Micro electromechanical device (MEMS) solid state
silicon accelerometer
22Accelerometer 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
23Gyroscope 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).
24Mechanical 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.
25Equations of Precession
- Angular Momentum vector H
- Torque vector T
- Torque is proportional to
- Angular Rate omega cross H plus
- A change in angular momentum
26Problems 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
27Gimbal 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
28Gimbal Lock
29Optical Gyroscope
- Measure difference in travel time of light
traveling in opposite directions around a
circular path
30Types
- Ring Laser Gyroscope
- Fiber Optic
31Ring 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.
32Lock 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
33Fiber Optic Gyroscope
- Measure phase difference of light traveling
through fiber optic path around axis of rotation
34Example Complete GPS/INS System
- Applanix POS LV-V4
- Used in Urbanscape Project
- Also includes wheel rate sensor
35Pulse 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
36Conceptual Drawing
37The Math
- d Distance from emitter/receiver to target
- C speed of light (299,792,458 m/s in a vacuum)
- ?t time of flight
38Determining Time of Flight
39From 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
40Error 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
41Example Pulse LIDAR Characteristics
- Sample specification from SICK
42Doppler 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
43Application of Doppler LIDAR
44Combined Sensor Systems
45Questions?
46References
- 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