GPS, Inertial Navigation and LIDAR Sensors Brian Clipp Urban 3D Modeling 9/26/06 Introduction GPS- The Global Positioning System Inertial Navigation • Accelerometers • Gyroscopes LIDAR- Laser Detection and Ranging Example.
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GPS, Inertial Navigation and LIDAR Sensors Brian Clipp Urban 3D Modeling 9/26/06 Introduction GPS- The Global Positioning System Inertial Navigation • Accelerometers • Gyroscopes LIDAR- Laser Detection and Ranging Example Systems 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 satellite’s orbital period is 12 hours 6 satellites visible in each hemisphere 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 Time of Signal Travel Determination Code is a pseudorandom sequence Use correlation with receiver’s code sequence at time shift dt to determine time of signal travel GPS Signal Formulation Signal Charcteristics Code and Carrier Phase Processing • Code used to determine user’s gross position • Carrier phase difference can be used to gain more accurate position Timing of signals must be known to within one carrier cycle Triangulation Equations Without Error 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 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 Good Geometric Degree of Precision Horizon Receiver Bad Geometric Degree of Precision Horizon Receiver Pseudorange Measurement Single satellite pseudorange measurement 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 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) Differential GPS WAAS/EGNOS Provide corrections based on user position Assumes atmospheric error is locally correlated Inertial Navigation Accelerometers measure linear acceleration Gyroscopes measure angular velocity Accelerometer Principles of Operation Newton’s Second Law • F = mA Measure force on object of known mass (proof mass) to determine acceleration a Direction of Acceleration w.r.t. Inertial Space Displacement Pickup Proof Mass (m) Spring Case Example Accelerometers Force Feedback Pendulous Accelerometer Sensitive Input Axis Permanent Magnet Restoring Coil Case Hinge Pendulous Arm Pick-Off Excitation Coil Example Accelerometers Micro electromechanical device (MEMS) solid state silicon accelerometer 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 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). 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. Equations of Precession Angular Momentum vector H Torque vector T A δH = Change in angular momentum B SPIN AXIS (at time t) SPIN AXIS (At time t = t + δt) Precession (rate ω) H H DISC O Torque is proportional to • Angular Rate omega cross H plus • A change in angular momentum 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 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 Gimbal Lock Optical Gyroscope Measure difference in travel time of light traveling in opposite directions around a circular path Beam Splitter Position at Y time t = t + δt Light Output Beam Splitter Position at time t = t X Light Input Ω Types Ring Laser Gyroscope Fiber Optic 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. 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 Fiber Optic Gyroscope Fiber Optic Coil Measure phase difference of light traveling through fiber optic path around axis of rotation Ω Coupling Lens Beam Splitter Light Source Detector Example Complete GPS/INS System Applanix POS LV-V4 Used in Urbanscape Project Also includes wheel rate sensor 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 Conceptual Drawing Sensor Case Photo Detector Target Laser Source Half Silvered Mirror Sensor Window Rotating Mirror Rotation Laser Beam The Math d = Distance from emitter/receiver to target C = speed of light (299,792,458 m/s in a vacuum) Δt = time of flight Determining Time of Flight Calculate Cross-Correlation of Measurement and Generated Signal Pulse generated by emitter Signal Magnitude Pulse detected at receiver time t 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 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 Example Pulse LIDAR Characteristics Sample specification from SICK 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 Application of Doppler LIDAR Speed Traps Combined Sensor Systems Questions? 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