Inertial Navigation Systems and GPS Juan Jacobo Van der Dys April 20 th, 2005.
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Transcript of Inertial Navigation Systems and GPS Juan Jacobo Van der Dys April 20 th, 2005.
Inertial Navigation SystemsandGPS
Juan Jacobo Van der Dys
April 20th, 2005
Outline• Introduction• Inertial Navigation Systems
– Definition– Determining Position– Determining Attitude– Inertial Platforms– Strapdown Systems– Gyro and Accelerometer errors and their
consequences.
• The money issue• Pseudo-attitude from GPS• The Kalman filter.
IntroductionThe five basic forms of navigation are:- Pilotage: Recognizing landmarks to know where you
are. Older than human kind.- Dead reckoning: Knowing where you started from,
some sort of heading and some estimate of speed.- Celestial Navigation: Knowing time and angle between
vertical and celestial objects.- Radio Navigation: rely on radio-frequency sources with
known locations.- Inertial Navigation: Knowing initial position, velocity,
attitude and measuring accelerations and attitude rates to determine position and attitude. No external references.
Inertial Navigation Systems
INS (or INU) = Navigation Computer
+ gyroscopes + acceleration
IMU (or IRU) = Inertial Sensors.
Once aligned to a set of reference axes (North, East, Down) the computer carries out continuous dead-reckoning calculations.
Determining Position
Courtesy of C.F.Savant Jr et. al.
acceleration ∫ ∫ position Newton’s Law
Determining AttitudeBased on Euler Angles
Kinematic differential equations
Courtesy of Wie, Bong
Courtesy of Wie, Bong
Why do we care about attitude?Instrument Flight Rules (IFR): Flying below
minimum weather requirements.
Guidance: Auto-pilots, cruise missiles, precision approaches.
Courtesy of Cessna Aircraft Company
Inertial PlatformsAn inertial platform uses gyros to maintain
accelerometers in a fixed attitude.
Courtesy of Dr. Walter Haussermann,Marshal Space Flight Center
Pros:• Simpler Gyros• Higher Accuracy• Self-alignment by
gyrocompassing• Sensor Calibration by
platform rotationsCons:• Complexity and cost.• Gimbal Mechanics.• Reliability.
Strapdown SystemsThe gyroscopes and accelerometers are rigidly
mounted to the vehicle structure so that they move with the vehicle.
Courtesy of Minneapolis-Honeywell
Pros:• Simpler structure, low cost,
lighter weight.• Ruggedness.• Reliability.Cons:• Alignment.• Sensor calibration.• Motion induced errors.• Strapdown computer.
ERRORS (and consequences)
From Anthony Lawrence “Modern Inertial Technology”
Errors• Scale Factor• Non-linearity• Asymmetry• Bias
– Change over time/temperature
– Tilt misalignment
• Random Drift/Walk• Dead Band, Threshold,
and Resolution• Hysteresis• Gyro acceleration
sensitivity.
From Anthony Lawrence “Modern Inertial Technology”
Precision/Accuracy is $$$• The better the sensor, the more
expensive it is.– Most of the time this also means
size and weight.
From Avidyne Corporation From Raytheon Company
Accumulated error correction• Airspeed/Baro-altitude,
– Δv ~ ∫abias
• Magnetic Field, is constant for short range flights.
• GPS:– Derive position (twice)
to compute acceleration
– Trajectory angle ~ velocity (heading - beta (side slip angle) +
airspeed) + wind.
– Flight path angle ~ pitch angle + alpha (angle of attack)
– In coordinated flight constant heading means zero roll angle.
aXt
2
2
Pseudo Attitude from GPS• Pseudo roll:
• Pseudo pitch:
• Pseudo yaw:Images from the QueenslandUniversity of Technology
The Kalman filter
From Portland State Aerospace Society
The state vector• Θ pitch• Φ roll• Ψ yaw• p• q• r• Xaccel bias• Yaccel bias• Zaccel bias• Xgyro bias• Ygyro bias• Zgyro bias• α angle of attack• β sideslip angle• Airspeed
The Kalman filterSensors:• Accelerometers• Gyros• GPS• Magnetometer• Airdata
Compute the results:– Read the sensors– Estimate signal covariance– Calculate gains– Compute state
Tuning the Kalman filter may be very challenging. Initializing can be tricky.
Conclusion
• GPS is a great aid for INS
• GPS allows engineers use inexpensive sensors and have good accuracy.
• System susceptible to GPS jamming (not liked by FAA).
• Requires lots of computer power.
ReferencesMohinder S. Grewal, "Global Positioning Systems, Inertial
Navigation, and Integration" Wiley-Interscience; Book&Disk edition (December 15, 2000)
Savant, C.F. et al. “Principles of Inertial Navigation” McGraw-Hill (1961)
Wie, Bong “Space Vehicle Dynamics and Control” AIAA Education Series (1998)
www.cessna.comLawrence, Anthony “Modern Inertial Technology” Springer-
Verlag (1993)Shephard, William et al. “Inertial Navigation” D Van
Nostrand Co. (1962)www.raytheon.comwww.bee.qut.edu.auhttp://psas.pdx.eduwww.avidyne.com
Questions?