GPS/INS explained

GPS/INS is the use of GPS satellite signals to correct or calibrate a solution from an inertial navigation system (INS). The method is applicable for any GNSS/INS system.

Overview

GPS/INS method

The GPS gives an absolute drift-free position value that can be used to reset the INS solution or can be blended with it by use of a mathematical algorithm, such as a Kalman filter. The angular orientation of the unit can be inferred from the series of position updates from the GPS. The change in the error in position relative to the GPS can be used to estimate the unknown angle error.

The benefits of using GPS with an INS are that the INS may be calibrated by the GPS signals and that the INS can provide position and angle updates at a quicker rate than GPS. For high dynamic vehicles, such as missiles and aircraft, INS fills in the gaps between GPS positions. Additionally, GPS may lose its signal and the INS can continue to compute the position and angle during the period of lost GPS signal. The two systems are complementary and are often employed together.[1]

Applications

GPS/INS is commonly used on aircraft for navigation purposes. Using GPS/INS allows for smoother position and velocity estimates that can be provided at a sampling rate faster than the GPS receiver. This also allows for accurate estimation of the aircraft attitude (roll, pitch, and yaw) angles. In general, GPS/INS sensor fusion is a nonlinear filtering problem, which is commonly approached using the extended Kalman filter (EKF)[2] or the unscented Kalman filter (UKF).[3] The use of these two filters for GPS/INS has been compared in various sources,[4] [5] [6] [7] [8] [9] [10] including a detailed sensitivity analysis.[11] The EKF uses an analytical linearization approach using Jacobian matrices to linearize the system, while the UKF uses a statistical linearization approach called the unscented transform which uses a set of deterministically selected points to handle the nonlinearity. The UKF requires the calculation of a matrix square root of the state error covariance matrix, which is used to determine the spread of the sigma points for the unscented transform. There are various ways to calculate the matrix square root, which have been presented and compared within GPS/INS application.[12] From this work it is recommended to use the Cholesky decomposition method.

In addition to aircraft applications, GPS/INS has also been studied for automobile applications such as autonomous navigation,[13] [14] vehicle dynamics control,[15] or sideslip, roll, and tire cornering stiffness estimation.[16] [17]

See also

References

Notes and References

  1. Book: Grewal, M. S.. Global Positioning, Inertial Navigation & Integration. 2007. John Wiley & Sons. New York. L. R. Weill . A. P. Andrew .
  2. Kalman. R. E.. R. S. Bucy. New Results in Linear Filtering and Prediction Theory. Journal of Basic Engineering. 1961. 83. 95–108. 10.1115/1.3658902. 8141345 .
  3. Julier. S.. J. Uhlmann. A New Extension of the Kalman Filtering to Non Linear Systems. SPIE Proceedings Series. 1997. 3068. 182–193. 10.1117/12.280797. 7937456.
  4. Crassidis. J. L.. Sigma-Point Kalman Filtering for Integrated GPS and Inertial Navigation. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, CA. 2005. 10.2514/6.2005-6052. 978-1-62410-056-7. 12664565.
  5. Fiorenzani. T.. etal. Comparative Study of Unscented Kalman Filter and Extended Kalman Filter for Position/Attitude Estimation in Unmanned Aerial Vehicles. Iasr-CNR. 2008. 08-08.
  6. Wendell. J.. J. Metzger . R. Moenikes . A. Maier . G. F. Trommer . A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems Based on Extended and Sigma-Point Kalman Filters. Journal of the Institute of Navigation. 2006. 53. 1.
  7. El-Sheimy. Naser . Eun-Hwan Shin . Xiaoji Niu. Kalman Filter Face-Off: Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial. Inside GNSS. March 2006. 48–54.
  8. St. Pierre. M.. D. Ing. Comparison between the unscented Kalman filter and the extended Kalman filter for the position estimation module of an integrated navigation information system. 2004 IEEE Intelligent Vehicles Symposium, Parma, Italy. June 2004.
  9. Gross. Jason. Yu Gu . Srikanth Gururajan . Brad Seanor . Marcello R. Napolitano . A Comparison of Extended Kalman Filter, Sigma-Point Kalman Filter, and Particle Filter in GPS/INS Sensor Fusion. AIAA Guidance, Navigation, and Control Conference, Toronto, Canada. August 2010. 10.2514/6.2010-8332. 978-1-60086-962-4.
  10. Gross. Jason N.. Yu Gu . Matthew Rhudy . Srikanth Gururajan . Marcello Napolitano . Flight Test Evaluation of GPS/INS Sensor Fusion Algorithms for Attitude Estimation. IEEE Transactions on Aerospace and Electronic Systems. July 2012. 48. 3. 2128–2139. 10.1109/taes.2012.6237583. 393165.
  11. Rhudy. Matthew. Yu Gu . Jason Gross . Marcello Napolitano . Sensitivity Analysis of EKF and UKF in GPS/INS Sensor Fusion. AIAA Guidance, Navigation, and Control Conference, Portland, OR. August 2011. 10.2514/6.2011-6491. 978-1-60086-952-5.
  12. Rhudy. Matthew. Yu Gu . Jason Gross . Marcello R. Napolitano . Evaluation of Matrix Square Root Operations for UKF within a UAV-Based GPS/INS Sensor Fusion Application. International Journal of Navigation and Observation. December 2011. 2011. 10.1155/2011/416828. free.
  13. Petovello. M. G.. M. E. Cannon . G. Lachapelle . J. Wang . C. K. H. Wilson . O. S. Salychev . V. V. Voronov . Development and Testing of a Real-Time GPS/INS Reference System for Autonomous Automobile Navigation. Proc. Of ION GPS-01, Salt Lake City, UT. September 2001.
  14. El-Sheimy. Naser . Eun-Hwan Shin . Xiaoji Niu. Kalman Filter Face-Off: Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial. Inside GNSS. March 2006. 48–54.
  15. Ryu. Jihan. J. Christian Gerdes. Integrating Inertial Sensors With Global Positioning System (GPS) for Vehicle Dynamics Control. Journal of Dynamic Systems, Measurement, and Control. June 2004. 126. 2. 243–254. 10.1115/1.1766026.
  16. Bevly. David M.. Jihan Ryu . J. Christian Gerdes . Integrating INS Sensors With GPS Measurements for Continuous Estimation of Vehicle Sideslip, Roll, and Tire Cornering Stiffness. IEEE Transactions on Intelligent Transportation Systems. December 2006. 7. 4. 483–493. 10.1109/tits.2006.883110. 206739497.
  17. Ryu. Jihan. Eric J. Rosseter . J. Christian Gerdes . Vehicle Sideslip and Roll Parameter Estimation Using GPS. AVED 2002 6th Int. Symposium on Advanced Vehicle Control, Hiroshima, Japan. 2002.

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