GPS/INS

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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.

Contents

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) [ citation needed ] 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

Related Research Articles

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<span class="mw-page-title-main">Sensor fusion</span> Combining of sensor data from disparate sources

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<span class="mw-page-title-main">UNSW School of Surveying and Geospatial Engineering</span>

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<span class="mw-page-title-main">Inertial navigation system</span> Continuously computed dead reckoning

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The unscented transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that is characterized only in terms of a finite set of statistics. The most common use of the unscented transform is in the nonlinear projection of mean and covariance estimates in the context of nonlinear extensions of the Kalman filter. Its creator Jeffrey Uhlmann explained that "unscented" was an arbitrary name that he adopted to avoid it being referred to as the “Uhlmann filter.”

<span class="mw-page-title-main">Pressure reference system</span> Flight instrument

Pressure reference system (PRS) is an enhancement of the inertial reference system and attitude and heading reference system designed to provide position angles measurements which are stable in time and do not suffer from long term drift caused by the sensor imperfections. The measurement system uses behavior of the International Standard Atmosphere where atmospheric pressure descends with increasing altitude and two pairs of measurement units. Each pair measures pressure at two different positions that are mechanically connected with known distance between units, e.g. the units are mounted at the tips of the wing. In horizontal flight, there is no pressure difference measured by the measurement system which means the position angle is zero. In case the airplane banks (to turn), the tips of the wings mutually change their positions, one is going up and the second one is going down, and the pressure sensors in every unit measure different values which are translated into a position angle.

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A synthetic air data system (SADS) is an alternative air data system that can produce synthetic air data quantities without directly measuring the air data. It uses other information such as GPS, wind information, the aircraft's attitude, and aerodynamic properties to estimate or infer the air data quantities. Though air data includes altitude, airspeed, pressures, air temperature, Mach number, and flow angles, existing known SADS primarily focuses on estimating airspeed, Angle of Attack, and Angle of sideslip. SADS is used to monitor the primary air data system if there is an anomaly due to sensor faults or system faults. It can also be potentially used as a backup to provide air data estimates for any aerial vehicle.

References

  1. ↑ Grewal, M. S.; L. R. Weill; A. P. Andrew (2007). Global Positioning, Inertial Navigation & Integration. New York: John Wiley & Sons.
  2. ↑ Kalman, R. E.; R. S. Bucy (1961). "New Results in Linear Filtering and Prediction Theory". Journal of Basic Engineering. 83: 95–108. doi:10.1115/1.3658902. S2CID   8141345.
  3. ↑ Julier, S.; J. Uhlmann (1997). "New extension of the Kalman filter to nonlinear systems". In Kadar, Ivan (ed.). Signal Processing, Sensor Fusion, and Target Recognition VI. Vol. 3068. pp. 182–193. doi:10.1117/12.280797. S2CID   7937456.
  4. ↑ Crassidis, J. L. (2005). "Sigma-Point Kalman Filtering for Integrated GPS and Inertial Navigation". AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, CA. doi:10.2514/6.2005-6052. ISBN   978-1-62410-056-7. S2CID   12664565.
  5. ↑ Fiorenzani, T.; et al. (2008). "Comparative Study of Unscented Kalman Filter and Extended Kalman Filter for Position/Attitude Estimation in Unmanned Aerial Vehicles". Iasr-CNR. 08–08.
  6. ↑ Wendell, J.; J. Metzger; R. Moenikes; A. Maier; G. F. Trommer (2006). "A Performance Comparison of Tightly Coupled GPS/INS Navigation Systems Based on Extended and Sigma-Point Kalman Filters". Journal of the Institute of Navigation. 53 (1).
  7. ↑ El-Sheimy, Naser; Eun-Hwan Shin; Xiaoji Niu (March 2006). "Kalman Filter Face-Off: Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial". Inside GNSS : 48–54.
  8. ↑ St. Pierre, M.; D. Ing (June 2004). "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.
  9. ↑ Gross, Jason; Yu Gu; Srikanth Gururajan; Brad Seanor; Marcello R. Napolitano (August 2010). "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. doi:10.2514/6.2010-8332. ISBN   978-1-60086-962-4.
  10. ↑ Gross, Jason N.; Yu Gu; Matthew Rhudy; Srikanth Gururajan; Marcello Napolitano (July 2012). "Flight Test Evaluation of GPS/INS Sensor Fusion Algorithms for Attitude Estimation". IEEE Transactions on Aerospace and Electronic Systems. 48 (3): 2128–2139. doi:10.1109/taes.2012.6237583. S2CID   393165.
  11. ↑ Rhudy, Matthew; Yu Gu; Jason Gross; Marcello Napolitano (August 2011). "Sensitivity Analysis of EKF and UKF in GPS/INS Sensor Fusion". AIAA Guidance, Navigation, and Control Conference, Portland, OR. doi:10.2514/6.2011-6491. ISBN   978-1-60086-952-5.
  12. ↑ Rhudy, Matthew; Yu Gu; Jason Gross; Marcello R. Napolitano (December 2011). "Evaluation of Matrix Square Root Operations for UKF within a UAV-Based GPS/INS Sensor Fusion Application". International Journal of Navigation and Observation. 2011. doi: 10.1155/2011/416828 .
  13. ↑ Petovello, M. G.; M. E. Cannon; G. Lachapelle; J. Wang; C. K. H. Wilson; O. S. Salychev; V. V. Voronov (September 2001). "Development and Testing of a Real-Time GPS/INS Reference System for Autonomous Automobile Navigation". Proc. Of ION GPS-01, Salt Lake City, UT.
  14. ↑ El-Sheimy, Naser; Eun-Hwan Shin; Xiaoji Niu (March 2006). "Kalman Filter Face-Off: Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial". Inside GNSS : 48–54.
  15. ↑ Ryu, Jihan; J. Christian Gerdes (June 2004). "Integrating Inertial Sensors With Global Positioning System (GPS) for Vehicle Dynamics Control". Journal of Dynamic Systems, Measurement, and Control. 126 (2): 243–254. doi:10.1115/1.1766026.
  16. ↑ Bevly, David M.; Jihan Ryu; J. Christian Gerdes (December 2006). "Integrating INS Sensors With GPS Measurements for Continuous Estimation of Vehicle Sideslip, Roll, and Tire Cornering Stiffness". IEEE Transactions on Intelligent Transportation Systems. 7 (4): 483–493. doi:10.1109/tits.2006.883110. S2CID   206739497.
  17. ↑ Ryu, Jihan; Eric J. Rosseter; J. Christian Gerdes (2002). "Vehicle Sideslip and Roll Parameter Estimation Using GPS". AVED 2002 6th Int. Symposium on Advanced Vehicle Control, Hiroshima, Japan.
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