# GPS/INS

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

### Problem

Inertial navigation systems usually can provide an accurate solution only for a short period of time. The INS accelerometers produce an unknown bias signal that appears as a genuine specific force. This is acceleration integrated twice against time and thus produces an error in position. Additionally, the INS software must use an estimate of the angular position of the accelerometers when conducting this integration. Typically, the angular position is tracked through an integration of the angular rate from the gyro sensors. These also produce unknown biases that affect the integration to get the position of the unit.

### 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]

## References

• US Patent No. 6900760
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 (Trans. of ASME). 83: 95–108. doi:10.1115/1.3658902.
3. ^ Julier, S.; J. Uhlmann (1997). "A New Extension of the Kalman Filtering to Non Linear Systems". SPIE Proceedings Series. 3068: 182–193.
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.
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.
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.
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.
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: 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 Trans. on Intelligent Transportation Systems. 7 (4): 483–493. doi:10.1109/tits.2006.883110.
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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