A Modified Second-Order Extended Kalman Filter for Positioning

P. Lu, X. Liu, J. Yang, S. Yang

Abstract:	Second-Order Extended Kalman Filter (EKF2) is an elaboration of Extended Kalman Filter (EKF) that takes the nonlinearity of the measurements models into consideration and performances better than EKF in accuracy and filtering, but the computational complexity of EKF2 is larger than EKF. In this paper, a low-complexity second-order extended Kalman filter algorithm (LEKF2) is proposed for GPS positioning having the same performance with EKF2 and almost the same complexity with EKF. The second-order Taylor expansions of measurements are used to derive the algorithm process according the Kalman theory, and then modifying the algorithm process, especially the Kalman Gain matrix and the error covariance matrix, to meet the requirements of stability and computational burden. The computation analyses show that the computations of LEKF2 are greatly reduced, e.g. a reduction of up to about 60% for EKF2 positioning algorithm, which is the same as EKF. The static and dynamic simulations of LEKF2, EKF and EKF2 show that they have similar performance and the second-order algorithms are better than first-order algorithm in filtering. Long time static testing under multipath improve LEKF2 stability and accuracy, meanwhile, dynamic tests under weak signal and multipath show that LEKF2 also does well at filtering. Hence, the proposed algorithm LEKF2 offers potential for low-cost hardware implementation for hybrid positioning and other applications and is greatly light on positioning computational load with a good performance.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	2807 - 2813
Cite this article:	Lu, P., Liu, X., Yang, J., Yang, S., "A Modified Second-Order Extended Kalman Filter for Positioning," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 2807-2813.
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