Abstract
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. A new version of Gaussian sum estimation algorithm is developed here based on high-order unscented Kalman filter (HUKF). A sigma point selection method, high-order unscented transformation (HUT) technique is proposed for the HUKF, which can approximate the Gaussian distributions more accurately. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We then go on to extend the use of the HUKF to discrete-time, nonlinear systems with additive, possibly non-Gaussian noise. The resulting filtering algorithm, called the Gaussian sum high-order unscented Kalman filter (GS-HUKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. It is corroborated in the theoretical analysis and the simulation that the proposed Gaussian sum HUKF has integrated advantages with respect to computational accuracy and time complexity for nonlinear non-Gaussian filtering problems.
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Lei Wang received his M.S. degree from Wuhan University of Science and Technology, China, in 2009. He is currently a teaching assistant at Anhui Science and Technology University and has been pursuing his Ph.D. degree since 2011 at the School of Instrument Science and Engineering, Southeast University, China. His research interests include nonlinear filtering and estimation, sensor fusion, and statistical signal processing.
Xianghong Cheng received her M.S. and Ph.D. degrees both in Precision Instrument and Mechanics from the Southeast University, China, in 1991 and 1998, respectively. She is currently a Professor in the School of Instrument Science and Engineering, Southeast University. As the first author or corresponding author she has published more than 40 peer reviewed technical papers in archival journals and conference proceedings. Her research interests include navigation system, general estimation theory, nonlinear optimal control theory, and nonlinear filtering.
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Wang, L., Cheng, X. Algorithm of gaussian sum filter based on high-order UKF for dynamic state estimation. Int. J. Control Autom. Syst. 13, 652–661 (2015). https://doi.org/10.1007/s12555-014-0114-4
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DOI: https://doi.org/10.1007/s12555-014-0114-4