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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 7905690, 10 pages
https://doi.org/10.1155/2017/7905690
Research Article

An Improved Unscented Kalman Filter for Discrete Nonlinear Systems with Random Parameters

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China
2College of Computer Science and Technology, Southwest University for Nationalities, Chengdu, Sichuan 610041, China

Correspondence should be addressed to Yue Wang; moc.361@100_euygnaw

Received 29 December 2016; Accepted 6 February 2017; Published 26 February 2017

Academic Editor: Delfim F. M. Torres

Copyright © 2017 Yue Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the nonlinear unscented Kalman filtering (UKF) problem for discrete nonlinear dynamic systems with random parameters. We develop an improved unscented transformation by incorporating the random parameters into the state vector to enlarge the number of sigma points. The theoretical analysis reveals that the approximated mean and covariance via the improved unscented transformation match the true values correctly up to the third order of Taylor series expansion. Based on the improved unscented transformation, an improved UKF method is proposed to expand the application of the UKF for nonlinear systems with random parameters. An application to the mobile source localization with time difference of arrival (TDOA) measurements and sensor position uncertainties is provided where the simulation results illustrate that the improved UKF method leads to a superior performance in comparison with the normal UKF method.