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

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.