A New Sigma-point Filter–Uniform Random Sampling Kalman Filter

Abstract

This paper is motivated by the problem of more accurately estimating the hidden state in nonlinear dynamic system. We propose a uniform random sampling Kalman filter(URSKF) which can be regarded as a Sigma-point filter based on the statistical linearization method. Compared with other Sigma-point filters, the uniform random sampling method used to obtain the deterministic points can match the any-order moment of the prior distribution with the moderately increasing sampling points and automatically capture the more rich statistical properties of the system after nonlinear function mapping. Moreover, the URSKF is a derivative and square-rooting free operation which avoid computing Jacobian matrix and failing the filtering process for not always guaranteeing the covariance matrix to be positive definite, such as UKF. Besides, the computation complexity is linearly related to the system dimension avoiding the curse of high dimension in the Gauss-Hermite Quadratute Filter(GHQF). The performance of this filter is demonstrated by an aircraft tracking model. The simulation results show the URSKF performs higher accurately than the Unscented Kalman Filter(UKF), Central Difference Kalman Filter(CDKF) and Cubature Kalman Filter(CKF).