A new method for nonlinear state estimation problem

Abstract

In this paper, a new filtering technique to solve a nonlinear state estimation problem has been developed with the help of the Gaussian integral. It is well known that for a nonlinear system, the prior and the posterior probability density functions (pdfs) are non-Gaussian in nature. However, in this work, they are assumed to be Gaussian; subsequently, the mean and the covariance are calculated. In the proposed method, nonlinear functions of process dynamics and measurements are expressed in a polynomial form with the help of the Taylor series expansion. In order to calculate the prior and the posterior mean and covariance, the functions are integrated over the Gaussian pdf with the Gaussian integral. The performance of the proposed method is tested on three nonlinear state estimation problems. The simulation results show that the proposed filter provides more accurate results than other existing deterministic sample point filters such as the cubature Kalman filter, the unscented Kalman filter, and the Gauss-Hermite filter.