Nonlinear State Estimation using Gaussian Integral

TL;DR

This paper introduces a novel nonlinear state estimation method that approximates nonlinear functions with Taylor series, uses Gaussian integrals for calculations, and outperforms existing filters in accuracy.

Contribution

A new filtering technique employing polynomial approximation and Gaussian integrals for improved nonlinear state estimation accuracy.

Findings

Outperforms cubature Kalman filter and unscented Kalman filter in simulations

Provides more accurate state estimates in nonlinear problems

Uses Taylor series expansion for nonlinear function approximation

Abstract

In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in nature. However, in this work, they are assumed as Gaussian and subsequently mean, and covariance of them are calculated. In the proposed method, nonlinear functions of process dynamics and measurement are expressed in a polynomial form with the help of 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 help of Gaussian integral. The performance of the proposed method is tested in two nonlinear state estimation problems. The simulation results show that the proposed filter provides more accurate result than other existing deterministic sample point filters such as cubature Kalman filter, unscented Kalman filter, etc.