Higher-Degree Stochastic Integration Filtering

TL;DR

This paper introduces higher-degree stochastic integration filters (SIF) for nonlinear Bayesian filtering, utilizing stochastic spherical-radial rules to achieve more accurate Gaussian integral evaluations, outperforming existing methods.

Contribution

The paper develops a novel fifth-degree SIF based on stochastic spherical-radial integration rules for improved nonlinear filtering accuracy.

Findings

Fifth-degree SIF outperforms existing stochastic and cubature filters.

The proposed method achieves asymptotically exact Gaussian integral evaluations.

Numerical comparisons demonstrate superior performance of the new filter.

Abstract

We obtain a class of higher-degree stochastic integration filters (SIF) for nonlinear filtering applications. SIF are based on stochastic spherical-radial integration rules that achieve asymptotically exact evaluations of Gaussian weighted multivariate integrals found in nonlinear Bayesian filtering. The superiority of the proposed scheme is demonstrated by comparing the performance of the proposed fifth-degree SIF against a number of existing stochastic, quasi-stochastic and cubature (Kalman) filters. The proposed filter is demonstrated to outperform existing filters in all cases.