A robust approach to sigma point Kalman filtering

TL;DR

This paper introduces a robust nonlinear state estimation method using sigma point approximation and MCMC simulation to handle model uncertainty, outperforming existing filters in numerical tests.

Contribution

It presents a novel robust sigma point Kalman filter that incorporates a minimax game framework and MCMC simulation for non-Gaussian models.

Findings

The proposed filter outperforms existing filters in numerical examples.

A sigma point approximation effectively characterizes the estimator.

MCMC simulation generates data from complex models.

Abstract

In this paper, we address a robust nonlinear state estimation problem under model uncertainty by formulating a dynamic minimax game: one player designs the robust estimator, while the other selects the least favorable model from an ambiguity set of possible models centered around the nominal one. To characterize a closed-form expression for the conditional expectation characterizing the estimator, we approximate the center of this ambiguity set by means of a sigma point approximation. Furthermore, since the least favorable model is generally nonlinear and non-Gaussian, we derive a simulator based on a Markov chain Monte Carlo method to generate data from such model. Finally, some numerical examples show that the proposed filter outperforms the existing filters.