State Estimation for Piecewise Affine State-Space Models

TL;DR

This paper introduces a novel filtering method for piecewise affine state-space models that approximates complex posterior distributions with a single normal distribution, outperforming the extended Kalman filter in simulations.

Contribution

It develops a new filter for PWASS models that uses moment matching to approximate the true posterior, improving estimation accuracy over EKF.

Findings

The proposed filter achieves lower RMSE than EKF in simulations.

The method effectively approximates mixture distributions with a single normal.

Numerical results demonstrate improved state estimation accuracy.

Abstract

We propose a filter for piecewise affine state-space (PWASS) models. In each filtering recursion, the true filtering posterior distribution is a mixture of truncated normal distributions. The proposed filter approximates the mixture with a single normal distribution via moment matching. The proposed algorithm is compared with the extended Kalman filter (EKF) in a numerical simulation where the proposed method obtains, on average, better root mean square error (RMSE) than the EKF.