Quantification of mismatch error in randomly switching linear state-space models

TL;DR

This paper quantifies the expected estimation error reduction of Switching Kalman Filters over mismatched single mode filters in linear dynamic systems, providing mathematical derivations and simulation validation.

Contribution

It introduces a method to analytically quantify the average error difference between SKF and mismatched KF in known systems, aiding filter selection.

Findings

Mathematical expressions for estimator error moments are derived.

Simulations confirm the accuracy of the theoretical error quantifications.

The approach helps optimize filter choice balancing accuracy and computational cost.

Abstract

Switching Kalman Filters (SKF) are well known for their ability to solve the piecewise linear dynamic system estimation problem using the standard Kalman Filter (KF). Practical SKFs are heuristic, approximate filters that are not guaranteed to have optimal performance and require more computational resources than a single mode KF. On the other hand, applying a single mode mismatched KF to a switching linear dynamic system (SLDS) results in erroneous estimation. This paper aims to quantify the average error an SKF can eliminate compared to a mismatched, single mode KF in a known SLDS before collecting measurements. Mathematical derivations for the first and second moments of the estimators errors are provided and compared. One can use these derivations to quantify the average performance of filters beforehand and decide which filter to run in operation to have the best performance in terms of estimation error and computation complexity. We further provide simulation results that verify our mathematical derivations.