Quantification of Mismatch Error in Randomly Switching Linear State-Space Models

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