  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.
