Switching Kalman Filters (SKF) are well known for solving switching linear dynamic system (SLDS), i.e., piecewise linear estimation problems. Practical SKFs are heuristic, approximate filters and require more computational resources than a single-mode Kalman filter (KF). On the other hand, applying a single-mode mismatched KF to an SLDS results in erroneous estimation. This paper quantifies the average error an SKF can eliminate compared to a mismatched, single-mode KF before collecting measurements. Derivations of 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.
The computation required for a switching Kalman Filter (SKF) increases exponentially with the number of system operation modes. In this paper, a computationally tractable graph representation is proposed for a switching linear dynamic system (SLDS) along with the solution of a minimum-sum optimization problem for clustering to reduce the switching mode cardinality offline, before collecting measurements. It is shown that upon perfect mode detection, the induced error caused by mode clustering can be quantified exactly in terms of the dissimilarity measures in the proposed graph structure. Numerical results verify that clustering based on the proposed framework effectively reduces model complexity given uncertain mode detection and that the induced error can be well approximated if the underlying assumptions are satisfied.
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