  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.
