A new smoothing algorithm for jump Markov linear systems

This paper presents a method for calculating the smoothed state distribution Jump Markov Linear Systems. More specifically, details novel two-filter smoother that provides closed-form expressions hybrid distribution. can be expressed as Gaussian mixture with known, but exponentially increasing, number of components time index increases. is accompanied by exponential growth in memory and computational requirements, which rapidly becomes intractable. To ameliorate this, we limit allowed terms employing likelihood reduction strategy, results computationally tractable, approximate The approximation error balanced against complexity order to provide an accurate practical smoothing algorithm compares favourably existing state-of-the-art approaches.