Dr Christopher Renton

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

Jump Markov linear systems (JMLS) are a useful model class for capturing abrupt changes in system behaviour that are temporally random, such as when a fault occurs. In many situations, accurate knowledge of the model is not readily available and can be difficult to obtain based on first principles. This paper presents a method for learning parameter values of this model class based on available input¿output data using the maximum-likelihood framework. In particular, the expectation¿maximisation method is detailed for this model class with attention given to a deterministic and numerically stable implementation. The presented algorithm is compared to state-of-the-art methods on several simulation examples with favourable results.