Expectation Correction for Smoothed Inference in Switching Linear Dynamical Systems

David Barber; 7(Nov):2515--2540, 2006.


We introduce a method for approximate smoothed inference in a class of switching linear dynamical systems, based on a novel form of Gaussian Sum smoother. This class includes the switching Kalman 'Filter' and the more general case of switch transitions dependent on the continuous latent state. The method improves on the standard Kim smoothing approach by dispensing with one of the key approximations, thus making fuller use of the available future information. Whilst the central assumption required is projection to a mixture of Gaussians, we show that an additional conditional independence assumption results in a simpler but accurate alternative. Our method consists of a single Forward and Backward Pass and is reminiscent of the standard smoothing 'correction' recursions in the simpler linear dynamical system. The method is numerically stable and compares favourably against alternative approximations, both in cases where a single mixture component provides a good posterior approximation, and where a multimodal approximation is required.


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