Expectation Correction for an augmented class of Switching Linear Gaussian Models

We consider approximate inference in a class of switching linear Gaussian State Space models which includes the switching Kalman Filter and the more general case of switch transitions dependent on the continuous hidden state. The method is a novel form of Gaussian sum smoother consisting of a single forward and backward pass, and compares favourably against a range of competing techniques, including sequential Monte Carlo and Expectation Propagation.