REPORT barber:rr05-71/IDIAP Construction and comparison of approximations for switching linear gaussian state space models Barber, David EXTERNAL PUBLIC Idiap-RR-71-2005 2005 IDIAP 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.