Abstract

We show how many different variants of Switching Kalman Filter models can be represented in a unified way, leading to a single, general-purpose inference algorithm. We then show how to find approximate Maximum Likelihood Estimates of the parameters using the EM algorithm, extending previous results on learning using EM in the non-switching case [DRO93, GH96a] and in the switching, but fully observed, case [Ham90]. 1 Introduction Dynamical systems are often assumed to be linear and subject to Gaussian noise. This model, called the Linear Dynamical System (LDS) model, can be defined as x t = A t x t\Gamma1 + v t y t = C t x t +w t where x t is the hidden state variable at time t, y t is the observation at time t, and v t ¸ N(0; Q t ) and w t ¸ N(0; R t ) are independent Gaussian noise sources. Typically the parameters of the model \Theta = f(A t ; C t ; Q t ; R t )g are assumed to be time-invariant, so that they can be estimated from data using e.g., EM [GH96a]. One of the main adva...

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