Localizing, forgetting, and likelihood filtering in state-space models

The context of this paper are cycle-free factor graphs such as hidden Markov models or linear state space models. The paper offers some observations and suggestions on ldquolocalizatingrdquo such models and their likelihoods. First, it is suggested that a localized version of the model likelihood, which is easily computed by forward sum-product message passing, may be useful for feature extraction and detection. Second, the notion of a ldquolocalrdquo model (local factor graph) is introduced. A first class of local models arises from exponential message damping and scale factors as in recursive least squares. A second class of local models arises from the problem of estimating the moment of a model switch from some known model A to some known model B. This problem can be solved by forward sum-product message passing in model A and backward sum-product message passing in model B. It is pointed out that this method is applicable to pulse position estimation for any pulse with a (deterministic or stochastic) state space model.