Generalized Linear and Gaussian State-Space Models

This letter generalizes the classical linear and Gaussian state-space model described by a dynamical and an observation model. We show that this model is actually a particular instance of a more general class of parameterized models based on pairwise Markov chains. The model we propose preserves the local properties of the original model, does not affect its computational properties and relies on additional parameters. These new parameters control some statistical properties related to the original model such as the markovianity of the hidden process or the conditional independence of the observations and facilitate modelling of more complex statistical dependencies. These parameters can be estimated from a sequence of observations and for any application relying on the classical model, we thus provide a more flexible alternative.