A Canonical Space-Time State Space Model: State and Parameter Estimation

The maximum likelihood estimation of a dynamic spatiotemporal model is introduced, centred around the inclusion of a prior arbitrary spatiotemporal neighborhood description. The neighborhood description defines a specific parameterization of the state transition matrix, chosen on the basis of prior knowledge about the system. The model used is inspired by the spatiotemporal ARMA (STARMA) model, but the representation used is based on the standard state-space model. The inclusion of the neighborhood into an expectation-maximization based joint state and parameter estimation algorithm allows for accurate characterization of the spatiotemporal model. The process of including the neighborhood, and the effect it has on the maximum likelihood parameter estimate is described and demonstrated in this paper.