On the Kalman filter with possibly degenerate and correlated errors Original Research Article

The Kalman filter is a very popular tool for estimation and prediction in the context of a state-space model. Sometimes it is necessary to formulate the state-space model in such a way that the model errors are correlated. The error dispersion matrix may even be singular. In this paper we establish a connection between prediction in the state-space model in this general set-up, and estimation in the general linear model. Subsequently we use the update equations in the general linear model to derive a generalization of the Kalman filter.