Kalman and Lainiotis Filters for Partially Time-Varying Models

The Kalman and the Lainiotis filters are integral parts of estimation theory, arising in linear estimation. They are related to time-varying state-space models which describe the relation between the state consisting of n elements and the observation (measurement) consisting of m elements. The equivalence of the Kalman and the Lainiotis filters means that they compute iteratively the same estimation statistics, i.e. state estimation and estimation error covariance. It is known from previous works that the time-varying Kalman filter outperforms the time-varying Lainiotis filter, in the sense that it is always faster. In this paper, the partially time-varying state-space models are considered, where the transition matrix is time-varying while the observation (measurement) matrix and the noises covariances are time-invariant. In this case, the Lainiotis filter is likely to be faster than the Kalman filter; in fact, the dimensions of the model determine which filter is the fastest.