Direct design of optimal filters from data

In the literature on filter design, the system whose state has to be estimated is usually assumed known. However, in most practical situations, this assumption does not hold, and a two-step procedure is adopted: 1) a model is identified from a set of noise-corrupted data; 2) on the basis of the identified model, a Kalman filter is designed. In this paper, the idea of directly identifying the filter from data is investigated. In previous works by the authors, it has been shown that the direct identification of the filter may be more convenient than the two-step design. In this paper, an approach for the direct design of optimal filters is proposed, where optimality refers to the minimization of a suitable worst-case estimation error. It is also shown that the Kalman filter is a particular case of the proposed approach.