Direct identification of optimal filters for LPV systems

Direct identification of filters for linear parameter varying (LPV) systems is considered. In the literature on filter design, the system whose state has to be estimated is usually assumed known. However, in most applications, this assumption does not hold, and a two-step procedure is adopted: 1) an LPV model is identified from a set of noise-corrupted data; 2) on the basis of the identified model, an LPV Kalman filter is designed. In this paper, the idea of directly identifying the LPV filter from data is investigated. In previous works by the authors, it has been shown that the direct identification may be more convenient than the two-step design. In some of these works, optimal filter design techniques for time invariant systems have been developed. In the present paper, an approach for the direct identification of optimal filters for LPV systems is proposed. The approach is developed within a Set Membership framework and optimality refers to minimizing the worst-case estimation error.