Direct Identification of Optimal SM-LPV Filters and Application to Vehicle Yaw Rate Estimation

In the literature on filter design, the system whose variables have to be estimated is assumed to be known. However, in most practical applications, this assumption does not hold, and a two-step approach is adopted: (1) a model is identified from data and (2) a filter is designed from the identified model. In this paper, a new approach, based on the direct identification of the filter from data, is considered. Such a direct approach is simpler and, especially in the presence of modeling uncertainty, more accurate than the two-step approach. A Set Membership (SM) method is developed, which allows the design of optimal filters for linear parametrically varying systems. The method is applied to estimation of vehicle yaw rate, a variable used by safety control systems to improve the vehicle stability. This application is interesting from an industrial point of view, since the availability of accurate yaw rate estimators, eliminating the need of the expensive physical sensors, could allow a significant cost reduction and, consequently, a larger diffusion of safety control systems.