Robustly optimal filter design for nonlinear systems

A relevant issue in filter design is that, in most practical situations, the system whose variables have to be estimated is not known, and a two-step procedure is adopted, based on model identification from data and filter design from the identified model. However, only approximate models can be identified from real data, and this approximation may lead to large estimation errors. In this paper, a new approach to filter design overcoming this important issue is considered, allowing the design of filters for nonlinear systems with suitable optimality and robustness properties. In particular, it is shown that the approach is intrinsically robust, since based on the direct design of the filter from a set of data generated by the system, avoiding the need of any (approximate) model. A result is also provided, allowing us to evaluate the trade-off between the estimation accuracy and the number of data required for filter design.