A new approach to optimal filter design for nonlinear systems

Optimal filters for nonlinear systems are in general difficult to derive or implement. The common approach is to use approximate solutions such as extended Kalman filters, ensemble filters or particle filters. However, no optimality properties can be guaranteed by these approximations, even the stability of the estimation error cannot often be ensured. Another relevant issue is that, in most practical situations, the system to filter is not known. In these situations, a two-step procedure is typically adopted, based on model identification from data and filter design from the identified model. However, the designed filter may display large performance deteriorations in the case of modeling errors. In this paper, a new approach overcoming these problems is proposed, allowing the design of optimal filters for nonlinear systems in both the cases of known and unknown system. The approach is based on the direct filter design from a set of data generated by the system. Simulated data are used if the system equations are known, experimental data are used otherwise. A bound on the number of data necessary to ensure a given filter accuracy is also provided, showing that the proposed approach is not affected by the curse of dimensionality.