Central Difference Formulation of Risk-Sensitive Filter

A numerically efficient algorithm for risk-sensitive filters (known to be robust to model uncertainties) of nonlinear plants, using central difference approximation is proposed. The proposed filter, termed central difference risk-sensitive filter (CDRSF), overcomes several disadvantages associated with the extended risk-sensitive filter (ERSF), reported earlier. The theory of formulation and the algorithm of the CDRSF are presented. With an example, it is demonstrated that the proposed new filter would give much better tracking performance compared to the ERSF for certain nonlinear systems. The CDRSF would be nearly as fast as the ERSF, thus making it more preferable for real-time applications compared to the risk-sensitive particle filter.