An Iterated Extended Risk-Sensitive Filters for Nonlinear Filtering Problems

The problem for filtering certain classes of systems which incorporate nonlinear, uncertainty initial condition is addressed. An extended risk-sensitive filter (ERSF) is reexamined and, new iterated version of that ERSF called the iterated extended risk sensitive filters (IERSF) is developed. An ERSF weakness specifically accumulation error in the computing of innovation steps due to approximating nonlinear functions at recently available prior estimate is presented. By using the IERSF with proper tuning of risk factor and local iteration, the filtering divergence may be overcome, and a stable, robust and unbiased estimation is obtained satisfactorily. The performance of IERSF is compared with the performance of ERSF through an application of nonlinear bimodal signal estimation problem. The IERSF results in reduced estimation error without increase in burden of the associated computational algorithm.