An efficient approach to highly non-linear estimation

This paper presents the theoretical development of a nonlinear adaptive filter based on a concept of filtering by approximated densities (FAD). The most common procedures for nonlinear estimation apply the extended Kalman filter. As opposed to conventional techniques the proposed recursive algorithm does not require any linearisation. The prediction uses a maximum entropy subject to constraints. Thus, the densities created are of an exponential type and depend on a finite number of parameters. The filtering yields recursive equations involving these parameters. The update applies the Bayes´ theorem. Through simulation on a generic exponential model, the proposed nonlinear filter proves to be superior to the extended Kalman filter and a class of nonlinear filters based on the partitioning algorithm.