A new approach to optimal nonlinear filtering

The classical approach to designing filters for systems where system equations are linear and measurement equations are nonlinear is to linearise measurement equations, and apply an extended Kalman filter (EKF). This results in suboptimal, biased, and often divergent filters. Many schemes proposed to improve the performance of the EKF concentrated on better linearisation techniques, iterative techniques and adaptive schemes. The improvements achieved were marginal and often reduced the bias and divergence problems but were far from optimal unbiased estimators. In this paper, we present a new approach to optimal nonlinear filtering in linear systems-nonlinear measurements case. It is based on approximation of evolved probability density functions using quasi-moments followed by numerical evaluation of Bayes´ conditional density equation