Approximate solutions of the nonlinear filtering problem

A comparison of the filter structures resulting from the consideration of different systems, both nonlinear models and linear models with correlated noise sequences, show an interesting similarity. Compared with the Kalman filter, these filter structures cause an apparent change in the linear system matrices, the noise covariance matrices, and in the form of the one-stage prediction. These modifications have interesting implications relative to adaptive filtering methods and system identification techniques.