A generalized algorithm for nonlinear state estimation using extended UFIR filtering

The unbiased finite impulse response (UFIR) filter provides better accuracy when the noise statistics are not fully known. Based on the UFIR approach, a generalized algorithm is developed for extended UFIR (EFIR) filtering of nonlinear models in discrete time state space. As well as the UFIR filter, the EFIR filter completely ignore the noise statistics and requires an optimal averaging horizon of N_opt points. The optimal horizon can be determined via measurements with much smaller efforts and cost than for the noise statistics. These properties of EFIR filtering are distinctive advantages against the extended Kalman filter (EKF). Extensive simulations confirm that the proposed iterative EFIR filtering algorithm is more successful in accuracy and more robust than EKF under the unknown noise statistics and model uncertainties.