An approach to nonlinear state estimation using extended FIR filtering

A new technique called extended finite impulse response (EFIR) filtering is developed to nonlinear state estimation in discrete time state space. The EFIR filter belongs to a family of unbiased FIR filters which completely ignore the noise statistics. An optimal averaging horizon of N_opt points required by the EFIR filter 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). A payment for this is an N_opt - 1 times longer operation which, however, can be reduced to that of the EKF by using parallel computing. Based on extensive simulations of diverse nonlinear models, we show that EFIR filtering is more successful in accuracy and more robust than EKF under the unknown noise statistics and model uncertainties.