Suboptimal FIR Filtering of Nonlinear Models in Additive White Gaussian Noise

The first- and second-order extended finite impulse response (EFIR1 and EFIR2, respectively) filters are addressed for suboptimal estimation of nonlinear discrete-time state-space models with additive white Gaussian noise. It is shown that, unlike the extended Kalman filter (EKF) and EFIR2 filter, the EFIR1 one does not require noise statistics and initial errors. Only within a narrow region around actual noise covariances, EFIR filters fall a bit short of EKF and they demonstrate better performance otherwise. It is shown that the optimal averaging interval for EFIR filters can be determined via measurement without a reference model in a learning cycle. We also notice that the second-order approximation can improve the local performance, but it can also deteriorate it. We thus have no recommendations about its use, at least for tracking considered as an example of applications.