In this correspondence, we propose an efficient estimator of optimal memory (averaging interval) for discrete-time finite impulse response (FIR) filters in state-space. Its crucial property is that only real measurements and the filter output are involved with no reference and noise statistics. Testing by the two-state polynomial model has shown a very good correspondence with predicted values. Even in the worst case of the harmonic model, the estimator demonstrates practical applicability.

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An extended unbiased finite impulse response (EFIR) filtering algorithm is examined for nonlinear discrete-time state-space models corrupted by additive white Gaussian noise. The algorithm is represented in the Kalman-like form ignoring noise statistics and initial errors, provided an averaging interval of N points. The first-order (EFIR1) and second-order (EFIR2) filters are compared to the relevant extended Kalman ones (EKF1 and EKF2) based on an example of 2D tracking. It is shown that EKF and EFIR produce similar errors under the ideal conditions and the former becomes lesser accurate otherwise. The contributions of the second-order expansions are shown to be indefinite.