Adaptive-Horizon Iterative UFIR Filtering Algorithm with Applications

The unbiased finite impulse response (UFIR) filter has strong engineering features for industrial applications, because it does not require the noise statistics and initial values. This filter minimizes the mean square error (MSE) on the optimal horizon of Nopt points and the real-time determination of <formula><tex>$N_\mathrm{opt}$</tex></formula> is an important issue. In this paper, a new strategy is proposed to adaptively estimate <formula><tex>$N_\mathrm{opt}$</tex></formula> in real time. A concept of the maximum allowed horizon is introduced referring to the fact that the current iteration with large horizon contains data from the previous iterations with small horizons. That allows selecting the target horizon in a single cycle of iterations and design the adaptive-horizon UFIR (AUFIR) filter. The proposed AUFIR filter is tested by a rotary pendulum system and a three degree-of-freedom helicopter system. Higher accuracy and robustness of the AUFIR filter are demonstrated in a comparison with the Kalman filter (KF), adaptive KF, and UFIR filter.