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 N_opt points, and the determination of N_opt is an important issue. In this paper, a new strategy is proposed to adaptively estimate N_opt 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 selection of the target horizon in a single cycle of iterations and a design of the adaptive-horizon UFIR (AUFIR) filter. The proposed AUFIR filter is tested by a rotary pendulum system and a 3-degree-of-freedom (DOF) 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.