An adaptive recursive filter.

An adaptive recursive digital filter is presented in which feedback and feedforward gains are adjusted adaptively to minimize a least square performance function on a sliding window averaging process. A two-dimensional version of the adaptive filter is developed and its performance compared with the optimal Wiener filter. The filter is shown to be effective in separating three diagonal trajectory streaks from a background of correlated noise added to white noise. Although the recursive adaptive filter approaches the optimal Wiener filter in performance, it does not require a priori statistical knowledge as does the Wiener filter to which it is compared. The results indicate that the recursive adaptive filter "learns" the statistics and adapts.