Recursive ldentification algorithm based on gradient method with application to adaptive bit detector

Because of its rapid convergence the recursive least squares (RLS) method is one of the most popular approaches to adjusting the coefficients of adaptive digital filters. The RLS method is, however, not always effective in practical applications where finite input‐output data are used because it is based on the matrix inversion lemma. The purpose of this paper is to present a new recursive algorithm to obtain the least square estimate of digital filter coefficient parameters on the basis of a finite number of data up to the present by incorporating a gradient approach in solving the normal equation. Although the proposed method is recursive, since it obtains the least square estimate by batch processing of data, it has batch processing merits which are not found in RLS, such as robustness against colored input and noise and smooth convergence to the real value. A method of automatically adjusting the tracking characteristic to time‐variable parameters is described and the effectiveness of this method is examined for the configuration of the FIR adaptive digital filter and the adaptive configuration of the bit detector.