Efficient recursive in order least squares FIR filtering and prediction

This paper is concerned with the efficient determination of the optimum, in the least squares sense, FIR filter on the basis of data samples of the input and desired response signals, by procedures recursive in the filter order. This situation typically arises when no a priori statistics are available and the system order is not known. The general multiinput-multioutput (multichannel) case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2S + 15m multiplications (mps) per order m, S being the number of samples. In the special case of linear prediction it calls for about S + 12m mps. Hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of Marple [1] and Morf et al. [2], respectively. Additionally, the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter.