Efficient order recursive algorithms for multichannel least squares filtering

Four efficient order-recursive algorithms for least-squares (LS) multichannel FIR filtering and multivariable system identification are developed. The need for such algorithms arises when the system model assigns an unequal number of delay elements to each input channel. All proposed schemes provide considerable improvements over overparametrization or the zero padding approach. First, a block-structures algorithm is derived. It operates on boxes, or blocks, whose dimensions successively increase until their size equals the number of input channels. As a result, it requires linear system solvers and matrix multiplications. The second algorithm manages to get free of block operations by proper decomposition of each block step involved in the first method into a number of scalar steps equal to the size of the block. The third and the fourth algorithms provide highly concurrent alternatives that reduce processing time by an order magnitude. An illustrative example from multichannel autoregressive spectral estimation is supplied