Efficient block implementation of exact sequential least-squares problems

An efficient blockwise algorithm, namely the block sequential least-squares (BSLS) algorithm, is presented for sequentially solving LS problems in realtime. The information is carried from block to block by iterating some correlation vectors. In the case of successive data blocks, the exactness of the BSLS algorithm is achieved at approximately the same computational requirement as characterizes the nonexact BFTF (block fast transversal filter) algorithm, which is significantly less than sample-by-sample RLS (recursive least squares) algorithms. However, the BSLS cannot accommodate the case of discontinuous blocks of data, which can be accommodated (at the expense of a nonexact solution) by the BFTF. It is shown that the BSLS algorithm allows efficient use of the FFT fast Fourier transform technique to make remarkable gains in computational complexity savings. Additionally, the BSLS algorithm can provide an improved numerical stability over the existing fast RLS algorithms. The numerical performance is illustrated by applications to adaptive equalization and online parameter identification