On the computational organization of fast sequential algorithms

Sequential Least-Squares (LS) methods play a prominent role in many digital signal processing applications. The conventional implementation of these schemes requires an amount of operations proportional to the square of the number of estimated parameters. In contrast a variety of existing fast algorithms offer a computational complexity proportional to the number of estimated parameters. Such schemes exist for both direct form and lattice-ladder filter structures. This paper offers a unified overview of fast sequential algorithms for LS FIR filters, implemented using a direct form realization, in the case of prewindowed multichannel signals. Although all these algorithms are theoretically equivalent, in practice they exhibit different performance due to round-off noise, incorrect initialization etc. The performance evaluation of all these shemes is still an area to be explored.