On the hierarchical least-squares algorithm

A so-called hierarchical recursive least-squares (HRLS) algorithm was suggested in a recent letter in an attempt to reduce the computational burden and improve the convergence rate of the classical RLS algorithm. The discussion of HRLS in the original letter, however, has several unclear points; in particular no clear explanation was offered for the good simulation results reported. In this letter we provide some analysis of the HRLS to determine when this algorithm may be expected to work or fail. It turns out that the input to the channel must be a white sequence, otherwise HRLS may yield grossly biased estimates of the channel FIR coefficients.