Exact analysis of the finite precision error generation and propagation in the FAEST and the fast transversal algorithms: A general methodology for developing robust RLS schemes

A New Multichannel Recursive Least Squares Algorithm for Very Robust and Efficient Adaptive Filtering

“…Updating of the filter coefficients The theoretical justification of the robustness of the algorithm goes beyond the scope of the present paper. It should, however, be mentioned that the new definitions proposed here are made after taking into account the finite precision error sources and error propagation properties of the posteriori RLS computational schemes under the scope of the general methodology introduced in [19][20][21][22][23]. However, the experimental results presented in the next section demonstrate the robustness of the algorithm in comparison to the numerical behavior of most of the previous multichannel RLS schemes.…”

“…Finally, formula (3.47) (or equivalently formula (3.42) demonstrates somewhat worst numerical behavior than the direct matrix inversion. However, it can be stabilized following the general method introduced in [22,23].…”

“…However, the experimental results presented in the next section demonstrate the robustness of the algorithm in comparison to the numerical behavior of most of the previous multichannel RLS schemes. Last, it should be mentioned that the proposed algorithm can be completely stabilized by using the general methodology introduced in [22,23]. Its stable form can run for millions of iterations without showing any sign of breaking.…”

“…And third, the particular structure of this scheme and the choice of the mathematical definitions behind it are made so as to eliminate the sources of generation and propagation of the finite precision error presented in [23]. Thus, the scheme presented here is very robust.…”

“…Moreover, the proposed algorithm can be stabilized by means of the general method introduced in [22,23] and can run for millions of iterations without showing any sign of breaking. It is worthwhile noticing that with this stabilization technique the proposed algorithm can track even nonstationary signals, such as music, speech, and environmental noise, very well without failing due to finite precision error problems.…”