Fast recursive total least squares algorithm for adaptive FIR filtering with input and output noises: coordinate relaxation approach

A computationally efficient recursive total least squares (RTLS) algorithm is developed for iteratively computing the TLS solution for adaptive FIR filtering with input and output noises. The developed algorithm is aimed at searching the minimum of the so-called constrained Rayleigh quotient (c-RQ) in which the last entry of the parameter vector is constrained to the negative one. The high computational efficiency of the developed algorithm is obtained by searching the minimal point of c-RQ alternately along every coordinate direction and using the well-known fast gain vector. In particular, the developed algorithm involves only the 8N + 19 MADs (number of multiplies, divides, and square roots). The performances of the developed algorithm are compared with the IP (inverse power iteration) and the well-known RLS algorithms via computer simulations.