Recursive total-least-squares adaptive filtering

In this paper a recursive total least squares (RTLS) adaptive filter is introduced and studied. The TLS approach is more appropriate and provides more accurate results than the LS approach when there is error on both sides of the adaptive filter equation; for example, linear prediction, AR modeling, and direction finding. The RTLS filter weights are updated in time O(mr) where m is the filter order and r is the dimension of the tracked subspace. In conventional adaptive filtering problems, r equals 1, so that updates can be performed with complexity O(m). The updates are performed by tracking an orthonormal basis for the smaller of the signal or noise subspaces using a computationally efficient subspace tracking algorithm. The filter is shown to outperform both LMS and RLS in terms of tracking and steady state tap weight error norms. It is also more versatile in that it can adapt its weight in the absence of persistent excitation, i.e., when the input data correlation matrix is near rank deficient. Through simulation, the convergence and tracking properties of the filter are presented and compared with LMS and RLS.