An extended inverse QR adaptive filtering algorithm

Abstract

A so-called inverse QR algorithm was recently introduced for recursive adaptive filtering under the exponentially weighted least-squares criterion. It has some attractive features, including the absence of inversions. The extension to the multi-channel case does require inversion however. We present a new derivation of the inverse QR algorithm, based on the technique of Sayed and Kailath, for reformulating the above adaptive filtering problem as a state-space estimation problem. A well-known square-root covariance algorithm for the latter problem is shown to directly give (a multi-channel version of) the inverse QR algorithm. A new extended square-root covariance algorithm is then applied to get a new inversion-free ‘extended inverse QR’ algorithm, even in the multi-channel case.