A so-called inverse QR algorithm was recently introduced for recursive
adaptive filtering under the exponentially weighted least-squares cri
terion. It has some attractive features, including the absence of inve
rsions. The extension to the multi-channel case does require inversion
however. We present a new derivation of the inverse QR algorithm, bas
ed 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 show
n to directly give (a multi-channel version of) the inverse QR algorit
hm. 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.