A numerically stable fast RLS algorithm for adaptive filtering andprediction based on the UD factorization

The use of UD factorization in adaptive RLS algorithms is interesting for its numeric robustness and because no square-root operations at all are involved. We describe a square root free fast RLS algorithm based on the UD factorization of the autocorrelation matrix. Numerous finite precision simulations tend to indicate that this algorithm is numerically stable. The algorithm requires 𝒪(𝒩) operations, where 𝒩 is the linear filter order