Reconciling fast RLS lattice and QR algorithms

Traditionally, there have been two groups of fast recursive least squares (RLS) algorithms, the fixed-order fast transversal filter (FTF) algorithms and the order-recursive fast lattice (FLA) algorithms. More recently, a third group of fast RLS algorithms has been introduced, the so-called fast QR RLS (FQR) algorithms. Although this group has been introduced as a third independent group of fast RLS algorithms, it is shown that the FQR algorithms and the FLA algorithms are essentially the same group of algorithms and that it is basically only the way in which these algorithms are derived that makes them appear to be different. However, the FQR algorithms are not identical to any particular member of the FLA group; although the same identities are used to update the same quantities, the way in which these identities are tied together to form a complete algorithm is different. However, various members within the FLA group itself also display such differences. In this way, the reconciliation brings out several interesting (e.g. numerical) aspects. Various new algorithms are discussed