Recursive Least Squares Filter - Lattice Recursive Least Squares Filter (LRLS)

Lattice Recursive Least Squares Filter (LRLS)

The Lattice Recursive Least Squares adaptive filter is related to the standard RLS except that it requires fewer arithmetic operations (order N). It offers additional advantages over conventional LMS algorithms such as faster convergence rates, modular structure, and insensitivity to variations in eigenvalue spread of the input correlation matrix. The LRLS algorithm described is based on a posteriori errors and includes the normalized form. The derivation is similar to the standard RLS algorithm and is based on the definition of . In the forward prediction case, we have with the input signal as the most up to date sample. The backward prediction case is, where i is the index of the sample in the past we want to predict, and the input signal is the most recent sample.