Multichannel adaptive least squares-relating the `Kalman´ recursive least squares (RLS) and least squares lattice (LSL) adaptive algorithms

A multichannel adaptive lattice algorithm is derived that provides a least-squares estimate of a primary signal in terms of the last p samples of m reference signals. The recursions developed are optimized for multichannel use and provide an algorithm with computational complexity O(pm²). In the single reference channel case (m=1), the algorithm simplifies to the O(p) least-squares lattice (LSL) algorithm. In the single filter tap case (p=1), the algorithm simplifies to the O(m ²) `Kalman´ recursive least-squares (RLS) algorithm. Hence, the general multichannel least-squares lattice (MLSL) presented provides an explicit relationship between, and common derivation of, both the LSL and RLS algorithms