This concept covers the exponentially-weighted (forgetting-factor) formulation of the Recursive Least Squares (RLS) adaptive lattice filter, within the domain of adaptive signal processing / statistical signal processing. It introduces a modified inner product that weights past samples by a factor lambda raised to increasing powers, so that contributions from the distant past are suppressed relative to recent samples, and shows that minimizing the resulting weighted sum-of-squares error is equivalent to an orthogonal projection under this new inner product, whose optimal combiner coefficients converge (for large sample counts) to the true forward and backward prediction-error coefficients. The concept relates this weighted least-squares/orthogonal-projection framework, built on vector-space projection theory, to the lattice-filter order-recursion (deriving order p+1 quantities from order p quantities) that underlies RLS adaptive filtering, distinguishing it from the earlier stationary stochastic lattice derivation by explicitly retaining time-index dependence (no expectation operator, no stationarity assumption) in the pre-windowed case.
This concept covers the exponentially-weighted (forgetting-factor) formulation of the Recursive Least Squares (RLS) adaptive lattice filter, within the domain of adaptive signal processing / statisti…