Recursive Least Squares (RLS) derives the optimal linear estimator of a random variable from a set of observed random variables by reformulating the classical orthogonal-projection solution (coefficient vector = R⁻¹p, where R is the autocorrelation matrix and p the cross-correlation vector) as a purely deterministic, data-based numerical linear algebra problem: minimizing the sum of squared errors over observed data samples up to index n, with no expectation operator, converges exactly (not merely in the mean) to the optimal coefficients as more data is incorporated. This belongs to adaptive filter theory in signal processing/estimation, positioned as an alternative to the LMS/gradient-search family of adaptive algorithms, trading higher computational cost and less structurally efficient implementation for exact convergence and faster convergence rate, independent of input eigenvalue spread.
Recursive Least Squares (RLS) derives the optimal linear estimator of a random variable from a set of observed random variables by reformulating the classical orthogonal-projection solution (coeffici…