This concept addresses adaptive lattice filtering in the domain of adaptive signal processing, extending the fixed-coefficient lattice filter (whose optimal reflection coefficient K_p is derived from correlation statistics of the forward and backward prediction errors) to a case where the input statistics are unknown or time-varying. The core mechanism is the Gradient Adaptive Lattice (GAL) algorithm: the mean-square prediction error is shown geometrically and algebraically to be a quadratic function of the reflection coefficient K, so a steepest-descent search on this quadratic surface—followed by a stochastic-gradient (LMS-style) approximation that replaces expectations with instantaneous data products—yields a recursive update rule for K_p at each lattice stage. This generalizes the earlier transversal-filter steepest-descent-to-LMS derivation to the lattice structure, with the added theoretical requirement of combining (summing) the forward and backward error quadratics before minimization to preserve the theoretical equality of the forward and backward optimal coefficients under convergence.
This concept addresses adaptive lattice filtering in the domain of adaptive signal processing, extending the fixed-coefficient lattice filter (whose optimal reflection coefficient K_p is derived from…