This concept covers the RLS lattice filter's time-update mechanism, in which forward and backward prediction error variances (sigma-squared terms) are order-recursively updated at each time index and used to derive the reflection coefficient delta. Because delta cannot be updated directly through order recursion, its time update instead relies on a general orthogonal-projection identity relating the projection error of an external vector onto a column space augmented by the unit basis vector pi(n) at time n to the corresponding projection error at time n-1, introducing an auxiliary angle parameter (expressed as a sine-squared quantity) that itself must be order-updated. This belongs to adaptive filtering theory within array/lattice signal processing, extending least-squares projection theory (column spaces, orthogonal projection and projection-error operators) to derive exact, non-approximate recursive adaptation rules for order-recursive lattice structures.
This concept covers the RLS lattice filter's time-update mechanism, in which forward and backward prediction error variances (sigma-squared terms) are order-recursively updated at each time index and…