Beyond lms: an overview of other adaptive filter algorithms

Rls algorithms

FIR adaptive filter algorithms with faster convergence. Since the Wiener solution can be obtained on one step by computing $W_{\mathrm{opt}}=R^{(-1)}P$ , most RLS algorithms attept to estimate $R^{(-1)}$ and $P$ and compute $W_{\mathrm{opt}}$ from these.

There are a number of $O(N^2)$ algorithms which are stable and converge quickly. A number of $O(N)$ algorithms have been proposed, but these are all unstable except for the lattice filter method. This isdescribed to some extent in the text. The adaptive lattice filter converges quickly and is stable, but reportedly has avery high noise floor.

Many of these approaches can be thought of as attempting to "orthogonalize" $R$ , or to rotate the data or filter coefficients to a domain where $R$ is diagonal, then doing LMS in each dimension separately , so that a fast-converging step size can be chosen in all directions.

Frequency-domain methods

Frequency-domain methods implicitly attempt to do this: