A Levinson-type algorithm for a class of non-Toeplitz systems with applications to multichannel IIR filtering

A very flexible Levinson-type recursion for a class of non-Toeplitz systems of linear equations is demonstrated. A complete solution is expressed as a linear combination of a partial solution and three auxiliary solutions. The class of systems possesses a special structure in that the coefficient matrices can be partitioned into four block Toeplitz submatrices. The number of multiplications and additions required to compute an n-dimensional solution is O(n²). The recursion is then applied to multichannel IIR filtering. Specifically, a lattice structure is established for linear minimum mean square error predictors having independently and arbitrarily specified numbers of poles and zeros. Next the recursion is used to develop a fast time and order recursive least-squares algorithm for ARX system identification. The novelty of the algorithm is that it can be used to efficiently determine parameter estimates of a family of ARX models