A QRD-Based Array Lattice Form for H^∞ Adaptive Filtering

Abstract

In this research note, we present an array lattice algorithm for H^∞ adaptive filtering, in which pre-arrays are transformed into post-arrays by J-unitary transformations regarding an indefinite signature matrix J. The array form is derived by factorization with respect to an indefinite Hermitian matrix, which functionally corresponds to the so-called conversion factor in recursive least-squares algorithms. The numerical stability of the array lattice form in finite-precision arithmetic is verified by simulation in comparison with the standard
H^∞ filter implementation.