Adaptive filtering is in principle intended for tracking nonstationary systems. However, most adaptive filtering algorithms have been designed for converging to a fixed unknown filter. When actually confronted with a non-stationary environment, they possess just one parameter (stepsize, window size) to adjust their tracking capability. In the stationary case of non-stationarity, the optimal fil...

Having recently shown that the LMS adaptive filtering technique can be viewed as an iterative linear equation solver applied to a time varying linear equation set directly related to the Wiener-Hopf equation, we address in this paper the question if a larger class of adaptive filtering algorithms can be formulated within the framework of the theory of iterative linear equation solvers. We show ...

We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate...

Abstract : In this paper we derive a new adaptive filtering algorithm. Starting from a general square−root formulation [1], we introduce a normalization transform to the updating scheme of the block−diagonal adaptive algorithm presented in [1]. This algorithm is efficiently implemented with a low complexity, the resulting algorithm is similar to the NLMS one. Simulations, in the context of mult...