Advanced Algorithms for Adaptive Filtering

In this paper, we evaluate the possibility to develop algorithms of adaptation for the applications system of acoustic echo cancellation, while maintaining equilibrium between its reduced calculation complexity and its adaptive performances. We present new algorithms versions of fast recursive least squares numerically stable (NS-FRLS). They are obtained by means of redundant formulas, available in the fast recursive least squares (FRLS) algorithms, to estimate numerical errors and to retroact them in an unspecified point of the algorithm in order to modify its numerical properties. These algorithms represent a very important load of calculation that needs to be reduced. we propose a new (M-SMFTF) algorithm for adaptive filtering with fast convergence and low complexity. It is the result of a simplified FTF type algorithm, where the adaptation gain is obtained only from the forward prediction variables and using a new recursive method to compute the likelihood variable. This algorithm presents a certain interest, for the adaptation of very long filters, like those used in the problems of echo acoustic cancellation, due to its reduced complexity, its numerical stability and its convergence in the presence of the speech signal. Its calculation complexity is of 6L (L is the finite impulse response filter length) and this is considerably reduced to (2L+4P) when we use a reduced P-size (P<<L) forward predictor. Key-Words: Fast RLS, NLMS, FNTF, Adaptive Filtering, Convergence Speed, Tracking capability.