Noise-robust normalised subband adaptive filtering

Proposed is a robust normalised subband adaptive filter (NSAF) for identifying a highly noisy system. The proposed NSAF reutilises a number of past weight vectors in adaptation, whereas the classical NSAF relies only on the immediately previous weight vector. A new constrained optimisation criterion is formulated so as to minimise the sum of the squared Euclidean norms of the changes between the weight vectors to be updated and the past weight vectors. The resultant NSAF exhibits robustness to noise in that it prevents the adaptive filter from fluctuating around an optimal solution. Through experiments, the proposed NSAF shows lower steady-state misalignment than the conventional NSAF while retaining comparable convergence rate, especially when noise gets severe.