Dually Regularized Recursive Prediction Error identification for acoustic feedback and echo cancellation

Recursive prediction error (RPE) identification algorithms are attractive alternatives to the traditional least-squares-based adaptive filtering algorithms for, e.g., room impulse response identification, in such applications as acoustic feedback and echo cancellation. It has however been observed that a recently proposed RPE algorithm suffers from numerical problems due to a scaling ambiguity in the calculation of the auxiliary variables. This problem is tackled by regularizing the identification of some of the auxiliary variables, which is called “dual regularization”. This leads to a class of Dually Regularized Recursive Prediction Error (DR-RPE) identification algorithms, with different choices of regularization methods (Tikhonov or Levenberg-Marquardt) and matrices (possibly incorporating prior knowledge). Simulation results confirm that the DR-RPE algorithms do not exhibit numerical problems, and as a consequence produce more accurate estimates of the room impulse response and of the auxiliary variables.