A robust fast recursive least squares adaptive algorithm

Very often, in the context of system identification, the error signal which is by definition the difference between the system and model filter outputs is assumed to be zero-mean, white, and Gaussian. In this case, the least squares estimator is equivalent to the maximum likelihood estimator and hence, it is asymptotically efficient. While this supposition is very convenient and extremely useful in practice, adaptive algorithms optimized on this, may be very sensitive to minor deviations from the assumptions. We propose here to model this error with a robust distribution and deduce from it a robust fast recursive least squares adaptive algorithm (least squares is a misnomer here but convenient to use). We then show how to successfully apply this new algorithm to the problem of network echo cancellation combined with a double-talk detector.