Robust adaptive filtering using recursive weighted least squares with combined scale and variable forgetting factors

In this paper, a new adaptive robustified filter algorithm of recursive weighted least squares with combined scale and variable forgetting factors for time-varying parameters estimation in non-stationary and impulsive noise environments has been proposed. To reduce the effect of impulsive noise, whether this situation is stationary or not, the proposed adaptive robustified approach extends the concept of approximate maximum likelihood robust estimation, the so-called M robust estimation, to the estimation of both filter parameters and noise variance simultaneously. The application of variable forgetting factor, calculated adaptively with respect to the robustified prediction error criterion, provides the estimation of time-varying filter parameters under a stochastic environment with possible impulsive noise. The feasibility of the proposed approach is analysed in a system identification scenario using finite impulse response (FIR) filter applications.