Abstract
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.
Highlights
Adaptive filtering represents a common tool in signal processing and control applications [1,2,3,4,5,6]
5 Conclusions The estimation problem of time-varying adaptive finite impulse response (FIR) filter parameters in the situations characterised by nonstationary and impulsive noise environments has been discussed in the article
The variable forgetting factor is determined by linear mapping of a suitably defined robust discrimination function, representing the ratio of robustified extended prediction error criterion, using M robust approach, and M robust type recursive estimate of noise variance
Summary
Adaptive filtering represents a common tool in signal processing and control applications [1,2,3,4,5,6]. The proposed suboptimal M robust estimator (6)–(8) is numerically simpler than the ones oriented towards solving the non-linear optimization problem in (5), but it still remains complex computation This method does not have an attractive recursive form and, is not computationally feasible as the RLS type estimators. The obtained algorithm in (3), (11), (16)–(18), represents the standard M robust RLS (RRLS), where the common approach is to estimate the unknown noise standard deviation, σ, by the MAD based scale factor in (9). This algorithm can be exactly derived by applying the Newton-Raphson iterative method for solving the non-linear optimization problem in (1), with the unit parameters s and ρ, respectively. The proposed parameter estimation algorithm (10)–(13) are derived from the M robust concept that is conservative, so the quality of parameter estimates may degrade without further adaptations of s and ρ variables
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