A Fractional-Order Gradient-Descent Total Least Mean P-Norm Adaptive Filtering Algorithm in Impulsive Noise Environments

Abstract

As a widely used method in the errors-in-variables (EIV) model, total least square (TLS) can work well for both input and output signals disturbed with noises. The TLS based adaptive filtering algorithms also have better performance than the least square based ones in the EIV system. However, their performance will deteriorate seriously in impulsive noise environments, since TLS cannot effectively suppress the large outliers in the noise. To address this problem, we present a cost function, called total least mean <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -norm (TLMP), and develop a fractional-order gradient-descent TLMP (FOGD-TLMP) algorithm in this brief. With the proposed cost function and the fractional-order derivative, FOGD-TLMP can deal well with impulsive noises in the EIV system. Furthermore, the local stability and computational complexity of the proposed algorithm are analyzed. Simulation results show that the proposed algorithm has better convergence performance than previous algorithms when the input and output signals are contaminated with impulsive noises.