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As a new addition to the recursive least squares (RLS) family filters, the state space recursive least squares (SSRLS) filter can achieve desirable performance by conquering some limitations of the standard RLS filter. However, when the system is contaminated by some non-Gaussian noises, the performance of SSRLS will get worse. The main reason for this is that the SSRLS is developed under the well-known minimum mean square error (MMSE) criterion, which is not very suitable for non-Gaussian situations. To address this issue, in this paper, we propose a new state space based linear filter, called the state space least p -power (SSLP) filter, which is derived under the least mean p -power error (LMP) criterion instead of the MMSE. With a proper p value, the SSLP can outperform the SSRLS substantially especially in non-Gaussian noises. Two illustrative examples are presented to show the satisfactory results of the new algorithm. [ABSTRACT FROM AUTHOR]

Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adapt then combine MCC and combine then adapt MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distributed estimation are in general based on the mean square error (MSE) criterion, which is desirable when the measurement noise is Gaussian. In non-Gaussian situations, especially for the impulsive-noise case, MCC based methods may achieve much better performance than the MSE methods as they take into account higher order statistics of error distribution. The proposed methods can also outperform the robust diffusion least mean p-power (DLMP) and diffusion minimum error entropy (DMEE) algorithms. The mean and mean square convergence analysis of the new algorithms are also carried out. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel error criterion for adaptive filtering, namely the smoothed least mean p -power (SLMP) error criterion, which aims to minimize the mean p -power of the error plus an independent and scaled smoothing variable . Some important properties of the SLMP criterion are presented. In particular, we show that if the smoothing variable is symmetric and zero-mean, and p is an even number, then the SLMP error criterion will become a weighted sum of the even-order moments of the error, and as the smoothing factor (i.e. the scale factor) is large enough, this new criterion will be approximately equivalent to the well-known mean square error (MSE) criterion. Based on the proposed error criterion, we develop a new adaptive filtering algorithm and its kernelized version, and derive a theoretical value of the steady-state excess mean square error (EMSE). Simulation results suggest that the new algorithms with proper choice of the smoothing factor may perform quite well. [ABSTRACT FROM AUTHOR]

• The steady-state complementary mean square deviation of the WL-RLS algorithm is analyzed. • The Lyapunov stability analysis of the WL-RLS algorithm for time-invariant system and noise-free output is performed. • Numerical stability analysis has been conducted, illustrating that the WL-RLS algorithm is numerically stable for λ < 1. The widely linear recursive least squares (WL-RLS) algorithm is useful for dealing with noncircular signals. In this paper, we focus on the theoretical prediction and stability of the WL-RLS algorithm. First, the steady-state complementary mean square deviation (CMSD) behavior under a time-varying system is analyzed, which is different from the traditional standard mean square analysis that takes the form of real-valued evolution. Second, the Lyapunov stability and numerical stability are taken into account to provide an in-depth understanding of the stability issue. Specifically, by employing the Lyapunov stability theory (LST) approach, we perform the stability analysis of the WL-RLS algorithm for time-invariant system and noise-free output, illustrating that the WL-RLS algorithm is exponentially convergent in the sense of Lyapunov. Moreover, the numerical stability is analyzed by considering the finite word-length effects, and it is shown that the WL-RLS algorithm is numerically stable when the forgetting factor λ < 1. Numerical simulations for system identification scenarios verify the accuracy of the steady-state theoretical prediction. [ABSTRACT FROM AUTHOR]

Although the least mean p th power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α -stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identification. To overcome these limitations, an enhanced recursive least mean p th power algorithm with logarithmic transformation (RLogLMP) is proposed in this paper. The proposed algorithm is adjusted to minimize the new cost function with the p -norm logarithmic transformation of the error signal. The logarithmic transformation, which can diminish the significance of outliers under α -stable noise environment, increases the robustness of the proposed algorithm and reduces the steady-state kernel error. Moreover, the proposed method improves the convergence rate by the enhanced recursive scheme. Finally, simulation results demonstrate that the proposed algorithm is superior to the LMP, NLMP, normalized least mean absolute deviation (NLMAD), recursive least squares (RLS) and nonlinear iteratively reweighted least squares (NIRLS) algorithms in terms of convergence rate and steady-state kernel error. [ABSTRACT FROM AUTHOR]