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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]

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]