Abstract
Kernel adaptive filtering (KAF) algorithms derived from the second moment of error criterion perform very well in nonlinear system identification under assumption of the Gaussian observation noise; however, they inevitably suffer from severe performance degradation in the presence of non-Gaussian impulsive noise and interference. To resolve this dilemma, we propose a novel robust kernel least logarithmic absolute difference (KLLAD) algorithm based on logarithmic error cost function in reproducing kernel Hilbert spaces, taking into account of the non-Gaussian impulsive noise. The KLLAD algorithm shows considerable improvement over the existing KAF algorithms without restraining impulsive interference in terms of robustness and convergence speed. Moreover, the convergence condition of KLLAD algorithm with Gaussian kernel and fixed dictionary is presented in the mean sense. The superior performance of KLLAD algorithm is confirmed by the simulation results.
Highlights
When the shape parameter is equal to 2 and the risk-sensitive parameter gradually tends to trivial, both generalized maximum correntropy criterion (GMCC) and minimum kernel risk-sensitive loss (MKRSL) algorithms reduce to the ordinary maximum correntropy criterion (MCC) algorithm. e constrained least mean logarithmic square (CLMLS) based
The kernel least logarithmic absolute difference algorithm based on the logarithmic error cost framework is proposed to achieve the nonlinear system identification in the impulsive interference environments, which are more frequently encountered in practical applications
We evaluated the performance of the proposed kernel least logarithmic absolute difference (KLLAD) algorithm in the context of impulsive noise by the simulation results
Summary
Kernel adaptive filters as a tremendous breakthrough of the conventional linear adaptive filters have been widely used in many practical nonlinear applications including time series prediction [1], acoustic echo cancellation [2], channel equalization [3], abnormal event detection [4], etc. e scheme of kernel adaptive filtering (KAF) is to map the original input data into high or infinite dimensional feature space via kernel function and apply the framework of typical linear adaptive filtering to the transformed data in the reproducing kernel Hilbert spaces (RKHS) leading to various KAF algorithms [5–8]. e kernel least-mean-square (KLMS) algorithm, as the benchmark among of KAF algorithms, is developed from the cost function of secondorder statistic of the error between the desired signal and instantaneous estimate under the assumption of Gaussian noise for its mathematical simplicity and convenience [9]. E kernel least-mean-square (KLMS) algorithm, as the benchmark among of KAF algorithms, is developed from the cost function of secondorder statistic of the error between the desired signal and instantaneous estimate under the assumption of Gaussian noise for its mathematical simplicity and convenience [9]. Nystrom kernel recursive generalized maximum correntropy (NKRGMC) with probability density rank-based quantization sampling algorithm was proposed to improve the convergence performance for impulsive noises [33]. Inspired by the family of linear adaptive filtering algorithms based on the logarithmic cost proposed in [37], our purpose is to extend this scheme into RKHS to obtain the robustness of KAF algorithm within non-Gaussian impulsive noise environment. The kernel least logarithmic absolute difference algorithm based on the logarithmic error cost framework is proposed to achieve the nonlinear system identification in the impulsive interference environments, which are more frequently encountered in practical applications. Identity matrix of size N × N is denoted by IN
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