Variable-Center Robust Kernel Adaptive Filtering Based on the Maximum Generalized Cauchy Kernel

doi:10.1109/tase.2026.3715964

Variable-Center Robust Kernel Adaptive Filtering Based on the Maximum Generalized Cauchy Kernel

2026-07-22

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DOI：10.1109/tase.2026.3715964

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Conventional generalized Gaussian kernel adaptive filtering usually employs a zero-centered kernel, which may lead to a mismatch between the kernel response and the error statistics when the error distribution is shifted by non-zero-mean noise or under heavy-tailed disturbances. A maximum generalized Cauchy kernel correntropy criterion is proposed to develop a variable-center kernel adaptive filtering algorithm, in which the center parameter is adaptively adjusted to compensate for the shift of the error distribution caused by biased noise. Furthermore, the variable center maximum Versoria criterion kernel adaptive filtering algorithm is derived as a special case under a specific parameter setting. The basic properties of these algorithms are analyzed. Numerical and field-testing results demonstrate the favorable estimation accuracy and robustness of the proposed algorithms in nonlinear system identification tasks. Note to Practitioners—State estimation under non-Gaussian and non-zero-mean noise remains a significant challenge in industrial sensing and control systems. Conventional Kalman filters often exhibit performance degradation when sensor measurements are corrupted by impulsive outliers or systematic biases. This paper proposes a variable-center kernel adaptive filtering algorithm based on the maximum generalized Cauchy kernel correntropy criterion, referred to as KMGCC-VC. The algorithm is designed to suppress heavy-tailed outliers through the generalized Cauchy kernel and to reduce the effect of non-zero-mean noise by adaptively adjusting the kernel center. Practitioners in battery management systems, radar/sonar target tracking, and autonomous robot localization may benefit from the following aspects: (1) Automatic bias compensation: The variable-center mechanism reduces the reliance on manual noise-mean estimation, thereby reducing commissioning time in field deployments; (2) Enhanced robustness: The generalized Cauchy kernel can provide stronger outlier attenuation than Gaussian-based alternatives in the tested impulsive-noise scenarios, thereby improving reliability when measurements are affected by sensor faults or electromagnetic interference; (3) Tunable robustness-efficiency trade-off: The shape parameter <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>, amplitude <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula>, and scale parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> allow practitioners to balance outlier suppression against convergence speed based on application requirements. In the tested implementation, the shape parameter <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> shows relatively strong sensitivity in the computational-cost analysis. Therefore, it can be prioritized during parameter tuning when a balance between robustness, accuracy, and computational cost is required. The algorithm is particularly suitable when measurement noise exhibits impulsive characteristics or unknown bias. In the tested benchmarks, these observations suggest a practical initial search range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a \in [{0.6, 1.7}], p \in [{1.4, 3.6}]$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda \in [{0.2, 0.6}]$ </tex-math></inline-formula>.

Keywords:

Robust estimation

variable center

maximum generalized Cauchy correntropy

probability of divergence

excess mean square error

Variable-Center Robust Kernel Adaptive Filtering Based on the Maximum Generalized Cauchy Kernel

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