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To enhance the performance of the diffusion robust adaptive filtering algorithm, this paper presents a novel loss function framework named the "Tanh cost function framework." By utilizing this framework, we are able to incorporate standard cost functions, devise novel cost functions, and introduce the associated diffusion algorithm. Moreover, the convergence of the algorithm is thoroughly analyzed. Furthermore, the proposed diffusion Tanh algorithm family is simulated in a system identification model to assess its performance, demonstrating superior performance compared to the standard diffusive algorithm. Notably, the DTHLMS within the diffusion tanh algorithm family exhibits superior performance over the mainstream robust diffusion algorithms. [ABSTRACT FROM AUTHOR]

Kernel adaptive filtering algorithms have been successfully applied in many areas, among which the fraction lower power order statistics error criterion (FLP) is a better choice due to its prominent performance in robust design. However, the growth of network size in kernel adaptive filtering affects the convergence rate and testing accuracy. This paper proposes a sparse Gaussian kernel adaptive filtering algorithm based on the Softplus function framework to address the network size. The framework is constituted by the fraction lower power order statistics error criterion and an improved novelty criterion. The exponential loss function is employed to describe a new novel criterion, which can accurately achieve fast classification and limit the data selection of the dictionary size. This new algorithm is called the kernel fraction lower power order statistics error criterion based on the Softplus function with a modified novelty criterion (SKFLP-MNC) algorithm. In particular, the proposed method is employed for the Mackey–Glass chaotic time series prediction and noise cancellation under the cases of Gaussian and non-Gaussian noise. Simulation results show that the filtering accuracy of the SKFLP-MNC algorithm, the dictionary size, and steady-state mean-squared errors rival some of the sparse kernel least mean square algorithms. [ABSTRACT FROM AUTHOR]

To make the zero attractor sign subband adaptive filter (ZA-SSAF) algorithm more suitable for sparse systems, where the impulse response is sparse and disturbed with impulse interference, this paper proposes an improved sign subband adaptive filtering algorithm that takes advantage of the splendid robustness of the arctangent function against impulse interference. Based on the ZA-SSAF algorithm, this algorithm introduces a proportionate coefficient matrix composed of a nonlinear function (the arctangent function) to assign different step sizes for the tap coefficients that need to be updated. The step size of the algorithm is updated in proportion to the magnitude of the weight coefficient in the adaptive process according to the relationship of the arctangent function, which greatly shortens the calculation convergence time and improves the overall convergence performance. The simulation results show that the proposed algorithm takes into account the trade-off between a faster convergence rate and a lower steady-state error and is superior to the traditional sign subband algorithm and zero attractor sign subband adaptive filtering algorithm in terms of the convergence rate and robustness against impulse noise. [ABSTRACT FROM AUTHOR]