In this paper, an affine projection maximum correntropy criterion with correntropy induced metric (APMCCCIM) algorithm is proposed for robust sparse adaptive filtering, and it is derived by using the cost function based on affine projection maximum correntropy criterion and correntropy induced metric to eliminate the adverse effects of impulsive noise on filter weight update in sparse systems. In order to further improve the convergence speed and steady-state misalignment of the proposed APMCCCIM algorithm, the variable step-size method is incorporated into the APMCCCIM algorithm. Hence, the variable step-size APMCCCIM (VSS-APMCCCIM) algorithm is presented. Besides, the computational complexity and the range of step-size of the proposed APMCCCIM algorithm are analyzed. Simulation results show that the proposed APMCCCIM and VSS-APMCCCIM algorithms have faster convergence speed and lower steady-state misalignment for sparse system identification and echo cancellation scenarios in the impulsive noise environments.

The reweighted zero-attracting least mean square (RZA-LMS) algorithm has good performance in sparse system identification. However, the convergence performance of the RZA-LMS algorithm degrades in the impulsive noise environment. In this brief, a reweighted zero-attracting least mean M-estimate (RZA-LMM) algorithm is proposed to address the issue. The RZA-LMM algorithm employs the M-estimate cost function with a sparsity-aware penalty term and is derived by using the unconstrained minimization method. In order to further enhance the convergence speed and reduce the steady-state error of the RZA-LMM algorithm, a variable step-size reweighted zero-attracting least mean M-estimate (VSSRZA-LMM) algorithm is proposed. The variable step-size scheme, which adopts the M-estimate cost function with a sparsity-aware penalty term and a constrained term of the step-size, is obtained by using the constrained minimization method. Besides, the mean-square stability is analyzed to obtain the range of the step-size, which guarantees the stabilization of the proposed algorithms. The computer simulation results show that the proposed RZA-LMM algorithm achieves better convergence performance than the RZA-LMS algorithm, and the proposed VSSRZA-LMM algorithm exhibits better convergence performance in terms of convergence speed and steady-state normalized mean square deviation (NMSD) than the RZA-LMM algorithm for sparse system identification in the impulsive noise environment.

The recursive general mixed-norm (RGMN) algorithm achieved excellent convergence performance in traditional unknown parameter identification application. However, it produces obvious estimation bias when dealing with the censored data collected from many practical scenarios. In this article, an RGMN algorithm for censored regression (CR-RGMN) is proposed for censored signal processing scenarios. The CR-RGMN algorithm utilizes a probit regression model to compensate for the sample bias caused by the sampling device. Then, a general form of the adaptive filter algorithm based on minimizing the convex mixture of $l_{a}$ and $l_{b}$ norms of the error is developed to identify the unknown parameter. The theoretical steady-state analysis in mean sense proves that the proposed CR-RGMN algorithm is unbiased, and the steady-state mean square deviation (MSD) is derived to predict the convergence behavior of the proposed algorithm. The computational complexities of the CR-RGMN and other algorithms are provided as well. Computer simulation results under robust parameter identification and channel equalization applications show that the proposed CR-RGMN algorithm achieves better performance in terms of convergence speed and steady-state MSD than the RGMN algorithm in censored data processing. And the theoretical analysis results are also verified.

Non-Gaussian colored input signal and censored observation are encountered frequently in many practical applications of adaptive signal processing. Conventional adaptive algorithms will face convergence performance degradation in such cases. To address the issue, the affine projection algorithm for censored regression (CR-APA) is proposed in this brief. The censored thresholds and the variance of the background noise are regarded as the prior knowledge to compensate for the bias caused by censored observation. By theoretical analysis, the range of the step size is derived to guarantee the stabilization of the CR-APA. Besides, the method of evolving projection order is employed to improve the convergence performance of the CR-APA. Computer simulations in system identification and echo cancellation applications are performed to demonstrate the better convergence performance of the proposed algorithms in censored data processing over competing algorithms, and to verify the improvement of the CR-APA by the method of evolving projection order. The proposed CR-APA and CR-EAPA can be used in engineering applications to make up for the hardware.

When the disturbance of impulsive noise exists in the multitask network, the convergence behavior of the traditional multitask diffusion affine projection (AP) algorithm (MD-APA) is significantly suppressed. To alleviate this problem, in this brief, a robust MD-APA is proposed based on maximum correntropy criterion (MCC), which is called MD-APMCC algorithm. Due to the shortcomings of the fixed kernel width, this brief adopts a robust adaptive kernel width strategy to increase the estimation behavior of the MD-APMCC algorithm. Besides, the convergence behavior of MD-APMCC algorithm is studied to derive the convergence range of step-size and the theoretical steady-state mean square deviation (MSD) of the whole network. The simulation verification demonstrates that the proposed MD-APMCC algorithm appears better estimation behavior than MD-APA and MD-APSA for multitask distributed estimation under impulsive noise interference, and the theoretical steady-state MSD of MD-APMCC algorithm is obtained through mean square analysis, which has been well verified by several simulations.