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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.

The least mean square (LMS) algorithm of graph signal processing (GSP) can be used for sensor signal processing due to its simplicity and low computational complexity, and the recursive least squares (RLS) algorithm of GSP can be applied to sensor signal processing since it has fast convergence rate. However, the GSP LMS algorithm has poor convergence performance, and the tracking performance of the GSP RLS algorithm turns weak after signal mutation. To solve the mentioned problems, we focus on the data-reuse strategy, aiming to improve the convergence/tracking performance of the related algorithms by reusing the same set of data several times, and thus, the GSP data-reuse LMS (GSP-DR-LMS) algorithm and the GSP data-reuse RLSs (GSP-DR-RLSs) algorithm are proposed. Moreover, to make the GSP-DR-LMS algorithm achieve better coordination between steady-state error and convergence rate, we propose the variable step size (VSS) strategy applicable to the GSP-DR-LMS algorithm, and thus, the GSP VSS-DR LMS algorithm is proposed. In addition, the performance analysis of the related algorithms is performed. Ultimately, we verify the superiority of the proposed algorithms in terms of convergence/tracking performance by performing computer simulations.

In order to address the performance degradation of the geometric algebra LMS algorithms (GA-LMS) in the face of non-Gaussian disturbances, this brief proposes a robust adaptive filtering algorithm based on hybrid maximum geometric algebra correntropy (HMGACC) perspective. Specially, we define the hybrid geometric algebra correntropy (HGAC) cost function, which can increase the flexibility of the correntropy. Secondly, we introduce a proportionality parameter to make the HGAC algorithm more general, which can be changed into a traditional single kernel GAC algorithm by changing the proportionality parameter. Furthermore, the addition of the proportionality parameter also allows for a non-fixed form of step-size, i.e., the step-size of the proposed algorithm in this brief is a hybrid step-size, which will be more useful for us to improve the performance of the algorithm. Finally, in the experimental simulations, the proposed algorithm can achieve better convergence and steady-state performance in comparison with other competing algorithms under different non-Gaussian disturbances, which confirms the feasibility of the proposed method.