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.

An adaptive least mean M-estimate algorithm for censored regression (CR-LMM) is presented for the robust parameter estimation of the censored regression system. To correct the bias produced by censored observation, the estimated error derived from the probit regression model is employed to construct an M-estimate cost function. It can expel the adverse impact of the impulsive noise and is solved by the unconstrained optimization method. Furthermore, the robust variable step-size (VSS) strategy, which is also predicted on the robust cost function, is also utilized to improve the convergence performance of the proposed CR-LMM algorithm, i.e., convergence speed and steady-state mean square deviation. The condition which guarantees the CR-LMM algorithm stability is obtained by analyzing the convergence in the mean and mean-square sense, and the theoretical steady-state result is also derived. Computer simulations in system identification scenarios are carried out to demonstrate that the proposed algorithms are superior to the existing algorithms in the impulsive environment with different background noise and the theoretical results are verified.