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Recently, maximum correntropy criterion (MCC) has been widely and successfully used in robust signal processing and machine learning, in which the correntropy is maximized instead of minimizing the popular mean square error (MSE) to improve the robustness with respect to outliers or impulsive noises. A lot of efforts have been devoted to derive different adaptive algorithms under MCC, but to date, little insight has been gained as to how the MCC solution will be influenced by outliers. In this paper, we investigate this problem and our focus is mainly on the parameter estimation of a simple linear errors-in-variables (EIVs) model with scalar variables. Under some conditions, we derive an upper bound on the absolute value of the estimation error and show that the MCC solution can get very close to the true value of the unknown parameter even with arbitrarily large outliers in both the input and output variables. Illustrative examples are provided to verify and clarify the theory. [ABSTRACT FROM AUTHOR]

A blocked proportionate normalized maximum correntropy criterion (PNMCC) is presented to improve the estimation behavior of the traditional maximum correntropy criterion (MCC) algorithm for identifying the blocked sparse systems. The proposed blocked MCC is implemented by constructing a new cost function based on a hybrid-norm constraint (HNC) of the filter coefficient vector to adaptively utilize the cluster-sparse characteristic of unknown systems, denoting as hybrid-norm constrained PNMCC (HNC-PNMCC). The proposed HNC-PNMCC algorithm is achieved by using the basis pursuit. Various simulations are brought out to confirm the validity of the HNC-PNMCC. Simulation results indicate that the HNC-PNMCC is better than the PNMCC, MCC, and sparse MCC with respect to the estimation performance for the cluster-sparse system identification under the impulsive noises. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel prognostic approach for remaining useful life estimation (RUL) with evolving joint prediction of continuous and discrete states which represent the signals and health states of systems respectively. The predictors are built with evolving capability of adapting structures and parameters online to capture the dynamic characteristics of systems during runtime. Moreover, the discrete states can be determined dynamically during the construction of the predictors for systems operating under different environments. In the testing phase, the optimum predictor for predicting continuous and discrete states jointly is chosen under the error and distance criteria. The RULs are estimated conveniently once the predicted signals fall into failure mode based on a distance metric. In order to validate the performance of the proposed approach, the widely used turbofan engine datasets are taken into consideration. Experimental results demonstrate the reasonability and superiority of the proposed approach compared to other approaches. [ABSTRACT FROM AUTHOR]

Compared with the least-mean-square algorithm, the least mean $p$th power algorithm shows a better robustness performance against impulsive noises such as the $\alpha$-stable noises. However, it still exhibits slow convergence rate and high kernel misadjustment. To overcome this drawback, a novel recursive logarithmic least mean $p$th (RLLMP) algorithm is proposed for the Volterra system identification under $\alpha$-stable noise environments. Instead of minimizing the $p$th power, the new algorithm aims to minimize the $p$th logarithmic cost, which makes it more robust against impulsive interferences. Furthermore, to enhance tracking performance, an improved variable forgetting factor (IVFF) algorithm (IVFF-RLLMP) is proposed, which is based on the robust estimation of outliers. Simulation results are presented to demonstrate the improved performance of the RLLMP and IVFF-RLLMP. [ABSTRACT FROM AUTHOR]