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Total least squares (TLS) method has been widely used in errors-in-variables (EIV) modeling tasks in which both input and output data are disturbed by noises, and adaptive filtering algorithm using TLS has shown significantly superior performance to classical least squares (LS) method in EIV system. The TLS essentially extends the minimum mean square error (MMSE) criterion to EIV model, which, however, may work poorly when noise is non-Gaussian (especially heavy-tailed distribution). Recently, an information theoretic learning (ITL) based minimum total error entropy (MTEE) adaptive filtering algorithm has been proposed, which extends the minimum error entropy (MEE) criterion to EIV model and shows desirable performance in non-Gaussian noise environments. However, due to complex mathematical expression, MTEE is computationally expensive and difficult to carry out the theoretical analysis. In this paper, we propose a new ITL-based criterion called maximum total correntropy (MTC) and develop a gradient-based MTC adaptive filtering algorithm. We analyze theoretically the local stability and steady-state performance of the proposed algorithm. Simulation results confirm the theoretical analysis and show the superior performance of MTC in heavy-tailed noises. Further, simulation comparisons between MTC and MTEE are presented. Compared with the MTEE, the MTC is mathematically more tractable and computationally much simpler while achieving similar or even better performance. [ABSTRACT FROM AUTHOR]

The state space recursive least squares (SSRLS) filter is a new addition to the well-known recursive least squares (RLS) family filters, which can achieve an excellent tracking performance by overcoming some limitations of the standard RLS algorithm. However, when the underlying system is disturbed by some heavy-tailed non-Gaussian impulsive noises, the performance of SSRLS will deteriorate significantly. The main reason for this is that the SSRLS is derived under the minimum mean square error (MMSE) criterion, which is not well-suited to estimation problems under non-Gaussian noises. To overcome this issue, we propose in this paper a novel linear filter, called the state space maximum correntropy (SSMC) filter, which is derived under the maximum correntropy criterion (MCC) instead of the MMSE. Since MCC is very suited to non-Gaussian signal processing, the SSMC performs very well in non-Gaussian noises especially when the signals are corrupted by impulsive noises. A simple illustrative example is presented to demonstrate the desirable performance of the new algorithm. [ABSTRACT FROM AUTHOR]