The Quarternion Maximum Correntropy Algorithm

The performance assessment of any control system plays a key role in industrial control systems. To meet the real-time requirements of modern control systems, a quick and accurate evaluation of the performance of a system is necessary. In this paper, a performance assessment method of a non-Gaussian control system based on mixture correntropy is proposed for non-Gaussian stochastic systems. Mixture correntropy can solve the problem of minimum entropy translation invariance. When the expected output of a system is unavailable, mixture correntropy combined with the estimation of distribution algorithm (EDA) is used for system identification and noise distribution estimation so as to calculate the benchmark of entropy-based performance assessment. When the expected output of a system is available, the mixture correntropy is directly used as the index to evaluate the performance of the system. To improve the real-time aspect of the performance assessment, an improved EDA is presented to obtain the evaluation index more quickly. For both Gaussian and non-Gaussian systems, the mixture correntropy and the improved identification algorithm are used for system performance assessment, and the results are compared with the minimum entropy index and the probability density function (PDF) curve coincident area index. The comparisons verify the rationality and effectiveness of the correntropy index and the rapidity of the improved EDA algorithm.

Section: Correntropy and Mixture Correntropy Indexmentioning

confidence: 99%

“…Correntropy [16][17][18] is a measure of similarity in the kernel space. The larger the correntropy between two sequences, the smaller the difference between them.…”

Section: Introductionmentioning

confidence: 99%

Performance Assessment of Non-Gaussian Control Systems Based on Mixture Correntropy

Zhang¹,

Wu²

2019

“…As it is well-known that MCC has been successfully applied in various non-Gaussian signal processing matters due to its robustness properties [ 5 , 6 , 8 , 22 ]. As a non-linear local similarity measure between two random variables x and y , the correntropy is defined by [ 2 , 3 ]:

where

denotes a shift-invariant Mercer kernel.…”

Section: Sgmcc Algorithmmentioning

confidence: 99%

“…The maximum correntropy criterion (MCC) [ 2 , 3 ] is one of the most popular optimization criteria in ITL due to its simplicity and robustness. Recently, it has been successfully applied in various signal processing scenarios, particularly the adaptive filtering [ 4 , 5 , 6 , 7 , 8 , 9 , 10 ].…”

Section: Introductionmentioning

confidence: 99%

A Smoothed Algorithm with Convergence Analysis under Generalized Maximum Correntropy Criteria in Impulsive Interference

Shi

Zhao

2019

The generalized maximum correntropy criterion (GMCC) algorithm is computationally simple and robust against impulsive noise but it suffers from slow convergence speed as it is derived and based on stochastic gradient, which only use the current data sample. In order to deal with this issue, a smoothed GMCC algorithm (SGMCC) is proposed. In the SGMCC algorithm, instead of taking the exponential weighted average of gradient vector to approximate the expectation of the gradient vector, we take the exponential weighted average of the variable step-size so that the SGMCC algorithm can be viewed as a sign GMCC algorithm with smoothed variable step-size. Moreover, convergence performance analyses are derived in terms of variable step-size, mean-square stability and steady-state behavior to demonstrate the robustness of the proposed algorithm. At last, simulation comparisons show that the proposed algorithm is robust against impulsive noise and converges fast with lower computational complexity. Also, for the steady-state behavior, simulation results verify that the simulated value matches well with the theoretical one.

“…The MCC aims at maximizing the similarity (measured by correntropy) between the model output and the desired response such that the adaptive model is as close as possible to the unknown system. It has been shown that, the MCC in terms of the stability and accuracy, is very robust with respect to impulsive noises [33][34][35][36][37][38][39]. Compared with the traditional Hammerstein adaptive filtering algorithms based on the MSE criterion, the new algorithm can achieve better performance especially in the presence of impulsive non-Gaussian noises.…”

Section: Introductionmentioning

confidence: 99%

Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion

Peng

Chen

et al. 2015

Abstract:The maximum correntropy criterion (MCC) has recently been successfully applied to adaptive filtering. Adaptive algorithms under MCC show strong robustness against large outliers. In this work, we apply the MCC criterion to develop a robust Hammerstein adaptive filter. Compared with the traditional Hammerstein adaptive filters, which are usually derived based on the well-known mean square error (MSE) criterion, the proposed algorithm can achieve better convergence performance especially in the presence of impulsive non-Gaussian (e.g., α-stable) noises. Additionally, some theoretical results concerning the convergence behavior are also obtained. Simulation examples are presented to confirm the superior performance of the new algorithm.