Adaptive identification under the maximum correntropy criterion with variable center

Abstract

The problem of identifying the parameters of a linear object in the presence of non-Gaussian noise is considered. The identification algorithm is a gradient procedure for maximizing the functional, which is a correntropy. This functionality allows you to get estimates that have robust properties. In contrast to the commonly used Gaussian kernels, the centers of which are at zero and effective for distributions with zero mean, the paper considers a modification of the criterion suitable for distributions with nonzero mean. The modification is to use correntropy with a variable center The use of Gaussian kernels with a variable center will allow us to estimate unknown parameters under Gaussian and non-Gaussian noises with zero and non-zero mean distributions and provide an opportunity to develop new technologies for data analysis and processing. It is important to develop a robust identification algorithm based on correntropy with variable center. Their properties in the identification of stationary and non-stationary objects are the subject of research. The goal is to develop a robust identification algorithm that maximizes the criterion of correntropy with a variable center using center configuration procedures and kernel width and to study its convergence in stationary and non-stationary cases under non-Gaussian noise. Expressions for steady-state value of the estimation error are obtained, which depend on the type of noise distribution and the degree of non-stationarity of the estimated parameters The following tasks are solved: to investigate the convergence of the algorithm and determine the conditions for the stability of the established identification process. Methods of estimation theory (identification) and probability theory are used. The following results were obtained: 1) the developed algorithm provides robust estimates in the presence of noises having a distribution with zero and non-zero mean; 2) its convergence was studied in stationary and non-stationary cases under conditions of Gaussian and non-Gaussian noise; 3) simulation of the algorithm was carried out. 1) the developed algorithm consists in the development of a robust identification algorithm that maximizes the criterion of correntropy with a variable center; 2) its convergence in stationary and non-stationary cases in the conditions of Gaussian and non-Gaussian noises is investigated; 3) simulation of the algorithm is performed. Conclusions: The results of the current study will improve existing data processing technologies based on robust estimates and accelerate the development of new computing programs in real time.

Keywords

• correntropy
• maximization
• functional
• gradient algorithm
• asymptotic estimation
• convergence
• identification accuracy
• steady state