Fuzzy C-means algorithm for parameter estimation of partitioned Markov chain impulsive noise model

Abstract

The partitioned Markov chain is a sample noise model that can represent impulsive noise in power substation including the time-correlation between the samples. In order to use this model, algorithms are needed to detect and to estimate the impulses characteristics, such as the duration, the samples values and the occurrence times of the impulses. Unsupervised learning of these characteristics is very complex, we propose then to use the fuzzy C-means algorithm to analyze impulses from substation measurements and to configure the partitioned Markov chain model by instantiating the transition matrix and by estimating the parameters of the Gaussian distributions associated with the Markov states. After simulating sequences of samples with our model, we noticed that the distribution of the impulsive noise characteristics and the power spectrum of the impulses are satisfyingly close to the measurements. The fuzzy C-means algorithm is appropriate to estimate the parameters required by the partitioned Markov chain model and to reduce the complexity of the parameter estimation.