Kybernetika 54 no. 5, 865-887, 2018

Efficient measurement of higher-order statistics of stochastic processes

Wladyslaw Magiera, Urszula Libal and Agnieszka WielgusDOI: 10.14736/kyb-2018-5-0865


This paper is devoted to analysis of block multi-indexed higher-order covariance matrices, which can be used for the least-squares estimation problem. The formulation of linear and nonlinear least squares estimation problems is proposed, showing that their statements and solutions lead to generalized `normal equations', employing covariance matrices of the underlying processes. Then, we provide a class of efficient algorithms to estimate higher-order statistics (generalized multi-indexed covariance matrices), which are necessary taking in mind practical aspects of the nonlinear treatment of the least-squares estimation problem. The algorithms are examined for different higher-order and non-Gaussian processes (time-series) and an impact of signal properties on covariance matrices is analysed.


nonlinear, covariance matrix, higher-order statistics, adaptive


15B51, 93E24, 15B05, 60G10, 60G15


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