Cumulant filters - a recursive estimation method for systems with non-Gaussian process and measurement noise

Abstract

Abdract -A recursive filtering technique for the state estimation of linear systems where the Gaussian assumption is not required for either the plant (process), initial condition, or measurement noise will he presented here. The approach requires the noise to be defined by their higherorder statistics (moments or cnmulants). Analogous to the Kalman filter time-update popagation of a covariance matrix, cumulants can he propagated in a similar fashion making use of Kronecker products and the fact that the cumulant of a sum of independent random variables is the sum of the individual cumulants. This allows for a straightfomard characterization of the statistics for the likelihood and the prior probability at the time of the measurement update of the filter. An experimental evaluation shows these cumulant-hased filters perform better than a default use of a Kalmau filter.

An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams

“…High order cumulants are used to analyze signal data, such as audio signals, for example in directionfinding methods of the multi-source signal (q-MUSIC algorithm) [4]. Additionally, high order cumulants are being used in signal filtering problems [5,6] or neu-roimaging signals analysis [7,8]. The neuroscience application often uses the Independent Components Analysis (ICA) [9], that can be evaluated by means of high order cumulant tensors [10,11].…”

Selected Methods for non-Gaussian Data Analysis

“…In this chapter, we will concentrate on multivariate higher order cumulants, applicable to analyse non-Gaussian distributed multivariate data. For their practical application in multivariate non-Gaussian data analysis refer to signals analysis, for example in signal filtering [207,208], finding the direction of received signals [17,18,19,20] and signal autocorrelation analysis [95]. Furthermore, those cumulants are used in hyper-spectral image analysis [47], financial data analysis [209,210] and neuroimage analysis [211,212].…”

Efficient Computation of Higher-Order Cumulant Tensors

“…Cumulants of the order of d > 2 have recently started to play an important role in the analysis of non-normally distributed multivariate data. Some potential applications of higher-order cumulants include signal filtering problems where the normality assumption is not required (see [25,32] and references therein). Another application is finding the direction of received signals [45,41,10,33] and signal auto-correlation analysis [37].…”