Moment Estimation Using a Marginalized Transform
Artikel i vetenskaplig tidskrift, 2012

We present a method for estimating mean and covariance of a transformed Gaussian random variable. The method is based on evaluations of the transforming function and resembles the unscented transform and Gauss-Hermite integration in that respect. The information provided by the evaluations is used in a Bayesian framework to form a posterior description of the parameters in a model of the transforming function. Estimates are then derived by marginalizing these parameters from the analytical expression of the mean and covariance. An estimation algorithm, based on the assumption that the transforming function can be described using Hermite polynomials, is presented and applied to the non-linear filtering problem. The resulting marginalized transform (MT) estimator is compared to the cubature rule, the unscented transform and the divided difference estimator. The evaluations show that the presented method performs better than these methods, more specifically in estimating the covariance matrix. Contrary to the unscented transform, the resulting approximation of the covariance matrix is guaranteed to be positive-semidefinite.

filtering theory


Kalman filter

gaussian filters

recursive estimation

statistical linearization

Bayes methods

hermite quadrature


Fredrik Sandblom

Chalmers, Signaler och system, Signalbehandling och medicinsk teknik

Lennart Svensson

Chalmers, Signaler och system, Signalbehandling och medicinsk teknik

IEEE Transactions on Signal Processing

1053-587X (ISSN) 1941-0476 (eISSN)

Vol. 60 12 6138-6150 6307890


Informations- och kommunikationsteknik


Elektroteknik och elektronik



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