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Moment Estimation Using a Marginalized Transform

Fredrik Sandblom (Institutionen för signaler och system, Signalbehandling) ; Lennart Svensson (Institutionen för signaler och system, Signalbehandling)
Ieee Transactions on Signal Processing (1053-587X). Vol. 60 (2012), 12, p. 6138-6150.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Bayes methods, filtering theory, Kalman filter, recursive estimation, statistical linearization, tracking, hermite quadrature, gaussian filters



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Denna post skapades 2013-01-02. Senast ändrad 2013-06-28.
CPL Pubid: 168830

 

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