Moment Estimation Using a Marginalized Transform
Journal article, 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

tracking

Kalman filter

gaussian filters

recursive estimation

statistical linearization

Bayes methods

hermite quadrature

Author

Fredrik Sandblom

Chalmers, Signals and Systems, Signalbehandling och medicinsk teknik, Signal Processing

Lennart Svensson

Chalmers, Signals and Systems, Signalbehandling och medicinsk teknik, Signal Processing

IEEE Transactions on Signal Processing

1053-587X (ISSN)

Vol. 60 12 6138-6150 6307890

Areas of Advance

Information and Communication Technology

Subject Categories

Electrical Engineering, Electronic Engineering, Information Engineering

DOI

10.1109/tsp.2012.2215605

More information

Created

10/7/2017