Open Access

Low Complexity Track Initialization from a Small Set of Non-Invertible Measurements

EURASIP Journal on Advances in Signal Processing20072008:756414

https://doi.org/10.1155/2008/756414

Received: 30 March 2007

Accepted: 15 November 2007

Published: 9 December 2007

Abstract

Target tracking from non-invertible measurement sets, for example, incomplete spherical coordinates measured by asynchronous sensors in a sensor network, is a task of data fusion present in a lot of applications. Difficulties in tracking using extended Kalman filters lead to unstable behavior, mainly caused by poor initialization. Instead of using high complexity numerical batch-estimators, we offer an analytical approach to initialize the filter from a minimum number of observations. This directly pertains to multi-hypothesis tracking (MHT), where in the presence of clutter and/or multiple targets (i) low complexity algorithms are desirable and (ii) using a small set of measurements avoids the combinatorial explosion. Our approach uses no numerical optimization, simply evaluating several equations to find the state estimates. This is possible since we avoid an over-determined setup by initializing only from the minimum necessary subset of measurements. Loss in accuracy is minimized by choosing the best subset using an optimality criterion and incorporating the leftover measurements afterwards. Additionally, we provide the possibility to estimate only sub-sets of parameters, and to reliably model the resulting added uncertainties by the covariance matrix. We compare two different implementations, differing in the approximation of the posterior: linearizing the measurement equation as in the extended Kalman filter (EKF) or employing the unscented transform (UT). The approach will be studied in two practical examples: 3D track initialization using bearingsonly measurements or using slant-range and azimuth only.

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Authors’ Affiliations

(1)
Department of Electrical and Computer Engineering, University of Connecticut
(2)
Sensor Networks and Data Fusion Group, FGAN e.V

Copyright

© Christian R. Berger et al. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.