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Proceedings Paper

Characterization of polar to Cartesian coordinates transformation and its effect on target track quality
Author(s): John E. Gray; Ali T. Alouani
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Paper Abstract

Target tracking with radar and sonar is done in either spherical or rectangular coordinates. Often tracking is done in one reference frame while filtering, usually Kalman, is done in another reference frame. It is commonly assumed that the probability density functions can be treated the same in both reference frames. An extended Kalman filter is used under this assumption that the probability density function of the measurements after conversion can be adequately characterized by the mean and standard deviation. The transformations from spherical coordinates (see manuscript) to Cartesian coordinates (see manuscript) is a non-linear transformation, so the statistical characteristics of the measurement process noise are changed significantly by the transformation. Thus, the characteristics which tracking filters are designed to optimize with respect to are changed as well by these coordinate transformations. Typical engineering practice uses approximations rather than exact solutions. The objective of this paper is to provide means to analytically characterize the probability density functions of these coordinate transformations. We then investigate the impact of approximating the noise statistics of these transformed coordinates on track quality.

Paper Details

Date Published: 7 May 2007
PDF: 14 pages
Proc. SPIE 6569, Acquisition, Tracking, Pointing, and Laser Systems Technologies XXI, 656902 (7 May 2007); doi: 10.1117/12.718467
Show Author Affiliations
John E. Gray, Naval Surface Warfare Ctr. (United States)
Ali T. Alouani, Tennessee Technological Univ. (United States)


Published in SPIE Proceedings Vol. 6569:
Acquisition, Tracking, Pointing, and Laser Systems Technologies XXI
Steven L. Chodos; William E. Thompson, Editor(s)

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