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The 3D complex damped exponential Cramer-Rao estimation bound and algorithms
Author(s): Matthew Pepin
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Paper Abstract

The desire for insightful and automated segmentation or decomposition of 3D Synthetic Aperture Radar (SAR) imagery, and other 3D collections of complex detect electromagnetic wave field data leads to decomposition models with a basis such at the 3D complex exponential. This paper presents the Cramer Rao Bound (CRB) for estimation of the sum of 3D complex damped exponentials including their complex amplitude, and complex frequency in three dimensions. Synthetic 3D rectangular wave …field and SAR data are decomposed into 3D damped exponentials to the CRB accuracy in examples. As in the 1D and 2D case the 3D case for a single exponential in rectangular coordinates can be directly related to the 3D Fourier Transform (FT) and its estimation accuracy. The use of SAR data presents several additional complexities. The use of linear flight path SAR is the most appropriate for complex damped exponentials, but is by the nature of SAR also approximate. Other SAR modalities such as circular, other curvilinear, or other non-uniformity ‡ight paths are prevalent but present a different multidimensional Impulse Response Function (IPR) and are expected to deviate for the accuracy of the CRB derived here. Additionally, sampling, interpolation, and corrections to an idealized ‡ight path are minimized or ignored in creating synthetic SAR data sets and in applying the 3D complex damped exponential decomposition to the data. The parameters of 3D complex damped exponentials will be estimated by several algorithms and their accuracy with be compared with the 3D complex damped exponential Cramer Rao bound.

Paper Details

Date Published: 14 May 2019
PDF: 16 pages
Proc. SPIE 10987, Algorithms for Synthetic Aperture Radar Imagery XXVI, 1098702 (14 May 2019); doi: 10.1117/12.2515545
Show Author Affiliations
Matthew Pepin, USAF, Retired (United States)


Published in SPIE Proceedings Vol. 10987:
Algorithms for Synthetic Aperture Radar Imagery XXVI
Edmund Zelnio; Frederick D. Garber, Editor(s)

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