The 3D Complex Damped Exponential Cramer-Rao Estimation Bound and Algorithms

摘要

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 ?eld data leads to decompositionmodels 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 complexfrequency in three dimensions. Synthetic 3D rectangular wave ?eld and SAR data are decomposed into 3Ddamped exponentials to the CRB accuracy in examples. As in the 1D and 2D case the 3D case for a singleexponential in rectangular coordinates can be directly related to the 3D Fourier Transform (FT) and its estimationaccuracy. The use of SAR data presents several additional complexities. The use of linear ?ight path SAR isthe most appropriate for complex damped exponentials, but is by the nature of SAR also approximate. OtherSAR modalities such as circular, other curvilinear, or other non-uniformity ?ight paths are prevalent but presenta di¤erent multidimensional Impulse Response Function (IPR) and are expected to deviate for the accuracyof the CRB derived here. Additionally, sampling, interpolation, and corrections to an idealized ?ight path areminimized or ignored in creating synthetic SAR data sets and in applying the 3D complex damped exponentialdecomposition to the data. The parameters of 3D complex damped exponentials will be estimated by severalalgorithms and their accuracy with be compared with the 3D complex damped exponential Cramer Rao bound.