Numerically Computing the KummerU Function and a Special Case of the Gauss Hypergeometric Function: With Application to the Computation of CFAR Threshholds for Dual Aperture SAR GMTI


  1. Sikaneta, I.S.
Corporate Authors
Defence R&D Canada - Ottawa, Ottawa ONT (CAN)
This report proposes new methods to compute the Kummer hypergeometric function of the second kind and to approximate a special case of the Gauss hypergeometric function. The Kummer hypergeometric function, Ψ(a, c; z), is computed for a, c ε R and x ε R+ although the proposed method can be extended to a, c, z ε C. The special case of the Gauss hypergeometric function is given by 2F1(μ+ν-1, ν-1/2; μ+1/2; x) where μ > | ν - 1 |, and where x ε R < 1. Numerical results of the proposed algorithms are compared with the capabilities of GSL., Mathematica.and Maple.. The evaluation of these functions is required for the dual aperture Synthetic Aperture Radar (SAR), Ground Moving Target Indication (GMTI), Constant False Alarm Rate (CFAR) problem. It is shown that the proposed methods provide a practical means for computing the CFAR thresholds over a wide range of the SAR GMTI statistical parameters and false alarm thresholds, even in very heterogeneous terrain. Additionally, this report shows how to handle infinite integrals that arise when the statistics of heterogeneous terrain are described by the product model. A C++ implementation of the developed algorithms is provided.

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Report Number
DRDC-OTTAWA-TR-2006-294 — Technical Report
Date of publication
01 Dec 2006
Number of Pages

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