ISAR cross-range scaling using a correlation based functional

Abstract

In this paper a technique for cross-range scaling of an ISAR image is proposed. Two suitable rows s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> and s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> , relative to the i-th and j-th range bin, are extracted from the range compressed hologram. Then a proper functional G(d(t)), where d(t) is the target rotation law, is evaluated on the complex vector hequiv[h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ...h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> , with h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> =s* <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ik</sub> s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">jk</sub> and k=1, ..., n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> , such that its maximization leads to motion rotation parameter estimation. It is shown how cross-range scaling may be obtained with an observation angle of few degrees. It is considered relevant that the scaling technique is applied to the hologram before motion compensation, so target translation estimation error does not affect rotation estimation. An efficient algorithm to evaluate the functional, based on nearest neighbor or linear interpolation, is then described. Finally, the effectiveness of the technique is tested on real data.