Optical reticle trackers with the multi-source discrimination capability by using independent component analysis

Abstract

Due to the simplicity and low cost, since only a few detectors are used, reticle trackers are still in use and are subject of further research. However, the major disadvantage of the reticle trackers has been proven to be sensitivity on the man-made clutters such as flares or jammers. To resolve this problem a beam splitter based modification of the optical trackers has been used successfully for tracking and discrimination of the several moving incoherent (heat) optical sources in the mathematical framework called independent component analyses (ICA). Here we further explore the theoretical basis of the coherent and partially coherent illumination by laser for the possibility of blind source de-mixing. An application of the partial coherence theory and Huygens–Fresnel principle is utilized to formulate the problem. When incoherence is assumed a linear ICA model is obtained while in the most general case of either partially or totally coherent optical radiation the resulting signal model is inherently nonlinear. It can be transformed into linear one under very special condition that assumes no relative motion between the radiating sources. In the most general case of partially coherent radiation, tracking of the several moving optical sources by using the beam splitter based reticle trackers is possible either by using ICA algorithms developed for undercomplete representation or by introduction of one additional sensor. The three conditions necessary for the ICA theory to work (statistical independence and non-Gaussianity of the source signals and nonsingularity of the mixing matrix) are shown to be fulfilled in principle for any kind of the reticle geometry. In relation to some IR counter–countermeasures algorithms which are based on the heuristic and sometimes unrealistic assumptions (target performs no maneuvering) the approach exposed here has been proven to be theoretically consistent without any special constraints imposed on the optical sources.