ASSOCIATION OF TOO SHORT ARCS USING ADMISSIBLE REGION
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The near-Earth space is filled with over 300,000 artificial debris objects with a diameter larger than one cm. For objects in GEO and MEO region, the observations are made mainly through optical sensors. These sensors take observations over a short time which cover only a negligible part of the object's orbit. Two or more such observations are taken as one single Too Short Arc (TSA). Each set of TSA from an optical sensor consists of several angles, the angles of right ascension, declination, along with the rate of change of the right ascension angle and the declination angle. However, such observational data obtained from one TSA because it is covering only a very small fraction of the orbit, is not sufficient for the complete initial determination of an object's orbit. For a newly detected unknown object, only TSAs are available with no information about the orbit of the object. Therefore, two or more such TSAs that belong to the same object are required for its orbit determination. To solve this correlation problem, the framework of the probabilistic Admissible Region is used, which restricts possible orbits based on a single TSA. To propagate the Admissible Region to the time of a second TSA, it is represented in closed-form Gaussian Mixture representation. This way, a propagation with an Extended Kalman filter is possible. To decide if two TSAs are correlated, that is if they belong to the same object, respectively, an overlap between the regions is found in a suitable orbital mechanic's based coordinate frame. To compute the overlap, the information measure of Kullback-Leibler divergence is used.