Daniel Lück, OKAPI:Orbits GmbH; Christopher Kebschull, OKAPI:Orbits GmbH; Harleen Kaur Mann, OKAPI:Orbits GmbH; Manuel Schubert, Institute of Space Systems, Technische Universität Braunschweig, Germany
Keywords: Correlation, Orbit Determination, Tracklet, Space Situational Awareness
Abstract:
An up-to-date catalogue is crucial for Space Situational awareness. To keep orbits of known objects accurate and find new objects regular observations have to be performed. Surveys of the geostationary region produce large numbers of short observation arcs or tracklets. They can be correlated to catalogued objects via a tracklet to orbit correlation process. If the observed object is not catalogued, an initial orbit determination can be attempted. Due to the length of the tracklet this might not lead to a satisfying result. Therefore, one tracklet should be correlated with at least one other tracklet to gather enough information for a precise initial orbit determination. As part of this work, a boundary value method for tracklet correlation was implemented. The goal was to find factors influencing the performance of the method. In the implemented method, angular positions from two observations are used to calculate an orbit. To evaluate the fit of an observation with the hypothesized orbit, their angular velocities are compared. The Mahalanobis distance between the angular velocities of the real observation and a simulated observation from the calculated orbit is used as a measurement of closeness between the orbit and the tracklet. When dealing with optical observations, the orbit between two observations is not uniquely determined. To find one unique orbit, the range to the object can be fixed for both observations. A downhill simplex algorithm was chosen to optimize the range and find the best-fitting orbit for two observations. When provided with several tracklets a correlation matrix is created containing the lowest possible Mahalanobis distance for every possible combination of two tracklets. The program was tested with simulated observations of 300 objects, covering geostationary and geotransfer orbits. For the simulation, perturbations due to geopotential, drag, solar radiation pressure, and third bodies were considered. The length of the tracklets varied between 30 and 120 seconds. The time between two observations was between 3 hours and 5 days. For the simulated survey campaign, 5 different sensor locations across the globe were used. The approach was shown to work well for observations less than a day apart. More than 90 percent of the tracklet pairs were identified. It worked decently well for observations that were multiple days apart. In this case, 60 percent of correlations were found. From the simulations, major influences on the quality of the correlation were identified. The main factors found to be affecting the fit between correlated tracklets are the time between observations, the orbit of the observed satellite, and the position of the observation on the satellite’s orbit. It was found that using this information can help in deciding which tracklets belong to the same object. Different methods were applied to the correlation matrix to find tracklet pairs belonging to the same object. The simplest way two decide whether two objects are correlated is by applying a fixed threshold on the Mahalanobis distance between them. This typically leads to a significant number of false positives and false negatives in case the data is from different sensors and objects. It was shown that it can be beneficial only to consider the best possible correlation for each tracklet. While this might lead to missing other correct correlations, one correlation is enough to calculate a preliminary orbit. The number of true positives can be improved by adjusting the threshold to the hypothesized orbit of the tracklet pair. A low threshold can be used for GEO objects, while a higher one is applied to GTO objects. This can improve the number of true correlations without affecting false positives.
Date of Conference: September 19-22, 2023
Track: Astrodynamics