Laura Pirovano, Surrey Space Centre, University of Surrey; Roberto Armellin, Surrey Space Centre; Jan Siminski, ESA/ESOC Space Debris Office; Tim Flohrer, ESA/ESOC Space Debris Office
Keywords: Data Association, Multi-Target Tracking, Differential Algebra
Abstract:
Untraced space debris are the principal threat to the functioning of operational satellites whose services have become a fundamental part of our daily life. Small debris between 1 and 10 cm are currently too small to be cataloged and are only detectable for a limited amount of time when surveying the sky. The very-short arc nature of the observations makes it very difficult to perform precise orbit determination with only one passage of the object over the observing station. For this reason the problem of data association becomes relevant: one has to find more observations of the same resident space object to precisely determine its orbit. The different lengths of observations defines the strategy to tackle the problem.
When Initial Orbit Determination (IOD) is possible, previous works [1] described a novel method that built on Differential Algebra (DA) to describe the uncertainty associated to the state of a satellite in an analytical way. In this way one would have continuum of possible candidate orbits – the Orbit Set (OS) – that fit in the observations within a prescribed accuracy and finding overlapping solutions between different observations was straightforward. To keep the analytical description accurate, the Automatic Domain Splitting (ADS) tool was introduce to create a mesh of polynomials over the domain of definition.
However, some observations may be too short or too uncertain to allow for a state and classical IOD methods fail. In these cases the Admissible Region (AR) method is the preferred approach. We then proposed a new method [2] that builds on the AR approach and exploits DA to estimate uncertainty ranges to discriminate between correlated and uncorrelated observations. The uncertainty is defined in six dimensions in spherical coordinates accounting for the orbit physical constraints and observations precision, thus determining again a continuum of candidate orbits, called Admissible States Region (ASR). The ASR has a much larger uncertainty than the OS given the lesser information contained in the observations. Performing data association is thus more challenging. This region is subsequently pruned when a new observation is acquired to remove the states that do not match with new observations. Whenever the intersection is the empty set, the temporary track is discarded. This framework is often referred to as the multi-target tracking (MTT) problem, which is the problem of jointly estimating the number of targets and their states from sensor data. This paper introduces a new description of the AR through DA to improve the computation time and compares three different approaches: DA-based initial value formulation (I-Cor), DA-based and boundary value formulations (B-Cor) and Coral, a software for which the optical correlation is based on [3]. Correlation are assessed on both synthetical and real optical observations obtained by ZimSMART on consecutive nights.
[1] Laura Pirovano, Daniele Antonio Santeramo, Roberto Armellin, Pierluigi Di Lizia, and Alexander Wittig. Probabilistic data association based on intersection of orbit sets. In 19th AMOS Conference, September 11-14, 2018,Maui, USA. Maui Economic Development Board, Inc., September 2018. Printed proceedings published by Curran Associates, Inc.
[2] Laura Pirovano and Roberto Armellin. Initial and boundary value formulations for multi-target tracking. In 1st ESA NEO and Debris Detection Conference, Darmstadt, ESOC, January 2019.
[3] Jan A. Siminski, Oliver Montenbruck, Hauke Fiedler, and Thomas Schildknecht. Short-arc tracklet association for geostationary objects. Advances in Space Research, 53:11841194, April 2014.
Date of Conference: September 17-20, 2019
Track: Astrodynamics