Benjamin Reifler, The University of Texas at Austin; Sehyun Yun, The University of Texas at Austin; Brandon Jones, University of Texas at Austin; Renato Zanetti, University of Texas at Austin
Keywords: multi-target tracking, label-partitioned GLMB filter, ensemble Gaussian mixture filter, sparse data, large satellite constellations
Abstract:
The continuing growth of the space object population in Earth orbit will lead to increasing demand on SSA sensor resources. This will increase data sparsity, as the frequency of observations of the average space object decreases. This will especially impact sensors with small fields of view (FoVs), which provide higher quality data than full-sky sensors, but can only observe a small portion of the sky at any time. This necessitates the development of multi-target tracking (MTT) algorithms that can maintain custody of a large population of objects given sparse data. This paper will cover work to track a simulated constellation containing thousands of satellites, configured to create high ambiguity in data association, with significant data sparsity using a label-partitioned generalized labeled multi-Bernoulli (GLMB) filter.
The GLMB filter is a closed-form solution to the Bayes multi-target filter recursion based on labeled random finite sets (RFSs). A labeled RFS is a set containing a random number of random vectors, each with a unique, discrete label. Labeled RFSs can represent the multi-target density of a population of distinctly identifiable objects. The GLMB RFS is a labeled RFS that maintains a table of measurement association hypotheses, referred to as components, and their associated weights. The number of components grows exponentially with each prediction and update, requiring costly truncation to remain computationally tractable.
This computational cost can be reduced by partitioning the label space to create many smaller MTT subproblems. These problems can be handled in parallel, allowing the use of high performance computing facilities. Label partitioning enables tractable large-scale MTT using the GLMB filter. It also enables the use of the GLMB filter with limited-FoV sensors. When too many objects are not observable at each timestep, runaway growth in the number of components can occur. This can be avoided by partitioning the label space based on which sensor’s FoV an object is most likely to appear in, and those objects that are not expected to be visible simply have their tracks propagated without the full GLMB prediction and update.
In this paper, the single-target filter used to predict and update individual tracks will be the ensemble Gaussian mixture filter (EnGMF). The EnGMF predictor uses particles, which can be converted to a Gaussian mixture (GM) via kernel density estimation to allow measurement update using a GM unscented Kalman filter. The EnGMF will help resolve ambiguity due to data sparsity by increasing track prediction accuracy.
The label-partitioned GLMB filter will be applied to two highly ambiguous tracking scenarios. The first is a pair of objects with consistently close spacing in the measurement space (one object following another in the same orbit). The second is a pair of objects with periodic conjunctions in the observation space (two objects in similar orbits with different eccentricities). These scenarios are a good test of the filter, because the constant ambiguity between the two objects generates many data association hypotheses. So far, the filter has been able to track these pairs of objects at varying levels of data sparsity, including observation gaps of up to 48 hours.
The tracking challenge will be increased by adding a constellation containing thousands of objects, simulation fidelity will be improved, and parameters such as the number of particles per track and the maximum number of GLMB components will be optimized to balance tracking performance and computation time. We will demonstrate and assess the filter’s ability to handle many different tracking subproblems simultaneously given sparse data.
Distribution Statement “A” (Approved for Public Release, Distribution Unlimited)
Date of Conference: September 14-17, 2021
Track: Conjunction/RPO