Trevor Wolf, The University of Texas at Austin; Brandon Jones, University of Texas at Austin
Keywords: Sensor Tasking, Initial Orbit Determination, Information Theory, Global Optimization
Abstract:
We consider the problem of optimally allocating tasks within a sensor network to acquire a newly detected space object in minimum time and with limited sensor resources. Initial target detections are often generated through electro-optical or radar sensors, which alone do not fully observe the state of a space object. Gaining custody of the object then requires either sufficient geometric diversity between multiple measurements or multiple sensing modalities. To facilitate data association between measurements, physics-informed assumptions allow for generating a representation of the feasible set of states from single measurements, known as the admissible region. The admissible region may be propagated forward and searched at future times to acquire the space object. However, this approach presents several critical challenges. First, the admissible region often necessitates informative priors for the eccentricity and semimajor axis of the object. However, quantitative bounds for these are often undetermined from single measurement tracks. Relaxing these bounds provides higher confidence that the object’s state is contained in the admissible region but drastically increases the hypervolume of dynamically feasible states associated to the target. The issue is compounded in many real cases where physical occlusions, shadowing, or limited sensor resources exclude the availability of timely follow-up observations, between which the feasible search space may grow and become too cumbersome to search with naive approaches.
In this work, we introduce a sensor allocation scheme to intelligently search a general feasible state set for rapidly acquiring a space object. The approach is adaptable for a heterogeneous network of both ground and space-based sensor resources. Our sensor scheduler uses a Finite Set Statistics (FISST) framework so that the set of feasible states associated to an un-tracked object is represented as a Probability Hypothesis Density (PHD) intensity function, which is approximated by a Gaussian Mixture Model (GMM) or a particle ensemble. The PHD filter recursion inherently allows for the ingestion of negative information contained in null detections as the feasible set of states is searched, information contained in true positive detections, as well as varying detection probabilities.
We use a receding time horizon scheduler, which jointly considers all available observing assets. The schedule optimization is formulated where candidate sensor/time combinations are represented as binary decision variables, and on-sky pointing directions are continuous angular coordinates. To mitigate the computational resources required for schedule optimization, we propagate the PHD intensity function off-line, and store its evolution at each candidate observation time. The propagation uses a multi-fidelity approach known as stochastic collocation, which manages the computational resources required for accurate uncertainty propagation by leveraging a suite of low- and high-fidelity dynamics models. The time history of the intensity function is projected into the Field of Regard (FoR) for each candidate sensor resource, and the projected GMM components are stored in a spatial database known as an R-Tree. The R-Tree structure allows efficient queries of the database so that many different sensor pointing directions may be tested quickly in the PHD filter recursion. For each receding horizon window, the optimized schedule minimizes a multi-objective generalization of the differential entropy of the posterior intensity function. This objective function contains numerous local minima, so we employ effective global optimization strategies such as Dual Simulated Annealing (DSA).
This work introduces a method for rapidly acquiring custody of a space object through intelligent sensor tasking. We will demonstrate the efficacy of our approach on several synthetic test cases relevant to the Space Domain Awareness (SDA) community. First, we will present a test case in which a well-constrained admissible region for a Geostationary (GEO) space object is immediately searched using a small network of electro-optical telescopes. We will extend this by augmenting the network with a ground-based satellite laser ranging system. Additionally, we will consider a realistic scenario in which there is an extended delay between the first detection and a follow-up observation. This challenging case will demonstrate the effectiveness of our approach for realistic space object search and recovery operations with a heterogeneous network of sensors. We may also consider scenarios in which the initial feasible set is not well constrained and different orbital regimes, including a Geostationary Transfer Orbit (GTO).
This research will produce important contributions to the SDA community. While much research has been placed in maintaining custody of tracked objects, there is limited work addressing sensor allocation for target acquisition, especially in considering a heterogeneous sensor network.
Date of Conference: September 19-22, 2023
Track: Space Domain Awareness