Applications of random finite set-based multi-target trackers in space situational awareness
Space situational awareness, the ability to accurately characterize and predict the state of the space environment, has become a topic of interest as the population of operational satellites increases. This trend is being driven by the deployment of large constellations of satellites that could consist of tens of thousands of satellites when fully deployed. Tracking space objects accurately is important for predicting and preventing collisions between objects, which can result in catastrophic damage to operational satellites and create debris clouds that endanger other satellites. However, tracking space objects is complicated due in part to the uncertain origins of measurements, a problem known as data ambiguity. While multiple target tracking algorithms that can handle data ambiguity exist, tracking in the space environment presents other challenges. The number of available observations per object is generally low due to the large number of objects relative to available sensor resources, and many observations are left uncorrelated due to the aforementioned data ambiguity problem. The recent rise of large constellations presents another problem in that the involved satellites will utilize low thrust propulsion systems to maintain formation, requiring maneuvering target tracking capabilities for optimal performance. In this dissertation we will analyze two problems that are representative of the space object tracking challenges that operators will face in the near future. We will show how applicable algorithms can developed using finite set statistics, a mathematical framework that allows a top-down approach to be employed in developing rigorous Bayes-optimal multi-target filters with desired functionalities.
The first problem we analyze is a large constellation tracking problem. We simulate a constellation of over 4,500 satellites in low Earth orbit and track them using a network of twelve ground-based myopic sensors. These sensors are tasked using a cost function that combines an information-theoretic reward. We also leverage tactical importance functions to enable the incorporation of mission-based objectives, like prioritization of objects at risk of collision, into the tasking logic. The collected data are processed using a labeled multi-Bernoulli filter. The state catalog estimate produced by the filter is used to motivate the next round of sensor tasking, resulting in an autonomous closed loop system for integrated tasking and tracking. After a five-day tracking period, the state catalog estimate is used to perform a conjunction analysis. We combine existing methods to produce a computationally efficient workflow for the filtering of close approaches between satellites and the quantification of risk.
The second problem we analyze is tracking multiple targets when maneuvering targets are present. Maneuvering targets deviate from their natural trajectories in unpredictable ways and generally require specialized tracking algorithms for best performance. A common method for tracking such targets is the interacting multiple model filter which maintains a bank of models to represent the possible dynamics of a target. Unknown dynamics can be represented as white noise processes through the concept of equivalent noise. This allows maneuvering space objects to be tracked efficiently, but this algorithm lacks the ability to characterize maneuvers. Using finite set statistics, we are able to develop a formulation of the generalized labeled multi-Bernoulli filter that allows for the integration of arbitrary dynamical models. This allows us to utilize data-adaptive methods that model unknown dynamics more specifically, allowing the filter to perform maneuver characterization in addition to maneuvering target tracking. We also develop a consider-based least squares maneuver estimation algorithm that models unknown dynamics using a single impulsive velocity change. The timing of this maneuver is estimated through a multiple hypothesis method. This method is integrated with our formulation of the generalized labeled multi-Bernoulli filter and applied to a simulated constellation of geostationary Earth orbiting satellites that includes a satellite performing an unknown maneuver.
Results in our large constellation tracking work showed that our integrated tasking and tracking algorithm was able to maintain custody of all simulated satellites. We were able to improve the accuracy of risk analysis by incorporating a measure of collision risk in the sensor tasking logic, but the improvement was marginal. We hypothesize that a more generalized optimization algorithm or different sensor architecture may allow mission objective-based tasking to exert greater influence. Our results for the maneuvering target tracking problem showed that we were able to characterize the maneuver dynamics with an acceptable level of accuracy. The absolute errors in our characterization were relatively high compared to the actual maneuvers, but we were able to maintain custody of all objects. Consistency metrics were stable through the occurrence of the maneuver, indicating accurate quantification of the estimated maneuver error uncertainty. Future work remains to scale this work up to a larger-scale scenario where maneuver detection will become a greater factor due to its impact on computational efficiency. Further work would also required to extend our algorithm to non-Gaussian state representations that are often utilized in low-Earth orbit tracking scenarios.