This website describes and contains a reference implementation of an algorithm for tasking sensors to investigate human-specified hypotheses about space objects (SOs). The goal is to improve the ability to evaluate internal- and physical- state hypotheses in cases where there are many objects and a collection of sensors with diverse capabilities.

To download and run the algorithm, see the Run the code page; for a brief description of the approach, see below.

Technical Approach

The approach can be broken down into two main steps:

  1. Generating a base plan using integer linear programming
  2. Generating a refined MCTS plan accounting for the object of interest

1. Integer Linear Program

The base integer linear programming approach aims to allocate sensors to space objects over a fixed period, maximizing the minimum observation count across all satellites. This ensures a fair distribution of observations, minimizing the disparity in how often each satellite is observed. By doing so, the approach satisfies the catalog maintenance objective for SDA.

Formally, the ILP is given by

\(\begin{aligned} \text{maximize} \quad & t \\ \text{subject to} \quad & X_{ijt} \in \{0,1\}^{I\times J \times T} \\ & X_{ijt} \preceq O \\ & t \preceq \sum_{j,t} X_{ijt} \\ & \sum_{i} X_{ijt} \preceq 1 \, . \end{aligned}\)

Here \(X_{ijt}\) is a binary 3-dimensional control variable representing whether or not observer \(j\) observes object \(i\) at time step \(t\), and \(O_{ijt}\) represents whether or not observer \(j\) is able to observe object \(i\) at time \(t\).

For ground based-sensors, the ILP plan can be visualized as follows: ILP-Plan .

Building on the ILP solution as a baseline, we assume the existence of an object of interest (OOI) in the catalogue, for which we seek to resolve a specific hypothesis. This work focuses on determining the true dynamic model the OOI is transitioning according to, for example due to drag configuration. To achieve this, we use Monte Carlo Tree Search (MCTS) applied to a belief Markov Decision Process (MDP). The goal of the MCTS solver is to minimize the entropy of the distribution over possible hypotheses while minimally disrupting the baseline catalogue maintenance plan.

Demo Results

To test the code we simulated 1600 seconds of trajectory, with a time step of 20 seconds. In this scenario, there are 5 SO’s, where one of them is the object of interest (OOI). The OOI moves in an unperturb nominal Keplerian orbit. However, an operator decides to investigate two competing hypothesis (in addition to the nominal): (i) the OOI deployed a set of small solar panels, which correspond to an area drag of 1, and (ii) the OOI deployed a larger set of solar panels, which corresponds to area drag of 5. In each decision point, the planning algorithm decides wheter to proceed with the nominal tasking plan, or change it to observe the OOI, with the goal of differentiating between the 3 hypotheses, and eventually deciding on the most probable one. The graph below shows the probability values for each hypothesis vs. time. As can be seen from the graph, it taks about 30 time steps to start differentiating between hypotheses, and the algorithm converges to the correct one with about \(75\%\) confidence.

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