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Update research.md
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oferdagan authored Sep 13, 2024
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Expand Up @@ -17,7 +17,6 @@ The approach can be broken down into two main steps:
The base integer linear programming approach aims to judiciously allocate sensors to space objects in a manner where the severity of the worst-case scenario is minimized.

Formally, the ILP is given by
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
$$
\begin{aligned}
\text{maximize} \quad & t \\
Expand All @@ -28,7 +27,7 @@ $$
\end{aligned}
$$

Here $$X_{ijt}$$ is a binary 3-dimensional control variable representing whether or not observer $j$ observers object $i$ at time step $t$, and $O_{ijt}$ represents whether or not observer $j$ *is able to* observe object $i$ at time $t$.
Here $$X_{ijt}$$ is a binary 3-dimensional control variable representing whether or not observer $$j$$ observers 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](../assets/images/ilp-plan-600.gif)
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