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@jemoka / Jemoka Knowledge Base / raw/concept/kbhaircraft_collision_avoidance.md
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--- title: "aircraft collision avoidance" source: https://www.jemoka.com/posts/kbhaircraft_collision_avoidance/ --- suppose we have some aircraft, let’s consider a sensor on this aircraft which is measuring the altitude: there’s a true altitude \(h_{t}\) that our system is at, and a measured altitude \(\hat{h}_{t}\), which has some relation. We can make a observation model through a linear conditional Gaussian: \begin{align} O \qty(o | s) &= O\qty(\hat{h} | h) \\ &= \mathcal{N}\qty(\hat{h} \mid f_{\theta}\qty(h), \sigma^{2}) \\ &= \mathcal{N}\qty(\hat{h} \mid \theta_{1} h + \theta_{2} \mid\sigma^{2}) \end{align} and then we can solve for our parameters \(\theta_{j}\)