---
title: "aircraft collision avoidance"
source: https://www.jemoka.com/posts/kbhaircraft_collision_avoidance/
---

suppose we have some aircraft, let&rsquo;s consider a sensor on this aircraft which is measuring the altitude:
there&rsquo;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) &amp;= O\qty(\hat{h} | h) \\ &amp;= \mathcal{N}\qty(\hat{h} \mid f_{\theta}\qty(h), \sigma^{2}) \\ &amp;= \mathcal{N}\qty(\hat{h} \mid \theta_{1} h + \theta_{2} \mid\sigma^{2}) \end{align}
and then we can solve for our parameters \(\theta_{j}\)
