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 \left(o | s\right) &= O\left(\hat{h} | h\right) \\ &= \mathcal{N}\left(\hat{h} \mid f_{\theta}\left(h\right), \sigma^{2}\right) \\ &= \mathcal{N}\left(\hat{h} \mid \theta_{1} h + \theta_{2} \mid\sigma^{2}\right) \end{align}
and then we can solve for our parameters \theta_{j}