I am studying the Kalman filter and its basic implementation, and it was asked to use the filter to estimate a signal observed in noise
$$y(n) = x(n) + v(n)$$
where $v(n) \sim \mathcal{N}(0, \sigma^2)$ and $x(n)$ is modeled as an ARMA(2,2) process
$$x(n) = b\_0 u(n) + b\_1 u(n-1) - a\_1 x(n-1) - a\_2 x(n-2).$$ 

The exercise is conceptually intersting, but I was wondering if there is an direct application for this case. I mean, which processes, in real life, can be modeled as an ARMA(2,2) and in which context the Kalman filter is used, not as a predictor, for a signal like $s(n)$?

Thanks!