I've been asked to give a quantitative confirmation of the Kalman filter that I develop.
My obvious first idea was to compare the residuals.
$$ \chi = {\lvert\lvert C \hat x - y \rvert\rvert}_2^2 $$
where $\hat x$ is the estimate of the state.
However, now that I think of it, the Kalman filter is obviously giving higher residuals. Due to the fact that least-squares by definition is minimizing this quantity...
I mean qualitatively the filter is performing well on simple simulated cases. But it is hard to tell on the real plant. So I'd like to have some quantitative verification.
Thanks so much!