Consider the following linear system
\begin{align} x_{t+1} = A x_t + w_t,\\ y_t = C x_t + v_t. \end{align}
If pair $(A, C)$ is not detectable, then how to prove $\mathrm{Cov}(x_t - \hat{x}_t)$ diverges?
Thanks!
2026-03-28 04:35:50.1774672550
How to prove the covariance of error in a Kalman filter diverges when the system is not detectable?
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