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Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)

We each have different life experiences to fuel our intuition, but try this one out: Let $\mathbf A = 1$ and $\mathbf Q = 0$, and $\mathbf C = 1$ -- i.e., the actual state variable just doesn't change,...
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