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Explain the Kalman filter and state-space models. What are the predict and update steps actually doing?

The Kalman filter is optimal Bayesian tracking under linear-Gaussian assumptions, and it is two steps repeated forever. The signal is explaining what the gain trades off and when the assumptions break. Here is the answer.

Updated Aug 2026 · Grounded in real Applied AI Engineer interview loops and written to a senior-engineer editorial bar.

The Kalman filter is optimal Bayesian tracking under linear-Gaussian assumptions, and it is two steps repeated forever. The signal is explaining what the gain trades off and when the assumptions break. Here is the answer.

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