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3

What you're experiencing is the transient lag of the Kalman Filter. The Kalman Filter, using the Measurement and Process Noise balances between begin very adaptive to being an aggressive smoother. In your case it means either having short lag with high error in steady state or having long lag with small error in steady state. In other words, either have low ...

1

If you carefully inspect the Kalman filtering equations, you come to realize that the actual value of the covariance matrix, process noise, and measurement noise aren't what affect the state updates. It's the ratios between them. So assuming that your process noise matrix reflects reality, then your intuition is correct -- using a measurement noise matrix ...

3

$Q_t$ is real-valued and positive definite, thus $Q_t^{-1}$ is real-valued and positive definite. Now it's just making up a lemma of the Cholesky decomposition: If $Q_t^{-1}$ is real-valued and positive definite, then there's some real-valued $q$ such that $q_t^T q_t = Q_t^{-1}$ (Cholesky decomposition) If that holds, then \$\left(q_t C_t \right)^T\left(q_t ...

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