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Kalman Filter
Kalman Filter
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The Kalman filter gives the optimal Bayesian estimate of a hidden state under a linear-Gaussian state-space model. What is the key property that makes the exact posterior also Gaussian at every time step?
Hide and think first
A.
The process and observation noises are assumed to be jointly independent of the hidden state at all times
B.
Linear transformations of Gaussians are Gaussian, and the Gaussian family is conjugate under linear-Gaussian observations
C.
The prior distribution on the initial state
x
0
is assumed to be a delta function, collapsing all uncertainty to a single point
D.
The noise covariance matrices
Q
and
R
are assumed diagonal, so all state and observation components are independent
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