Recursive Bayesian estimation: Difference between revisions

Revision as of 15:20, 22 January 2006

Revision as of 04:25, 26 February 2006

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:[[Image:HMMKalmanFilterDerivation.png|463-239|Hidden Markov Model]]

Because of the Markov assumption, the true state is conditionally independent of all earlier states given the immediately previous state.

:<math>p(\textbf{x}_k|\textbf{x}_0,...,\textbf{x}_{k-1}) = p(\textbf{x}_k|\textbf{x}_{k-1})</math>

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:<math>p(\textbf{z}_k|\textbf{Z}_{k-1}) = \int p(\textbf{z}_k|\textbf{x}_k) p(\textbf{x}_k|\textbf{Z}_{k-1}) d\textbf{x}_k</math>

is an unimportant normalisation term.

== Applications ==