Recursive Bayesian estimation: Difference between revisions

Revision as of 08:48, 21 October 2009

Revision as of 02:57, 21 April 2010

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

The probability distribution of updatedupdate is proportional to the product of the measurement likelihood and the predicted state.

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

= \alpha\,p(\textbf{z}_k|\textbf{x}_k) p(\textbf{x}_k|\textbf{Z}_{k-1})