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Just correctet the "=\alpha" to "\propto" |
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The probability distribution of update is proportional to the product of the measurement likelihood and the predicted state.
:<math> p(\textbf{x}_k|\textbf{z}_{1:k}) = \frac{p(\textbf{z}_k|\textbf{x}_k) p(\textbf{x}_k|\textbf{z}_{1:k-1})}{p(\textbf{z}_k|\textbf{z}_{1:k-1})}
</math>
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