- #1
zyh
- 137
- 0
hi, everyone, I have a problem when I learn the Bayesian tracking in an Hidden Markov model. Firstly ,the Hidden Markov model is represented here:
http://en.wikipedia.org/wiki/Recursive_Bayesian_estimation
secondly, the problem I encounted is in the follow formula ONE
[tex]$P(X_{i}|y_{0},\ldots,y_{i-1})=\int P(X_{i},X_{i-1}|y_{0},\ldots,y_{i-1})dX_{i-1}$
[/tex]
and then get formula TWO
[tex]$=\int P(X_{i}|X_{i-1},y_{0,\ldots}y_{i-1})P(X_{i-1}|y_{0},\ldots y_{i-1})dX_{i-1}$[/tex]
then get the formula Three
[tex]$=\int P(X_{i}|X_{i-1})P(X_{i-1}|y_{0},\ldots y_{i-1})dX_{i-1}$[/tex]
How can I get the formula Two to three. why
[tex]$P(X_{i}|X_{i-1},y_{0,\ldots}y_{i-1})=P(X_{i}|X_{i-1})$[/tex]
Thank you very much for reading my post, any suggestion is appreciated.
http://en.wikipedia.org/wiki/Recursive_Bayesian_estimation
secondly, the problem I encounted is in the follow formula ONE
[tex]$P(X_{i}|y_{0},\ldots,y_{i-1})=\int P(X_{i},X_{i-1}|y_{0},\ldots,y_{i-1})dX_{i-1}$
[/tex]
and then get formula TWO
[tex]$=\int P(X_{i}|X_{i-1},y_{0,\ldots}y_{i-1})P(X_{i-1}|y_{0},\ldots y_{i-1})dX_{i-1}$[/tex]
then get the formula Three
[tex]$=\int P(X_{i}|X_{i-1})P(X_{i-1}|y_{0},\ldots y_{i-1})dX_{i-1}$[/tex]
How can I get the formula Two to three. why
[tex]$P(X_{i}|X_{i-1},y_{0,\ldots}y_{i-1})=P(X_{i}|X_{i-1})$[/tex]
Thank you very much for reading my post, any suggestion is appreciated.