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Topic: Question about sequential Monte Carlo
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fl

Posts: 90
Registered: 10/8/05
Question about sequential Monte Carlo
Posted: Jun 24, 2014 2:05 PM
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Hi,

I read a paper on mixture Kalman filter, which is a simplified particle filter.
It has a sequential Monte Carlo algorithm table to generate importance weight

FOR j=1,...,m DO
1. Draw a sample z_t^(j) from a trial distribution q(z_t|Z_(t-1)^(j), Y_t) and let
Z_t^(j)=(Z_(t-1)^(j), z_t^(j));
2. Compute the importance weight w_t^(j)=w_(t-1)^(j)*p(Z_t^(j)|Y_t)/[p(Z_(t-1)|Y_(t-1)^(j)*q(z_t|Z_(t-1)^(j), Y_t)]
END

My questions are:
1. I do not understand:
let Z_t^(j)=(Z_(t-1)^(j), z_t^(j));

It simply adds sample z_t^(j) to set Z_(t-1)^(j) and get Z_(t)^(j) ?
The element number of Z_(t)^(j) will get continuous increased with t increases?

2. I find that line 2 above uses p(Z_t^(j)|Y_t) with Z_(t)^(j)
If question 1 is solved, how to get p(Z_t^(j)|Y_t)?

I am new to this topic even though I have some probability knowledge. Although
I know Kalman filter, it seems that these new stuff is very difficult. I have spent a lot of time on particle filter, I still feel it difficult on sequential sampling. Please explain it to me if you could.

Thanks a lot.



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