Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.


fl
Posts:
90
Registered:
10/8/05


Question about sequential Monte Carlo
Posted:
Jun 24, 2014 2:05 PM


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_tZ_(t1)^(j), Y_t) and let Z_t^(j)=(Z_(t1)^(j), z_t^(j)); 2. Compute the importance weight w_t^(j)=w_(t1)^(j)*p(Z_t^(j)Y_t)/[p(Z_(t1)Y_(t1)^(j)*q(z_tZ_(t1)^(j), Y_t)] END
My questions are: 1. I do not understand: let Z_t^(j)=(Z_(t1)^(j), z_t^(j));
It simply adds sample z_t^(j) to set Z_(t1)^(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.



