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**pvn** ok - get that now (i've done some experiments): many thanks.

Could you explain importance sampling to me? i understand that if its hard to draw samples from p(x) for example, then instead you sample from q(x), and then weight by p(x)/q(x). What i don't get is how i calculate p(x)?

All i have in my particle filter is the approx to the posterior at any given step represented by my particles, p(x). in my case these are the x,y co-ordinates of an object i'm tracking. i'd like to re-sample in order to get more particles in the high probability region, because a bunch of them have died (i.e. gone to 0 probability or thereabouts). My standard re-sampling algorithm just creates new duplicate particles with the same state space values as the old ones, drawn in accordance to the pdf.

What i want it to do is give me new particles with new state space values (e.g. to get an estimate of an accelerometer bias for example). So i could do importance sampling and generate some completely new samples from my importance distribution q(x-new). But then how do i work out p(x-new) for that sample? All i have is the existing samples. Do i use the nearby samples to calculate a value for p(x)?

i've just got a feeling that i'm missing something fundamental here...