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The choice of the importance density is crucial in order to obtain a good estimate of the posterior pdf.
However, because it is often difficult to draw samples from the posterior pdf, an importance density is used to generate the samples.
On Aneraccurate projectimportancele filter resamples 14.9% of the time andensitytandard partisle filter 19.4%, that is, an increase of 30% beneficiale former anotthe latter.
Nevertheless, the closer the importance density is from the true posterior density, the slower the set will degenerate; a good choice of importance density reduces the need for resampling.
It is well known that the optimal importance density is pileft({ {boldsymbol{x}}}_{k}|{ {boldsymbol{x}}}^{(i)}_{0 k-1}, { y}_{1 k}right) = pleft({ {boldsymbol{x}}}_{k}|{ {boldsymbol{x}}}^{(i)}_{k-1}, { y}_{k}right), in the sense that it minimizes the variance of importance weights.
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The transition prior and the importance density are both modeled with normal distributions.
Importance sampling can be highly efficient if a good importance sampling density is constructed.
The importance sampling density is then constructed using nonparametric wavelet density estimation technique.
Using information from the analytical study, an importance sampling density is proposed.
A nonparametric estimation of the optimal importance sampling density is then obtained using the MEDE technique.
Assuming importance density to be equal to the prior density, weight update is recursively computed as w t j ∝ w t - 1 j p z t | x t j. (4).
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