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Stochastic Filtering for Diffusion Processes With Level Crossings
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DOI：10.1109/TAC.2011.2157404.png)
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摘要
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We provide a general framework for computing the state density of a noisy system given the sequence of hitting times of predefined thresholds. Our method relies on eigenfunction expansion corresponding to the Fokker-Planck operator of the diffusion process. For illustration, we present a particular example in which the state and the noise are one-dimensional Gaussian processes and observations are generated when the magnitude of the observed signal is a multiple of some threshold value. We present numerical simulations confirming the convergence and the accuracy of the recovered density estimator. Applications of the filtering methodology will be illustrated.
Keyword:
Diffusion processes
Fokker-Planck equation
nonlinear filtering
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IF:
7
论文数:
1.3W
被引数:
6.7W
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