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Probability density evolution filter
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DOI：10.1016/j.probengmech.2022.103325.png)
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Abstract
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Based on probability density evolution method (PDEM) and Bayes' law, a new filter strategy is proposed, in which the prior probability of system state of interest is predicted by solving the generalized density evolution equation (GDEE), the posterior probability of system state is then updated in terms of Bayesian formula. Furthermore, a Chebyshev polynomial-based collocation method is developed to obtain numerical solutions of the prior probability. Three illustrative examples are finally presented to validate the probability density evolution filter (PDEF). Overall, PDEF evolves the prior probability through a differential equation, and exhibits accuracy close to PF without any resampling algorithm.
Keywords:
Probabilitydensityevolutionmethod
Bayes
Particlefilter
UKF
Spectralmethod
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