  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 general density evolution equation (GDEE),
the posterior probability of system state is then updated in terms of Bayes
formula. Furthermore, a Chebyshev polynomial-based collocation method is
employed to obtain numerical solutions of the prior probability. An
illustrative example is finally presented to validate the probability density
evolution filter (PDEF) in comparison to particle filter (PF) and UKF. Overall,
PDEF exhibits accuracy close to PF without any resampling algorithm.
