  In this paper, we construct a type of interacting particle systems to
approximate a class of stochastic different equations whose coefficients depend
on the conditional probability distributions of the processes given partial
observations. After proving the well-posedness and regularity of the particle
systems, we establish a quantitative convergence result for the empirical
measures of the particle systems in the Wasserstein space, as the number of
particles increases. Moreover, we discuss an Euler--Maruyama scheme of the
particle system and validate its strong convergence. A numerical experiment is
conducted to illustrate our results.
