  Stochastic filtering refers to estimating the probability distribution of the
latent stochastic process conditioned on the observed measurements in time. In
this paper, we introduce a new class of convergent filters that represent the
filtering distributions by their moments. The key enablement is a quadrature
method that uses orthonormal polynomials spanned by the moments. We prove that
this moment-based filter is asymptotically exact in the order of moments, and
show that the filter is also computationally efficient and is in line with the
state of the art.
