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.

翻译：随机滤波是指在时间上根据观测到的测量值估计潜在随机过程的条件概率分布。本文提出了一类新的收敛型滤波器，该类滤波器通过矩来表示滤波分布。其关键实现是一种利用矩张成的正交多项式进行数值积分的方法。我们证明了这种基于矩的滤波器在矩阶数上是渐近精确的，并表明该滤波器在计算效率方面同样表现出色，与当前最先进的技术水平相当。