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:随机滤波是指基于时间序列中的观测值估计潜在随机过程的概率分布。本文介绍一种新的滤波器类型,它通过矩表示滤波分布。关键是采用由矩张成的正交多项式执行的积分方法。我们证明该基于矩的滤波器在矩的阶数方面是渐近准确的,并且表明此滤波器也具有计算效率,在技术领域内达到了最新水平。