论文标题
使用功率力矩的多元非高斯贝叶斯过滤器
A Multivariate Non-Gaussian Bayesian Filter Using Power Moments
论文作者
论文摘要
在本文中，我们使用功率力矩将结果扩展到单变量的非高斯贝叶斯过滤器上，该系统可以是线性或非线性的多变量系统。这样做会引入几个具有挑战性的问题，例如密度替代物的积极参数化，这不仅是滤波器设计的问题，而且是多维汉堡臂矩问题之一。我们提出了密度替代物的参数化，并证明了其存在，altivstellensatz和唯一性。基于它，我们通过提出的密度替代物分析了密度估计的矩误差。提出了关于非高斯贝叶斯过滤问题的连续和离散处理问题的讨论，以激发有关系统状态连续参数化的研究。给出了估计不同类型的多元密度函数的仿真结果，以验证我们所提出的过滤器。据我们所知，提出的过滤器是第一个实现多元贝叶斯滤波器，将系统状态参数化为连续函数，这仅要求真实的状态为lebesgue commentable。
In this paper, we extend our results on the univariate non-Gaussian Bayesian filter using power moments to the multivariate systems, which can be either linear or nonlinear. Doing this introduces several challenging problems, for example a positive parametrization of the density surrogate, which is not only a problem of filter design, but also one of the multiple dimensional Hamburger moment problem. We propose a parametrization of the density surrogate with the proofs to its existence, Positivstellensatz and uniqueness. Based on it, we analyze the errors of moments of the density estimates by the proposed density surrogate. A discussion on continuous and discrete treatments to the non-Gaussian Bayesian filtering problem is proposed to motivate the research on continuous parametrization of the system state. Simulation results on estimating different types of multivariate density functions are given to validate our proposed filter. To the best of our knowledge, the proposed filter is the first one implementing the multivariate Bayesian filter with the system state parameterized as a continuous function, which only requires the true states being Lebesgue integrable.
