A Bayesian update method for exponential family projection filters with non-conjugate likelihoods

IF 2.5 3区 计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS
Muhammad Fuady Emzir
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引用次数: 0

Abstract

The projection filter is one of the approximations to the solution of the optimal filtering problem. It approximates the filtering density by projecting the dynamics of the square-root filtering density onto the tangent space of the square-root parametric density manifold. While the projection filters for exponential and mixture families with continuous measurement processes have been well studied, the continuous-discrete projection filtering algorithm for non-conjugate priors has received less attention. In this paper, we introduce a simple Riemannian optimization method to be used for the Bayesian update step in the continuous-discrete projection filter for exponential families. Specifically, we show that the Bayesian update can be formulated as an optimization problem of α-Rényi divergence, where the corresponding Riemannian gradient can be easily computed. We demonstrate the effectiveness of the proposed method via two highly non-Gaussian Bayesian update problems.
非共轭似然指数族投影滤波器的贝叶斯更新方法
投影滤波器是求解最优滤波问题的一种近似方法。它通过将平方根滤波密度的动态投影到平方根参数密度流形的切空间来近似滤波密度。虽然针对连续测量过程的指数族和混合族的投影滤波算法已经得到了很好的研究,但针对非共轭先验的连续离散投影滤波算法却很少受到关注。本文介绍了一种简单的黎曼优化方法,用于指数族连续离散投影滤波器的贝叶斯更新步骤。具体来说,我们证明了贝叶斯更新可以被表述为α- rsamnyi散度的优化问题,其中相应的黎曼梯度可以很容易地计算出来。我们通过两个高度非高斯贝叶斯更新问题证明了所提出方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Systems & Control Letters
Systems & Control Letters 工程技术-运筹学与管理科学
CiteScore
4.60
自引率
3.80%
发文量
144
审稿时长
6 months
期刊介绍: Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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