Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformations, such as those occurring in nonlinear filtering and smoothing problems, using tabulated message passing rules. In this contribution, we provide general forward (filtering) and backward (smoothing) approximate Gaussian message passing rules for deterministic nonlinear transformation nodes in arbitrary factor graphs fulfilling a Markov property, based on numerical quadrature procedures for the forward pass and a Rauch-Tung-Striebel-type approximation of the backward pass. These message passing rules can be employed for deriving many algorithms for solving nonlinear problems using factor graphs, as is illustrated by the proposition of a nonlinear modified Bryson-Frazier (MBF) smoother based on the presented message passing rules.
翻译:系数图最近作为信号处理、估计和控制的表示和构建算法的统一框架日益受到注意。在系数图工具箱中似乎没有很好探讨的一种能力是能够处理非线性非线性变换,例如非线性过滤和平滑问题,使用列表式电文传递规则。在这一贡献中,我们提供了一般前向(过滤)和后向(移动)近似高斯电文传递规则,用于在满足马尔科夫属性的任意系数图中确定非线性非线性变换节点,其依据是前方电传口的数字二次转换程序和后方电传口的Rauch-Tung-Striebel-类型近似。这些电文传递规则可用于利用系数图得出许多非线性问题的算法,正如根据电文传递规则提出的非线性修改的Bryson-Frazier(MBF)光化提议所显示的那样。