On Approximate Nonlinear Gaussian Message Passing On Factor Graphs
This work addresses a gap in factor graph methods for nonlinear filtering and smoothing, offering a tool for deriving algorithms in signal processing and control, but it is incremental as it builds on existing factor graph frameworks.
The paper tackles the problem of handling deterministic nonlinear transformations in factor graphs for signal processing and estimation, providing forward and backward approximate Gaussian message passing rules based on numerical quadrature and Rauch-Tung-Striebel approximations, and illustrates this with a nonlinear modified Bryson-Frazier smoother.
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.