Iterative Approximate Nonlinear Inference via Gaussian Message Passing on Factor Graphs

Factor graphs are graphical models able to represent the factorization of probability density functions. By visualizing conditional independence statements, they provide an intuitive and versatile interface to sparsity exploiting message passing algorithms as a unified framework for constructing algorithms in signal processing, estimation, and control in a mix-and-match style. Especially, when assuming Gaussian distributed variables, tabulated message passing rules allow for easy automated derivations of algorithms. This letter's contribution consists in the combination of statistical or Jacobian-based linearization approaches to handling nonlinear factors with efficient message parametrizations in a Gaussian message passing setting. Tabulated message passing rules for a multivariate nonlinear factor node are presented that implement a re-linearization about the most current belief (marginal) of each adjacent variable. When utilized in a nonlinear Kalman smoothing setting, the iterated nonlinear modified Bryson-Frazier smoother is recovered, while retaining the flexibility of the factor graph framework. This application is illustrated by deriving an input estimation algorithm for a nonlinear system.