“Robust Incremental Online Inference Over Sparse Factor Graphs:
Beyond the Gaussian Case”
by
D.M. Rosen,
M. Kaess,
and
J.J. Leonard.
In IEEE Intl. Conf. on Robotics and Automation, ICRA, (Karlsruhe,
Germany), May 2013.

Abstract

Many online inference problems in robotics and AI are characterized by
probability distributions whose factor graph representations are sparse.
While there do exist some computationally efficient algorithms (e.g.
incremental smoothing and mapping (iSAM) or Robust Incremental
least-Squares Estimation (RISE)) for performing online incremental maximum
likelihood estimation over these models, they generally require that the
distribution of interest factors as a product of Gaussians, a rather
restrictive assumption. In this paper, we investigate the possibility of
performing efficient incremental online estimation over sparse factor
graphs in the non-Gaussian case. Our main result is a method that
generalizes iSAM and RISE by removing the assumption of Gaussian factors,
thereby significantly expanding the class of distributions to which these
algorithms can be applied. The generalization is achieved by means of a
simple algebraic reduction that under relatively mild conditions
(boundedness of each of the factors in the distribution of interest)
enables an instance of the general maximum likelihood estimation problem
to be reduced to an equivalent instance of least-squares minimization that
can be solved efficiently online by application of iSAM or RISE. Through
this construction we obtain robust, computationally efficient, and
mathematically correct incremental online maximum likelihood estimators
for non-Gaussian distributions over sparse factor graphs.