Degenerate Gaussian factors for probabilistic inference

TL;DR

This paper introduces a generalized Gaussian factor representation that handles linear dependencies among variables, enabling accurate probabilistic inference in degenerate Gaussian networks with minimal additional computational cost.

Contribution

It proposes a new parametrized Gaussian factor that relaxes positive-definite constraints, extending inference capabilities to degenerate Gaussian networks.

Findings

Effective handling of degeneracies in Gaussian networks

Extension of statistical operations to degenerate cases

Application to recursive state estimation in robotics

Abstract

In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian parametrisations where the positive-definite constraint of the covariance matrix has been relaxed. For this purpose, we derive various statistical operations and results (such as marginalisation, multiplication and affine transformations of random variables) that extend the capabilities of Gaussian factors to these degenerate settings. By using this principled factor definition, degeneracies can be accommodated accurately and automatically at little additional computational cost. As illustration, we apply our methodology to a representative example involving recursive state estimation of cooperative mobile robots.