Degenerate Gaussian factors for probabilistic inference

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 a generalisation of traditional Gaussian parametrisations where the positive-definite constraint (of covariance and precision matrices) has been relaxed. For this purpose, we derive various statistical operations and results (such as marginalisation, multiplication and affine transformations of random variables) which 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.