Degenerate Gaussian factors for probabilistic inference
This work addresses a specific technical bottleneck in probabilistic inference for Gaussian models, offering an incremental improvement for applications like robotics.
The paper tackles the problem of performing probabilistic inference in Gaussian networks with linear dependencies among variables by proposing a parametrized factor that relaxes the positive-definite constraint on covariance matrices, enabling accurate and computationally efficient handling of degeneracies, as demonstrated in a state estimation example for cooperative mobile robots.
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.