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.

Efficient approximations of the multi-sensor labelled multi-Bernoulli filter

In this paper, we propose two efficient, approximate formulations of the multi-sensor labelled multi-Bernoulli (LMB) filter, which both allow the sensors' measurement updates to be computed in parallel. Our first filter is based on the direct mathematical manipulation of the multi-sensor, multi-object Bayes filter's posterior distribution. Unfortunately, it requires the division of probability distributions and its extension beyond linear Gaussian applications is not obvious. Our second filter is based on covariance intersection and it approximates the multi-sensor, multi-object Bayes filter's posterior distribution using the geometric mean of each sensor's measurement-updated distribution. This filter can be used for distributed fusion under non-linear conditions; however, it is not as accurate as our first filter. In both cases, we approximate the LMB filter's measurement update using an existing loopy belief propagation algorithm, which we adapt to account for object existence. Both filters have a constant complexity in the number of sensors, and linear complexity in both number of measurements and objects. This is an improvement on an iterated-corrector LMB filter, which has linear complexity in the number of sensors. We evaluate both filters' performances on simulated data and the results indicate that the filters are accurate.