Gaussian Variational Inference with Covariance Constraints Applied to Range-only Localization

Accurate and reliable state estimation is becoming increasingly important as robots venture into the real world. Gaussian variational inference (GVI) is a promising alternative for nonlinear state estimation, which estimates a full probability density for the posterior instead of a point estimate as in maximum a posteriori (MAP)-based approaches. GVI works by optimizing for the parameters of a multivariate Gaussian (MVG) that best agree with the observed data. However, such an optimization procedure must ensure the parameter constraints of a MVG are satisfied; in particular, the inverse covariance matrix must be positive definite. In this work, we propose a tractable algorithm for performing state estimation using GVI that guarantees that the inverse covariance matrix remains positive definite and is well-conditioned throughout the optimization procedure. We evaluate our method extensively in both simulation and real-world experiments for range-only localization. Our results show GVI is consistent on this problem, while MAP is over-confident.