Stein Variational Gradient Descent for Non-Bayesian Particle Flow

Bayes’ rule provides an undoubtedly powerful framework for statistical inference; however, the assumptions inherent in Bayesian filtering often cannot be realized in physical systems. Oftentimes, the true Bayesian posterior probability density function (pdf) is infinite-dimensional and lacks tractable implementations, in addition to errors induced by inaccurate realizations of the prior and likelihood pdfs. Though particlebased methods can provide versatile and computationally efficient approximations of Bayes’ rule, they lack the theoretical ability to mitigate estimation errors incurred by erroneous measurement modeling. This work merges Stein Variational Gradient Descent, a nonlinear particle flow update scheme, with generalized variational inference, a method for formulating optimal non-Bayesian posteriors, to produce tractable variational posterior pdfs that remain robust to modeling errors. The new framework is demonstrated to outperform conventional filtering approaches in a simplified relative spacecraft navigation scenario.