Nonlinear Particle Flow for Constrained Bayesian Inference
Kyle J. Craft, Kyle J. DeMars · 2024
A common problem faced in the estimation of dynamic systems is the accurate and statistically consistent incorporation of nonlinear state constraints. Both linear estimators, such as the Kalman filter and its many alterations, and Bayes' rule succumb to various deficiencies when attempting to tractably approximate a set of parameters subject to both equality and inequality constraints. As a result, a novel particle flow measurement update is proposed utilizing Stein variational gradient descent, which seeks to transport the approximating particle ensemble from the prior density to the constrained Bayesian posterior. Two heuristic methods, one for equality constraints and one for inequality constraints, are proposed and evaluated that ensure the constraints are satisfied and that the true Bayesian posterior probability density is accurately approximated. For visualization and qualitative analysis, the methods are first applied to a two-dimensional example problem. Estimator performance is then evaluated in a constrained scenario common in dynamic systems, sequential estimation of the attitude quaternion.