A nonparametric belief solution to the Bayes tree

We relax parametric inference to a nonparametric representation towards more general solutions on factor graphs. We use the Bayes tree factorization to maximally exploit structure in the joint posterior thereby minimizing computation. We use kernel density estimation to represent a wider class of constraint beliefs, which naturally encapsulates multi-hypothesis and non-Gaussian inference. A variety of new uncertainty models can now be directly applied in the factor graph, and have the solver recover a potentially multi-modal posterior. For example, data association for loop closure proposals can be incorporated at inference time without further modifications to the factor graph. Our implementation of the presented algorithm is written entirely in the Julia language, exploiting high performance parallel computing. We show a larger scale use case with the well known Victoria park mapping and localization data set inferring over uncertain loop closures.