Variational Bayesian data fusion of multi-class discrete observations with applications to cooperative human-robot estimation

A new method is presented for fusing conventional continuous sensor observations with discrete multi-categorical state-dependent information, which can be furnished by humans in many cooperative human-robot interaction problems. The hybrid likelihood function for mapping between continuous hidden states and categorical observations are specified via softmax models. Although softmax models avoid discretization of continuous states, they are challenging to implement for real-time data fusion since they are not analytically integrable. An approximation based on variational Bayesian (VB) methods is presented here to obtain fast closed-form Gaussian solutions to the desired posteriors in cases where the hidden continuous states have Gaussian pdfs. A joint human-robot target localization example illustrates the properties and utility of the VB hybrid fusion strategy, which also applies more generally to inference in hybrid Bayesian networks and mixture models.