Categorical soft data fusion via variational Bayesian importance sampling with applications to cooperative search

Abstract

This paper considers Bayesian data fusion with categorical 'soft sensor' information, such as human input in cooperative multi-agent search applications. Previous work studied variational Bayesian (VB) hybrid data fusion, which produces optimistic posterior covariance estimates and requires simple Gaussian priors with softmax likelihoods. Here, a new hybrid fusion procedure, known as variational Bayesian importance sampling (VBIS), is introduced to combine the strengths of VB and fast Monte Carlo methods to produce more reliable Gaussian posterior approximations for Gaussian priors and softmax likelihoods. VBIS is then generalized to problems involving complex Gaussian mixture priors and multimodal softmax observation models to obtain reliable Gaussian mixture posterior approximations. The utility and accuracy of the VBIS fusion method is demonstrated on a multitarget search problem for a real cooperative human-automaton team.

Decentralized Information-Rich Planning and Hybrid Sensor Fusion for Uncertainty Reduction in Human-Robot Missions

“…The likelihood functions p(z r,j k |x i ) and p(z h,j k |x i ) are modeled here via multimodal softmax (MMS) models, which enable simple piecewise linear representations of "continuous-to-discrete" probability surface mappings. 8 The top left of Figure 4(b) shows an example 2D MMS model of a triangular probability of detection region for a camera-based target detector mounted to a robot agent facing east. This particular MMS likelihood model has the form ∈ {"next to", "around", "far from"}.…”

“…As discussed in [8], fast Monte Carlo importance sampling techniques can be used to obtain accurate GM approximations for the required posteriors on the left-hand sides of Equations (20) and (21) when the righthand sides contain GM priors and MMS likelihoods. This leads to a recursive approximate Bayesian fusion strategy in which the priors and posteriors in (20) and (21) are always represented as GMs, thus ensuring that human and robot agents can incorporate new information from each other in a consistent and compact form.…”

“…Set q(x i ) using variational Bayes method (see [8]) end if 1. Draw N samples x 1 i , ..., x N i from q(x i ) 2.…”

“…Draw N samples x 1 i , ..., x N i from q(x i ) 2. Evaluate importance weights ω 1 , ..., ω N (see [8] …”

“…For updates via Equation (21), a variational Bayes algorithm is used to determine a q close to the true posterior, which can shift far away from the modes of the input GM when human agents make "surprising" observations (in such cases, severe sample degeneracy could result if q were instead set to the m th component of the input GM). A more detailed description of Algorithm 3, including further details on the selection of q and evaluation of the importance weights ω n in step 2, can be found in [8]. Figure 4 illustrates some typical fusion results using Algorithm 3 .…”