  Humans cannot always be treated as oracles for collaborative sensing. Robots
thus need to maintain beliefs over unknown world states when receiving semantic
data from humans, as well as account for possible discrepancies between
human-provided data and these beliefs. To this end, this paper introduces the
problem of semantic data association (SDA) in relation to conventional data
association problems for sensor fusion. It then develops a novel probabilistic
semantic data association (PSDA) algorithm to rigorously address SDA in general
settings, unlike previous work on semantic data fusion which developed
heuristic techniques for specific settings. PSDA is further incorporated into a
recursive hybrid Bayesian data fusion scheme which uses Gaussian mixture priors
for object states and softmax functions for semantic human sensor data
likelihoods. Simulations of a multi-object search task show that PSDA enables
robust collaborative state estimation under a wide range of conditions where
semantic human sensor data can be erroneous or contain significant reference
ambiguities.
