  In object tracking and state estimation problems, ambiguous evidence such as
imprecise measurements and the absence of detections can contain valuable
information and thus be leveraged to further refine the probabilistic belief
state. In particular, knowledge of a sensor's bounded field-of-view can be
exploited to incorporate evidence of where an object was not observed. This
paper presents a systematic approach for incorporating knowledge of the
field-of-view geometry and position and object inclusion/exclusion evidence
into object state densities and random finite set multi-object cardinality
distributions. The resulting state estimation problem is nonlinear and solved
using a new Gaussian mixture approximation based on recursive component
splitting. Based on this approximation, a novel Gaussian mixture Bernoulli
filter for imprecise measurements is derived and demonstrated in a tracking
problem using only natural language statements as inputs. This paper also
considers the relationship between bounded fields-of-view and cardinality
distributions for a representative selection of multi-object distributions,
which can be used for sensor planning, as is demonstrated through a problem
involving a multi-Bernoulli process with up to one-hundred potential objects.

Signal Processing;Robotics