This paper introduces and solves a problem of maintaining the
distribution of hidden targets that move outside the field of view
while a sensor sweep is being performed, resulting in a substantial
generalization of visibility-based pursuit-evasion games. Our solution
first applies information space concepts to dramatically reduce the
general complexity so that information is processed only when the
shadow region (all points invisible to the sensors) changes
combinatorially or targets pass in and out of the field of view. The
cases of distinguishable, partially distinguishable, and completely
indistinguishable targets are handled. Depending on whether the
targets move nondeterministically or probabilistically, more specific
classes of problems are formulated. For each case, efficient
filtering algorithms are introduced, implemented, and demonstrated
that provide critical information for tasks such as counting, herding,
pursuit-evasion, and situational awareness.
