Counting Moving Bodies Using Sparse Sensor Beams

Abstract—This paper examines the problem of determining the distribution of a number of indistinguishable moving bodies lo-cated in regions separated by sensor beams that can detect whether a body moves across them. We characterize the conditions under which an exact distribution of bodies can be determined, and com-pute bounds on the expected number of sensor observations re-quired to determine this exact distribution for a certain movement model of the bodies. Note to Practitioners —Consider a building in which the rooms are separated by sensors that detect crossings, such as turnstiles (or laser tripwires, pressure-sensitive floors, etc.). If the number of occupants in each room is known initially, it is easy to use the data from the turnstiles to keep the population of each room up-to-date. However, if the number of occupants in each room is not known initially, the data from the turnstiles can be used to determine the population in each room. This paper approximates how long it will take to accumulate the data needed to determine these populations. Index Terms—Filtering, robots, tracking. I