Analysis of Deterministic Tracking of Multiple Objects Using a Binary Sensor Network

Let consider a set of anonymous moving objects to be tracked in a binary sensor network. This article studies the problem of associating deterministically a track revealed by the sensor network with the trajectory of an unique anonymous object, namely the multiple object tracking and identification (MOTI) problem. In our model, the network is represented by a sparse connected graph where each vertex represents a binary sensor and there is an edge between two sensors if an object can pass from one sensed region to another one without activating any other sensor. The difficulty of MOTI lies in the fact that the trajectories of two or more objects can be so close that the corresponding tracks on the sensor network can no longer be distinguished (track merging), thus confusing the deterministic association between an object trajectory and a track. The article presents several results. We first show that MOTI cannot be solved on a general graph of ideal binary sensors even by an omniscient external observer if all the objects can freely move on the graph. Then we describe restrictions that can be imposed a priori either on the graph, on the object movements, or on both, to make the MOTI problem always solvable. In the absence of an omniscient observer, we show how our results can lead to the definition of distributed algorithms that are able to detect when the system is in a state where MOTI becomes unsolvable.