On the Deterministic Tracking of Moving Objects with a Binary Sensor Network

Let consider a set of anonymous moving objects to be tracked in a binary sensor network. This paper 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 remaining sensor. The difficulty of MOTI lies in the fact that trajectories of two or more objects can be so close (track merging) that the corresponding tracks on the sensor network can no longer be distinguished, thus confusing the deterministic association between an object trajectory and a track. The paper 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 some restrictions that can be imposed a priori either on the graph, on the object movements or both, to make MOTI problem always solvable. We also discuss the consequences of our results and present some related open problems.