Multi-target tracking and identification by a vector of sensors

Diverse security applications often require monitoring of a narrow passage, such as an indoor corridor, a tunnel, a bridge; either to protect critical assets at the end of such a passage or to control the passage over it, or both. Often, sensors are arranged in a vector along such a passage and are capable of registering the crossing of a target but not its identity. In this paper, we consider coordinated tracking by such a vector of sensors where each sensor learns timings of objects passing at monitored spots from its predecessors. Hence, the problem we are solving could be formulated as an assignment or matching of target identities to arrival times of the targets at the subsequent sensors in a vector. We introduce a cost function that is the sum of squares of the difference between each target´s predicted and observed arrival time at each sensor. We use target´s speed as computed from the arrival times of the target at previous two sensors to predict the time of arrival at the current sensor. In such a scheme, the simple matching algorithm that sorts predicted and actual arrival times in two separated lists and then matches both lists by positions minimizes this and similar cost functions for each sensor locally in O(n log n) time. We have also developed more costly algorithms that yield higher quality global solution at the cost of communication, computation and memory. In the paper, we evaluate analytically, and by simulations, different variants of this matching algorithm and their complexity and performance.