Spatial and temporal robustness for scheduling a target tracking mission using wireless sensor networks

•This work studies multi-target tracking under spatial uncertainty.•The problem is extended to a biobjective problem with spatio-temporal uncertainty.•The proposed approach is based on epsilon constraint and bisection methods.•The proposed?algorithms have been implemented and the results have been analyzed. Robust scheduling for target tracking with a wireless sensor network (WSN), focuses on the deployment of a WSN in a remote area to monitor a set of moving targets. Each sensor operates on a battery and is able to communicate with reachable sensors in the network. The targets are typically moving vehicles (planes, trains, cars,…) passing through the area. In order to monitor the targets, an activation schedule is sought such that the sensor network is continuously collecting data about the targets. Additionally, the transfer of the data collected to a base station deployed near the network also has to be planned. In this work, we consider that the trajectories of the targets are estimated. i.e., during the mission, at each time instant t, there is a given position where the target is expected. However, such estimations are inaccurate and deviations can occur. In this work, we formulate the problem of spatial robust scheduling. The aim is to produce an activation schedule for the sensors such that the targets are covered as long as they remain no farther from their estimated positions than a maximized value, called the spatial stability radius of the schedule. Afterwards, we formulate the spatio-temporal robustness problem. It is a bi-objective problem, with a spatial stability radius and a temporal stability radius for covering delays and advances. Two algorithms are proposed to solve these problems, and we show their efficiency through several numerical experiments.