A Lagrangean relaxation based sensor deployment algorithm to optimize quality of service for target positioning

The target positioning service is one of useful applications for wireless sensor networks. So far, most papers considered traditional uniform quality of services (QoS) for target positioning in sensing fields. However, it is possible that all regions in a sensing field have different requirements for target positioning accuracy. We also concern the terrain of sensing fields might have some limitations for placing sensors. Therefore, this paper proposes a generic framework for the sensor deployment problem supporting differential quality of services (QoS) for target positioning to all regions in a sensing field. We define weighted error distance as metric of quality of positioning services. This problem is to optimize the QoS level for target positioning under the limitations of budget and discrimination priorities of regions, where locations and sensing radiuses of all sensors should be determined. We formulate the problem as a nonlinear integer programming problem where the objective function is to minimize of the maximum weighted error distance subject to the complete coverage, deployment budget, and discrimination priority constraints. A Lagrangean relaxation (LR) based heuristic is developed to solve the NP-hard problem. Experimental results reveal that the proposed framework can provide better quality of services for positioning than the previous researches, which only handles uniform QoS requirements. Moreover we evaluate the performance of proposed algorithm. As well as we adopt the previous algorithm, ID-CODE, as the benchmark to examine the proposed heuristic. The results show the proposed algorithm is very effective in terms of deployment cost.

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