Cooperative Localization in Hybrid Active and Passive Wireless Sensor Networks With Unknown Tx Power

Abstract

Hybrid active and passive wireless sensor networks (HWSNs) gain advantages in extending the network lifetime and reducing the overall cost. Because the passive sensors without battery harvest the energy from distributed active sensor signal beam, and only a few active sensors can maintain a large-scale network. Thus, how to track the passive sensor’s location is essential for network management. Since the active sensors are sparsely deployed, cooperative localization which employs passive sensors to locate themselves together is a promising solution. In this paper, we analyze the energy beam generated by the active sensors on the cooperative localization accuracy of the passive sensors. We consider the spatial-temporal cooperative localization based on the received signal strength (RSS) model with unknown Tx power information of each sensor due to the limited processing capabilities, circuit complexity and energy constraints. We formulate the Fisher information matrix (FIM) and the corresponding Cramér-Rao lower bound (CRLB) for the static full connected network and dynamic spatial-temporal recursive network. Accordingly, energy beamforming schemes are proposed to optimize localization accuracy and energy efficiency problems. For the optimal localization problem, we derive the closed-form solution of the optimal energy beamforming wave. For the optimal energy efficiency problem, we propose a semi-definite programming (SDP) solution to achieve optimal energy consumption with a self-calibration method, which can address the over-relax problem. Extensive simulation results indicate that our proposed beamforming schemes have high localization accuracy and lower power consumption compared with the existing power allocation-based schemes.