Penalized Maximum Likelihood Based Localization for Unknown Number of Targets Using WSNs: Terrestrial and Underwater Environments

This paper proposes a multiple target localization scheme using a clustered wireless sensor network (WSN) for terrestrial and underwater environments. In the considered system, sensors measure the total energy emitted by the targets and transmit quantized versions of their measurements to a data central device (DCD) with the help of intermediate cluster-heads (CHDs), which employ decode-and-forward relaying (DFR). Upon data collection from sensors, the DCD performs the localization process, which involves estimating the number and positions of the targets. Data transmission from the sensors to CHDs takes place through an imperfect medium, which is characterized by a Rician fading model. The penalized maximum likelihood estimator (PMLE), also known as regularized maximum likelihood estimation (MLE), is applied at the DCD to provide optimal estimates of the number and locations of targets. Furthermore, a suboptimal estimator is derived from PMLE that offers comparable performance under certain operating conditions, but with significantly reduced computational complexity. Cramer-Rao lower bound (CRLB) is derived to serve as an asymptotic benchmark for the root mean square error (RMSE) of the estimators in addition to the centroid-based localization benchmark. Monte Carlo simulation is used to evaluate the performance of the proposed estimation techniques under various system conditions. The results show that PMLE can effectively estimate the number and locations of the targets. Furthermore, it is shown that the RMSE of the proposed estimators approaches the CRLB for a large number of sensors and a high signal-to-noise ratio.