Penalized Maximum Likelihood Based Localization for Unknown Number of
Targets Using WSNs: Terrestrial and Underwater Environments
Abstract
This paper proposes a multiple targets 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 assistance of
intermediate cluster-heads (CHDs), which employ decode-and-forward
relaying (DFR). Upon data collection from the sensors, the DCD performs
the localization process, which involves estimating the number and
positions of the targets. The data transmission from the sensors to the
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 for the number and
locations of targets. Furthermore, a suboptimal estimator is derived
from PMLE, which can offer comparable performance under certain
operating conditions 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 is an effective tool for estimating the number
and locations of the targets. Additionally, it is demonstrated that the
RMSE of the proposed estimation approaches the CRLB for a large number
of sensors and high signal-to-noise ratio.