Maximum Likelihood Estimators for Three-Dimensional Rigid Body Localization in Internet of Things Environments

Different from the conventional point source localization, rigid body localization (RBL) not only aims to estimate the position of the target but also to acquire the attitude information, which is also essential information in many Internet of Things (IoT) applications, such as the virtual reality systems, smart parking systems. This paper develops three maximum likelihood estimators (MLEs) for the RBL purpose in 3 dimensional space via a single base station. The MLEs are designed for the RBL framework, which adopts the direction of arrival (DoA) of the signal from a small scale wireless sensor network (SSWSN) mounted on the surface of the rigid target as measurement and can be realized by a single base station. The three MLEs respectively exploit the SSWSN topology information, the DoA measurement information only, as well as the equality constraint of the rotation matrix and the DoA measurement information. In addition, we implement the modified Guass-newton algorithm for the MLEs of the rotation matrix and the translation vector. Simulations show that the proposed MLE fusing the equality constraint of the rotation matrix and the DoA measurement information most approaches the Cramer-Rao Lower Bound and also outperforms the other two MLEs in terms of convergence success rate and the computational cost.