Location is one of the basic information required for underwater optical wireless sensor networks (UOWSNs) for
three main purposes: 1) Relating the sensing measurements with precise sensor positions, 2) Enabling efficient routing techniques by exploiting the sensor locations, and 3) Sustaining link connectivity
and performance via pointing and alignment mechanisms between the nodes. Even though various two-dimensional
UOWSNs localization methods have been proposed in the past, the directivity of optical wireless communications and three dimensional (3D) deployment of sensors require to develop 3D underwater localization methods. Therefore, we propose a robust 3D localization method for partially connected UOWSNs with a limited number of anchors. The proposed method achieves an accurate 3D localization of all the nodes in the network by using a novel low-rank matrix approximation and outliers removal method. The performance of the proposed method is compared
with the well known iterative majorization approach. The numerical results indicate that the proposed method outperforms the iterative majorization method substantially.