Manifold Learning With Localized Procrustes Analysis Based WSN Localization

In this letter, we propose a novel system for localization of a wireless sensor network using the localized Procrustes analysis with manifold learning. Due to different environmental factors, such as noise and fading, the internode distances calculated by the received signal strength indicator are erroneous and may not satisfy the $L2$ norm. The nodes seemingly lie on an unknown high-dimensional manifold that satisfies the Riemannian manifold assumption. Thus, the problem of localization is transformed into the problem of nonlinear dimensionality reduction. The location of the nodes can be learned through a manifold learning algorithm like Isomap. However, the coordinates so obtained needed to be transformed to obtain the correct locations of the nodes. We use the localized Procrustes analysis in order to align the relative locations to the absolute or global locations. The localized Procrustes analysis considers each sensor node's neighborhood and computes distinct parameters for each sensor based on the transformation parameters of the anchors present in its neighborhood. Experiment results show that our proposed system outperformed existing localization schemes and can localize the nodes with a better accuracy up to 31.27% in contrast to the least square optimization method.