Relative Positioning via Iterative Locally Linear Embedding: A Distributed Approach Toward Manifold Learning Technique

A novel and distributed version of locally linear embedding (LLE) for the relative positioning of sensor nodes in wireless sensor networks is under focus. The proposed algorithm is iterative in nature and exploits the range and bearing estimates between a sensor and its
$k$
-nearest neighbors forming a local neighborhood that is then utilized in a cooperative fashion to map the whole network. As a result, a partially connected network is localized with every sensor having an estimate of all the sensor positions in the network. It is shown that the proposed distributed mechanism of LLE does not compromise the accuracy of estimation when compared with conventional centralized LLE.