Coordinates Determination of Submerged Sensors Using Cayley-Menger Determinant

This paper investigates the problem of localizing submerged sensors and provides a new mechanism to determine the coordinates of those sensors using only one beacon node. In underwater wireless sensor networks (UWSN), precise coordinate of the sensors that actuate or collect data is vital, as data without the knowledge of its actual origin has limited value. Mostly, multi-lateration technique is used to determine the location of the sensors with respect to three or more known beacon nodes where distance between them is measured considering the roundtrip time of acoustic signal. However, this method of measuring distances gives erroneous results due to a number of factors, including relative angular stand of the nodes. In this study, a new method of determining the underwater distances between beacon and sensor nodes has been presented using combined radio and acoustic signals, which has better immunity from multipath fading. Moreover, Cayley-Menger determinant is used to determine the coordinates of the nodes where none of nodes have a priori knowledge about its location. Simulation results validate the proposed mathematical models by computing coordinates of sensor nodes with negligible errors.