The Effect and Analysis of Cayley-Menger Determinant on Coordinates Determination of Sensors

Abstract

In this paper, we study the localization problem in large-scale underwater sensor networks. We present a method to calculate the sensor node coordinate using single floating beacon node. In underwater wireless sensor networks to determine the specific coordinate of the sensors that collect data is essential. The collected data gives limited value into the actual origin. Trilateration or multilateration techniques is used to determine the location of the sensors with respect to more known beacon nodes and measure the distance between sensor and beacon using acoustic signal(considered the roundtrip time).This method do not measure correct distance between sensor and beacon . In this study, we determined the underwater distances between beacon and sensor nodes using combined radio and acoustic signals, which has better immunity from multipath fading. Cayley-Menger determinant is used to determine the coordinates of the nodes. The simulations and field evaluations show a good estimation of the beacon node positions. Computing coordinates of sensor nodes with negligible errors.