Embracing Localization Inaccuracy with a Single Beacon

Abstract

This paper illustrates a new mechanism to determine the coordinates of the sensors using a beacon node and determines the definitive error associated with it. In UWSNs (underwater wireless sensor networks), actual and precise location of the deployed sensors which accumulate data is vital, because the accumulated data without the location information has less significance. Moreover it has limited value in the domain of location based services. In UWSN, trilateration or multilateration is exploited to assess the location of the deployed hosts; having three or more reference nodes to localize a deployed sensor is not pragmatic at all. On the other hand, nonlinear equations are usually solved in conventional method where degree-of-freedom is uncertain to lead to an exclusive solution. In this paper, associated localization inaccuracies has been shown for a unique configuration where a single beacon is used to determine the coordinates of three deployed sensors simultaneously. Cayley-Menger determinant is used for the configuration and system of nonlinear distance equations have been linearized for better accuracy and convergence. Simulations with Euclidean distances validate the propounded model and reflect the acquired accuracies in sensors' coordinates and bearings. Moreover, an experiment has been conducted with ultrasonic sensors in terrestrial environments to validate the proposed model; the associated inaccuracies were found to be generated from the distance measurement errors; on the other hand, considering Euclidean distances proves the model to be precise and accurate.

Non Parallelism and Cayley-Menger Determinant in Submerged Localization

“…The proposed algorithm in [9] was to determine the coordinates of the submerged sensors with a single beacon; the problem domain was considered to be in parallel state which is only possible in perfect world. However, in [7] Cayley-Menger determinant has been used for non-parallel state situation. Following sections iterates the proposed algorithm for parallel and non-parallel states.…”

“…3D positioning system in [6] requires four separate positions to determine the coordinates of the beacon. This paper analyzed the method proposed in [7] to determine the coordinates of underwater sensors with a single beacon where Cayley-Menger determinant is used for non-parallel situation and validates the method with simulation and experimentation. Recently, localization of submerged sensors for non-parallel states has been proposed in [8].…”

ANFIS-EKF-Based Single-Beacon Localization Algorithm for AUV

“…The literature in [11] fuses the Rauch-Tung-Striebel smoother into EKF, and a linear time-varying single-beacon navigation model is used to enhance KF performance in [12]. In addition to filtering estimation methods, there are many other methods that can be used for single-beacon localization, such as modified LS [13,14], Cayley-Menger determinant configuration [15], the second-order time difference of arrival model [16], the phase difference coordinate solution equation [17], and virtual LBL [18][19][20]. In addition, PF can also be used solely to track an underwater target from a maneuver surface vehicle, but the computation complexity is much greater than EKF [21].…”