3D Tdoa Problem Solution with Four Receiving Nodes

Abstract

Time difference of arrival (TDOA) positioning methods have experienced growing importance over the last few years due to their multiple applications in local positioning systems (LPSs). While five sensors are needed to determine an unequivocal three-dimensional position, systems with four nodes present two different solutions that cannot be discarded according to mathematical standards. In this paper, a new methodology to solve the 3D TDOA problems in a sensor network with four beacons is proposed. A confidence interval, which is defined in this paper as a sphere, is defined to use positioning algorithms with four different nodes. It is proven that the separation between solutions in the four-beacon TDOA problem allows the transformation of the problem into an analogous one in which more receivers are implied due to the geometric properties of the intersection of hyperboloids. The achievement of the distance between solutions needs the application of genetic algorithms in order to find an optimized sensor distribution. Results show that positioning algorithms can be used 96.7% of the time with total security in cases where vehicles travel at less than 25 m/s.

Local Wireless Sensor Networks Positioning Reliability Under Sensor Failure

“…This means that in these sensor deployments a sensor fault will cause the unavailability of TOA architectures with 4 sensors and TDOA architectures with 5 sensors. However, our finding in [13] has determined that an unequivocal solution for these systems with a possible sensor failure -3 sensors in TOA and 4 sensors in TDOA-can be achieved under an optimized node localization. As a consequence, an optimized sensor distribution can guarantee the availability of the system in sensor failure conditions through the consideration of a methodology to enhance the system properties in these situations.…”

“…As a consequence, the position determination by means of iterative methods provides a unique solution that it might not match with the real target location. Nevertheless, we have shown in [13] that the optimal solution can be achieved by maximizing the radius of convergence of the initial iteration point which forces the iterative method to converge to the real solution in a high confidence interval. It has been demonstrated that this fact coincides with the maximization of the distance between the two possible solutions in LPS.…”

“…The application of this process to sensors k and l to complete the four-sensor 3D TDOA problem solution in [13] generates the range difference matrix (∆R):…”

“…In one of our previous works [13], we have demonstrated that a reliable unique solution to the intersection of three hyperboloids or spheres can be obtained through the maximization of the distance between the two potential solutions in a defined environment by means of Genetic Algorithms (GA). We achieve this result by applying Taylor-based algorithms [14] from an initial iteration point which must be close enough to the final solution.…”

Refinement of TOA Localization with Sensor Position Uncertainty in Closed-Form

“…With the rise of the fifth-generation communication system (5G), Internet of things, automatic pilot and unmanned aerial vehicle, localization continues to receive great attention [1][2][3][4]. Based on different type of measurements, the common localization methods estimate the source position using time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), Doppler frequency, Fingerprint and received signal strength (RSS) [5][6][7][8][9][10][11][12][13]. To improving the accuracy further, a series of hybrid method is developed by combining several kinds of measurements [14][15][16].…”