scholarly journals 3D Tdoa Problem Solution with Four Receiving Nodes

Sensors ◽  
2019 ◽  
Vol 19 (13) ◽  
pp. 2892 ◽  
Author(s):  
Javier Díez-González ◽  
Rubén Álvarez ◽  
Lidia Sánchez-González ◽  
Laura Fernández-Robles ◽  
Hilde Pérez ◽  
...  
Keyword(s):  
Genetic Algorithms ◽  
Confidence Interval ◽  
Sensor Network ◽  
Three Dimensional ◽  
Time Difference ◽  
Problem Solution ◽  
Time Difference Of Arrival ◽  
Geometric Properties ◽  
Positioning Systems

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.

scholarly journals A Virtualization Approach to Correct Systematic Errors in Measured TDOA and FDOA for Low Orbit Dual-Satellite Positioning Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Gang Li ◽  
Min Zhou ◽  
Hongwen Tang ◽  
Hongbin Chen
Keyword(s):  
Systematic Errors ◽  
Time Difference ◽  
Frequency Difference ◽  
Reference Station ◽  
Virtual Reference ◽  
Time Difference Of Arrival ◽  
Positioning Accuracy ◽  
Positioning Systems ◽  
Location System ◽  
Measured Time

The low-orbit dual-satellite passive location system provides a cost-efficient and easy implementation platform, by which positions of unknown emitters on the Earth can be determined through measuring both the time and the frequency differences by two low-orbit satellites in space. However, in reality, this dual-satellite location system has low positioning accuracy because of the existence of systematic errors. In this paper, in order to address the problem of low positioning accuracy in low-orbit dual-satellite systems, a virtualization approach, consisting of the establishment of the virtual reference station and virtual frequency conversion, is proposed to correct systematic errors in the system. Specifically, we first analyze the coming source of systematic errors in the dual-satellite location system, and then, a virtual reference station and virtual frequency are constructed to correct errors in the measured time difference of arrival and the frequency difference of arrival, respectively. Simulation results show that systematic errors caused by the measured time difference of arrival can be significantly reduced, and the correction efficiency, defined as a ratio between remaining errors after implementing the proposed method over uncorrected ones, for the measured frequency difference of arrival, largely relies on both the virtual frequency and the transmission frequency of reference stations.

scholarly journals Optimal Sensor Formation for 3D Cooperative Localization of AUVs Using Time Difference of Arrival (TDOA) Method

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4442 ◽  
Author(s):  
Xu Bo ◽  
Asghar Razzaqi ◽  
Xiaoyu Wang
Keyword(s):  
Autonomous Underwater Vehicles ◽  
Information Matrix ◽  
Three Dimensional ◽  
Time Difference ◽  
Cooperative Localization ◽  
Evaluation Function ◽  
Time Difference Of Arrival ◽  
Single Target ◽  
Novel Method ◽  
Localization Systems

The cooperative localization of submerged autonomous underwater vehicles (AUVs) using the Time Difference of Arrival (TDOA) measurements of surface AUV sensors is an effective method for many applications of AUVs. Proper positioning of the sensors to maximize the observability of the AUVs is very critical for cooperative localization. In this paper, a novel method for obtaining the optimal formation of sensor AUVs has been presented for the three-dimensional (3D) cooperative localization of targets using the TDOA technique. An evaluation function for estimating the optimal formation has been derived based on Fisher Information Matrix (FIM) theory for a single target as well as multiple-target cooperative localization systems. An iterative stepping algorithm has been followed to solve the evaluation function and obtain the optimal positions of the sensors. The algorithm ensured that the computation complexity should remain limited, even when the number of sensor AUVs is increased. Various simulation examples are then presented to calculate the optimal formation for different systems/situations. The effect of the position of the reference sensor and operating depth of the target AUVs on the optimal formation of the sensors has also been studied, and conclusions are drawn. For implementation of the proposed method for more practical scenarios, a simulation example is also presented for cases when the target’s position is only known with uncertainty.

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