Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint
Finding the position of a radiative source based on time-difference-of-arrival (TDOA) measurements from spatially separated receivers has been widely applied in sonar, radar, mobile communications and sensor networks. For the nonlinear model in the process of positioning, Taylor series and other nov...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-03-01
|
| Series: | Sensors |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1424-8220/18/3/778 |
| _version_ | 1818035073712128000 |
|---|---|
| author | Bonan Jin Xiaosu Xu Tao Zhang |
| author_facet | Bonan Jin Xiaosu Xu Tao Zhang |
| author_sort | Bonan Jin |
| collection | DOAJ |
| description | Finding the position of a radiative source based on time-difference-of-arrival (TDOA) measurements from spatially separated receivers has been widely applied in sonar, radar, mobile communications and sensor networks. For the nonlinear model in the process of positioning, Taylor series and other novel methods are proposed. The idea of cone constraint provides a new way of solving this problem. However, these approaches do not always perform well and are away from the Cramer-Rao-Lower-Bound (CRLB) in the situations when the source is set at the array edge, the noise in measurement is loud, or the initial position is biased. This paper presents a weighted-least-squares (WLS) algorithm with the cone tangent plane constraint for hyperbolic positioning. The method adds the range between the source and the reference sensor as a dimension. So, the space-range frame is established. Different from other cone theories, this paper sets the reference sensor as the apex and finds the optimal source estimation on the cone. WLS is used for the optimal result from the measurement plane equations, a vertical constraint and a cone constraint. The cone constraint equation is linearized by a tangent plane. This method iterates through loops and updates the tangent plane, which approximates the truth-value on the cone. The proposed algorithm was simulated and verified under various conditions of different source positions and noises. Besides, some state-of-the-art algorithms were compared in these simulations. The results show that this algorithm is accurate and robust under poor external environment. |
| first_indexed | 2024-12-10T06:49:16Z |
| format | Article |
| id | doaj.art-bce79b5e09354637a6a3277c1f167c56 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-12-10T06:49:16Z |
| publishDate | 2018-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-bce79b5e09354637a6a3277c1f167c562022-12-22T01:58:36ZengMDPI AGSensors1424-82202018-03-0118377810.3390/s18030778s18030778Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane ConstraintBonan Jin0Xiaosu Xu1Tao Zhang2Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, ChinaKey Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, ChinaKey Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, ChinaFinding the position of a radiative source based on time-difference-of-arrival (TDOA) measurements from spatially separated receivers has been widely applied in sonar, radar, mobile communications and sensor networks. For the nonlinear model in the process of positioning, Taylor series and other novel methods are proposed. The idea of cone constraint provides a new way of solving this problem. However, these approaches do not always perform well and are away from the Cramer-Rao-Lower-Bound (CRLB) in the situations when the source is set at the array edge, the noise in measurement is loud, or the initial position is biased. This paper presents a weighted-least-squares (WLS) algorithm with the cone tangent plane constraint for hyperbolic positioning. The method adds the range between the source and the reference sensor as a dimension. So, the space-range frame is established. Different from other cone theories, this paper sets the reference sensor as the apex and finds the optimal source estimation on the cone. WLS is used for the optimal result from the measurement plane equations, a vertical constraint and a cone constraint. The cone constraint equation is linearized by a tangent plane. This method iterates through loops and updates the tangent plane, which approximates the truth-value on the cone. The proposed algorithm was simulated and verified under various conditions of different source positions and noises. Besides, some state-of-the-art algorithms were compared in these simulations. The results show that this algorithm is accurate and robust under poor external environment.http://www.mdpi.com/1424-8220/18/3/778conepositioningrobustTaylorTDOAWLS |
| spellingShingle | Bonan Jin Xiaosu Xu Tao Zhang Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint Sensors cone positioning robust Taylor TDOA WLS |
| title | Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint |
| title_full | Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint |
| title_fullStr | Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint |
| title_full_unstemmed | Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint |
| title_short | Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint |
| title_sort | robust time difference of arrival tdoa localization using weighted least squares with cone tangent plane constraint |
| topic | cone positioning robust Taylor TDOA WLS |
| url | http://www.mdpi.com/1424-8220/18/3/778 |
| work_keys_str_mv | AT bonanjin robusttimedifferenceofarrivaltdoalocalizationusingweightedleastsquareswithconetangentplaneconstraint AT xiaosuxu robusttimedifferenceofarrivaltdoalocalizationusingweightedleastsquareswithconetangentplaneconstraint AT taozhang robusttimedifferenceofarrivaltdoalocalizationusingweightedleastsquareswithconetangentplaneconstraint |