Measurement Along the Path of Unmanned Aerial Vehicles for Best Horizontal Dilution of Precision and Geometric Dilution of Precision
In the zenith-horizon placement for achieving minimum geometric dilution of precision (GDOP), one access node or sensor is positioned along the z-axis, while the remaining nodes are placed symmetrically on a three-dimensional (3D) cone. This configuration yields the minimum GDOP at the cone’s tip, w...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-06-01
|
| Series: | Sensors |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1424-8220/25/13/3901 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849427584833552384 |
|---|---|
| author | Yanwu Ding Dan Shen Khanh Pham Genshe Chen |
| author_facet | Yanwu Ding Dan Shen Khanh Pham Genshe Chen |
| author_sort | Yanwu Ding |
| collection | DOAJ |
| description | In the zenith-horizon placement for achieving minimum geometric dilution of precision (GDOP), one access node or sensor is positioned along the z-axis, while the remaining nodes are placed symmetrically on a three-dimensional (3D) cone. This configuration yields the minimum GDOP at the cone’s tip, which we term the designated min-GDOP point. However, in practical localization applications, the unknown node is not necessarily located at this designated min-GDOP point; instead, it may be situated anywhere within an area. As a result, evaluating localization accuracy across the entire area, rather than at a single point, is more relevant. Averaged horizontal dilution of precision (HDOP) and GDOP across the region provide more meaningful metrics for system-wide performance than values computed only at a specific location. Although many recent positioning applications leverage multiple unmanned aerial vehicles (UAVs), many established fixed sensor deployments predate the widespread adoption of UAVs. This paper proposes a novel approach with a single UAV working in conjunction with existing fixed access nodes for positioning. This approach offers improved adaptability for fixed infrastructure while circumventing the expense of establishing entirely new UAV systems, thus providing a valuable compromise. We investigate the criteria of average HDOP and GDOP over the given area. The objective is to determine optimal UAV positions along the flight path that minimize the average HDOP and/or GDOP across the area. Due to the analytical complexity, we employ numerical methods. Our simulation results demonstrate that minimizing average HDOP and GDOP often requires different UAV positions, depending on the number of access nodes and the size of the area. Consequently, achieving simultaneous minimization of both metrics with a single UAV trajectory is generally infeasible. When minimizing the average HDOP with a small number of access nodes, aligning the UAV’s XY-plane angle with those of the stationary nodes, offset by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>60</mn><mo>∘</mo></msup></semantics></math></inline-formula>, proves advantageous. This angular alignment becomes less critical as the number of access nodes increases. For scenarios where both HDOP and GDOP are important, UAV placement can be optimized by selecting appropriate trade-offs. Additionally, we quantify how increasing the number of access nodes improves the average HDOP and GDOP over the specified area. |
| format | Article |
| id | doaj-art-4be73249d4724ec8a3dc828dce236a25 |
| institution | Kabale University |
| issn | 1424-8220 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj-art-4be73249d4724ec8a3dc828dce236a252025-08-20T03:28:59ZengMDPI AGSensors1424-82202025-06-012513390110.3390/s25133901Measurement Along the Path of Unmanned Aerial Vehicles for Best Horizontal Dilution of Precision and Geometric Dilution of PrecisionYanwu Ding0Dan Shen1Khanh Pham2Genshe Chen3Department of Electrical and Computer Engineering, Wichita State University, Wichita, KS 67260, USAIntelligent Fusion Technology, Germantown, MD 20874, USAAir Force Research Laboratory, Albuquerque, NM 87108, USAIntelligent Fusion Technology, Germantown, MD 20874, USAIn the zenith-horizon placement for achieving minimum geometric dilution of precision (GDOP), one access node or sensor is positioned along the z-axis, while the remaining nodes are placed symmetrically on a three-dimensional (3D) cone. This configuration yields the minimum GDOP at the cone’s tip, which we term the designated min-GDOP point. However, in practical localization applications, the unknown node is not necessarily located at this designated min-GDOP point; instead, it may be situated anywhere within an area. As a result, evaluating localization accuracy across the entire area, rather than at a single point, is more relevant. Averaged horizontal dilution of precision (HDOP) and GDOP across the region provide more meaningful metrics for system-wide performance than values computed only at a specific location. Although many recent positioning applications leverage multiple unmanned aerial vehicles (UAVs), many established fixed sensor deployments predate the widespread adoption of UAVs. This paper proposes a novel approach with a single UAV working in conjunction with existing fixed access nodes for positioning. This approach offers improved adaptability for fixed infrastructure while circumventing the expense of establishing entirely new UAV systems, thus providing a valuable compromise. We investigate the criteria of average HDOP and GDOP over the given area. The objective is to determine optimal UAV positions along the flight path that minimize the average HDOP and/or GDOP across the area. Due to the analytical complexity, we employ numerical methods. Our simulation results demonstrate that minimizing average HDOP and GDOP often requires different UAV positions, depending on the number of access nodes and the size of the area. Consequently, achieving simultaneous minimization of both metrics with a single UAV trajectory is generally infeasible. When minimizing the average HDOP with a small number of access nodes, aligning the UAV’s XY-plane angle with those of the stationary nodes, offset by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>60</mn><mo>∘</mo></msup></semantics></math></inline-formula>, proves advantageous. This angular alignment becomes less critical as the number of access nodes increases. For scenarios where both HDOP and GDOP are important, UAV placement can be optimized by selecting appropriate trade-offs. Additionally, we quantify how increasing the number of access nodes improves the average HDOP and GDOP over the specified area.https://www.mdpi.com/1424-8220/25/13/3901geometric dilution of precisionGDOPHDOPDOPVDOPgeometric matrix |
| spellingShingle | Yanwu Ding Dan Shen Khanh Pham Genshe Chen Measurement Along the Path of Unmanned Aerial Vehicles for Best Horizontal Dilution of Precision and Geometric Dilution of Precision Sensors geometric dilution of precision GDOP HDOP DOP VDOP geometric matrix |
| title | Measurement Along the Path of Unmanned Aerial Vehicles for Best Horizontal Dilution of Precision and Geometric Dilution of Precision |
| title_full | Measurement Along the Path of Unmanned Aerial Vehicles for Best Horizontal Dilution of Precision and Geometric Dilution of Precision |
| title_fullStr | Measurement Along the Path of Unmanned Aerial Vehicles for Best Horizontal Dilution of Precision and Geometric Dilution of Precision |
| title_full_unstemmed | Measurement Along the Path of Unmanned Aerial Vehicles for Best Horizontal Dilution of Precision and Geometric Dilution of Precision |
| title_short | Measurement Along the Path of Unmanned Aerial Vehicles for Best Horizontal Dilution of Precision and Geometric Dilution of Precision |
| title_sort | measurement along the path of unmanned aerial vehicles for best horizontal dilution of precision and geometric dilution of precision |
| topic | geometric dilution of precision GDOP HDOP DOP VDOP geometric matrix |
| url | https://www.mdpi.com/1424-8220/25/13/3901 |
| work_keys_str_mv | AT yanwuding measurementalongthepathofunmannedaerialvehiclesforbesthorizontaldilutionofprecisionandgeometricdilutionofprecision AT danshen measurementalongthepathofunmannedaerialvehiclesforbesthorizontaldilutionofprecisionandgeometricdilutionofprecision AT khanhpham measurementalongthepathofunmannedaerialvehiclesforbesthorizontaldilutionofprecisionandgeometricdilutionofprecision AT genshechen measurementalongthepathofunmannedaerialvehiclesforbesthorizontaldilutionofprecisionandgeometricdilutionofprecision |