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Published on: September 28, 2018
Covariant Approach to the Geometric Dilution of Precision
Ramón Serrano Montesinos1, Joan Josep Ferrando1,2, Juan Antonio Morales-Lladosa1,2
1Departament d'Astronomia i Astrofísica, Universitat de València, 46100 Burjassot, València, Spain.
Sensors (Basel, Switzerland)
|August 13, 2026
Summary
A new covariant formulation for the Frequency Geometric Dilution of Precision (FGDOP) scalar is derived within a Relativistic Positioning System (RPS). This method uses observable frequencies and emitter angles for enhanced positioning accuracy.
Area of Science:
- Relativistic Positioning Systems
- Geodesy
- Navigation Systems
Background:
- Geometric Dilution of Precision (GDOP) is a critical factor in positioning accuracy.
- Relativistic effects and frequency ratios are often overlooked in traditional positioning systems.
- A covariant formulation for GDOP within a Relativistic Positioning System (RPS) is needed.
Purpose of the Study:
- To present a covariant formulation of the Geometric Dilution of Precision (GDOP) matrix within a Relativistic Positioning System (RPS).
- To compute the Frequency Geometric Dilution of Precision (FGDOP) scalar using observable quantities.
- To provide a closed-form expression for the FGDOP scalar and clarify its geometric interpretation.
Main Methods:
- Developed a covariant formulation for the GDOP matrix in the framework of RPS.
- Introduced the Frequency Geometric Dilution of Precision (FGDOP) matrix and Gram matrix concepts.
- Utilized the tensor form of the FGDOP matrix and its trace to derive a closed-form FGDOP scalar.
Main Results:
- Computed the FGDOP scalar using receiver-emitter frequency ratios, received frequencies, and angular separation.
- Obtained a closed-form expression for the FGDOP scalar, extending previous matrix calculations.
- Recovered the geometric interpretation of the GDOP scalar in terms of volumes and areas on the celestial sphere.
Conclusions:
- The covariant formulation provides a robust method for calculating FGDOP in RPS.
- The derived FGDOP scalar offers a more comprehensive measure of positioning accuracy by incorporating relativistic effects.
- The geometric interpretation aids in understanding the impact of emitter configuration on positioning precision.
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