Algebraic analysis of Doppler-based positioning with application to LEO satellites
Ferranti, Luca ; Astrom, Kalle LU
; Oskarsson, Magnus
LU
and Prol, Fabricio Dos Santos
(2025)
15th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2025
In Proceedings of the 15th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2025
- Abstract
In this paper we revisit positioning from Doppler measurements, using techniques from algebraic geometry to produce new theoretical insights and efficient localization algorithms. First, we give a full characterization of the problem, identifying for each problem their minimal configurations, that is the minimum number of receivers and transmitters to have a finite number of solutions. We also study the degree of each configuration. Finally, we show how these algebraic techniques can be applied to obtain an accurate position estimation in challenging environments, such as in the presence of noise and outliers. We also describe how the derived optimized algebraic solver can be integrated in a positioning engine for Low Earth Orbit... (More)
In this paper we revisit positioning from Doppler measurements, using techniques from algebraic geometry to produce new theoretical insights and efficient localization algorithms. First, we give a full characterization of the problem, identifying for each problem their minimal configurations, that is the minimum number of receivers and transmitters to have a finite number of solutions. We also study the degree of each configuration. Finally, we show how these algebraic techniques can be applied to obtain an accurate position estimation in challenging environments, such as in the presence of noise and outliers. We also describe how the derived optimized algebraic solver can be integrated in a positioning engine for Low Earth Orbit position, navigation and timing (LEO PNT) systems.
(Less)
- author
- Ferranti, Luca
; Astrom, Kalle
LU
; Oskarsson, Magnus
LU
and Prol, Fabricio Dos Santos
- organization
-
- Lund Laser Centre, LLC
- LTH Profile Area: Photon Science and Technology
- Computer Vision and Machine Learning (research group)
- LU Profile Area: Nature-based future solutions
- LU Profile Area: Light and Materials
- LU Profile Area: Proactive Ageing
- LU Profile Area: Natural and Artificial Cognition
- LTH Profile Area: AI and Digitalization
- LTH Profile Area: Engineering Health
- Stroke Imaging Research group (research group)
- ELLIIT: the Linköping-Lund initiative on IT and mobile communication
- eSSENCE: The e-Science Collaboration
- Mathematical Imaging Group (research group)
- Mathematics (Faculty of Engineering)
- publishing date
- 2025
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- algebraic geometry, Doppler, LEO PNT, minimal problems, robust estimation, satellite positioning
- host publication
- Proceedings of the 15th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2025
- series title
- Proceedings of the 15th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2025
- editor
- Nurmi, Jari ; Lohan, Simona ; Ometov, Aleksandr ; Klus, Lucie ; Mutschler, Christopher and Torres-Sospedra, Joaquin
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 15th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2025
- conference location
- Tampere, Finland
- conference dates
- 2025-09-15 - 2025-09-18
- external identifiers
-
- scopus:105022150436
- ISBN
- 9798331556808
- DOI
- 10.1109/IPIN66788.2025.11213444
- language
- English
- LU publication?
- yes
- id
- 89697cc2-d457-4134-b6c9-4ba4feb0a217
- date added to LUP
- 2026-02-09 15:12:27
- date last changed
- 2026-02-09 15:12:57
@inproceedings{89697cc2-d457-4134-b6c9-4ba4feb0a217,
abstract = {{<p>In this paper we revisit positioning from Doppler measurements, using techniques from algebraic geometry to produce new theoretical insights and efficient localization algorithms. First, we give a full characterization of the problem, identifying for each problem their minimal configurations, that is the minimum number of receivers and transmitters to have a finite number of solutions. We also study the degree of each configuration. Finally, we show how these algebraic techniques can be applied to obtain an accurate position estimation in challenging environments, such as in the presence of noise and outliers. We also describe how the derived optimized algebraic solver can be integrated in a positioning engine for Low Earth Orbit position, navigation and timing (LEO PNT) systems.</p>}},
author = {{Ferranti, Luca and Astrom, Kalle and Oskarsson, Magnus and Prol, Fabricio Dos Santos}},
booktitle = {{Proceedings of the 15th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2025}},
editor = {{Nurmi, Jari and Lohan, Simona and Ometov, Aleksandr and Klus, Lucie and Mutschler, Christopher and Torres-Sospedra, Joaquin}},
isbn = {{9798331556808}},
keywords = {{algebraic geometry; Doppler; LEO PNT; minimal problems; robust estimation; satellite positioning}},
language = {{eng}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{Proceedings of the 15th International Conference on Indoor Positioning and Indoor Navigation, IPIN 2025}},
title = {{Algebraic analysis of Doppler-based positioning with application to LEO satellites}},
url = {{http://dx.doi.org/10.1109/IPIN66788.2025.11213444}},
doi = {{10.1109/IPIN66788.2025.11213444}},
year = {{2025}},
}