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Asymptotically efficient GNSS trilateration

Vincent, François and Chaumette, Eric and Charbonnieras, Christophe and Israel, Jonathan and Aubault, Marion and Barbiero, Franck Asymptotically efficient GNSS trilateration. (2017) Signal Processing, 133. 270-277. ISSN 0165-1684

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Official URL: https://doi.org/10.1016/j.sigpro.2016.11.027

Abstract

Localization based on the reception of radio-frequency waveforms is a crucial problem in many civilian or military applications. It is also the main objective of all Global Navigation Satellite System (GNSS). Given delayed and Doppler shifted replicas of the satellites transmitted signals, the most widespread approach consists in a suboptimal two-step procedure. First, estimate the delays and Dopplers from each satellite independently, then estimate the user position and speed thanks to a Least Square (LS) minimization. More accurate and robust techniques, such as a direct Maximum Likelihood (ML) maximization, that exploit the links in between the different channels exist but suffer from an heavy computational burden that prevent their use in real time applications. Two-steps procedures with an appropriate Weighted LS (WLS) minimization are shown to be asymptotically equivalent to the ML procedure. In this paper, we develop a closed-form expression of this WLS asymptotically efficient solution. We show that this simple expression is the sum of two terms. The first one, depending on the pseudo-ranges is the widespread used WLS solution. The second one is a Doppler-aided corrective term that should be taken into account to improve the position estimation when the observation time increases.

Item Type:Article
HAL Id:hal-01428433
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National d'Études Spatiales - CNES (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE)
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Deposited On:22 Oct 2020 12:13

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