Asymptotically efficient GNSS trilateration
Résumé
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.
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