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Robust Covariance Matrix Estimation and Sparse Bias Estimation for Multipath Mitigation

Lesouple, Julien and Barbiero, Franck and Faurie, Frédéric and Sahmoudi, Mohamed and Tourneret, Jean-Yves Robust Covariance Matrix Estimation and Sparse Bias Estimation for Multipath Mitigation. (2018) In: 31st International Technical meeting and showcase of GNSS technology, products and services (ION GNSS+ 2018), 24 September 2018 - 28 September 2018 (Miami, Floride, United States).

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Official URL: https://doi.org/10.33012/2018.15864

Abstract

Multipath is an important source of error when using global navigation satellite systems (GNSS) in urban environment, leading to biased measurements and thus to false positions. This paper treats the GNSS navigation problem as the resolution of an overdetermined system, which depends on the receiver's position, velocity, clock bias, clock drift, and possible biases affecting GNSS measurements. We investigate a sparse estimation method combined with an extended Kalman filter to solve the navigation problem and estimate the multipath biases. The proposed sparse estimation method assumes that only a part of the satellites are affected by multipath, i.e., that the unknown bias vector is sparse in the sense that several of its components are equal to zero. The natural way of enforcing sparsity is to introduce an ℓ1 regularization ensuring that the bias vector has zero components. This leads to a least absolute shrinkage and selection operator (LASSO) problem, which is solved using a reweighted-ℓ1 algorithm. The weighting matrix of this algorithm is defined as functions of the carrier to noise density ratios and elevations of the different satellites. Moreover, the smooth variations of multipath biases versus time are enforced using a regularization based on total variation. For estimating the noise covariance matrix, we use an iterative reweighted least squares strategy based on the so-called Danish method. The performance of the proposed method is assessed via several simulations conducted on different real datasets.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Proceedings of the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation ISSN: 2331-5954 ISBN: 0-936406-10-0 https://www.ion.org/publications/abstract.cfm?articleID=15864
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National d'Études Spatiales - CNES (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Ecole Nationale de l'Aviation Civile - ENAC (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Thales (FRANCE)
Other partners > Telecom ParisTech (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > M3 Systems (FRANCE)
Laboratory name:
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Deposited On:20 Feb 2020 11:51

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