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Fast error analysis of continuous GNSS observations with missing data / M.S. Bos in Journal of geodesy, vol 87 n° 4 (April 2013)  

Public [article]  inJournal of geodesy > vol 87 n° 4 (April 2013) . - pp 351 - 360 Titre : Fast error analysis of continuous GNSS observations with missing data Type de document : Article/Communication Auteurs : M.S. Bos, Auteur ; R. Fernandes, Auteur ; S. Williams, Auteur ; Luisa Bastos, Auteur Année de publication : 2013 Article en page(s) : pp 351 - 360 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] bruit (théorie du signal) [Termes IGN] classification par maximum de vraisemblance [Termes IGN] données GNSS [Termes IGN] matrice de covariance [Termes IGN] série temporelle [Termes IGN] traitement de données GNSS Résumé : (Auteur) One of the most widely used method for the time-series analysis of continuous Global Navigation Satellite System (GNSS) observations is Maximum Likelihood Estimation (MLE) which in most implementations requires O(n3) operations for n observations. Previous research by the authors has shown that this amount of operations can be reduced to O(n2) for observations without missing data. In the current research we present a reformulation of the equations that preserves this low amount of operations, even in the common situation of having some missing data. Our reformulation assumes that the noise is stationary to ensure a Toeplitz covariance matrix. However, most GNSS time-series exhibit power-law noise which is weakly non-stationary. To overcome this problem, we present a Toeplitz covariance matrix that provides an approximation for power-law noise that is accurate for most GNSS time-series. Numerical results are given for a set of synthetic data and a set of International GNSS Service (IGS) stations, demonstrating a reduction in computation time of a factor of 10–100 compared to the standard MLE method, depending on the length of the time-series and the amount of missing data. Numéro de notice : A2013-218 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0605-0 Date de publication en ligne : 02/12/2012 En ligne : https://doi.org/10.1007/s00190-012-0605-0 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=32356 [article]

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Fast error analysis of continuous GPS observations / M. Bos in Journal of geodesy, vol 82 n° 3 (March 2008)  

Public [article]  inJournal of geodesy > vol 82 n° 3 (March 2008) . - pp 157 - 166 Titre : Fast error analysis of continuous GPS observations Type de document : Article/Communication Auteurs : M. Bos, Auteur ; R. Fernandes, Auteur ; S. Williams, Auteur ; et al., Auteur Année de publication : 2008 Article en page(s) : pp 157 - 166 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] bruit blanc [Termes IGN] classification par maximum de vraisemblance [Termes IGN] données GPS [Termes IGN] incertitude des données [Termes IGN] série temporelle Résumé : (Auteur) It has been generally accepted that the noise in continuous GPS observations can be well described by a power-law plus white noise model. Using maximum likelihood estimation (MLE) the numerical values of the noise model can be estimated. Current methods require calculating the data covariance matrix and inverting it, which is a significant computational burden. Analysing 10 years of daily GPS solutions of a single station can take around 2 h on a regular computer such as a PC with an AMD AthlonTM 64 X2 dual core processor. When one analyses large networks with hundreds of stations or when one analyses hourly instead of daily solutions, the long computation times becomes a problem. In case the signal only contains power-law noise, the MLE computations can be simplified to a O(N log N) process where N is the number of observations. For the general case of power-law plus white noise, we present a modification of the MLE equations that allows us to reduce the number of computations within the algorithm from a cubic to a quadratic function of the number of observations when there are no data gaps. For time-series of three and eight years, this means in practise a reduction factor of around 35 and 84 in computation time without loss of accuracy. In addition, this modification removes the implicit assumption that there is no environment noise before the first observation. Finally, we present an analytical expression for the uncertainty of the estimated trend if the data only contains power-law noise. Copyright Springer Numéro de notice : A2008-167 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-007-0165-x En ligne : https://doi.org/10.1007/s00190-007-0165-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29162 [article]

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