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A drift line bias estimator: ARMA-based filter or calibration method, and its application in BDS/GPS-based attitude determination / Zhang Liang in Journal of geodesy, vol 90 n° 12 (December 2016)
[article]
Titre : A drift line bias estimator: ARMA-based filter or calibration method, and its application in BDS/GPS-based attitude determination Type de document : Article/Communication Auteurs : Zhang Liang, Auteur ; Hou Yanqing, Auteur ; Wu Jie, Auteur Année de publication : 2016 Article en page(s) : pp 1331 - 1343 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Traitement du signal
[Termes IGN] échantillonnage de signal
[Termes IGN] erreur systématique
[Termes IGN] estimateur
[Termes IGN] étalonnage des données
[Termes IGN] filtrage du signal
[Termes IGN] positionnement ponctuel précis
[Termes IGN] signal BeiDou
[Termes IGN] signal GPSRésumé : (Auteur) The multi-antenna synchronized receiver (using a common clock) is widely applied in GNSS-based attitude determination (AD) or terrain deformations monitoring, and many other applications, since the high-accuracy single-differenced carrier phase can be used to improve the positioning or AD accuracy. Thus, the line bias (LB) parameter (fractional bias isolating) should be calibrated in the single-differenced phase equations. In the past decades, all researchers estimated the LB as a constant parameter in advance and compensated it in real time. However, the constant LB assumption is inappropriate in practical applications because of the physical length and permittivity changes of the cables, caused by the environmental temperature variation and the instability of receiver-self inner circuit transmitting delay. Considering the LB drift (or colored LB) in practical circumstances, this paper initiates a real-time estimator using auto regressive moving average-based (ARMA) prediction/whitening filter model or Moving average-based (MA) constant calibration model. In the ARMA-based filter model, four cases namely AR(1), ARMA(1, 1), AR(2) and ARMA(2, 1) are applied for the LB prediction. The real-time relative positioning model using the ARMA-based predicting LB is derived and it is theoretically proved that the positioning accuracy is better than the traditional double difference carrier phase (DDCP) model. The drifting LB is defined with a phase temperature changing rate integral function, which is a random walk process if the phase temperature changing rate is white noise, and is validated by the analysis of the AR model coefficient. The auto covariance function shows that the LB is indeed varying in time and estimating it as a constant is not safe, which is also demonstrated by the analysis on LB variation of each visible satellite during a zero and short baseline BDS/GPS experiment. Compared to the DDCP approach, in the zero-baseline experiment, the LB constant calibration (LBCC) and MA approaches improved the positioning accuracy of the vertical component, while slightly degrading the accuracy of the horizontal components. The ARMA(1, 0) model, however, improved the positioning accuracy of all three components, with 40 and 50 % improvement of the vertical component for BDS and GPS, respectively. In the short baseline experiment, compared to the DDCP approach, the LBCC approach yielded bad positioning solutions and degraded the AD accuracy; both MA and ARMA-based filter approaches improved the AD accuracy. Moreover, the ARMA(1, 0) and ARMA(1, 1) models have relatively better performance, improving to 55 % and 48 % the elevation angle in ARMA(1, 1) and MA model for GPS, respectively. Furthermore, the drifting LB variation is found to be continuous and slowly cumulative; the variation magnitudes in the unit of length are almost identical on different frequency carrier phases, so the LB variation does not show obvious correlation between different frequencies. Consequently, the wide-lane LB in the unit of cycle is very stable, while the narrow-lane LB varies largely in time. This reasoning probably also explains the phenomenon that the wide-lane LB originating in the satellites is stable, while the narrow-lane LB varies. The results of ARMA-based filters are better than the MA model, which probably implies that the modeling for drifting LB can further improve the precise point positioning accuracy. Numéro de notice : A2016-805 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0926-5 En ligne : http://dx.doi.org/10.1007/s00190-016-0926-5 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=82593
in Journal of geodesy > vol 90 n° 12 (December 2016) . - pp 1331 - 1343[article]Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix / Gaël Kermarrec in Journal of geodesy, vol 90 n° 9 (September 2016)
[article]
Titre : Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix Type de document : Article/Communication Auteurs : Gaël Kermarrec, Auteur ; Steffen Schön, Auteur Année de publication : 2016 Article en page(s) : pp 793 – 805 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Termes IGN] compensation par moindres carrés
[Termes IGN] corrélation
[Termes IGN] données GPS
[Termes IGN] estimateur
[Termes IGN] matrice de covariance
[Termes IGN] matrice diagonale
[Termes IGN] pondération
[Termes IGN] positionnement différentiel
[Termes IGN] positionnement par GPS
[Termes IGN] régression
[Termes IGN] série temporelle
[Vedettes matières IGN] Traitement de données GNSSRésumé : (auteur) Based on the results of Luati and Proietti (Ann Inst Stat Math 63:673–686, 2011) on an equivalence for a certain class of polynomial regressions between the diagonally weighted least squares (DWLS) and the generalized least squares (GLS) estimator, an alternative way to take correlations into account thanks to a diagonal covariance matrix is presented. The equivalent covariance matrix is much easier to compute than a diagonalization of the covariance matrix via eigenvalue decomposition which also implies a change of the least squares equations. This condensed matrix, for use in the least squares adjustment, can be seen as a diagonal or reduced version of the original matrix, its elements being simply the sums of the rows elements of the weighting matrix. The least squares results obtained with the equivalent diagonal matrices and those given by the fully populated covariance matrix are mathematically strictly equivalent for the mean estimator in terms of estimate and its a priori cofactor matrix. It is shown that this equivalence can be empirically extended to further classes of design matrices such as those used in GPS positioning (single point positioning, precise point positioning or relative positioning with double differences). Applying this new model to simulated time series of correlated observations, a significant reduction of the coordinate differences compared with the solutions computed with the commonly used diagonal elevation-dependent model was reached for the GPS relative positioning with double differences, single point positioning as well as precise point positioning cases. The estimate differences between the equivalent and classical model with fully populated covariance matrix were below the mm for all simulated GPS cases and below the sub-mm for the relative positioning with double differences. These results were confirmed by analyzing real data. Consequently, the equivalent diagonal covariance matrices, compared with the often used elevation-dependent diagonal covariance matrix is appropriate to take correlations in GPS least squares adjustment into account, yielding more accurate cofactor matrices of the unknown. Numéro de notice : A2016-654 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-016-0911-z En ligne : http://dx.doi.org/10.1007/s00190-016-0911-z Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=81856
in Journal of geodesy > vol 90 n° 9 (September 2016) . - pp 793 – 805[article]MIDAS robust trend estimator for accurate GPS station velocities without step detection / Geoffrey Blewitt in Journal of geophysical research : Solid Earth, vol 121 n° 3 (March 2016)
[article]
Titre : MIDAS robust trend estimator for accurate GPS station velocities without step detection Type de document : Article/Communication Auteurs : Geoffrey Blewitt, Auteur ; Corné Kremer, Auteur ; William C. Hammond, Auteur ; Julien Gazeaux , Auteur Année de publication : 2016 Article en page(s) : pp 2054 - 2068 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale
[Termes IGN] Amérique du nord
[Termes IGN] coordonnées GPS
[Termes IGN] estimateur
[Termes IGN] méthode robuste
[Termes IGN] série temporelle
[Termes IGN] station GPS
[Termes IGN] valeur aberrante
[Termes IGN] vitesseRésumé : (auteur) Automatic estimation of velocities from GPS coordinate time series is becoming required to cope with the exponentially increasing flood of available data, but problems detectable to the human eye are often overlooked. This motivates us to find an automatic and accurate estimator of trend that is resistant to common problems such as step discontinuities, outliers, seasonality, skewness, and heteroscedasticity. Developed here, Median Interannual Difference Adjusted for Skewness (MIDAS) is a variant of the Theil‐Sen median trend estimator, for which the ordinary version is the median of slopes vij = (xj–xi)/(tj–ti) computed between all data pairs i > j. For normally distributed data, Theil‐Sen and least squares trend estimates are statistically identical, but unlike least squares, Theil‐Sen is resistant to undetected data problems. To mitigate both seasonality and step discontinuities, MIDAS selects data pairs separated by 1 year. This condition is relaxed for time series with gaps so that all data are used. Slopes from data pairs spanning a step function produce one‐sided outliers that can bias the median. To reduce bias, MIDAS removes outliers and recomputes the median. MIDAS also computes a robust and realistic estimate of trend uncertainty. Statistical tests using GPS data in the rigid North American plate interior show ±0.23 mm/yr root‐mean‐square (RMS) accuracy in horizontal velocity. In blind tests using synthetic data, MIDAS velocities have an RMS accuracy of ±0.33 mm/yr horizontal, ±1.1 mm/yr up, with a 5th percentile range smaller than all 20 automatic estimators tested. Considering its general nature, MIDAS has the potential for broader application in the geosciences. Numéro de notice : A2016--176 Affiliation des auteurs : LASTIG LAREG+Ext (2012-mi2018) Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1002/2015JB012552 Date de publication en ligne : 12/02/2016 En ligne : https://doi.org/10.1002/2015JB012552 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=91799
in Journal of geophysical research : Solid Earth > vol 121 n° 3 (March 2016) . - pp 2054 - 2068[article]Documents numériques
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MIDAS robust trend estimator ... - pdf éditeurAdobe Acrobat PDF Convex programming approach to robust estimation of a multivariate Gaussian model / Samuel Balmand (2016)
Titre : Convex programming approach to robust estimation of a multivariate Gaussian model Type de document : Article/Communication Auteurs : Samuel Balmand , Auteur ; Arnak Dalalyan, Auteur Editeur : Ithaca [New York - Etats-Unis] : ArXiv - Université Cornell Année de publication : 2016 Importance : 31 p. Format : 21 x 30 cm Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Statistiques
[Termes IGN] distribution de Gauss
[Termes IGN] estimateur
[Termes IGN] matrice de covariance
[Termes IGN] méthode des moindres carrés
[Termes IGN] valeur aberranteRésumé : (auteur) Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often considered as a prototype for testing new algorithms or theoretical frameworks. In this paper, we develop a nonasymptotic approach to the problem of estimating the parameters of a multivariate Gaussian distribution when data are corrupted by outliers. We propose an estimator efficiently computable by solving a convex program|that robustly estimates the population mean and the population covariance matrix even when the sample contains a signi?cant proportion of outliers. Our estimator of the corruption matrix is provably rate optimal simultaneously for the entry-wise `1-norm, the Frobenius norm and the mixed `2=`1 norm. Furthermore, this optimality is achieved by a penalized square-root-of-least-squares method with a universal tuning parameter (calibrating the strength of the penalization). These results are partly extended to the case where p is potentially larger than n, under the additional condition that the inverse covariance matrix is sparse. Note de contenu : bibliographie Numéro de notice : P2016-001 Affiliation des auteurs : ENSG+Ext (2012-2019) Thématique : MATHEMATIQUE Nature : Preprint nature-HAL : Préprint DOI : 10.48550/arXiv.1512.04734 Date de publication en ligne : 06/02/2016 En ligne : https://doi.org/10.48550/arXiv.1512.04734 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=91897 Documents numériques
en open access
Convex programming approach... - pdf auteurAdobe Acrobat PDF
Titre : Filtrage de Kalman à bruits corrélés pour le positionnement précis Type de document : Mémoire Auteurs : Ulrich Mambou Kuipou, Auteur Editeur : Le Mans : Ecole Supérieure des Géomètres et Topographes ESGT Année de publication : 2016 Importance : 75 p. Format : 21 x 30 cm Note générale : bibliographie
Mémoire présenté en vue d'obtenir le diplôme d'Ingénieur CNAM, Spécialité Géomètre et TopographeLangues : Français (fre) Descripteur : [Vedettes matières IGN] Traitement du signal
[Termes IGN] analyse de variance
[Termes IGN] auscultation topographique
[Termes IGN] bruit blanc
[Termes IGN] corrélation temporelle
[Termes IGN] estimateur
[Termes IGN] étalonnage des données
[Termes IGN] filtre de Kalman
[Termes IGN] méthode de Monte-Carlo par chaînes de Markov
[Termes IGN] méthode des moindres carrés
[Termes IGN] méthode du maximum de vraisemblance (estimation)
[Termes IGN] précision du positionnement
[Termes IGN] topométrie de précisionRésumé : (auteur) Le filtre de Kalman à bruits corrélés peut être considéré comme une alternative aux solutions de filtrage classique, car il améliore la précision du positionnement. Les applications de ce nouveau filtre seraient très intéressantes pour le couplage de mesures dans les domaines suivants : photogrammétrie, télédétection aérienne, bathymétrie et «mobile mapping». L’objectif visé par ce travail de fin d’études, est d’évaluer les performances du filtre de Kalman à bruits corrélés dans une expérience d’auscultation. Dans l’optique de mettre en évidence la puissance de ce filtre, il y a lieu d’estimer par le maximum de vraisemblance, d’une part la variance du modèle d’évolution et d’autre part la corrélation des modèles (même corrélation de bruits, pour les modèles d’évolution et d’observation) en fixant au préalable une structure de corrélation aux dits modèles. Note de contenu : Introduction
1- Expérience de Bogatin
2- Méthode de calibration et résultat du filtrage de Kalman
3- Bruits corrélés : estimation et filtrage de Kalman à bruits corrélés
4- Applications sur des données réellesNuméro de notice : 24612 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Mémoire ingénieur ESGT Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92178 Documents numériques
en open access
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