Single-receiver single-channel multi-frequency GNSS integrity: outliers, slips, and ionospheric disturbances

Teunissen, Peter; Bakker, Peter F. de

doi:10.1007/s00190-012-0588-x

Cited by 56 publications

(27 citation statements)

References 31 publications

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“…The research has recently revealed the hardware delays to be temporally variable and different for each observation type (Collins et al 2010;Laurichesse et al 2009;Liu et al 2004;Odijk et al 2012;Teunissen and de Bakker 2013). When linear combination is applied, code and phase hardware delays are lumped together in b .…”

Section: Observation Equations Of the Single-frequency Pppmentioning

confidence: 99%

Single-frequency precise point positioning: an analytical approach

Sterle

Stopar

Prešeren

2015

J Geod

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An analytical approach to single-frequency precise point positioning (PPP) is discussed in this paper. To obtain highest precision results, all biases must be eliminated or modelled to centimetre level. The use of the GRAPHIC ionosphere-free linear combination that is based on single-frequency phase and code observations eliminates the ionosphere bias; however, the rank deficient GaussMarkov model is obtained. We explicitly determine rank deficiency of a Gauss-Markov model as a number of all ambiguity clusters, each of them defined as a set of all ambiguities overlapping in time. On the basis of S-transformation we prove that the single-frequency PPP represents an unbiased estimator for station coordinates and troposphere parameters, while it presents a biased estimator for ambiguities and receiver-clock error parameters. Additionally we describe the estimable parameters in each ambiguity cluster as the differences between ambiguity parameters and the sum of receiver-clock parameters with one of the ambiguities. We also show that any other particular solution on the basis of S-transformation is obtained only when the common leastsquares estimation in single step is applied. The recursive least-squares estimation with parameter pre-elimination only determines the vector of unknowns as possible to transform through S-transformation, whereas the same does not hold for the cofactor matrix of unknowns. For a case study, we present our method on GPS data from 19 permanent stations (14 IGS and 5 EPN) in Europe, for 89 consecutive days in the beginning of 2013. The static case study revealed the precision of daily coordinates as 7.6, 11.7 and 19.6 mm for N , E and U , respectively. The accuracies of the N , E and U components were determined as 6.9, 13.5 and 31.4 mm, respectively, and were calculated using the Helmert transformation of weighted-mean daily single-frequency PPP and IGb08 coordinates. The estimated convergence times were relatively diverse, expanding from 1.75 h (CAGL) to 5.25 h (GRAZ) for the horizontal position with the 10-cm precision threshold, and from 1.00 h (GRAS) to 3.25 h (BZRG) for the height component with a 20-cm precision threshold. The convergence times were shown to be strongly correlated to the remaining unmodelled biases in the GRAPHIC linear combination, primarily with multipath, where the correlation coefficient for the horizontal position was determined as ρ P = 0.68 and for height as ρ U = 0.85. The comparison to the model where raw observations are used (C, L) and where the ionosphere bias is mitigated with global ionosphere models (GIM) revealed the supremacy of the proposed single-frequency PPP method based on the GRAPHIC linear combination in both the static and the semi-kinematic case study. In the static case study, the proposed singlefrequency PPP model was superior both in terms of precision and accuracy. In the semi-kinematic case study, the usage of raw observations with GIM would improve results only when multipath and noise of code observations would prevail over the remaini...

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Section: Observation Equations Of the Single-frequency Pppmentioning

confidence: 99%

Single-frequency precise point positioning: an analytical approach

Sterle

Stopar

Prešeren

2015

J Geod

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“…In DIA, the detection process aims to decide by using a overall test whether some kind of bias or outlier is present; the identification process serves to decide in which channel of the measurement and/or process vector and at which epoch the bias/outlier occurred; in the adaptation process, the detected bias/outlier are corrected or discarded. The DIA methods have found widely applications in the geodetic community, e.g., to detect GNSS pseudorange outliers, phase cycle slips or ionospheric disturbances (Teunissen 1998;Teunissen and De Bakker 2013), station coordinate discontinuities (Perfetti 2006), etc. Also, by inversing the power function of the test, a concept called minimal detectable bias/outlier, some kind of reliability measure, can be derived which can be used to evaluate the strength of the measurement model (De Jong 2000;Koch 2015;Teunissen 1998), and hence further to conduct the design of the measurement model (Salzmann 1991).…”

Section: Introductionmentioning

confidence: 99%

Accuracy improvement by implementing sequential measurement update in robust Kalman filter

Chang

Wang

2015

Acta Geod Geophys

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A robust Kalman filter based on Chi square test with sequential measurement update is proposed. This approach can not only handle outliers in part or even individual measurement channel, but can also further improve the accuracy especially when a novel ordering strategy in processing the measurement elements is adopted. The accuracy improvement can be attributed to the higher statistical efficiency, i.e., an increased probability of correctly resisting the outlying measurement elements and retaining the good ones. The accuracy improvement of the proposed method is illustrated by a simulating example.

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“…Despite their different applications, all of the aforementioned arrays are, however, utilized for the purpose of the same functionality, that is, providing accurate corrections for the users. Ensuring the integrity and reliability of the corrections, even at the pre-analysis level, is therefore of great importance, see e.g., Teunissen (1998); Teunissen and de Bakker (2012).Integrity monitoring and quality control of the GNSS array model is the topic of this contribution. We confine our study to the single-epoch scenario as it is indeed the ultimate goal of the near real-time applications and, at the same time, brings us conservative thresholds of the reliability measures of the corresponding multi-epoch scenario.…”

mentioning

confidence: 99%

Single-Epoch GNSS Array Integrity: An Analytical Study

Khodabandeh

Teunissen

2015

VIII Hotine-Marussi Symposium on Mathematical Geodesy

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In this contribution we analyze the integrity of the GNSS array model through the socalled uniformly most powerful invariant (UMPI) test-statistics and their corresponding minimal detectable biases (MDBs). The model considered is characterized by multiple receivers/satellites with known coordinates where the multi-frequency carrier-phase and pseudo-range observables are subject to atmospheric (ionospheric and tropospheric) delays, receiver and satellite clock biases, as well as instrumental delays. Highlighting the role played by the model's misclosures, analytical multivariate expressions of a few leading teststatistics together with their MDBs are studied that are further accompanied by numerical results of the three GNSSs GPS, Galileo and BeiDou. Keywords Array model • GNSS misclosures • Integrity • Minimal detectable bias (MDB) • Uniformly most powerful invariant (UMPI) test-statistic IntroductionThe notion of the GNSS array model, here, refers to an array of antennas tracking the multi-frequency carrier-phase/pseudo-range observables in the presence of atmospheric effects. The coordinates of antennas and satellites are assumed to be known. The definition presented is rather general in the sense that even the medium-scale control networks can also be considered as an array. Examples of such are the continuously operating reference (Teunissen 2010(Teunissen , 2012, and the ground based augmentation systems (GBASs) supporting safe flight procedures such as landing, departure and surface operations at an airport (Khanafseh et al. 2012;Giorgi et al. 2012). Despite their different applications, all of the aforementioned arrays are, however, utilized for the purpose of the same functionality, that is, providing accurate corrections for the users. Ensuring the integrity and reliability of the corrections, even at the pre-analysis level, is therefore of great importance, see e.g., Teunissen (1998); Teunissen and de Bakker (2012).Integrity monitoring and quality control of the GNSS array model is the topic of this contribution. We confine our study to the single-epoch scenario as it is indeed the ultimate goal of the near real-time applications and, at the same time, brings us conservative thresholds of the reliability measures of the corresponding multi-epoch scenario. Our strategy commences with the model's misclosures. Although the GNSS misclosures can be treated as diagnostic tools in

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Single-receiver single-channel multi-frequency GNSS integrity: outliers, slips, and ionospheric disturbances

Cited by 56 publications

References 31 publications

Single-frequency precise point positioning: an analytical approach

Single-frequency precise point positioning: an analytical approach

Accuracy improvement by implementing sequential measurement update in robust Kalman filter

Single-Epoch GNSS Array Integrity: An Analytical Study

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