Integer estimability in GNSS networks

Khodabandeh, Amir; Teunissen, Peter

doi:10.1007/s00190-019-01282-6

Cited by 26 publications

(10 citation statements)

References 29 publications

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“…The first use of the HNF for solving rank-defect ILS problems was given in Teunissen and Odijk (2003). Later use of the HNF can be found in Khodabandeh and Teunissen (2019); Tagliaferro (2021).…”

Section: Obtaining Z Through Integer Sweepingmentioning

confidence: 99%

PPP–RTK theory for varying transmitter frequencies with satellite and terrestrial positioning applications

Teunissen

Khodabandeh

2022

J Geod

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In this contribution, we generalize PPP–RTK theory by allowing the transmitters to transmit on different frequencies. The generalization is based on the integer-estimability theory of Teunissen (A new GLONASS FDMA model. GPS Solutions, 2019). As the theory and associated algorithms provided are generally applicable, they apply to satellite-based carrier-phase positioning as well as to terrestrial interferometric sensory networks. Based on an identification of the constraints imposed on the admissible ambiguity transformations by PPP–RTK, a fundamental network+user condition is found that determines whether PPP–RTK is possible or not. The discriminating contributions of both the network and user observation equations to this PPP–RTK condition are analysed, followed by a description of PPP–RTK enabling classes of measurement scenarios.

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Section: Obtaining Z Through Integer Sweepingmentioning

confidence: 99%

PPP–RTK theory for varying transmitter frequencies with satellite and terrestrial positioning applications

Teunissen

Khodabandeh

2022

J Geod

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“…and that PPP single-receiver ambiguity resolution should be seen as a special case of network DD ambiguity resolution (Khodabandeh and Teunissen 2019). Denoting the reference satellite as s 0 , the SD float ambiguity can be expressed as, where Δd s,s 0 and ΔN s,s 0 r refer to SD UPD and integer part between satellites, and Δd s,s 0 is provided in UPD products.…”

Section: Estimation Of Updmentioning

confidence: 99%

Calibrating receiver-type-dependent wide-lane uncalibrated phase delay biases for PPP integer ambiguity resolution

Cui

Pan

Wang

et al. 2021

J Geod

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Wide-lane (WL) uncalibrated phase delay (UPD) is usually derived from Melbourne–Wübbena (MW) linear combination and is a prerequisite in Global Navigation Satellite Systems (GNSS) precise point positioning (PPP) ambiguity resolution (AR). MW is a linear combination of pseudorange and phase, and the accuracy is limited by the larger pseudorange noise which is about one hundred times of the carrier phase noise. However, there exist inconsistent pseudorange biases which may have detrimental effect on the WL UPD estimation, and further degrade user-side ambiguity fixing. Currently, only the large part of pseudorange biases, e.g., the differential code bias (DCB), are available and corrected in PPP-AR, while the receiver-type-dependent biases have not yet been considered. Ignoring such kind of bias, which could be up to 20 cm, will cause the ambiguity fixing failure, or even worse, the incorrect ambiguity fixing. In this study, we demonstrate the receiver-type-dependent WL UPD biases and investigate their temporal and spatial stability, and further propose the method to precisely estimate these biases and apply the corrections to improve the user-side PPP-AR. Using a large data set of 1560 GNSS stations during a 30-day period, we demonstrate that the WL UPD deviations among different types of receivers can reach ± 0.3 cycles. It is also shown that such kind of deviations can be calibrated with a precision of about 0.03 cycles for all Global Positioning System (GPS) satellites. On the user side, ignoring the receiver-dependent UPD deviation can cause significant positioning error up to 10 cm. By correcting the deviations, the positioning performance can be improved by up to 50%, and the fixing rate can also be improved by 10%. This study demonstrates that for the precise and reliable PPP-AR, the receiver-dependent UPD deviations cannot be ignored and have to be handled.

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“…Several equivalent methods with different variants were proposed by Collins et al (2008), Ge et al (2008), and Laurichesse et al (2009), and the satellite phase biases are provided as the corrections to the users to construct double-differenced ambiguities by using the S-system theory (Khodabandeh and Teunissen 2019). PPP-AR can significantly improve the positioning precision anywhere around the world with an extent of 30-60% but the contribution to shortening convergence time is marginal (Ge et al 2008;Hu et al 2020;Li et al 2016).…”

Section: Introductionmentioning

confidence: 99%

PPP-RTK considering the ionosphere uncertainty with cross-validation

Cui

et al. 2022

Satell Navig

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With the high-precision products of satellite orbit and clock, uncalibrated phase delay, and the atmosphere delay corrections, Precise Point Positioning (PPP) based on a Real-Time Kinematic (RTK) network is possible to rapidly achieve centimeter-level positioning accuracy. In the ionosphere-weighted PPP–RTK model, not only the a priori value of ionosphere but also its precision affect the convergence and accuracy of positioning. This study proposes a method to determine the precision of the interpolated slant ionospheric delay by cross-validation. The new method takes the high temporal and spatial variation into consideration. A distance-dependent function is built to represent the stochastic model of the slant ionospheric delay derived from each reference station, and an error model is built for each reference station on a five-minute piecewise basis. The user can interpolate ionospheric delay correction and the corresponding precision with an error function related to the distance and time of each reference station. With the European Reference Frame (EUREF) Permanent GNSS (Global Navigation Satellite Systems) network (EPN), and SONEL (Système d'Observation du Niveau des Eaux Littorales) GNSS stations covering most of Europe, the effectiveness of our wide-area ionosphere constraint method for PPP-RTK is validated, compared with the method with a fixed ionosphere precision threshold. It is shown that although the Root Mean Square (RMS) of the interpolated ionosphere error is within 5 cm in most of the areas, it exceeds 10 cm for some areas with sparse reference stations during some periods of time. The convergence time of the 90th percentile is 4.0 and 20.5 min for horizontal and vertical directions using Global Positioning System (GPS) kinematic solution, respectively, with the proposed method. This convergence is faster than those with the fixed ionosphere precision values of 1, 8, and 30 cm. The improvement with respect to the latter three solutions ranges from 10 to 60%. After integrating the Galileo navigation satellite system (Galileo), the convergence time of the 90th percentile for combined kinematic solutions is 2.0 and 9.0 min, with an improvement of 50.0% and 56.1% for horizontal and vertical directions, respectively, compared with the GPS-only solution. The average convergence time of GPS PPP-RTK for horizontal and vertical directions are 2.0 and 5.0 min, and those of GPS + Galileo PPP-RTK are 1.4 and 3.0 min, respectively.

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Integer estimability in GNSS networks

Cited by 26 publications

References 29 publications

PPP–RTK theory for varying transmitter frequencies with satellite and terrestrial positioning applications

PPP–RTK theory for varying transmitter frequencies with satellite and terrestrial positioning applications

Calibrating receiver-type-dependent wide-lane uncalibrated phase delay biases for PPP integer ambiguity resolution

PPP-RTK considering the ionosphere uncertainty with cross-validation

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