Network-Based Stochastic Model for Instantaneous GNSS Real-Time Kinematic Positioning

Próchniewicz, D.; Szpunar, R.; Brzeziński, Aleksander

doi:10.1061/(asce)su.1943-5428.0000188

Cited by 11 publications

(10 citation statements)

References 24 publications

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“…Such analysis may be beneficial for establishing, e.g., an advanced stochastic model of positioning [42]. The characteristic of stochastic properties is followed by presentation of the observation model of multi-constellation relative kinematic positioning.…”

Section: Gsat0201 (5-mentioning

confidence: 99%

On the Applicability of Galileo FOC Satellites with Incorrect Highly Eccentric Orbits: An Evaluation of Instantaneous Medium-Range Positioning

2018

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This study addresses the potential contribution of the first pair of Galileo FOC satellites sent into incorrect highly eccentric orbits for geodetic and surveying applications. We began with an analysis of the carrier to noise density ratio and the stochastic properties of GNSS measurements. The investigations revealed that the signal power of E14 & E18 satellites is higher than for regular Galileo satellites, what is related to their lower altitude over the experiment area. With regard to the noise of the observables, there are no significant differences between all Galileo satellites. Furthermore, the study confirmed that the precision of Galileo data is higher than that of GPS, especially in the case of code measurements. Next analysis considered selected domains of precise instantaneous medium-range positioning: ambiguity resolution and coordinate accuracy as well as observable residuals. On the basis of test solutions, with and without E14 & E18 data, we found that these satellites did not noticeably influence the ambiguity resolution process. The discrepancy in ambiguity success rate between test solutions did not exceed 2%. The differences between standard deviations of the fixed coordinates did not exceed 1 mm for horizontal components. The standard deviation of the L1/E1 phase residuals, corresponding to regular GPS and Galileo, and E14 & E18 satellite signals, was at a comparable level, in the range of 6.5-8.7 mm. The study revealed that the Galileo satellites with incorrect orbits were fully usable in most geodetic, surveying and many other post-processed applications and may be beneficial especially for positioning during obstructed visibility of satellites. This claim holds true when providing precise ephemeris of satellites.

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Section: Gsat0201 (5-mentioning

confidence: 99%

On the Applicability of Galileo FOC Satellites with Incorrect Highly Eccentric Orbits: An Evaluation of Instantaneous Medium-Range Positioning

2018

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“…They are based on the assumption that residual observation errors not included in the functional model can be equivalently captured by the fully populated VC matrix [ 47 ]. These models, mainly dedicated to kinematic positioning, use a priori values of individual errors [ 48 , 49 , 50 ], the residual observations from previous epochs [ 51 , 52 ] or the atmospheric correction errors estimation determined from the network of reference stations [ 53 ].…”

Section: Introductionmentioning

confidence: 99%

Empirical Stochastic Model of Multi-GNSS Measurements

Próchniewicz

Wezka

Kozuchowska

2021

Sensors

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The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

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“…Instantaneous, or single-epoch, high-precision GNSS is resistant to satellite signal interruptions which take place frequently in urban and other GNSS-difficult areas and thus is valued in time-and safety-critical applications. Singleepoch decimeter-level or better positioning is premised on ambiguity-fixed carrier-phase data and is thus mostly promised for ultra-short-baseline solutions (e.g., preferably < 10 km) (e.g., Odolinski et al 2015;Prochniewicz et al 2016;Teunissen et al 2014). This is because precise enough ambiguity estimates for both successful integer-cycle resolution and high-precision positioning are hardly achievable in case of single epochs of data.…”

Section: Introductionmentioning

confidence: 99%

Toward global instantaneous decimeter-level positioning using tightly coupled multi-constellation and multi-frequency GNSS

Geng

Guo

Chang

et al. 2018

J Geod

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Autonomous driving represents one of the emerging applications that require both high-precision positions and highly critical timeliness to reach stringent safety standards. We develop a method to potentially achieve global instantaneous decimeter-level positioning by virtue of tightly coupled multi-GNSS triple-frequency observations contributing to precise point positioning (PPP). Inter-system phase biases (ISPBs) for two wide-lane observables are first computed for each station to form inter-GNSS resolvable ambiguities, and then correspondingly two wide-lane fractional-cycle biases (FCBs) are computed for each satellite to recover the integer property of single-station ambiguities. With both ISPB and FCB products, we can accomplish tightly coupled multi-GNSS PPP wide-lane ambiguity resolution (PPP-WAR) using only a single epoch of triple-frequency observations on a global scale. To verify this method, we used 1 month of GPS/BeiDou/Galileo/QZSS data from 107 globally distributed stations and 1 h of such multi-GNSS data collected on a vehicle moving in an urban area. We found that both ISPB and FCB products could be estimated every 24 h with high precisions of around or below 0.1 cycles; 83-98% of their day-today variations fell within 0.1 cycles, facilitating their precise predictions for real-time applications. Using these corrections, we achieved both instantly and reliably ambiguity-fixed solutions at 91.2% of all epochs at the 107 stations on average; the resultant single-epoch positions reached a mean accuracy of 0.22 m, 0.18 m and 0.63 m for the east, north and up components, respectively, in case of abundant triple-frequency observations from over 15 satellites. Similarly, for the vehicle-borne test, we obtained instantaneous PPP-WAR solutions at 99.31% of all epochs and achieved a positioning accuracy of 0.29, 0.35 and 0.77 m for the east, north and up components, respectively, which improved significantly the identification of road lanes as opposed to other single-epoch solutions. Finally, we expect that the prospect of instantaneous PPP-WAR in aiding driverless vehicles can be more promising if, whenever possible, integrated with inertial sensors and/or smoothed through multi-epoch data.

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Network-Based Stochastic Model for Instantaneous GNSS Real-Time Kinematic Positioning

Cited by 11 publications

References 24 publications

On the Applicability of Galileo FOC Satellites with Incorrect Highly Eccentric Orbits: An Evaluation of Instantaneous Medium-Range Positioning

On the Applicability of Galileo FOC Satellites with Incorrect Highly Eccentric Orbits: An Evaluation of Instantaneous Medium-Range Positioning

Empirical Stochastic Model of Multi-GNSS Measurements

Toward global instantaneous decimeter-level positioning using tightly coupled multi-constellation and multi-frequency GNSS

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