On a Measure for the Discernibility between Different Ambiguity Solutions in the Static-Kinematic GPS-Mode

Euler, Hans-Jiirgen; Schaffrin, Burkhard

doi:10.1007/978-1-4612-3102-8_26

Cited by 146 publications

(76 citation statements)

References 2 publications

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“…Independently of the chosen threshold, the impact of misspecifying the stochastic model up to neglecting correlations on the ratio test de ned as R = (Euler and Scha rin 1991) can be assessed. We call x A, x ,x A, x the two vectors of integer candidates that are corresponding to the two smallest values of the distance between the oat and two xed ambiguity vectors in the metric of the covariance matrix.…”

Section: Impact On Ambiguity Resolution Of Fullymentioning

confidence: 99%

Fully populated VCM or the hidden parameter

Kermarrec

Schön

2017

Journal of Geodetic Science

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Least-squares estimates are trustworthy with minimal variance if the correct stochastic model is used. Due to computational burden, diagonal models that neglect correlations are preferred to describe the elevation dependency of the variance of GPS observations. In this contribution, an improved stochastic model based on a parametric function to take correlations between GPS phase observations into account is presented. Built on an adapted and exible Mátern function accounting for spatiotemporal variabilities, its parameters can be xed thanks to Maximum Likelihood Estimation or chosen apriori to model turbulent tropospheric refractivity uctuations. In this contribution, we will show in which cases and under which conditions corresponding fully populated variance covariance matrices (VCM) replace the estimation of a tropospheric parameter. For this equivalence "augmented functional versus augmented stochastic model" to hold, the VCM should be made su ciently large which corresponds to computing small batches of observations. A case study with observations from a medium baseline of 80 km divided into batches of 600 s shows improvement of up to 100 mm for the 3Drms when fully populated VCM are used compared with an elevation dependent diagonal model. It con rms the strong potential of such matrices to improve the least-squares solution, particularly when ambiguities are let oat.

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Section: Impact On Ambiguity Resolution Of Fullymentioning

confidence: 99%

Fully populated VCM or the hidden parameter

Kermarrec

Schön

2017

Journal of Geodetic Science

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“…This validation on the basis of statistical tests utilizing observation residuals for float and fixed solutions makes possible to verify whether or not the estimated ambiguities may be consider valid (by using the so-called acceptance or integer test) as well as if more that one set of ambiguities pass the acceptance test whether the estimated ambiguities can be considered sufficiently more likely than other for the chosen level of significance α (the so-called discrimination test) (Euler and Schaffrin, 1991;Tiberius et al, 1997). Ambiguity validation for the test data was carried out by using the following discrimination tests: the ratio test (R-ratio, T R ) (Euler and Schaffrin, 1991), the F-ratio test (T F ) (Counselman and Abbot, 1989), and the difference test (D-test, T D ) (Tiberius and De Jonge, 1995). These tests work very well and provide the effective performance of validation, also when they are carried out without the acceptance test (Verhagen, 2004).…”

Section: Application Parameters and Solution Algorithmmentioning

confidence: 99%

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

Próchniewicz

2014

Artificial Satellites

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ABSTRACT. The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

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“…In this research, the popular R-ratio (Euler and Schaffrin, 1991;Leick, 2004) is used and a threshold value is set to two.…”

Section: S H E N Gy U E J I a N D O T H E R Smentioning

confidence: 99%

First Preliminary Fast Static Ambiguity Resolution Results of Medium-Baseline with Triple-Frequency Beidou Wavebands

Wang

et al. 2014

J. Navigation

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Fast high precision relative Global Navigation Satellite System (GNSS) positioning is very important to various applications and ambiguity resolution is a key requirement. It has been a continuing challenge to determine and fix GNSS carrier-phase ambiguity, especially for medium-and long-distance baselines. In past research, with dual-frequency band Global Positioning System (GPS), it is almost impossible for fast ambiguity resolution of mediumand long-distance baselines mainly due to the ionospheric and tropospheric effects. With the launch of the BeiDou system, triple-frequency band GNSS observations are available for the first time. This research aims to test the ambiguity resolution performance with BeiDou triplefrequency band observations. In this research, two mathematical models are compared: zenith tropospheric delay as an unknown parameter versus corrected tropospheric delay. The ambiguity resolution performance is investigated in detail with BeiDou observations. Different distance baselines are tested: 45 km, 70 km and 100 km and the performances are investigated with different elevation cut-off angles. Also the performance with BeiDou alone and combined BeiDou and GPS are compared. Experimental results clearly show that with practical observations of triple-frequency bands, ambiguity of medium-or long-distance baselines can be fixed. The results also show that: the performance of ambiguity resolution with an elevation cutoff angle of 20°is much better than that of 15°; The performance with tropospheric effect corrected is slightly better than that with tropospheric effect as an estimated parameter; Dual-frequency band GPS observations will benefit ambiguity resolution of integrated BeiDou and GPS. K E Y WO R D S 1. BeiDou.2. Ambiguity resolution. 3. Medium-and long-distance baselines. 4. Ionosphere.5. Troposphere.

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On a Measure for the Discernibility between Different Ambiguity Solutions in the Static-Kinematic GPS-Mode

Cited by 146 publications

References 2 publications

Fully populated VCM or the hidden parameter

Fully populated VCM or the hidden parameter

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

First Preliminary Fast Static Ambiguity Resolution Results of Medium-Baseline with Triple-Frequency Beidou Wavebands

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