GPS signal diffraction modelling: the stochastic SIGMA- δ model

Brunner, Fritz K.; Hartinger, Horst; Troyer, L.

doi:10.1007/s001900050242

Cited by 174 publications

(80 citation statements)

References 2 publications

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“…It is well known that the observational noise is basically related to the power of the satellite signal at the receiver, and the stochastic properties of GNSS data can be described as a function of this indicator [43,44]. Furthermore, it was also confirmed that the carrier to noise density ratio (C/N0) for BDS-IGSO and GEO satellites, which are characterised by a much higher altitude, is 3-4 dB-Hz lower than common BDS-MEO satellites [45,46].…”

Section: Signal Powermentioning

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: Signal Powermentioning

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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“…Traditionally, data processing for precise GPS positioning is invariably performed using the least squares (LS) method. The quality of LS solutions depends on the model's formulation regarding GPS observations, including both a functional model, which describes the mathematical relationships between the GPS measurements and unknown parameters, and a stochastic model, which tells us the statistical properties of the measurements (Han and Rizos, 1995;Rizos, 1997;Brunner et al, 1999). Over the past two decades, the functional models for GPS measurements have been investigated in considerable detail.…”

Section: Introductionmentioning

confidence: 99%

An improvement of GPS height estimations: stochastic modeling

2005

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The results of GPS positioning depend on both functional and stochastic models. In most of the current GPS processing programs, however, the stochastic model that describes the statistical properties of GPS observations is usually assumed that all GPS measurements have the same accuracy and are statistically independent. Such assumptions are unrealistic. Although there were only a few studies modeling the effects on the GPS relative positioning, they are restricted to short baselines and short session lengths. In this paper, the stochastic modeling for IGS long-baseline positioning (with 24-hour session) is analyzed in the GAMIT software by modified stochastic models. Results show that any mis-specifications of stochastic model result in unreliable GPS baseline results, and the deviation of baseline estimations reaches as much as 2 cm in the height component. Using the stochastic model of satellite elevation angle-based cosine function, the precision of GPS baseline estimations can be improved, and the GPS baseline component is closest to the reference values, especially GPS height.

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“…Figure 7 shows a typical diffraction situation for a short baseline (100 m), reported by Brunner et al (1999). The rover station is close to a narrow building, which totally obstructs the direct signal from PRN01 during the first 30 min of the session.…”

Section: Limitation Of Sigma Modelsmentioning

confidence: 98%

An extended weight model for GPS phase observations

Wieser

Brünner

2014

Earth Planet Sp

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Low elevation data may be included in the processing of small scale engineering GPS applications, in order to improve satellite geometry and reduce the required observation time. Careful weighting of the phase observations is needed then, because of increased noise and systematic errors. The measured carrier-to-noise-power-density ratio (C/N0) has proven to be an excellent tool for the estimation of the random errors of the phase observables. In this paper an extended weight model using robust estimation is presented, in particular the Danish Method. This model combines the information inherent in C/N0 and the residuals of the double differenced phase observations in order to model random errors and signal distortion effects.

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GPS signal diffraction modelling: the stochastic SIGMA- δ model

Cited by 174 publications

References 2 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

An improvement of GPS height estimations: stochastic modeling

An extended weight model for GPS phase observations

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