Characterizing noise in daily GPS position time series with overlapping Hadamard variance and maximum likelihood estimation

Xu, Caijun; Yue, Dongjie

doi:10.1080/00396265.2016.1163830

Cited by 4 publications

(5 citation statements)

References 34 publications

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“…One of the most crucial indicators of atomic clock performance is frequency stability, which is usually expressed by Allan and Hadamard variances. As for the frequency, drift is easily ignored by the Allan variance, and the Hadamard variance is insensitive to linear frequency drift [ 16 , 17 ]. The Hadamard variance adopts the second difference of the fractional frequencies.…”

Section: Methodsmentioning

confidence: 99%

Characteristics of Onefold Clocks of GPS, Galileo, BeiDou and GLONASS Systems

Maciuk

Lewińska

et al. 2021

Sensors

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This research is focused on searching for frequency and noise characteristics for available GNSS (Global Navigation Satellite Systems). The authors illustrated frequency stability and noise characteristics for a selected set of data from four different GNSS systems. For this purpose, 30-s-interval clock corrections were used for the GPS weeks 1982–2034 (the entirety of 2018). Firstly, phase data (raw clock corrections) were preprocessed for shifts and removal of outliers; GLONASS and GPS satellites characterize a smaller number of outliers than BeiDou and Galileo clock products. Secondly, frequency and Hadamard deviation were calculated. This study concludes that the stability of GPS and Galileo is better than that of BDS (BeiDou Navigation Satellite System) and GLONASS. Regarding noise, the GPS, Galileo, and BDS clocks are affected by the random walk modulation noise (RWFM), flashing frequency modulation noise (FFM), and white frequency modulation noise (WFM), whereas the GLONASS clocks are mainly affected only by WFM.

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Section: Methodsmentioning

confidence: 99%

Characteristics of Onefold Clocks of GPS, Galileo, BeiDou and GLONASS Systems

Maciuk

Lewińska

et al. 2021

Sensors

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“…Hackl et al [25] reveal that Allan variance is an alternative and accurate method to estimate the rate uncertainty for South African TrigNet network. Due to the good confidence in dealing with divergent noise, Xu and Yue [26] adopted a modified Allan variance approach called overlapping Hadamard variance (OHVAR) to infer the noise components of daily PPP position time series of 12 International GNSS Service (IGS) sites in China. They found that the dominate power-law noise inferred by OHVAR agrees well with that inferred by MLE.…”

Section: Introductionmentioning

confidence: 99%

Characteristics of seasonal variations and noises of the daily double-difference and PPP solutions

Maciuk

Varna

2020

Journal of Applied Geodesy

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Long term GNSS observations provided by networks of the continuously operating reference stations (CORS) allow for determination of the global and local tectonic plate movements and seasonal variations. In recent years, PPP (Precise Point Positioning) technique has become increasingly popular and most likely in the future will replace relative positioning with CORS stations. In this paper, we discuss the difference of the velocity and seasonal component estimates of 25 Latvian CORS stations on the basis of daily PPP solutions from the Nevada Geodetic Laboratory and double-difference solutions from the Institute of Geodesy and Geoinformatics of the University of Latvia. Time series of each coordinate component for 9-year time period were determined by the usage of the Tsview software and seasonal existence of linear, annual, semi-annual factors and their uncertainties were determined. Breaks (e. g., antenna and receiver changes) were also taken into account. We then assessed the noise characteristics of these time series with the use of overlapping Hadamard variance (OHVAR). The result shows that OHVAR is computationally cheap, and the dominating power-law noise, including flicker and random walk. However Hadamard deviation of the PPP and double-difference solutions scatters differently for a whole year averaging time due to the different GNSS data strategies.

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“…However, these dynamics can only be modelled to some reasonable degree and possibly mitigate some errors with correct stochastic and functional models (He et al, 2017). The stochastic as done by (Klos et al, 2014;He et al, 2016;Xu andYue, 2017) Klos et al (2014) who analysed more than 40 stations belonging to the ASG-EUPOS and EPN networks with 5 years of observations from the area of Sudeten, concluded that the WN+PL noise best describes the error sources for most of the analysed stations. Elsewhere, Goudarzi et al (2015) analysed the behaviour of noise in 112 continuously operating GPS (CGPS) position time series in the eastern part of North America and found out that WN+FN is the best model that describes the stochastic part of the position time series.…”

mentioning

confidence: 99%

“…Elsewhere, Goudarzi et al (2015) analysed the behaviour of noise in 112 continuously operating GPS (CGPS) position time series in the eastern part of North America and found out that WN+FN is the best model that describes the stochastic part of the position time series. Xu and Yue (2017) in their assessment of the noise characteristics of daily position time series from 12 International GNSS Service sites located in China concluded that the noise model of most sites can be characterized by a combination of WN+FN.…”

mentioning

confidence: 99%

“…However, removing outliers using designated threshold or criterion can't detect or remove some outliers (He et al, 2017). Therefore, so that realistic uncertainty can be assigned, maximum Likelihood estimation (Bos et al, 2008(Bos et al, , 2013, overlapping Hadamard variance (OHVAR) (Xu and Yue, 2017), Least squares variance component estimation (LS-VCE) (Amiri-Simkooei et al, 2007) and Alan Variance (Niu et al, 2014) are often used to estimate the optimal noise characteristics in GNSS time series.…”

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confidence: 99%

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Preliminary assessment of the effect of noise on velocity uncertainty on the Nigerian permanent GNSS network

Bawa¹

2019

Acta Geodynamica Et Geomaterialia

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With the evolution of GNSS technology, geodynamic activities can appropriately be modelled nowadays. GNSS derived time series from which velocities and their uncertainties are derived, are vital derivatives in geodynamic modelling processes. Therefore, understanding all the stochastic properties is crucial. Assuming that GNSS coordinate time series is characterized by only white noise may lead to underestimation of velocity uncertainties. In this contribution, noise behaviour of NigNET tracking stations position time series was examined by adopting WN, FL+WN, WN+RW, WN+PL. Using the maximum likelihood estimate (MLE), Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) the quality of stochastic model or the goodness of fit of a stochastic model is determined. The results of this study show that the combination of white plus flicker noise is the best model for describing the stochastic part of NigNET tracking stations position time series.

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Characterizing noise in daily GPS position time series with overlapping Hadamard variance and maximum likelihood estimation

Cited by 4 publications

References 34 publications

Characteristics of Onefold Clocks of GPS, Galileo, BeiDou and GLONASS Systems

Characteristics of Onefold Clocks of GPS, Galileo, BeiDou and GLONASS Systems

Characteristics of seasonal variations and noises of the daily double-difference and PPP solutions

Preliminary assessment of the effect of noise on velocity uncertainty on the Nigerian permanent GNSS network

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