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Investigation of performance improvement in GNSS PPP-RTK ambiguity resolution via Gaussian overbounding for heavy-tailed error modeling.

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Title: Investigation of performance improvement in GNSS PPP-RTK ambiguity resolution via Gaussian overbounding for heavy-tailed error modeling.
Authors: Li, Yuan1 (AUTHOR) yuaen.li@connect.polyu.hk, Yan, Penggao1 (AUTHOR) peng-gao.yan@connect.polyu.hk, Hsu, Li-Ta1 (AUTHOR) lt.hsu@polyu.edu.hk
Source: Advances in Space Research. Apr2026, Vol. 77 Issue 7, p7634-7649. 16p.
Subjects: Monte Carlo method, Error probability, Global Positioning System, Random noise theory, Wireless geolocation systems
Abstract: • This paper first investigates the performance improvement of Gaussian overbound in GNSS PPP-RTK ambiguity resolution regarding the correct fix rate, miss detection rate, and positioning error. • This paper develops a single-epoch weighted least squares PPP-RTK simulation platform to validate the overbound method under various heavy-tailed errors. • This paper uses Monte Carlo simulations and real experiments to demonstrate that the overbound method can reduce the ambiguity miss detection rate and increase positioning reliability under heavy-tailed error distribution. Global Navigation Satellite System (GNSS) is essential for many autonomous system applications. Its degradation directly threatens the operational safety. Precise Point Positioning (PPP) based on real-time kinematic (RTK) networks (PPP-RTK) is a popular candidate for providing precise positioning service. This technology needs to resolve integer ambiguities of GNSS carrier phase measurements, which is key to achieving centimeter-level accuracy (also known as a fixed solution). However, there are times when the fixed solution is falsely locked to an incorrect set of integers, leading to errors of several meters. This miss detection can occur even when a rigorous ambiguity resolution (AR) algorithm, such as the least squares ambiguity decorrelation adjustment (LAMBDA) method, is applied. This is sometimes because GNSS measurements often exhibit heavy-tailed error distributions. To address this issue, this paper investigates the use of a Gaussian overbounding method to stochastically model the noise of pseudorange and carrier phase measurements. The Gaussian overbounding method can better describe the tail characteristics of the error distribution, aiming to reduce the miss detection rate of AR and thereby improve positioning performance. A PPP-RTK simulation platform is developed to validate the effectiveness of the Gaussian overbounding method under various degrees of heavy-tailed error distribution scenarios. Through Monte Carlo simulations, we demonstrate that the overbound-based stochastic model can reduce the miss detection rate under heavy-tailed distributions and mitigate the degradation of AR reliability caused by underestimating measurement uncertainty, serving as a confirmation and complement to existing studies. Real experiments demonstrate that the 3D RMSE of the fixed solution decreases by 18.34 % on average. [ABSTRACT FROM AUTHOR]
Copyright of Advances in Space Research is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Investigation of performance improvement in GNSS PPP-RTK ambiguity resolution via Gaussian overbounding for heavy-tailed error modeling.
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  Data: <searchLink fieldCode="AR" term="%22Li%2C+Yuan%22">Li, Yuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yuaen.li@connect.polyu.hk</i><br /><searchLink fieldCode="AR" term="%22Yan%2C+Penggao%22">Yan, Penggao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> peng-gao.yan@connect.polyu.hk</i><br /><searchLink fieldCode="AR" term="%22Hsu%2C+Li-Ta%22">Hsu, Li-Ta</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lt.hsu@polyu.edu.hk</i>
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  Data: <searchLink fieldCode="JN" term="%22Advances+in+Space+Research%22">Advances in Space Research</searchLink>. Apr2026, Vol. 77 Issue 7, p7634-7649. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Error+probability%22">Error probability</searchLink><br /><searchLink fieldCode="DE" term="%22Global+Positioning+System%22">Global Positioning System</searchLink><br /><searchLink fieldCode="DE" term="%22Random+noise+theory%22">Random noise theory</searchLink><br /><searchLink fieldCode="DE" term="%22Wireless+geolocation+systems%22">Wireless geolocation systems</searchLink>
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  Label: Abstract
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  Data: • This paper first investigates the performance improvement of Gaussian overbound in GNSS PPP-RTK ambiguity resolution regarding the correct fix rate, miss detection rate, and positioning error. • This paper develops a single-epoch weighted least squares PPP-RTK simulation platform to validate the overbound method under various heavy-tailed errors. • This paper uses Monte Carlo simulations and real experiments to demonstrate that the overbound method can reduce the ambiguity miss detection rate and increase positioning reliability under heavy-tailed error distribution. Global Navigation Satellite System (GNSS) is essential for many autonomous system applications. Its degradation directly threatens the operational safety. Precise Point Positioning (PPP) based on real-time kinematic (RTK) networks (PPP-RTK) is a popular candidate for providing precise positioning service. This technology needs to resolve integer ambiguities of GNSS carrier phase measurements, which is key to achieving centimeter-level accuracy (also known as a fixed solution). However, there are times when the fixed solution is falsely locked to an incorrect set of integers, leading to errors of several meters. This miss detection can occur even when a rigorous ambiguity resolution (AR) algorithm, such as the least squares ambiguity decorrelation adjustment (LAMBDA) method, is applied. This is sometimes because GNSS measurements often exhibit heavy-tailed error distributions. To address this issue, this paper investigates the use of a Gaussian overbounding method to stochastically model the noise of pseudorange and carrier phase measurements. The Gaussian overbounding method can better describe the tail characteristics of the error distribution, aiming to reduce the miss detection rate of AR and thereby improve positioning performance. A PPP-RTK simulation platform is developed to validate the effectiveness of the Gaussian overbounding method under various degrees of heavy-tailed error distribution scenarios. Through Monte Carlo simulations, we demonstrate that the overbound-based stochastic model can reduce the miss detection rate under heavy-tailed distributions and mitigate the degradation of AR reliability caused by underestimating measurement uncertainty, serving as a confirmation and complement to existing studies. Real experiments demonstrate that the 3D RMSE of the fixed solution decreases by 18.34 % on average. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Advances in Space Research is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.asr.2026.01.099
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 7634
    Subjects:
      – SubjectFull: Monte Carlo method
        Type: general
      – SubjectFull: Error probability
        Type: general
      – SubjectFull: Global Positioning System
        Type: general
      – SubjectFull: Random noise theory
        Type: general
      – SubjectFull: Wireless geolocation systems
        Type: general
    Titles:
      – TitleFull: Investigation of performance improvement in GNSS PPP-RTK ambiguity resolution via Gaussian overbounding for heavy-tailed error modeling.
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            NameFull: Li, Yuan
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            NameFull: Yan, Penggao
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            NameFull: Hsu, Li-Ta
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            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
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