Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation
Global navigation satellite systems (GNSS) are an important tool for positioning, navigation, and timing (PNT) services. The fast and high-precision GNSS data processing relies on reliable integer ambiguity fixing, whose performance depends on phase bias estimation. However, the mathematic model of...
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| Format: | Article |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/522 |
| _version_ | 1797571523748298752 |
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| author | Yumiao Tian Maorong Ge Frank Neitzel |
| author_facet | Yumiao Tian Maorong Ge Frank Neitzel |
| author_sort | Yumiao Tian |
| collection | DOAJ |
| description | Global navigation satellite systems (GNSS) are an important tool for positioning, navigation, and timing (PNT) services. The fast and high-precision GNSS data processing relies on reliable integer ambiguity fixing, whose performance depends on phase bias estimation. However, the mathematic model of GNSS phase bias estimation encounters the rank-deficiency problem, making bias estimation a difficult task. Combining the Monte-Carlo-based methods and GNSS data processing procedure can overcome the problem and provide fast-converging bias estimates. The variance reduction of the estimation algorithm has the potential to improve the accuracy of the estimates and is meaningful for precise and efficient PNT services. In this paper, firstly, we present the difficulty in phase bias estimation and introduce the sequential quasi-Monte Carlo (SQMC) method, then develop the SQMC-based GNSS phase bias estimation algorithm, and investigate the effects of the low-discrepancy sequence on variance reduction. Experiments with practical data show that the low-discrepancy sequence in the algorithm can significantly reduce the standard deviation of the estimates and shorten the convergence time of the filtering. |
| first_indexed | 2024-03-10T20:42:17Z |
| format | Article |
| id | doaj.art-b3c8a518940d46a2b8b2a44aeea298a9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:42:17Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b3c8a518940d46a2b8b2a44aeea298a92023-11-19T20:37:08ZengMDPI AGMathematics2227-73902020-04-018452210.3390/math8040522Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias EstimationYumiao Tian0Maorong Ge1Frank Neitzel2Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, ChinaInstitute of Geodesy and Geoinformation Science, Technische Universität Berlin, 10623 Berlin, GermanyInstitute of Geodesy and Geoinformation Science, Technische Universität Berlin, 10623 Berlin, GermanyGlobal navigation satellite systems (GNSS) are an important tool for positioning, navigation, and timing (PNT) services. The fast and high-precision GNSS data processing relies on reliable integer ambiguity fixing, whose performance depends on phase bias estimation. However, the mathematic model of GNSS phase bias estimation encounters the rank-deficiency problem, making bias estimation a difficult task. Combining the Monte-Carlo-based methods and GNSS data processing procedure can overcome the problem and provide fast-converging bias estimates. The variance reduction of the estimation algorithm has the potential to improve the accuracy of the estimates and is meaningful for precise and efficient PNT services. In this paper, firstly, we present the difficulty in phase bias estimation and introduce the sequential quasi-Monte Carlo (SQMC) method, then develop the SQMC-based GNSS phase bias estimation algorithm, and investigate the effects of the low-discrepancy sequence on variance reduction. Experiments with practical data show that the low-discrepancy sequence in the algorithm can significantly reduce the standard deviation of the estimates and shorten the convergence time of the filtering.https://www.mdpi.com/2227-7390/8/4/522GNSS phase biassequential quasi-Monte Carlovariance reduction |
| spellingShingle | Yumiao Tian Maorong Ge Frank Neitzel Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation Mathematics GNSS phase bias sequential quasi-Monte Carlo variance reduction |
| title | Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation |
| title_full | Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation |
| title_fullStr | Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation |
| title_full_unstemmed | Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation |
| title_short | Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation |
| title_sort | variance reduction of sequential monte carlo approach for gnss phase bias estimation |
| topic | GNSS phase bias sequential quasi-Monte Carlo variance reduction |
| url | https://www.mdpi.com/2227-7390/8/4/522 |
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