Tikhonov Regularization Based Modeling and Sidereal Filtering Mitigation of GNSS Multipath Errors

In Global Navigation Satellite System (GNSS) relative positioning applications, multipath errors are non-negligible. Mitigation of the multipath error is an important task for precise positioning and it is possible due to the repeatability, even without any rigorous mathematical model. Empirical mod...

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Bibliographic Details
Published inRemote sensing (Basel, Switzerland) Vol. 10; no. 11; p. 1801
Main Authors Chang, Guobin, Chen, Chao, Yang, Yuanxi, Xu, Tianhe
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.11.2018
Subjects
Algorithms
bootstrap
Earthquakes
Error analysis
Filtration
Global navigation satellite system
GNSS
Kalman filters
Lagrange multiplier
Linear algebra
Mathematical models
Methods
Mitigation
multipath
Navigation
Phase measurement
Regularization
Remote sensing
sidereal filtering
Smoothness
Statistical methods
Tikhonov regularization
New York
United States > US
China
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Summary:In Global Navigation Satellite System (GNSS) relative positioning applications, multipath errors are non-negligible. Mitigation of the multipath error is an important task for precise positioning and it is possible due to the repeatability, even without any rigorous mathematical model. Empirical modeling is required for this mitigation. In this work, the multipath error modeling using carrier phase measurement residuals is realized by solving a regularization problem. Two Tikhonov regularization schemes, namely with the first and the second order differences, are considered. For each scheme, efficient numerical algorithms are developed to find the solutions, namely the Thomas algorithm and Cholesky rank-one update algorithm for the first and the second differences, respectively. Regularization parameters or Lagrange multipliers are optimized using the bootstrap method. In experiment, data on the first day are processed to construct a multipath model for each satellite (except the reference one), and then the model is used to correct the measurement on the second day, namely following the sidereal filtering approach. The smoothness of the coordinates calculated using the corrected measurements is improved significantly compared to those using the raw measurement. The efficacy of the proposed method is illustrated by the actual calculation.
ISSN:2072-4292
2072-4292
DOI:10.3390/rs10111801