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Open AccessArticle

Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation

by Yumiao Tian 1,*, Maorong Ge 2,3,* and Frank Neitzel 2,*
Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China
Institute of Geodesy and Geoinformation Science, Technische Universität Berlin, 10623 Berlin, Germany
Section 1.1: Space Geodetic Techniques, GFZ German Research Centre for Geosciences, 14473 Potsdam, Germany
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(4), 522;
Received: 29 February 2020 / Revised: 16 March 2020 / Accepted: 18 March 2020 / Published: 3 April 2020
(This article belongs to the Special Issue Stochastic Models for Geodesy and Geoinformation Science)
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. View Full-Text
Keywords: GNSS phase bias; sequential quasi-Monte Carlo; variance reduction GNSS phase bias; sequential quasi-Monte Carlo; variance reduction
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Tian, Y.; Ge, M.; Neitzel, F. Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation. Mathematics 2020, 8, 522.

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