Abstract
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.
Highlights
Global navigation satellite systems (GNSS) are widely used in positioning, navigation, and timing (PNT) services
The measurement data were collected at Global PositioningSystem (GPS) time (GPST) 9:00–10:00 a.m. on day of year (DOY) 180 of 2018 with an epoch interval of 30 seconds
This article presented the problem of solving the mathematical models in GNSS phase bias estimation, which is essential for fast and precise GNSS data processing; it developed a fast and efficient algorithm by combining the GNSS data processing procedure and the sequential quasi-Monte Carlo (SQMC) method
Summary
Global navigation satellite systems (GNSS) are widely used in positioning, navigation, and timing (PNT) services. The accuracy of the precise positioning can reach the level of centimeters and satisfy a pervasive use in civil and military applications. GNSS is being developed at a fast pace, and the systems in full operation at present include the United States of America (USA)’s Global Positioning. System (GPS) and Russia’s Global Navigation Satellite System (GLONASS). The basic principle of GNSS data processing is to mathematically solve the interesting PNT parameters in the observation models with measurements of the distances between GNSS satellites and receivers. The bias estimation plays an important role in the quality of the final PNT services [3,4,5]. Reducing the variance of the bias estimates can more precisely recover the measurements and improve the service quality
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