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

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.

Nonlinear Regression-Based GNSS Multipath Dynamic Map Construction and Its Application in Deep Urban Areas

“…GNSS code measurements represent the range obtained by multiplying the propagation time of the signal from the satellite to the receiver by the speed of light. The pseudorange code measurement of the i th satellite at time t can be modeled using (1).…”

“…G LOBAL navigation satellite systems (GNSSs) are widely used in positioning, navigation, and timing services [1] Manuscript received 31 Pai Wang is with the School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.…”

“…This is because RAIM assumes that no more than one failure is detected at a time, which is not true in urban environments-most signals received in an urban canyon are easily corrupted by multipath and NLOS errors [7]. Smoothing techniques based on carrier phase variation [8], [9] also enable more accurate positioning, but they require an accurate absolute position solution and a sufficient number of good signals for initialization [1], which are impractical and challenging requirements in urban environments [6].…”

Carrier Phase Residual Modeling and Fault Monitoring Using Short-Baseline Double Difference and Machine Learning

“…Code measurements provide information about the absolute distance between a satellite and a user as described in (1). The carrier phase measurements, which are shown in (2), provide higher resolution distance information, but it is difficult to resolve the integer ambiguities that are inherent in the measurements, so they are often used as a relative metric unless the ambiguities are resolved [17]. Doppler measurements provide the LOS doppler frequency between the satellite and the user.…”