Stochastic Models of Very High-Rate (50 Hz) GPS/BeiDou Code and Phase Observations

Yuanming Shu,Rongxin Fang,Jingnan Liu

doi:10.3390/rs9111188

Abstract

In recent years, very high-rate (10–50 Hz) Global Navigation Satellite System (GNSS) has gained a rapid development and has been widely applied in seismology, natural hazard early warning system and structural monitoring. However, existing studies on stochastic models of GNSS observations are limited to sampling rates not higher than 1 Hz. To support very high-rate GNSS applications, we assess the precisions, cross correlations and time correlations of very high-rate (50 Hz) Global Positioning System (GPS)/BeiDou code and phase observations. The method of least-squares variance component estimation is applied with the geometry-based functional model using the GNSS single-differenced observations. The real-data experimental results show that the precisions are elevation-dependent at satellite elevation angles below 40° and nearly constant at satellite elevation angles above 40°. The precisions of undifferenced observations are presented, exhibiting different patterns for different observation types and satellites, especially for BeiDou because different types of satellites are involved. GPS and BeiDou have comparable precisions at high satellite elevation angles, reaching 0.91–1.26 mm and 0.13–0.17 m for phase and code, respectively, while, at low satellite elevation angles, GPS precisions are generally lower than BeiDou ones. The cross correlation between dual-frequency phase is very significant, with the coefficients of 0.773 and 0.927 for GPS and BeiDou, respectively. The cross correlation between dual-frequency code is much less significant, and no correlation can be found between phase and code. Time correlations exist for GPS/BeiDou phase and code at time lags within 1 s. At very small time lags of 0.02–0.12 s, time correlations of 0.041–0.293 and 0.858–0.945 can be observed for phase and code observations, respectively, indicating that the correlations in time should be taken into account in very high-rate applications.

Highlights

The adjustment of Global Navigation Satellite System (GNSS) observations, e.g., in GNSS relative positioning or precise point positioning, is based on functional and stochastic models [1]
Various studies have been conducted to improve our knowledge of the GNSS stochastic model by estimating unknown components of thevariance matrix, which is generally known as variance component estimation (VCE)
This paper aims to study the stochastic models of very high-rate data from two GNSS constellations, namely Global Positioning System (GPS) and BeiDou

Summary

Introduction

The adjustment of Global Navigation Satellite System (GNSS) observations, e.g., in GNSS relative positioning or precise point positioning, is based on functional and stochastic models [1]. The stochastic model, represented by the (co)variance matrix, reflects the precisions, cross correlations between observation types and time correlations. Tiberius and Kenselaar [9] presented reasonably simple VCE formulas and analyzed stochastic models of GPS observables on a zero baseline. Li et al [10] assessed the stochastic models of GPS measurements collected by different types of receivers on ultra-short baselines, and identified the existence of elevation dependence of precisions, time correlations and cross correlations between observation types. They pointed out that the stochastic model should be specified for the receiver and observation types. For more studies on GNSS stochastic models, the readers can refer to Teunissen and Amiri-Simkooei [13]

Objectives

Methods

Results

Conclusion