LS-VCE Applied to Stochastic Modeling of GNSS Observation Noise and Process Noise

Pengyu Hou,Jiuping Zha,Teng Liu,Baocheng Zhang

doi:10.3390/rs14020258

Abstract

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is able to jointly estimate the variances of observation noise and process noise. The method is flexible since it is based on the least-squares variance component estimation (LS-VCE), enabling users to estimate the variance components that they are specifically interested in. We apply the proposed method to estimate the variances for the dual-frequency GNSS observation noise and for the process noise of the receiver code bias (RCB). We also investigate the impact of the stochastic model upon parameter estimation, ambiguity resolution, and positioning. The results show that the precision of GNSS observations differs in systems and frequencies. Among the dual-frequency GPS, Galileo, and BDS code observations, the precision of the BDS B3 observations is highest (better than 0.2 m). The precision of the BDS phase observations is better than two millimeters, which is also higher than that of the GPS and Galileo observations. For all three systems, the RCB process noise ranges from 0.5 millimeters to 1 millimeter, with a data sampling rate of 30 s. An improper stochastic model of the observation noise results in an unreliable ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP), thus adversely affecting the assessment of the ambiguity resolution and positioning performance. An inappropriate stochastic model of RCB process noise disturbs the estimation of the receiver clock and the ionosphere delays and is thus harmful for timing and ionosphere retrieval applications.

Highlights

Introduction published maps and institutional affilChoosing the proper mathematical models, including a functional model, a dynamic model, and a stochastic model, is essential for global navigation satellite systems (GNSS)data processing [1,2]
This paper focuses on the least-squares variance component estimation (LS-VCE) which is capable of unifying many VCE methods [13,18]
By comparing our realistic stochastic model with the empirical stochastic model that is commonly adopted in real-time kinematic (RTK) positioning, we analyzed the impact of the stochastic model on parameter estimation, ambiguity resolution, and positioning

Summary

Introduction

Introduction published maps and institutional affilChoosing the proper mathematical models, including a functional model, a dynamic model, and a stochastic model, is essential for global navigation satellite systems (GNSS)data processing [1,2]. Choosing the proper mathematical models, including a functional model, a dynamic model, and a stochastic model, is essential for global navigation satellite systems (GNSS). The functional model describes the relationships between observations and unknown parameters, while the dynamic model specifies the time evolution of unknown parameters [3,4]. A considerable number of studies have established various functional and dynamic models for GNSS positioning, navigation, and timing applications [5,6,7]. The stochastic model, which describes the random characteristics of a system, is usually unknown or only partly known. A realistic stochastic model ensures the best linear unbiased estimation, determines an accurate precision description of the unknown parameters, and allows reliable quality control [3,8]. It is of great importance to establish a realistic stochastic model for GNSS applications

Methods

Results

Discussion

Conclusion