引用本文: 边少锋, 刘一, 纪兵, 周威. 北斗三号卫星观测信息高度角相关随机模型统计特性分析[J]. 武汉大学学报 ( 信息科学版), 2022, 47(10): 1615-1624.
BIAN Shaofeng, LIU YI, JI Bing, ZHOU Wei. Analysis of Statistic Testing of Elevation-Dependent Stochastic Models of BDS-3 Satellite Observation[J]. Geomatics and Information Science of Wuhan University, 2022, 47(10): 1615-1624.
 Citation: BIAN Shaofeng, LIU YI, JI Bing, ZHOU Wei. Analysis of Statistic Testing of Elevation-Dependent Stochastic Models of BDS-3 Satellite Observation[J]. Geomatics and Information Science of Wuhan University, 2022, 47(10): 1615-1624.

## Analysis of Statistic Testing of Elevation-Dependent Stochastic Models of BDS-3 Satellite Observation

• 摘要: 观测信息随机模型在参数估计、质量控制和精度评定过程中具有重要作用,准确的观测信息随机模型是北斗精密定位的基础。首先,利用简化的Helmert方差分量估计方法估计北斗三号卫星观测信息精度,并拟合模型系数；然后,利用全局检验和$\omega$检验对基于分段函数、正弦函数、余弦函数和指数函数的随机模型进行统计检验,分析随机模型统计特性；最后,利用精密单点定位（precise point positioning,PPP）检验各随机模型对定位性能的影响。实验结果表明,北斗三号卫星的伪距和载波相位观测值精度均与高度角相关,且观测类型不同,相关程度不同；基于指数函数的随机模型在拟合误差、全局检验和$\omega$检验中均表现出最优的性能,全局检验浮点解和固定解的误警率仅为5.1%和4.9%,$\omega$检验伪距和载波相位最大误警率分别为5.8%和6.8%,PPP收敛时间最短,定位精度最高。基于指数函数的随机模型能够准确描述北斗观测信息精度,提高北斗三号卫星精密定位结果的精度和可靠性。

Abstract:
Objectives  The stochastic model of observation information describes the accuracy of observation information and its correlation, and also plays an important role in parameter estimation, quality control and accuracy evaluation. In the process of global navigation satellite system (GNSS) precision positioning, an accurate stochastic model is essential for improving the accuracy of float solution, enhancing the success rate of ambiguity resolution, increasing the accuracy of gross error detection, and obtaining the accurate and reliable positioning results.
Methods  An optimization method for stochastic model of BeiDou navigation satellite system (BDS) is proposed by handling the properties of four classic elevation-dependent stochastic models based on the relationship between BDS satellite observation information and elevation. Firstly, the accuracy of BDS four-frequency observation information is evaluated by the simplified Helmert variance estimation method. Then, the model parameters could be fitted based on the estimated precision of observation information. Finally, the statistical characteristics of four stochastic models, including piecewise function, sine function, cosine function and exponential function, are tested by the overall test and ω-test methods.
Results  The results show that the accuracy of pseudorange and carrier phase for BDS-3 satellite are related to elevation, and the correlation degree is different by GNSS observation types. The stochastic model of exponential function shows the best performance in the fitting error, the overall test and the ω-test. The maximum fitting errors of pseudorange and carrier phase are 0.029 m and 5.484 mm, respectively. The false alarm rates of the overall test for the float solution and the fixed solution are 5.1 % and 4.9 %, respectively. In addition, the maximum false alarm rates of the ω-test are 5.8 % for the pseudorange and 6.8 % for the carrier phase.
Conclusions  The stochastic model of exponential function can get the shortest convergence time and the highest positioning accuracy for BDS-3 quad-frequency precise point positioning. It can also accurately describe the accuracy of BDS observation information and improve the accuracy and reliability of BDS precise positioning results.

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