﻿ 变异系数赋权法确定GNSS系统硬件延迟
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 大地测量与地球动力学  2019, Vol. 39 Issue (12): 1287-1292  DOI: 10.14075/j.jgg.2019.12.014

### 引用本文

YUAN Xingming. A Variation Coefficient Weighting Method to Determine the Difference Code Bias Estimation of GNSS System[J]. Journal of Geodesy and Geodynamics, 2019, 39(12): 1287-1292.

### Foundation support

Research Project of Teaching Reform of Shandong Vocational College of Industry, No.2017RW13.

### 第一作者简介

YUAN Xingming, lecturer, majors in engineering survey and deformation monitoring, E-mail:yuanxingming1986@126.com.

### 文章历史

1. 山东工业职业学院建筑与信息工程系，山东省淄博市张北路69号，256414

1 GNSS硬件延迟计算模型

 $\begin{array}{*{20}{c}} {\rho = P - \frac{{0.4028}}{{{f^2}}} \times F\left( z \right) \times }\\ {{\rm{VTEC}} + c\left( {{\rm{d}}s - {\rm{d}}r} \right) + \varepsilon } \end{array}$ (1)
 $\begin{array}{*{20}{c}} {\rho = \lambda \left( {N + \phi } \right) + \frac{{0.4028}}{{{f^2}}} \times F\left( z \right) \times }\\ {{\rm{VTEC}} + c\left( {{\rm{d}}s - {\rm{d}}r} \right) + \varepsilon } \end{array}$ (2)

 ${\rm{VTEC}} = k\left( {{P_2} - {P_1}} \right) + ck\left( {{\rm{d}}s - {\rm{d}}r} \right)$ (3)
 ${\rm{VTEC}} = k\left( {{L_1} - {L_2}} \right) + ck\left( {{\rm{d}}s - {\rm{d}}r} \right)$ (4)

 ${\rm{VTEC}} = k\left( {{{\bar P}_2} - {{\bar P}_1}} \right) + ck({\rm{d}}s - {\rm{d}}r)$ (5)

 $\begin{array}{*{20}{c}} {{\rm{VTEC}} = \sum\limits_{i = 0}^4 {\sum\limits_{m = 0}^i {\left( {A_n^m\cos m{\lambda ^\prime } + } \right.} } }\\ {\left. {B_n^m\sin m{\lambda ^\prime }} \right) \times P_n^m\sin \varphi } \end{array}$ (6)

 $\begin{array}{*{20}{c}} {k\left( {{{\bar P}_2} - {{\bar P}_1}} \right) + ck({\rm{d}}s - {\rm{d}}r) = }\\ {\sum\limits_{i = 0}^4 {\sum\limits_{m = 0}^i {\left( {A_n^m\cos m{\lambda ^\prime } + B_n^m\sin m{\lambda ^\prime }} \right)} } \times P_n^m\sin \varphi } \end{array}$ (7)

 $\mathit{\boldsymbol{V}} = \mathit{\boldsymbol{B\hat x}} - \mathit{\boldsymbol{l}}$ (8)

 $\mathit{\boldsymbol{P}} = \sigma _0^2{\mathit{\boldsymbol{D}}_0} = {\mathit{\boldsymbol{Q}}^{ - 1}}$ (9)

 $\sum\limits_{i = 1}^n {{d_i}} = 0$ (10)

1) 等精度定权。当某一历元观测的卫星个数为n时，可以组成(n-1)个双差观测值。若不考虑观测值卫星间及历元间的任何相关性，并认为原始观测值的精度相同，即近似认为各系统观测值为等权观测值，将权矩阵看成是单位阵[9]

2) 高度角定权。高度角随机模型是利用观测值的高度角为变量构成高度角的函数，即

 $\sigma = f\left( {{\rm{elv}}} \right)$ (11)

 ${\sigma ^2} = 1/{\sin ^2}\left( {{\rm{elv}}} \right)$ (12)

 $P = \frac{{\sigma _0^2}}{{{\sigma ^2}}}$ (13)

 $P = {\sin ^2}\left( {{\rm{elv}}} \right)$ (14)
2 变异系数赋权法

 $V = \frac{{{\sigma ^2}}}{{\bar x}}$ (15)

 $\begin{array}{*{20}{c}} {\bar x = \frac{1}{n}\sum\limits_{i = 1}^n {{x_i}} }\\ {{\sigma _j} = \sqrt {\frac{1}{{n - 1}}\sum\limits_{i = 1}^n {{{\left( {{x_i} - \bar x} \right)}^2}} } ,i = 1,2, \cdots ,n} \end{array}$ (16)

 $w = \frac{V}{{\mathit{\Sigma }{V_i}}}$ (17)

 $\mathit{\boldsymbol{H}} = b\mathop {\mathit{\boldsymbol{q}}}\limits_{n \times m} \times \mathop {\mathit{\boldsymbol{w}}}\limits_{m \times 1} ,\mathit{\boldsymbol{P}} = {\rm{diag}}\left( \mathit{\boldsymbol{H}} \right)$ (18)

 ${q_{ij}} = \frac{{{x_{ij}}}}{{\sum\limits_{j = 1}^m {{x_{ij}}} }}$ (19)

 图 1 变异系数赋权计算观测值权的流程 Fig. 1 Flowchart of calculating the weight of observing values by variation coefficient weighting

3 实验分析

 $\gamma = \sqrt {\frac{{\left[ {\Delta \Delta } \right]}}{n}}$ (20)

 ${\sigma _{外}} = \sqrt {\frac{{\left[ {vv} \right]}}{r}}$ (21)

 图 2 2种方法的GNSS-DCB残差对比 Fig. 2 Comparison of GNSS-DCB residual difference of the two methods

 ${\rm{ST}}{{\rm{D}}^j} = \sqrt {\frac{{\sum\limits_{i = 1}^n {{{\left( {{\rm{d}}{s^{i,j}} - {\rm{d}}{{\bar s}^{i,j}}} \right)}^2}} }}{{n - 1}}} ,i = 1,2, \cdots ,n$ (22)

 图 3 2种方法差值对比 Fig. 3 Comparison of difference of the two methods

 图 4 2种方法2016年doy 184~190GNSS-DCB的稳定性 Fig. 4 Stability of GNSS-DCB of the two methods during doy 184 to 190 of 2016

4 结语

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A Variation Coefficient Weighting Method to Determine the Difference Code Bias Estimation of GNSS System
YUAN Xingming1
1. Department of Architecture and Information Engineering, Shandong Vocational College of Industry, 69 Zhangbei Road, Zibo 256414, China
Abstract: This paper studies the stochastic model of DCB for GNSS systems by post-processing phase smoothed code data. To resolve the problem of estimating the uncertainty of the parameters of the weight of the elevation angle and the equal-accuracy, the paper presents a weighted method, i.e., variation coefficient weighting, to effectively influence the stochastic model. The index weights are determined according to the decision matrix of the index value of the evaluation object. Preliminary results show that: 1) The fitting precision of the model is related to observation data and the station location. The more stable the ionospheric variation of the station position and the adequacy of the observational data, the better the model fitting accuracy. 2) The model fitting accuracy is better than by the weight of elevation angle using variation coefficient weighting. 3) In the accuracy and stability of parameter estimation, the variation coefficient weighting method is superior to the method of the weight of elevation angle, and the calculation accuracy of single-day data can be improved by 0.2 ns.
Key words: phase smoothing; DCB; weight of elevation angle; variation coefficient weighting