VLBI、卫星网和地面网联合平差的数学模型

佘彬彬

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VLBI、卫星网和地面网联合平差的数学模型

佘彬彬

文章导航 > 武汉大学学报 ● 信息科学版 > 1989 > 14(1): 27-37

佘彬彬. VLBI、卫星网和地面网联合平差的数学模型[J]. 武汉大学学报 ● 信息科学版, 1989, 14(1): 27-37.

引用本文:

佘彬彬. VLBI、卫星网和地面网联合平差的数学模型[J]. 武汉大学学报 ● 信息科学版, 1989, 14(1): 27-37.

She Binbin. New Approaches to the Combination of Terrestrial Networks with Satellite Networks and VLBI Base Lines[J]. Geomatics and Information Science of Wuhan University, 1989, 14(1): 27-37.

Citation:

She Binbin. New Approaches to the Combination of Terrestrial Networks with Satellite Networks and VLBI Base Lines[J]. Geomatics and Information Science of Wuhan University, 1989, 14(1): 27-37.

VLBI、卫星网和地面网联合平差的数学模型

佘彬彬

New Approaches to the Combination of Terrestrial Networks with Satellite Networks and VLBI Base Lines

She Binbin

摘要: 本文同时顾及地面网尺度系统误差和卫星网尺度系统误差对各自网点坐标的影响,对联合平差中常用的两种7参数转换模型:Bursa模型和Molodensky模型进行了分析比较,在此基础上,提出了一种新的7参数转换模型;建立了甚长基线(VLBI)、卫星网和地面网联合平差的数学模型,并用模拟数据进行了数值分析,得到了一些有益结论。
- 甚长基线 /
- 卫星网 /
- 地面网 /
- 联合平差 /
- 数学模型 /
- 数值分析
Abstract: In this paper, some analyses and comparisions have been made on the two widelyused transformation models:the bursa model and the Molodensky model, with the consi-deration of the effects of the systematic scale errors of both terrestrial and satellite networks.On the basis of it, an improved transformation model (named WTS model) with sevenparameters has been proposed. Considering the high scale accuracy of VLBI Base Lineswhose scale error can be neglected with respect to that of terres trial and satellite networks,two equivalent models for combing VLBI base lines, satellite network and terrestrial networkhave been developed, in which two scale bias parameters corresponding to the terrestrialnatwork and the satellite network respectively have been considered. Some numerical analyseshave been made using these models, and the results have been compared with the corres-ponding results obtained from the combined adjustment of terrestrial and satellite network.The main conclusions are as follows:As there exist significant scale biases both in the terrestrial network and the satellitenetwork, and the scale biases of each network affects its coordinates in a different way,the relative scale parameter of the existing transformation models with seven parameters,such as the Bursa model,the Moledensky model etc., cannot absorb the scale biases ofthe two networks completely, thus resulting in systematic biases of the estimated translationparameters. The WTS model put forward in this paper has the minimum biases of theestimted translation parameters compared with the well-known Bursa model and the Mo-lodensky model. The influences of the scale biases upon the translation parameters and the estimatedcoordinates of the terrestrial network cannot be eliminated in the combined adjustmentswith only terrestrial and satellite data. Therefore,extra observations with higt scale accuracyshould be added. Compared with terrestrial and satellite networks VLBI base lines can beused to provide the scale standard (its scale biases is regarded as zero) for both terrestri-al and satellite networks. By using the models presented in this paper, it is possible toobtain the unbiased estimators of the translation parameters and the two scale parametersof the sattellite network and terrestrial network as well as the three rotation parameters,so that the transformation of the terrestria1 newtork into the satellite geocentric systemcan be realized and the influnce of scale biases upon the coordinates of the terrestYial geo-datic network can be eliminated.
- VLBI /
- satellite network /
- terrestrial network /
- combined adjustment /
- mathematical model /
- numerical analyses

[1]	王乐洋, 余航. 火山Mogi模型反演的总体最小二乘联合平差方法 . 武汉大学学报 ● 信息科学版, 2018, 43(9): 1333-1341. doi: 10.13203/j.whugis20160469
[2]	王乐洋, 余航. 总体最小二乘联合平差 . 武汉大学学报 ● 信息科学版, 2016, 41(12): 1683-1689. doi: 10.13203/j.whugis20140670
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[6]	许才军, 王华, 程鹏飞, 张莉. 天文大地网与GPS2000网联合平差的地壳形变改正研究 . 武汉大学学报 ● 信息科学版, 2005, 30(1): 34-37.
[7]	童小华, 刘大杰. 道路曲线数字化数据的联合平差模型 . 武汉大学学报 ● 信息科学版, 2001, 26(1): 64-69.
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[9]	王建华. 基于模糊综合评判原理建立制图基本资料选择评价数学模型 . 武汉大学学报 ● 信息科学版, 1992, 17(2): 86-96.
[10]	周忠谟, 晁定波, 刘乃苓. 卫星网与地面网在高斯平面坐标系统中的转换模型 . 武汉大学学报 ● 信息科学版, 1991, 16(1): 92-96.
[11]	周忠谟, 晁定波. 论卫星网与地面网在高斯平面坐标系统中的联合平差问题 . 武汉大学学报 ● 信息科学版, 1991, 16(4): 65-71.
[12]	单杰, 李德仁. 摄影测量与大地测量观测值联合平差的质量分析 . 武汉大学学报 ● 信息科学版, 1990, 15(4): 6-15.
[13]	张永生. 近景光束法自由网联合平差的实际精度 . 武汉大学学报 ● 信息科学版, 1989, 14(2): 100-108.
[14]	祝国瑞. 应用数学模型推断地图上河流的选取程度 . 武汉大学学报 ● 信息科学版, 1989, 14(4): 47-51.
[15]	许才军. 卫星网与地面网联合平差中随机模型的估计 . 武汉大学学报 ● 信息科学版, 1989, 14(3): 35-45.
[16]	单杰. 联合平差中大地测量观测值的数学模型 . 武汉大学学报 ● 信息科学版, 1988, 13(4): 105-111.
[17]	王有年. 用于近景摄影测量的联合平差程序系统CAS-C . 武汉大学学报 ● 信息科学版, 1987, 12(2): 64-72.
[18]	周忠谟, 晁定波. GPS空间基线向量网与地面控制网的联合平差模型 . 武汉大学学报 ● 信息科学版, 1987, 12(2): 20-28.
[19]	周忠谟. 在地面三角网中布设卫星观测站的最低精度要求 . 武汉大学学报 ● 信息科学版, 1986, 11(3): 30-36.
[20]	周忠谟, 晁定波. 地面网和卫星网联合平差的数学模型 . 武汉大学学报 ● 信息科学版, 1985, 10(4): 1-7.

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VLBI、卫星网和地面网联合平差的数学模型

佘彬彬

收稿日期: 1987-12-24
刊出日期: 1989-01-05

关键词:

甚长基线 /

卫星网 /

地面网 /

联合平差 /

数学模型 /

数值分析

摘要: 本文同时顾及地面网尺度系统误差和卫星网尺度系统误差对各自网点坐标的影响,对联合平差中常用的两种7参数转换模型:Bursa模型和Molodensky模型进行了分析比较,在此基础上,提出了一种新的7参数转换模型;建立了甚长基线(VLBI)、卫星网和地面网联合平差的数学模型,并用模拟数据进行了数值分析,得到了一些有益结论。

English Abstract

New Approaches to the Combination of Terrestrial Networks with Satellite Networks and VLBI Base Lines

She Binbin

Received Date: 1987-12-24
Publish Date: 1989-01-05

Keywords:

Abstract: In this paper, some analyses and comparisions have been made on the two widelyused transformation models:the bursa model and the Molodensky model, with the consi-deration of the effects of the systematic scale errors of both terrestrial and satellite networks.On the basis of it, an improved transformation model (named WTS model) with sevenparameters has been proposed. Considering the high scale accuracy of VLBI Base Lineswhose scale error can be neglected with respect to that of terres trial and satellite networks,two equivalent models for combing VLBI base lines, satellite network and terrestrial networkhave been developed, in which two scale bias parameters corresponding to the terrestrialnatwork and the satellite network respectively have been considered. Some numerical analyseshave been made using these models, and the results have been compared with the corres-ponding results obtained from the combined adjustment of terrestrial and satellite network.The main conclusions are as follows:As there exist significant scale biases both in the terrestrial network and the satellitenetwork, and the scale biases of each network affects its coordinates in a different way,the relative scale parameter of the existing transformation models with seven parameters,such as the Bursa model,the Moledensky model etc., cannot absorb the scale biases ofthe two networks completely, thus resulting in systematic biases of the estimated translationparameters. The WTS model put forward in this paper has the minimum biases of theestimted translation parameters compared with the well-known Bursa model and the Mo-lodensky model. The influences of the scale biases upon the translation parameters and the estimatedcoordinates of the terrestrial network cannot be eliminated in the combined adjustmentswith only terrestrial and satellite data. Therefore,extra observations with higt scale accuracyshould be added. Compared with terrestrial and satellite networks VLBI base lines can beused to provide the scale standard (its scale biases is regarded as zero) for both terrestri-al and satellite networks. By using the models presented in this paper, it is possible toobtain the unbiased estimators of the translation parameters and the two scale parametersof the sattellite network and terrestrial network as well as the three rotation parameters,so that the transformation of the terrestria1 newtork into the satellite geocentric systemcan be realized and the influnce of scale biases upon the coordinates of the terrestYial geo-datic network can be eliminated.

佘彬彬. VLBI、卫星网和地面网联合平差的数学模型[J]. 武汉大学学报 ● 信息科学版, 1989, 14(1): 27-37.

引用本文:

佘彬彬. VLBI、卫星网和地面网联合平差的数学模型[J]. 武汉大学学报 ● 信息科学版, 1989, 14(1): 27-37.

She Binbin. New Approaches to the Combination of Terrestrial Networks with Satellite Networks and VLBI Base Lines[J]. Geomatics and Information Science of Wuhan University, 1989, 14(1): 27-37.

Citation:

She Binbin. New Approaches to the Combination of Terrestrial Networks with Satellite Networks and VLBI Base Lines[J]. Geomatics and Information Science of Wuhan University, 1989, 14(1): 27-37.