| GPS多差相位观测量数学相关性的分析表示 |
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| 引用本文： | 张传定,吴晓平,郝金明,何海波.GPS多差相位观测量数学相关性的分析表示[J].测绘学报,2004,33(3):221-227. |
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| 作者姓名： | 张传定 吴晓平 郝金明 何海波 |
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| 作者单位： | 中国科学院,测量与地球物理研究所,湖北,武汉,430077;信息工程大学,测绘学院,河南,郑州,450052;信息工程大学,测绘学院,河南,郑州,450052 |
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| 基金项目： | 国家自然科学基金
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王宽诚教育基金 |
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| 摘 要： | 给出了GPS载波相位测量中Ⅰ个测站同步观测S颗相同卫星0个观测历元所在弧段内单差、双差、三差乃至更高次差分相位观测量之间数学相关性的分析表示.它克服了多条基线同时求解时无法精确顾及多差相位观测量之间相关性的缺陷,使得单、多基线矢量解算无需用大型矩阵求逆就能得到相关权阵,只需列出误差方程,组成法矩阵后求解有限个待估参数,从而极大地提高了求解速度,具有重要的实用价值.
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| 关 键 词： | GPS 双差 多次差分 协因数矩阵 Toeplitz矩阵 矩阵的Kronecker积 解析逆矩阵 |
| 文章编号： | 1001-1595(2004)03-0221-07 |
An Analytical Stochastic Model of Multi-differences GPS Carrier Phase Data |
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| ZHANG Chuan-ding.An Analytical Stochastic Model of Multi-differences GPS Carrier Phase Data[J].Acta Geodaetica et Cartographica Sinica,2004,33(3):221-227. |
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| Authors: | ZHANG Chuan-ding |
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| Institution: | ZHANG Chuan-ding~ |
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| Abstract: | Differential technique is a good method for GPS positioning. Suppose that for differential GPS, two or more receivers collect simultaneous measurements from common satellites at each epoch, and all carrier phase observables have same normally distributed. The purpose of this paper is to obtain an analytical probability distribution of the single-, double-, triple- and multi-differences. The variance-covariance matrix Q can be expressed as Kronecker products of several small matrices, so the inverse matrix of Q is equal to Kronecker products of inverse of several small matrices. Moreover, these small matrixes are circular or symmetric Toeplitz matrix, so their inverse matrices have analytical solutions. The analytical model ISO2002 proposed in this paper to compute the inverse matrix of Q was shown to be very effective. |
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| Keywords: | GPS double-difference multi-difference variance-covariance matrix Toeplitz matrix Kronecker product analytical inverse |
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