引用本文: 王乐洋, 许光煜. 系数矩阵误差对地壳应变参数反演的影响[J]. 武汉大学学报 ( 信息科学版), 2017, 42(10): 1453-1460.
WANG Leyang, XU Guangyu. The Effect of the Random Coefficient Matrix on Adjustment of the Inversion of Crustal Strain Parameters Model[J]. Geomatics and Information Science of Wuhan University, 2017, 42(10): 1453-1460.
 Citation: WANG Leyang, XU Guangyu. The Effect of the Random Coefficient Matrix on Adjustment of the Inversion of Crustal Strain Parameters Model[J]. Geomatics and Information Science of Wuhan University, 2017, 42(10): 1453-1460.

## The Effect of the Random Coefficient Matrix on Adjustment of the Inversion of Crustal Strain Parameters Model

• 摘要: 针对地壳应变参数反演模型中系数矩阵含随机和非随机元素及观测数据存在相关性等情况，以部分变量误差（partial-errors-in-variables，PEIV）模型为基础，采用了地壳应变参数反演的加权总体最小二乘算法，该算法不受系数矩阵和权矩阵结构的限制，能够快速、有效解决系数矩阵含有随机误差的模型问题。结合推导得到的最小二乘改正项公式，对地壳反演模型中坐标点误差对反演参数求解的影响进行了分析。通过对模拟数据和川滇地区的实际数据进行处理，得出系数矩阵误差对地壳应变参数反演的影响主要受GPS站点坐标值量级以及应变参数量级的牵制。

Abstract: Theweighted total least squares method based on partial errors-in-variables (PEIV for short) model is used to solve the inversion parameters of crustal strain model. It not only considers the error of observation (displacement or velocity field), but also the error effects from the coefficient matrix, generally composed of monitoring points coordinates. When taking the special structure of the coefficient matrix in the geodetic inversion model into account, we insure that the repeated coordinates have the same residual and that the constants are not allocated any correction. The method usedin this paper can meet these requirements as it separates the random elements from the constant elements taking advantage of the partial errors-in-variables model. All calculation formulae for crust strain (rate) parameters inversion based on partial errors-in-variables using monitoring point displacement or velocity fields are deduced. In addition, the derivate correction of weighted least squares (WLS) is used to analyze the effect of the random coefficient. The discrepancy between the weighted least squares solution and WTLS solution was also investigated. Because of the complexity of the WTLS solution, we propose a formulation to relate the WLS\and WTLS solutions based on Xu (J Geod 86:661-675, 2012). A simulation using data from the Sichuan-Yunnan region permits a comparison and analysis of the effect of the random design matrix. The experimental results reveal that the effect of the random coefficient matrix on adjustment of the inversion of crustal strain (rate) parameters model is mainly depend on the order of value of the GPS coordinates and the crustal strain parameters themselves.

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