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

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.