基于非线性Gauss-Markov模型与广义EIV模型的矿区高程拟合方法研究

Research on the Method of Mine Elevation Anomaly Fitting Based on Nonlinear Gauss-Markov Model and Generalized EIV Model

论文以矿区沉降观测的高程异常拟合为案例,分别基于非线性Gauss-Markov(GM)模型和广义EIV(error-in-variables,EIV)模型详细推导了煤矿开采沉陷区高程异常拟合方法。通过实测数据和仿真数据表明:在实测实验中,由于是等权的方式,广义EIV模型与非线性GM模型的估计结果一致且精度相当,与文献[8]的结论一致,表明了论文方法的正确性;在仿真实验中,广义EIV模型的参数与外推检核点的高程异常估值的均方根均小于非线性GM模型的结果。这也表明在加权条件下,广义EIV模型处理精度要优于最小二乘法的仿真数据处理精度。因此,应结合实际情况,选择合理的方法进行矿区高程异常拟合。

In this paper,the elevation anomaly fitting method for mine subsidence observation is derived in detail based on the nonlinear Gauss-Markov(GM)model and the generalized EIV(error-in-variables,EIV)model,respectively,as a case study.The measured and simulated data show that,(1)in the measured experiments,the estimation results of the generalized EIV model and the nonlinear GM model are consistent and of comparable accuracy due to the equal-weight approach,which is consistent with the findings of the literature[8],indicating the rightness of the method in this paper;(2)in the simulated experiments,the root mean square of the parameters of the generalized EIV model and the elevation anomaly valuation of the extrapolated check points are smaller than that of the nonlinear GM model results.This also indicates that under the weighted condition,the processing accuracy of the generalized EIV model is better than that of the least squares method for the simulation data.Therefore,a reasonable method should be selected to fit the elevation anomaly in the mine area,taking into account the actual situation.