半参数测量平差模型参数的二阶段估计

Two stage estimation of parameter for semiparametric survey ad-justment models

本文首先利用自然样条函数法,找到符合条件的非参数自然插值样条函数。其次利用核函数并综合最小二乘法建立了参数x和S非参数的估计量x、S,讨论了窗宽参数h的选取方法。最后,用一个模拟的平差算例从估值的稳定性、均方差等方面与最小二乘法进行了比较,结果说明,半参数测量模型能更接近于真实情况。

Considering the Semiparametric surveying adjustment models L = Bx + S + A,x ∈ Rd is a d-vector of unknown parameters, S is an unknown Borel function. Firstly, using natural cubic spline methods, find natural cubic spline funcion of nonpara-metric component S. Secondly, the estimators of parameters β and S are derived by using the kernel function and least square method, and we also discuss the approach of bandwidth choice in the Semi-parametric surveying adjustment models;Finally,a simulated adjustment problem is constructed to explain this method. The new method presented in this paper shows an effective way of solving the problem, the estimated values are nearer to their theoretical ones than by the adjustment method of least squares.