引用本文: 王乐洋, 赵英文. 非线性平差精度评定的自适应蒙特卡罗法[J]. 武汉大学学报 ( 信息科学版), 2019, 44(2): 206-213, 220.
WANG Leyang, ZHAO Yingwen. Adaptive Monte Carlo Method for Precision Estimation of Nonlinear Adjustment[J]. Geomatics and Information Science of Wuhan University, 2019, 44(2): 206-213, 220.
 Citation: WANG Leyang, ZHAO Yingwen. Adaptive Monte Carlo Method for Precision Estimation of Nonlinear Adjustment[J]. Geomatics and Information Science of Wuhan University, 2019, 44(2): 206-213, 220.

## 非线性平差精度评定的自适应蒙特卡罗法

• 摘要: 针对现有的非线性平差精度评定理论中，蒙特卡罗法模拟次数的选择不具有客观性，无法对结果进行直接控制，以及没有同时考虑到平差参数估值、随机量改正数和单位权方差估值的有偏性等问题，把自适应蒙特卡罗法融入到非线性平差精度评定理论中。通过基于自适应蒙特卡罗法的估值偏差计算和参数估值协方差阵计算，设计了非线性平差精度评定一套理论完整的算法流程。基于对偶变量的思想，提出了参数估值偏差计算的对偶自适应蒙特卡罗法。直线拟合模型和椭圆拟合模型两个算例结果表明，非线性平差精度评定的自适应蒙特卡罗法能获得稳定且合理的精度评定结果，具有更强的适用性；对偶自适应蒙特卡罗法计算估值偏差的收敛速度更快，效率更高。

Abstract: Among existing theories on precision estimation of nonlinear adjustment, the simulation number of Monte Carlo method generally is chosen subjectively and its result also cannot be controlled directly. Besides those, the biases of parameter estimates, corrections of observations and the estimate of variance of unit weight are not taken into consideration simultaneously. The adaptive Monte Carlo method is combined with precision estimation of nonlinear adjustment for solving problems given above in this paper. By calculating biases of estimates and covariances matrix of parameter estimates, the complete process of precision estimation based on adaptive Monte Carlo is given. With the help of the term of antithetic variates, the antithetic and adaptive Monte Carlo algorithm is proposed for biases of parameter estimates. Results from two examples of straight line fitting model and ellipse fitting model show that the adaptive Monte Carlo method in this paper can obtain the stable and reasonable effects for precision estimation of nonlinear adjustment with extensive applicability, the antithetic and adaptive Monte Carlo in this paper is better at convergence and computational efficiency for calculating biases of parameter estimates.

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