Adaptive Monte Carlo Method for Precision Estimation of Nonlinear Adjustment

WANG Leyang; ZHAO Yingwen

doi:10.13203/j.whugis20170064

Volume 44 Issue 2

Feb. 2019

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Geomatics and Information Science of Wuhan University > 2019 > 44(2): 206-213, 220. > DOI: 10.13203/j.whugis20170064

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. DOI: 10.13203/j.whugis20170064

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Adaptive Monte Carlo Method for Precision Estimation of Nonlinear Adjustment

WANG Leyang^{1, 3, 4,},
ZHAO Yingwen^{1, 2}

1.
Faculty of Geomatics, East China University of Technology, Nanchang 330013, China
2.
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
3.
Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, East China University of Technology, Nanchang 330013, China
4.
Key Laboratory for Digital Land and Resources of Jiangxi Province, East China University of Technology, Nanchang 330013, China

Funds:

The National Natural Science Foundation of China 41874001

The National Natural Science Foundation of China 41664001

Support Program for Outstanding Youth Talents in Jiangxi Province 20162BCB23050

the National Key Research and Development Program of China 2016YFB0501405

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Author Bio:
WANG Leyang, PhD, associate professor, specializes in geodetic inversion and geodetic data processing.E-mail::wleyang@163.com
Received Date: August 15, 2018
Published Date: February 04, 2019

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Abstract

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.
- adaptive Monte Carlo method,
- nonlinear adjustment,
- precision estimation,
- Gauss-Helmert

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References

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