Adaptive Monte Carlo Method for Precision Estimation of Nonlinear Adjustment

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.