The Optimization Algorithms To Enhance Efficiency Of Weighted Total Least Squares And Its Application In Surveying Data Processing

The weighted total least squares(WTLS)is a relatively rigorous method used for estimating parameters in EIV model,which has a higher precision of parameter estimation.However,estimating parameters by WTLS requires complicated calculations and with low computational efficiency,particularly when processing large data sets.In order to simplify algorithm of WTLS and improve the computational efficiency,this paper aims at the structural characteristics of the coefficient matrix in EIV model,derived an optimization algorithm by using the LS criterion and matrix partitioning,which without the Lagrange factor.The proposed optimization algorithm has less matrix operations involved in the process of calculation because it effectively reduces dimension of cofactor matrix for coefficient matrix and avoids estimating the random error of coefficient matrix during the iterative process,which is conducive to improving computational efficiency.Based on partial errors-in-variables(PEIV)model,an optimization algorithm is derived by applying the LS criterion for the situation where a large number of random elements appear repeatedly in the coefficient matrix.The proposed optimization algorithm is simple in the concept,easy in the implementation,and there is no need to estimate the random error of the coefficient matrix and reconstruct matrix in the iterative process,has fewer matrix operations and higher calculation efficiency than other existing algorithms.In addition,in order to improve calculation efficiency of the algorithm more effectively,this paper analyzed the difference in the derivation process between the LS criterion is applied to EIV(PEIV)model and Gauss-Markov model,and derived an approximate algorithm.At the same time,this paper also studies the condition that the LS directly replace the WTLS to estimate the unknown parameters of EIV model.The application of the approximate algorithm and the alternative method can achieve a good balance between the precision of parameter estimation and computational efficiency.Finally,the precision of parameter estimation and computational performance of the proposed algorithms are verified by measured data and simulated data,respectively.The results show that the two optimization algorithms have the same precision of parameter estimation as other existing algorithms,but computation more efficient.When the coefficient matrix exhibits structural characteristics,the optimization algorithm based on EIV model has relatively more advantages in computational efficiency.When the random elements of the coefficient matrix account for a large number and appear repeatedly,the optimization algorithm based on PEIV model is more applicable.