Sterling interpolation method for precision estimation of total least squares

Abstract

The randomness of the biases of parameter estimates, residuals and some variables is seldom considered for calculating covariance matrix of parameter estimates in total least squares (TLS) iterative algorithm. There are few studies on the precision estimation with the approximate probability distribution method of function in the TLS. In order to get more reasonable precision information for the TLS adjustment, the derivative-free Sterling interpolation method is introduced and implemented. The errors-in-variables (EIV) model and its TLS algorithm are introduced. The TLS iterative algorithm is combined with the Sterling interpolation, and two kinds of schemes for calculating biases of the TLS parameter estimates and approximate mean squared error matrix are designed. The method is used to four examples: line fitting model, coordinate transformation model, auto-regression model and variation function model. Comparing the results with the scaled unscented transformation (SUT) method, the feasibility and effectiveness of the Sterling interpolation method in the TLS precision estimation are verified. The Sterling interpolation method has fewer parameters than the SUT method, and it is simpler to implement. And the scheme two in this paper can be applied to the case where some matrix elements are nonlinear functions of the observation. The application of the precision estimation is expanded by this method, and the theory for precision estimation of TLS is further improved.