TLS algorithm for GPS height fitting based on robust estimation

Abstract

Application mathematical model for GPS height fitting problem, rational fitting model and accurate parameters of fitting model have impact on the final fitting accuracy. It is known that researchers are used to applying least squares (LS) to establish Gauss–Markov model (G–M model) for computation parameters of mathematical models to realise GPS height fitting. The premise of establishing G–M model based on LS is under the assumptions that coefficient matrix of fitting model is error-free, and random error exists only in observation data. However, two kinds of factors mean that this hypothesis does not exist exactly: first, both coefficient matrix and observation data of control points have random error unavoidably; second, gross error may exist in observation data. In this paper, a solution is presented to solve the problems due to these factors. To take into account random error both in coefficient matrix and observation data while computing the parameters, method of establishing G–M model based on total least squares (TLS) is discussed, and to take into account that the accuracy of observation data is unequal because of gross error, method of applying TLS algorithm to compute parameters based on robust estimation is proposed. We cite instances to prove that the solution is feasible, in the instance, weight of control point which contains gross error is computed by iteration. And the numerical results from our experiment clearly demonstrate that compared with LS and TLS, mean square error of parameters which is computed by the robust TLS is more accurate, and conclusions can be drawn that application robust TLS for GPS height fitting is more scientific.