Abstract: In the robust weighted total least squares(RWTLS) algorithm, its robustness of the robust model is highly related to the initial values. If the least squares or total least squares estimates is used as the initial value, it will be affected by gross error, and certainly impacted the robust characteristics of RWTLS estimates. Considering the correlation between the observed vector and the coefficient matrix, we first deduce the weighted least-squares solution of Partial-EIV model, and a new RWTLS algorithm of correlated observation is proposed to solve the initial values of robust iterations by using the median parameter method. Then the median parameter method is used to determine the initial value, and on this basis we propose a new robust estimated method, which is based on the standardized residual error and considered the influence of gross error both on observation and structure spaces. The experiment results show that the proposed estimated method has a good performance to resist gross error, and the presented solution is more accurate than the traditional method for line fitting, and with the increase of the number of gross errors, the stability of the algorithm is superior to the traditional method.