A mixed weighted least squares and weighted total least squares adjustment method and its geodetic applications

A mixed weighted least squares (WLS) and weighted total least squares (WTLS) (mixed WLS-WTLS) method is presented for an errors-in-variables (EIV) model with some fixed columns in the design matrix. The numerical computational scheme and an approximate accuracy assessment method are also provided. It is extended from the mixed Least squares (LS)-Total least squares (TLS) method to deal with the case that the random columns are corrupted by heteroscedastic correlated noises. The mixed WLS-WTLS method can improve the computational efficiency compared with the existing WTLS methods without loss of accuracy, particularly when the fixed columns are far more than random ones. The Bursa transformation and parallel lines fitting examples are carried out to demonstrate the performance of the proposed algorithm. Since the mixed WLS-WTLS problem includes both the WLS and the WTLS problem, it will have a more wide range of applications.