Weighted Total Least Squares Method for Joint Adjustment Model with Weight Scaling Factor

In regard to the joint adjustment problem with different types of dataset, the functional model of each type of dataset is affected by random errors, which indicates the observation vector and coefficient matrix are not error-free. In this paper, the weight total least squares (WTLS) method is applied to joint adjustment model. An iterative WTLS method for joint adjustment model is derived, which uses the weight scaling factor to adjust the contribution of each type of dataset. In view of the determination of the weight scaling factor, more schemes are designed, which includes the minimum discrimination function method. The results show that the prior unit weight variance method and the total least squares variance component estimation (TLS-VCE) method have their limitations. When the prior information is inaccurate or the variance components are not estimable while using the TLS-VCE method, the minimum discriminate function method with \mathop \mathop \sum \limits_i = 1 \limits^n_1 \left| \widehat \bar e_1_i \right| + \mathop \mathop \sum \limits_j = 1 \limits^n_2 \left| \widehat \bar e_2_j \right| as its discriminate function can achieve the relative effective results.