Abstract:A total least square with partial random parameter adjustment problem occurs if some of the estimated parameters in an adjustment problem have priori random information and the error equation coefficient matrix contains observation errors. This paper proposes a function model of total least squares adjustment with additional partial random parameters. The model has general adaptability. The algorithms formula of parameter estimation and accuracy evaluation are derived, and the steps of computation are presented, which can process the data that only partial (from 0 to all) parameter has random prior information. The feasibility, reliability and correctness of the algorithms are demonstrated by several examples and comparative analysis. The proposed algorithms have advantages in iterative convergence times.