Abstract:The coefficient matrix is the functions of some independent variables in the polynomial fitting model. According to the solution of the partial errors-in-variables(Partial EIV) model, the random elements that are the functions of independent variables of the coefficient matrix are extracted. Considering the quadratic terms of the Taylor expansion, the cofactor matrix,which is the functions of independent variables, is obtained by the law of covariance propagation. The experiments show that the results obtained by the method of this paper are similar to those obtained by the method of existed non-linear total least squares method when the elements of coefficient matrix are no more individual independent variables. This provides a method of structuring the weight matrix of random vectors.