An Aggregate Function Method for Weighted Total Least Squares with Inequality Constraints

When the variance-covariance matrix of the error is fairly symmetric and positively definite, parameter estimation and accuracy assessment of weighted total least squares adjustment with inequality constraints(ICWTLS) are investigated in this paper. First, the problem of minimizing the residual sum of squares are converted to an optimization problem with only the model parameters under the total least squares, and all the inequality constraints are transformed into an equivalent aggregate constraint. Accordingly, the ICWTLS problem is converted to unconstrained optimization problem by a penalty function approach and is then solved by BFGS optimization method. Then, the observation equation and constraints function are expanded to the first order Taylor series and the linear approximation between the solution and observations is derived as well as the approximate dispersion matrix of the solution under the variance propagation law. Finally, a numerical simulation is given to indicate the validity and feasibility of this method.