A Regularized Solution and Statistical Properties ofIll-Posed Problem with Equality Constraints

Proper equality constraints between parameters can improve the accuracy of a leastsquare solution,eliminate the deficiencies of free networks and improve the solution of an ill-posed problem,therefore we proposes the ill-posed adjustment model with equality con-straints.First,we established a regularization rule and developed a solution through the La-grange multiplier method.Next,we evaluated its statistical properties to show that this so-lution is biased and has a smaller mean square error(MSE)than that of the constrained leastsquare problem solution.Then we propese a rule that minimizes the MSE of the estimates tochoose both a regularization factor and numerical algorithm.Finally,we use a simulated ex-ample and another control net to verify the feasibility of the algorithms and test the statisticalproperties of the solution.