The Least-Squares Method With Data Uncertainties

The Least-Squares method is effective for solving the parameter estimation problem.Thispaper studies the parameter estimation with part bounded data uncertainties,and solves theextension for the bounded errors-in-variables models. The estimation with part bounded datauncertainties is posed and solved in the paper for efficiently computating.That is to consider thecase to which only selected block of the coefficient matrix is subject to perturbations,while theremainings are known precisely.Its superior performance is due to the fact that the new methodguarantees that the effect of the uncertainties will never be unnecessarily over-estimated,beyondwhat is reasonably assumed by the a-prior bounds,consequently,overly conservative designs,aswell as overly sensitive designs,are avoided.In contrast to the BDU estimation,once the worst-caseperturbation is identified,the solution cannot be characterized by the orthogonalitycondition.Another performance in the paper is to extend the bounded errors-in-variables model tothe one in which the right observation vectors is also subject to the perturbations.We introduce theSVD decomposition of the coefficient matrix,and achieve the optimal solution. Numerical resultsshow the methods the paper proposes are effective for computating some problem with datauncertainties.