The parameter-weighted square of the error matrix E is used as a basis for total least squares optimization, i.e.,  is utilized either instead of   or in supplementation to it. the multiplicity of the solution and computational aspects are presented in concise form, in comparison to the conventional methods of total least sqrares, model least squares and their unified iterative algorithms. solving the parameter-weighted total least squares iteratively, the puocess of iteration is characterized by good convergence properties compared to the unweighted total least squares algorithm. incremental solutions, analytic and numerical, provide additional computational speed improvements for fast identification in adaptive control.