Classical Least Squares Method for Inequality Constrained PEIV Model

  Objectives  The inequality constrained partial errors-in-variables(ICPEIV) model is mainly solved by linear approximation method and nonlinear programming algorithms. The linear approximation method is computationally inefficient and the nonlinear programming algorithms are complicated because they are based on optimization theory. The nonlinear programming algorithms are impracticable to apply in surveying fields because the connections between nonlinear programming methods and classical adjustment have not been established.

  Methods  Under the total least squares(TLS) criterion, the inequality constrained TLS problem is transformed into the quadratic programming according to the Kuhn-Tucker condition. Then an improved Jacobian iteration approach is proposed to solve the quadratic programming.

  Results  The proposed method does not require the linearization process and has the same form with the classical least squares which is easy to code.

  Conclusions  The numerical examples show that the proposed method is efficient in computation and concise in form and it is a beneficial extension of classical least squares theory.