Automated least-squares adjustment of triangulation-trilateration figures

Two nonlinear horizontal survey adjustment problems, one for a triangle and the other for a quadrilateral, were analyzed in Smith and Varnes (1987) using traditional methods. This paper demonstrates a new approach to solve such problems by direct least-squares minimization using an optimization package that resides within a widely available spreadsheet program, requiring no Taylor series expansion, matrices, or programming. By adopting an alternative ellipsoid perspective on constrained least-squares estimation, the present approach establishes a one-to-one correspondence between least-squares adjustment in surveying and "reliability index" calculation in structural/geotechnical engineering. This connection then allows adjustment problems to benefit from recently developed spreadsheet methods for reliability calculation. The new approach is conceptually and computationally more direct and efficient than traditional procedures found in the existing literature and can handle both conditional and parametric adjustment problems. All adjustment results given by the new approach are virtually identical to those previously given by conventional methods.