Analysis of the Nonlinear Parametric Least-Squares Adjustment via an Isomorphic Geometrical Setup with Tensor Structure

Abstract

Abstract : The parametric adjustment model expresses n observables in terms of u parameters, where the structure linking the two groups is in general nonlinear. This model can be expanded in the Taylor series based on an initial set of parameters. The standard treatment includes only the first-order partial derivatives of the observables with respect to the parameters, constituting a linearized model which is resolved via normal equations as mandated by the linearized model which is resolved via normal equations as mandated by the least-squares criterion. If necessary, the solution is iterated upon using the same linearized model in conjunction with an updated set of parameters. In this study, the resolution of a nonlinear adjustment model is addressed through an isomorphic geometrical setup with tensor structure and notation, represented by a u-dimensional model surface embedded in a flat n-dimensional observational space.