Abstract
The resolution of a nonlinear parametric 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”. Then observations correspond to the observational-space coordinates of the pointQ, theu initial parameters correspond to the model-surface coordinates of the “initial” pointP, and theu adjusted parameters correspond to the model-surface coordinates of the “least-squares” point\(\bar P\). The least-squares criterion results in a minimum-distance property implying that the vector\(\bar P\)Q must be orthogonal to the model surface. The geometrical setup leads to the solution of modified normal equations, characterized by a positive-definite matrix. The latter contains second-order and, optionally, thirdorder partial derivatives of the observables with respect to the parameters. This approach significantly shortens the convergence process as compared to the standard (linearized) method.
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Blaha, G., Bessette, R.P. Nonlinear least-squares method via an isomorphic geometrical setup. Bull. Geodesique 63, 115–137 (1989). https://doi.org/10.1007/BF02519146
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DOI: https://doi.org/10.1007/BF02519146