Nonlinear Adjustment with or without Constraints, Applicable to Geodetic Models
Final rept. 4 Mar 1987-3 Mar 1989
NOVA UNIV OCEANOGRAPHIC CENTER DANIA FL
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This study concentrates on the least-squares resolution of the parametric adjustment model. In general this model may occur in a linear or a nonlinear form, and may or may not have constraints associated with it. The constraints, if present, may be linear or nonlinear. Furthermore, two basic categories of constraints are available, namely the familiar equality constraints i.e., exact relations which must be fulfilled by the parameters, and the relatively new category of inequality constraints. With the exception of the inequality constraints, which are treated in the linear version in conjunction with the linear parametric model, the adjustment model and the eventual equality constraints are presented here in the nonlinear version. But in every case, the least-squares solution is achieved via an isomorphic geometrical setup with tensor structure and notation. This is possible due to the fact that in the geometrical context the least-squares criterion translates into the minimum-distance property, which, in turn, entails an orthogonal projection of the observational point onto the pertinent model surface. Keywords Nonlinear constraints Equality constraints Inequality constraints Least squares method Tensor analysis Metric tensor Associated metric tensor Minimum distance Observational space Model surface Model hyperplane Nonlinear mathematical model.
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