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

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.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1988
Accession Number
ADA208219

Entities

People

  • Georges Blaha

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Cartesian Coordinates
  • Classification
  • Computations
  • Convergence
  • Coordinate Systems
  • Covariance
  • Earth Sciences
  • Equations
  • Geometry
  • Nonlinear Dynamics
  • Notation
  • Observation
  • Security
  • Standards
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Computational Modeling and Simulation

Technology Areas

  • Space