A Model Comparison in Least Squares Collocation.

Abstract

In the model equation of least squares collocation there appears a random signal, s', which is of the same physical nature as the observations whereas the signal to be estimated, s, is only linked to the model through its correlation with s'. This Model (1) is compared with the least squares estimation Model (2), where the signal to be estimated is directly part of the model with a coefficient matrix R. The basic differences of these two models in the framework of physical geodesy are pointed out by analyzing the validity of the equation s' = Rs, that transforms one model into the other, for different cases. For clarification purposes least squares filtering, prediction and collocation are discussed separately. In filtering problems the coefficient matrix R becomes the unit matrix and by this the two models become identical. For prediction and collocation problems the relation s' = Rs is only fulfilled in the global limit where s becomes either a continuous function on the earth or an infinite set of spherical harmonic coefficients.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1976
Accession Number
ADA033066

Entities

People

  • Reiner Rummel

Organizations

  • Ohio State University

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Air Force
  • Artificial Satellites
  • Coefficients
  • Covariance
  • Equations
  • Filtration
  • Frequency
  • Frequency Domain
  • Gravity
  • Gravity Anomalies
  • Grids
  • Integral Equations
  • Linear Systems
  • Low Noise
  • Noise
  • Spherical Harmonics
  • White Noise

Readers

  • Computational Modeling and Simulation
  • Space Exploration and Orbital Mechanics.
  • Statistical inference.