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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1976
- Accession Number
- ADA033066
Entities
People
- Reiner Rummel
Organizations
- Ohio State University