APPLICATION OF SIMILARITY TRANSFORMATIONS IN GEODETIC MONITORING NETWORKS

Abou Halima, Hisham; Rahil, Abo El Hassan F.

doi:10.21608/erjm.2001.71135

APPLICATION OF SIMILARITY TRANSFORMATIONS IN GEODETIC MONITORING NETWORKS

Document Type : Original Article

Authors

¹ Assistant Professor, faculty of Engineering, Mansoura University, Egypt

² Associate Professor, faculty of Engineering, Shebin El-Kom, Minufiya University, Egypt.

10.21608/erjm.2001.71135

Abstract

Similarity transformation are useful in the detection of deformation and for the
connexion of geodetic networks. The estimated netpoints coordinates and their
covariance matrix can be transformated from one computational base to another
without repeating the adjustment process via an similarity transformation. The
derivation of the transformation matrices is closely connected with the properties of
generalised matrix inverses which have been mentioned in connection with inner
constriants.
The main objective of this paper is to introduce the partial trace minimization
approach as an proposed general solution technique for free geodetic net work. In
addition the problem of transforming regular covariance matrix into a singular one
with the required rank deficiency and vice verse will be solved. The structure of the
transformation tnatrices for different datum defects have been deduced. Finally the
use of similarity transformation to transform a covariance matrix from one
computational base to another is introduced and disussed.Two numerical examples
representing simulated and real geodetic networks were given in order to illustrate the
application and the efficiency of the underlying theoretical concept

Keywords