APPLICATION OF SIMILARITY TRANSFORMATIONS IN GEODETIC MONITORING NETWORKS | ||||
| ERJ. Engineering Research Journal | ||||
| Article 6, Volume 24, Issue 4, October 2001, Page 97-113 PDF (556.58 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/erjm.2001.71135 | ||||
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| Authors | ||||
| Hisham Abou Halima1; Abo El Hassan F. Rahil2 | ||||
| 1Assistant Professor, faculty of Engineering, Mansoura University, Egypt | ||||
| 2Associate Professor, faculty of Engineering, Shebin El-Kom, Minufiya University, Egypt. | ||||
| 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 | ||||
| Similarity transformation , Computational base , Innere constraints; Transformation matrix , Partial trace minimization ,Datum - points | ||||
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