Basic principles for the theory of reliability and gross error detection methodology in networks with correlated observations

Aim of project
The main objective of the research is to provide theoretical basis for the analysis of network reliability and to develop the methodology of gross error detection in the systems with correlated observations. The investigations that have been carried out until now show that such systems when transformed to decorrelated form display slightly different properties than those of their original form. For that reason, it becomes difficult to find suitable and physically interpretable reliabi-lity measures. Difficulties arise also in the process of gross error detection in such systems.

The research will cover systems with different levels of external defect (local networks, partly tied-up networks, completely tied-up networks) and with different types of constraints, i.e. the conditions set upon unknown parameters, such as distorting conditions and non-distorting conditions. Although theoretically we might operate with semi-positive definite covariance matrices for observations, only positive definite matrices will be taken into consideration. The investigations will be based on a linear parametric model.

The research is aimed at practical applications in engineering surveys. Theoretical findings should be useful in solving engineering survey tasks where highly reliable networks are required. This requirement is specifically important in geodetic monitoring of displacements and deformations in engineering structures to evaluate their level of safety.

Expected results
Theoretical findings: Formulation of reliability-oriented properties of the systems with correlated observations;

Proposal of reliability measures and methods of gross error detection in the above systems. Publications:

A monograph summing up the results of the research (main findings to be submitted either to the Journal of Geodesy or to Geodesy and Cartography);

A chapter in the next edition of “Reliability of geodetic networks” (in Polish) by W. Prószyński and M. Kwaśniak, publications of Warsaw University of Technology, 2002;

A chapter in an academic manual on mathematical models in deformation monitoring and analysis, currently under preparation;

Several papers presented at scientific conferences (both in Poland and abroad). Scientific promotion of academic staff :

At least one of the research assistants will gather the material for his doctoral thesis.