Another approach to reliability measures for systems with correlated observations

Abstract

An approach to internal reliability analysis is presented which, compared to existing approaches, offers further insight into the system responses to observation gross errors. The proposed reliability measures are defined on the diagonal and non-diagonal elements of the modified reliability matrix being an oblique projector. It maps the observations into the least squares residuals, both expressed as multiples of the a priori standard deviations of the observations. The system responses to a single gross error, such as the local, the quasi-global or the global response, are discussed and their consistency with non-correlation case is proved. Also, the reliability criteria interpretable in terms of those responses are proposed. They enable one to evaluate the observation systems with correlated and uncorrelated observations with respect to internal reliability. An attempt is also made to relate the global responses to reliability numbers that are the basis for determining the magnitude of the minimal detectable bias. Some differences of the new reliability measures in relation to existing measures are indicated. A numerical example is provided, showing the reliability analysis for a simulated horizontal network (distances, angles and GPS vectors), with given covariance matrix for GPS-vector components. In addition, a reliability analysis is presented for a simple leveling network being a study case for other authors referred to in this paper.