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In safety-critical applications, deformation monitoring systems are required to issue timely alerts when a deformation beyond a critical threshold occurs. Only a very small probability of failing to issue an alert when in fact one should have been given, is acceptable. This probability is referred to as integrity risk. In this contribution, we show how to evaluate this risk, thereby taking the intimate link between testing and estimation into account. Using a simple example, the basic integrity components of deformation monitoring are introduced and illustrated. The integrity risk is then formulated for the generalized case where multiple-hypothesis testing is involved. As monitoring systems, in addition to issuing timely alerts, are also required to provide deformation estimates, it is also crucial to assess their confidence levels. In doing so, the statistical testing, that preceded the estimation of the deformation parameters, needs to be accounted for. As this is not the customary procedure followed in practice, we show how the combined estimation and testing can be probabilistically accounted for, and thereby demonstrate that the customary practice can give a too optimistic outcome of the stated confidence levels. The presented methodology is worked out and numerically illustrated by means of two deformation examples. [ABSTRACT FROM AUTHOR]

The Minimal Detectable Bias (MDB) is an important diagnostic tool in data quality control. The MDB is traditionally computed for the case of testing the null hypothesis against a single alternative hypothesis. In the actual practice of statistical testing and data quality control, however, multiple alternative hypotheses are considered. We show that this has two important consequences for one's interpretation and use of the popular MDB. First, we demonstrate that care should be exercised in using the single-hypothesis-based MDB for the multiple hypotheses case. Second, we show that for identification purposes, not the MDB, but the Minimal Identifiable Bias (MIB) should be used as the proper diagnostic tool. We analyse the circumstances that drive the differences between the MDBs and MIBs, show how they can be computed using Monte Carlo simulation and illustrate by means of examples the significant differences that one can experience between detectability and identifiability. [ABSTRACT FROM AUTHOR]

In the past few decades the Global Positioning System (GPS) has been the number one positioning tool in a range of Geodesy and Geophysics applications. GPS modernisation from dual-frequency to triple-frequency signals has lately also been complemented by global GLObal' naya NAvigatsionnaya Sputnikovaya Sistema (GLONASS), Galileo and BeiDou Navigation Satellite System (BDS), as well as the regional Quasi-Zenith Satellite system (QZSS) and Navigation with Indian Constellation (NavIC). Single-frequency receivers, in particular, need ionospheric models to be able to precisely determine positions, and by making use of ionospheric models one can also speed up the parameter convergence for dual- and multi-frequency GNSS applications. [Extracted from the article]