In this contribution, we propose a method for statistically evaluating the risk in a deformation monitoring system. When the structure under monitoring moves beyond tolerance, the monitor system should issue an alert. Only a very small probability is acceptable of the system telling us that no change beyond a critical threshold has taken place, while in reality it has. This probability is referred to as integrity risk. We provide a formulation of integrity risk where the interaction between estimation and testing is taken into account, implying the use of conditional probabilities. In doing so, we assumed different scenarios with the alerts being dependent on both the identified hypothesis and the threat that the estimated size of deformations entails. It is hereby highlighted that a correct risk evaluation requires estimation and testing being considered together, as they are typically intimately linked. In practice, one may, however, find it simpler computation-wise to neglect the estimation–testing link. For this case, we provide an approximation of the integrity risk. This approximation may provide a too optimistic or pessimistic description of the integrity risk depending on the testing procedure and tolerances of the structure at hand. Monitoring systems, besides issuing timely alerts, are also required to provide threat estimates together with their corresponding probabilistic properties. As the testing outcome determines how the threat gets estimated, the threat estimator will then inherit the statistical properties of both estimation and testing. We derive the threat estimator b¯ _j and its probability density function, taking the contributions from combined estimation and testing into account. It is highlighted that although the threat estimator under the identified hypothesis H_j, i.e., b^ _j, is normally distributed, the estimator b¯ _j is not. It is explained that working with b^ _j instead of b¯ _j, thus ignoring the estimation–testing link, may provide a too optimistic description of the threat estimator’s quality. The presented method is illustrated by means of two simple deformation examples.

As parameter estimation and statistical testing are often intimately linked in the processing of observational data, the uncertainties involved in both estimation and testing need to be properly propagated into the final results produced. This necessitates the use of conditional distributions when evaluating the quality of the resulting estimator. As the conditioning should be on the identified hypothesis as well as on the corresponding testing outcome, omission of the latter will result in an incorrect description of the estimator’s distribution. In this contribution, we analyse the impact this omission or approximation has on the considered distribution of the estimator and its integrity risk. For a relatively simple observational model it is mathematically proven that the rigorous integrity risk exceeds the approximation for the contributions under the null hypothesis, which typically has a much larger probability of occurrence than an alternative. Actual GNSS-based positioning examples confirm this finding. Overall we observe a tendency of the approximate integrity risk being smaller than the rigorous one. The approximate approach may, therefore, provide a too optimistic description of the integrity risk and thereby not sufficiently safeguard against possibly hazardous situations. We, therefore, strongly recommend the use of the rigorous approach to evaluate the integrity risk, as underestimating the integrity risk in practice, and also the risk to do so, cannot be acceptable particularly in critical and safety-of-life applications.

Google Location Timeline, once activated, allows to track devices and save their locations. This feature might be useful in the future as available data for evidence in investigations. For that, the court would be interested in the reliability of these data. The position is presented in the form of a pair of coordinates and a radius, hence the estimated area for tracked device is enclosed by a circle. This research focuses on the assessment of the accuracy of the locations given by Google Location History Timeline, which variables affect this accuracy and the initial steps to develop a linear multivariate model that can potentially predict the actual error with respect to the true location considering environmental variables. The determination of the potential influential variables (configuration of mobile device connectivity, speed of movement and environment) was set through a series of experiments in which the true position of the device was recorded with a reference Global Positioning System (GPS) device with a superior order of accuracy. The accuracy was assessed measuring the distance between the Google provided position and the de facto one, later referred to as Google error. If this Google error distance is less than the radius provided, we define it as a hit. The configuration that has the largest hit rate is when the mobile device has GPS available, with a 52% success. Then the use of 3G and 2G connection go with 38% and 33% respectively. The Wi-Fi connection only has a hit rate of 7%. Regarding the means of transport, when the connection is 2G or 3G, the worst results are in Still with a hit rate of 9% and the best in Car with 57%. Regarding the prediction model, the distances and angles from the position of the device to the three nearest cell towers, and the categorical (non-numerical) variables of Environment and means of transport were taking as input variables in this initial study. To evaluate the usability of a model, a Model hit is defined when the actual observation is within the 95% confidence interval provided by the model. Out of the models developed, the one that shows the best results was the one that predicted the accuracy when the used network is 2G, with 76% of Model hits. The second model with best performance had only a 23% success (with the mobile network set to 3G).

In this paper, a novel statistical approach is presented for time-of-arrival (TOA) estimation based on first path (FP) pulse detection using a sub-Nyquist sampling ultra-wide band (UWB) receiver. The TOA measurement accuracy, which cannot be improved by averaging of the received signal, can be enhanced by the statistical processing of a number of TOA measurements. The TOA statistics are modeled and analyzed for a UWB receiver using threshold crossing detection of a pulse signal with noise. The detection and estimation scheme based on the Generalized Likelihood Ratio Test (GLRT) detector, which captures the full statistical information of the measurement data, is shown to achieve accurate TOA estimation and allows for a trade-off between the threshold level, the noise level, the amplitude and the arrival time of the first path pulse, and the accuracy of the obtained final TOA.

Precise Point Positioning (PPP) is a popular Global Positioning System (GPS) processing strategy, thanks to its high precision without requiring additional GPS infrastructure. Single-Frequency PPP (SF-PPP) takes this one step further by no longer relying on expensive dual-frequency GPS receivers, while maintaining a relatively high positioning accuracy. The use of GPS-only SF-PPP for lane identification and mapping on a motorway has previously been demonstrated successfully. However, the performance was shown to depend strongly on the number of available satellites, limiting the application of SF-PPP to relatively open areas. We investigate whether the applicability can be extended by moving from using only GPS to using multiple Global Navigation Satellite Systems (GNSS). Next to GPS, the Russian GLONASS system is at present the only fully functional GNSS and was selected for this reason. We introduce our approach to multi-GNSS SF-PPP and demonstrate its performance by means of several experiments. Results show that multi-GNSS SF-PPP indeed outperforms GPS-only SF-PPP in particular in case of reduced sky visibility.