Reliable Bounding Zones and Inconsistency Measures for GPS Positioning using Geometrical Constraints

Reliable confidence domains for Global Navigation Satellite System (GNSS) positioning and inconsistency measures of the observations are of great importance for any navigation system, especially for safety critical applications. In this work, deterministic error bounds are introduced in form of intervals to assess remaining observation errors. The intervals can be computed based on expert knowledge or based on a sensitivity analysis of the measurement correction process. Using convex optimization, bounding zones are computed for GPS positioning using the geometrical constraints imposed by the observation intervals. The bounding zone is a convex polytope, where exploiting only the navigation geometry, confidence domain is computed in form of zonotope. We show that the relative volume between the polytopes and the zonotope is an inconsistency measures. Small polytope volume indicates bad consistency of the observations. In extreme cases empty sets are obtained which indicates large outliers. We determine the observation intervals via sensitivity analysis of the Klobuchar ionospheric model and Saastamoinen tropospheric model. The remaining errors are treated as white noise. We explain how the shape and the volume of the polytope are related to the positioning geometry. We show that this assignment has to be interpreted with care. Furthermore, we propose a new concept of Minimum Detectable Biases (MDB). Taking GPS data from simulations and real experiments, a comparison analysis between the proposed deterministic bounding method and the classical least-squares adjustment has been conduct in terms of accuracy and reliability. This helps validating that our proposed deterministic bound methods shows high internal and external reliability compared to the probabilistic approaches and that it provides rigorous inconsistency measures.

Almost complete convergence for the sequence of approximate solutions in linear calibration problem with α-mixing random data

In this work, we propose a stochastic method which gives an estimated solution for a linear calibration problem with ?-mixing random data. We establish exponential inequalities of Fuk Nagaev type, for the probability of the distance between the approximate solutions and the exact one. Furthermore, we build a confidence domain for the so mentioned exact solution. To check the validity of our results, a numerical example is proposed.

The Psychological Impact of Dental Aesthetics in Patients with Juvenile Idiopathic Arthritis Compared with Healthy Peers: A Cross-Sectional Study

This study aimed to assess whether dental aesthetics had a different impact on the psychosocial domains of adolescents with juvenile idiopathic arthritis (JIA) as compared with healthy peers. Fifty JIA patients and eighty controls aged between 13 and 17 years were enrolled. The Psychosocial Impact of Dental Aesthetics Questionnaire (PIDAQ) was administered along with tools for the self-assessment of malocclusion and self-esteem. An objective evaluation of malocclusion severity was performed through a clinical evaluation with the Dental Aesthetic Index (DAI). The sample was divided according to the DAI stages of malocclusion severity; a two-way analysis of variance (ANOVA) was performed to assess whether there was a difference in the studied variables according to the malocclusion and the presence of JIA. The results showed no interaction between the malocclusion severity and the presence of JIA in all analyzed variables (all p > 0.05). According to the DAI stages, the Dental Self-Confidence domain of the PIDAQ and the Perception of Occlusion Scale showed statistically significant differences only within the controls (p = 0.027 and p = 0.014, respectively). Therefore, JIA adolescents seem to be less concerned about their dental aesthetics compared with healthy peers, and clinicians should take particular care when proposing orthodontic treatments aiming only to improve dental aesthetics.

Analysis of Noise-Induced Bifurcations in the Stochastic Tritrophic Population System

A problem on the analysis of the noise-induced transitions in stochastically forced tritrophic population systems is considered. We study this problem on the basis of the conceptual “prey–predator-top predator” model which possesses coexisting attractors (limit cycles) and exhibits noise-induced transitions between them. For the parametric analysis of noise-induced phenomena in this nonlinear 3D model, we suggest a constructive approach combining the stochastic sensitivity function technique and confidence domain method. We show how increasing noise causes stochastic bifurcations, generation of mixed-mode oscillations, and transitions from order to chaos.