Widely linear estimation for multisensor quaternion systems with mixed uncertainties in the observations

The optimal widely linear state estimation problem for quaternion systems with multiple sensors and mixed uncertainties in the observations is solved in a unified framework. For that, we devise a unified model to describe the mixed uncertainties of sensor delays, packet dropouts and uncertain observations by using three Bernoulli distributed quaternion random processes. The proposed model is valid for linear discrete-time quaternion stochastic systems measured by multiple sensors and it allows us to provide filtering, prediction and smoothing algorithms for estimating the quaternion state through a widely linear processing. Simulation results are employed to show the superior performance of such algorithms in comparison to standard widely linear methods when mixed uncertainties are present in the observations.     

Reliability of the ALPHA environmental questionnaire and its association with physical activity in female fibromyalgia patients: the al-Ándalus project

Physical activity attenuates the symptoms of fibromyalgia, and its level is oftentimes associated with the perceived environment of fibromyalgia patients. Within this context, we aimed to study the reliability of the Spanish version of the Assessing Levels of Physical Activity (ALPHA) environmental questionnaire and the mode of commuting questionnaire. We also studied the association between the perceived environment and mode of commuting with physical activity levels among female fibromyalgia patients in Spain. Test–retest reliability was judged by the intra-class correlation coefficient (ICC), weighted kappa statistic, Spearman correlations and the proportion of agreement. We calculated bivariate Pearson’s correlations between environmental sum scores and physical activity measured by both International Physical Activity Questionnaire (IPAQ) and accelerometry. More than 70% of the scales and items showed a good reliability regarding the ICC, the weighted kappa, the Spearman correlation and the percentage of inter-agreement (higher than 50%). The perceived environment assessed with the ALPHA showed a low correlation with both IPAQ and accelerometry. The Spanish version of the ALPHA environmental questionnaire proved to be reliable and showed a weak degree of association with physical activity in female fibromyalgia patients.