Moderate Geomagnetic Storm Condition, WAAS Alerts and real GPS Positioning Quality

The most significant part of the Wade Area Augmentation System (WAAS) integrity data consists of the User Differential Range Error (UDRE) and the Grid Ionospheric Vertical Error (GIVE). WAAS solutions are not completely appropriate to determine the GIVE term within the entire wade area coverage zone taking in account real irregular structure of the ionosphere. It leads to the larger confidence bounding terms and lower expected positioning availability in comparison to the reality under geomagnetic storm conditions and system outages. Thus a question arises: is the basic WAAS concept appropriate to provide the same efficiency of the integrity monitoring for both “global differential correction (i.e. clock, ephemeris etc)” and “local differential correction (i.e. ionoshrere, troposhpere and multipath)”? The aim of this paper is to compare official WAAS integrity monitoring reports and real positioning quality in US coverage zone (CONUS) and Canada area under geomagnetic storm conditions and system outages. In this research we are interested in comparison between real GPS positioning quality based on one-frequency C/A ranging mode and HAL (VAL) values which correspond to the LP, LPV and LPV200 requirements. Significant mismatch of the information between WAAS integrity data and real positioning quality was unfolded as a result of this comparison under geomagnetic storms and system outages on February, 2011 and June 22, 2015. Based on this result we think that in order to achieve high confidence of WAAS positioning availability alerts real ionospheric measurements within the wide area coverage zone must be involved instead of the WAAS GIVE values. The better way to realize this idea is to combine WAAS solutions to derive “global differential corrections” and LAAS solutions to derive “local differential corrections”

Point derivations for Lipschitz functions andClarke's generalized derivative

Clarke's generalized derivative $f^0(x,v)$ is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed $x\in X$ and fixed $v\in E$ the function $f^0(x,v)$ is continuous and sublinear in $f\in Lip(X,d)$. It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz's product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given

A method of truncated codifferential with application to some problems of cluster analysis

A method of truncated codifferential descent for minimizing continuously codifferentiable functions is suggested. The convergence of the method is studied. Results of numerical experiments are presented. Application of the suggested method for the solution of some problems of cluster analysis are discussed. In numerical experiments Wisconsin Diagnostic Breast Cancer database was used