No Perfect Outdoors: Towards a Deep Profiling of GNSS-Based Location Contexts

While both outdoor and indoor localization methods are flourishing, how to properly marry them to offer pervasive localizability in urban areas remains open. Recently, proposals on indoor–outdoor detection have made the first step towards such an integration, yet complicated urban environments render such a binary classification incompetent. Fortunately, the latest developments in Android have granted us access to raw GNSS measurements, which contain far more information than commonly derived GPS location indicators. In this paper, we explore these newly available measurements in order to better characterize diversified urban environments. Essentially, we tackle the challenges introduced by the complex GNSS data and apply a deep learning model to identify representations for respective location contexts. We further develop two preliminary applications of our deep profiling: one, we offer a more fine-grained semantic classification than binary indoor–outdoor detection; and two, we derive a GPS error indicator that is more meaningful than that provided by Google Maps. These results are all corroborated by our extensive data collection and trace-driven evaluations.

On the Adaptive Numerical Solution to the Darcy–Forchheimer Model

We considered a primal-mixed method for the Darcy–Forchheimer boundary value problem. This model arises in fluid mechanics through porous media at high velocities. We developed an a posteriori error analysis of residual type and derived a simple a posteriori error indicator. We proved that this indicator is reliable and locally efficient. We show a numerical experiment that confirms the theoretical results.

Analysis of estimators for Stokes problem using a mixed approximation

In this work, we introduce the steady Stokes equations with a new boundary condition, generalizes the Dirichlet and the Neumann conditions. Then we derive an adequate variational formulation of Stokes equations. It includes algorithms for discretization by mixed finite element methods. We use a block diagonal preconditioners for Stokes problem. We obtain a faster convergence when applying the preconditioned MINRES method. Two types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true discretization error. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like Adina system.

Numerical Simulation of a Nonlinear Problem Arising in Heat Transfer and Magnetostatics

We present a numerical model that comprises a nonlinear partial differential equation. We apply an adaptive stabilised mixed finite element method based on an a posteriori error indicator derived for this particular problem. We describe the numerical algorithm and some numerical results.

Influence of accuracy estimation of frequency characteristics of radar targets on the results of identifying the geometric shape of local reflectors

The issues of introducing broadband technologies in civil and special purpose radar systems are considered. The popularity of these technologies for solving a number of practical problems determines the relevance of research related to a detailed analysis of long-range portraits of observed objects at a new qualitative level. The influence of the systematic error of the measuring channel on the reliability of the identification of the geometric shape of the local reflectors of the observation object using the results of broadband radar sounding is studied. The created broadband radar measuring channel with linear frequency modulation of the signal based on the method of generalized heterodyning is described. A technique is proposed for compensating systematic measurement errors for a channel of a given type using calibration spheres. The systematic error in measuring the frequency characteristics of the sphere is estimated, and an error indicator for estimating the frequency characteristics of objects is proposed. The dependence of the statistical indicators of the identification results of the geometric shape of local reflectors on the specified indicator is given. The possibility of identifying the geometric shape of local reflectors of objects by the parameters of their frequency characteristics has been experimentally confirmed. The results can be used to assess the reliability of identifying the geometric shape of local reflectors at the stage of calibration of the measuring channel, as well as to decide on the feasibility of implementing algorithms for identifying the geometric shape of local reflectors on an existing radar.

Cross-Gramian-based dominant subspaces

A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspaces projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work, we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.

An Error Indicator Based on a Wave Dispersion Analysis for the Vibration Modes of Isotropic Elastic Solids Discretized by Energy-Orthogonal Finite Elements

This paper studies the dispersion of elastic waves in isotropic media discretized by the finite element method. The element stiffness matrix is split into basic and higher order components which are respectively related to the mean and deviatoric components of the element strain field. This decomposition is applied to the elastic energy of the finite element assemblage. By a dispersion analysis the higher order elastic energy is related to the elastic energy error for the propagating waves. An averaged correlation is proposed and successfully tested as an error indicator for finite element vibration eigenmodes.