Error bounds for wireless localization in NLOS environments

An efficient and accurate method to evaluate the fundamental error bounds for wireless sen-sor localization is proposed. While there already exist efficient tools like Cram`er-Rao lower bound (CRLB) and position error bound (PEB) to estimate error limits, in their standard formulation they all need an accurate knowledge of the statistic of the ranging error. This requirement, under Non-Line-of-Sight (NLOS) environments, is impossible to be met a priori. Therefore, it is shown that collecting a small number of samples from each link and applying them to a non-parametric estimator, like the Gaussian kernel (GK), could lead to a quite accurate reconstruction of the error distribution. A proposed Edgeworth Expansion method is employed to reconstruct the error statistic in a much more efficient way with respect to the GK. It is shown that with this method, it is possible to get fundamental error bounds almost as accurate as the theoretical case, i.e. when a priori knowledge of the error distribution is available. Therein, a technique to determine fundamental error limits – CRLB and PEB – onsite without knowledge of the statistics of the ranging errors is proposed.

Identifying Domains of Applicability of Machine Learning Models for Materials Science

We present an extension to the usual machine learning process that allows for the identification of the domain of applicability of a fitted model, i.e., the region in its domain where it performs most accurately. This approach is applied to several vastly different but commonly used materials representations (namely the n-gram approach, SOAP, and the many body tenor representation), which are practically indistinguishable based on performance using a single error statistic. Moreover, these models appear unsatisfactory for screening applications as they fail to reliably identify the ground state polymorphs. When applying our newly developed analysis for each of the models, we can identify the domain of applicability for each model according to a simple set of interpretable conditions. We show that identification of the domain of applicability in the prediction of the formation energy enables a more accurate ground-state search - a crucial step for the discovery of novel materials.

Identifying Domains of Applicability of Machine Learning Models for Materials Science

We present an extension to the usual machine learning process that allows for the identification of the domain of applicability of a fitted model, i.e., the region in its domain where it performs most accurately. This approach is applied to several vastly different but commonly used materials representations (namely the n-gram approach, SOAP, and the many body tenor representation), which are practically indistinguishable based on performance using a single error statistic. Moreover, these models appear unsatisfactory for screening applications as they fail to reliably identify the ground state polymorphs. When applying our newly developed analysis for each of the models, we can identify the domain of applicability for each model according to a simple set of interpretable conditions. We show that identification of the domain of applicability in the prediction of the formation energy enables a more accurate ground-state search - a crucial step for the discovery of novel materials.

Identifying Domains of Applicability of Machine Learning Models for Materials Science

We present an extension to the usual machine learning process that allows for the identification of the domain of applicability of a fitted model, i.e., the region in its domain where it performs most accurately. This approach is applied to several vastly different but commonly used materials representations (namely the n-gram approach, SOAP, and the many body tenor representation), which are practically indistinguishable based on performance using a single error statistic. Moreover, these models appear unsatisfactory for screening applications as they fail to reliably identify the ground state polymorphs. When applying our newly developed analysis for each of the models, we can identify the domain of applicability for each model according to a simple set of interpretable conditions. We show that identification of the domain of applicability in the prediction of the formation energy enables a more accurate ground-state search - a crucial step for the discovery of novel materials.

Consistency and representativeness of integrated water vapour from ground-based GPS observations and ERA-Interim reanalysis

This study examines the consistency and representativeness differences of daily integrated water vapour (IWV) data from ERA-Interim reanalysis and GPS observations at 120 global sites over a 16-year period (1995–2010). Various comparison statistics are analysed as a function of geographic, topographic, and climatic features. A small (±1 kg m−2) bias is found in the reanalysis across latitudes (moist in northern and southern midlatitudes and dry in the tropics). The standard deviation of daily IWV differences is generally below 2 kg m−2 but peaks in the northern and southern storm-track regions. In general, the larger IWV differences are explained by increased representativeness errors, when GPS observations capture some small-scale variability that is not resolved by the reanalysis. A representativeness error statistic is proposed which measures the spatiotemporal variability in the vicinity of the GPS sites, based on reanalysis data at the four surrounding grid points. It allows to predict the standard deviation of daily IWV differences with a correlation of 0.73. In general, representativeness differences can be reduced by temporal averaging and spatial interpolation from the four surrounding grid points. A small number of outlying cases (15 sites) which do not follow the general tendencies are further examined. It is found that their special topographic and climatic features strongly enhance the representativeness errors (e.g. steep topography, coastlines, and strong seasonal cycle in monsoon regions). Discarding these sites significantly improves the global ERA-Interim and GPS comparison results. The selection of sites a priori, based on the representativeness error statistic, is able to detect 11 out of the 15 sites and improve the comparison results by 20 % to 30 %.

Consistency and representativeness of integrated water vapour from ground-based GPS observations and ERA-Interim reanalysis

This study examines the consistency and representativeness differences of daily IWV data from ERA-Interim reanalysis and GPS observations at 120 global sites over a 16-year period (1995–2010). Various comparison statistics are analysed as a function of geographic, topographic, and climatic features. A small (±1 kg m−2) bias is found in the reanalysis across latitudes (moist in northern and southern mid-latitudes and dry in the tropics). The standard deviation of daily IWV differences is generally below 2 kg m−2 but peaks in the northern and southern storm-tracks regions. In general, the larger IWV differences are explained by increased representativeness errors, when GPS observations capture some small-scale variability that is not resolved by the reanalysis. A representativeness error statistic is proposed which measures the spatiotemporal variability in the vicinity of the GPS sites, based on reanalysis data at the four surrounding grid points. It allows to predict the standard deviation of daily IWV differences with a correlation of 0.73. In general, representativeness differences can be reduced by temporal averaging and spatial interpolation from the four surrounding grid points. A small number of outlying cases (15 sites) which don’t follow the general tendencies are further examined. It is found that their special topographic and climatic features strongly enhance the representativeness errors (e.g. steep topography and coast-lines, strong seasonal cycle in monsoon regions). Discarding these sites significantly improves the global ERA-Interim and GPS comparison results. The selection of site a priori, based on the representativeness error statistic, is able to detect 11 out of the 15 sites and improve the comparison results by 20 to 30 %.