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The adaptive inverse distance weighting (IDW) interpolation method shows improved computational advantages for building high-precision 3D geological models. However, in the case of varying geological borehole distribution characteristics, the statistical range of local adjacent points and the type of membership function are two important factors that affect the adaptive calculation of the weight power value in the IDW method. Therefore, this study attempts to build a general adaptive IDW model unaffected by the spatial distribution of geological boreholes sample data. This study uses a combination of nearest neighbor point statistics and membership function mapping to modify the IDW weights automatically. Moreover, it investigates the accuracy of IDW interpolation under two types of nearest neighbor point statistics ranges (fixed number and area) and three types of membership functions (triangle, trapezoidal, and Gaussian) interactions. The results showed that fixing the search window to determine the local neighbor statistics range and utilizing the triangle membership function to map adjustment weights exhibit strong distribution patterns. The minimum interpolation relative error for 10 sample boreholes reached 0.86%, whereas the average minimum interpolation relative error was 18.80%. Each borehole achieved optimal interpolation accuracy. The research findings significantly impact building adaptive spatial interpolation techniques and high-precision 3D geological models. [ABSTRACT FROM AUTHOR]

Along with the IoT technology, the importance of indoor positioning is increasing, but the accuracy of the traditional fingerprint positioning algorithm is negatively affected by the complex indoor environment. This issue of low indoor spatial geolocation localization accuracy when the signal is collected away from the present stage occurs due to the signal instability of the iBeacon in the traditional fingerprint localization algorithm, which generates a variety of factors such as object blocking and reflection, multipath effect, etc., as well as the scarcity of reference fingerprint data points. In response, this study proposes an inverse distance-weighted optimization WKNN algorithm for indoor localization based on the GM(1,1) model. By implementing GM(1,1) model pre-process leveling, the original fingerprint library was reconstructed into a large-capacity fingerprint database using the inverse distance-weighted interpolation method. The local inverse distance-weighted interpolation was used for interpolation, combined with the WKNN algorithm to complete the coordinate solution in real time. This effectively solved the issue of low localization accuracy caused by the large fluctuation of the received signal strength (RSS) sampling measurement data and the existence of few reference fingerprint datapoints in the fingerprint database. The results show that this algorithm reduced the average positioning error by 5.9% compared with ordinary kriging (OK) interpolation leveling and reduced the average positioning error by 18.2% compared with the indoor spatial location accuracy of the original fingerprint database, which can effectively improve the positioning accuracy and provide technical support for indoor location and navigation services. [ABSTRACT FROM AUTHOR]

The mapping of a survey variable throughout a continuum or for finite populations of units is usually performed from a model-dependent perspective. Nevertheless, when a sample of locations/units is selected by a probabilistic sampling scheme, the complex task of modelling can be avoided by using the inverse distance weighting interpolator and deriving the properties of maps in a design-based perspective. Conditions ensuring consistency of maps can be derived mainly based on some obvious assumptions about the pattern of the survey variable throughout the study region as well from the feature of the sampling scheme adopted to select locations/units. Nevertheless, in a design-based setting the totals of the survey variable for a set of domains partitioning the study region are commonly estimated by traditional estimators such as the Horvitz–Thompson estimator in the case of finite populations or the Monte-Carlo estimator in the case of continuous populations or by related estimators exploiting the information of auxiliary variables. That necessarily gives rise to different total estimates with respect to those achieved from the resulting maps as the sum of the interpolated values within domains. To obtain non-discrepant results, a harmonization of maps is here suggested, in such a way that the resulting totals arising from maps coincide with those achieved by traditional estimation. The capacity of the harmonization procedure to maintain consistency is argued theoretically and checked by a simulation study performed on some real populations. [ABSTRACT FROM AUTHOR]

Along with the IoT technology, the importance of indoor positioning is increasing, but the accuracy of the traditional fingerprint positioning algorithm is negatively affected by the complex indoor environment. This issue of low indoor spatial geolocation localization accuracy when the signal is collected away from the present stage occurs due to the signal instability of the iBeacon in the traditional fingerprint localization algorithm, which generates a variety of factors such as object blocking and reflection, multipath effect, etc., as well as the scarcity of reference fingerprint data points. In response, this study proposes an inverse distance-weighted optimization WKNN algorithm for indoor localization based on the GM(1,1) model. By implementing GM(1,1) model pre-process leveling, the original fingerprint library was reconstructed into a large-capacity fingerprint database using the inverse distance-weighted interpolation method. The local inverse distance-weighted interpolation was used for interpolation, combined with the WKNN algorithm to complete the coordinate solution in real time. This effectively solved the issue of low localization accuracy caused by the large fluctuation of the received signal strength (RSS) sampling measurement data and the existence of few reference fingerprint datapoints in the fingerprint database. The results show that this algorithm reduced the average positioning error by 5.9% compared with ordinary kriging (OK) interpolation leveling and reduced the average positioning error by 18.2% compared with the indoor spatial location accuracy of the original fingerprint database, which can effectively improve the positioning accuracy and provide technical support for indoor location and navigation services.

When the Permanent Scatterer (PS) technique is utilized to compensate the Atmospheric Phase (AP) for Ground-Based Interferometric Synthetic Aperture Radar (GB-InSAR) images, a proper parametric model should be built to describe the AP. However, for some interferograms, the AP may nonlinearly vary with the PS range, and this cannot be effectively compensated via the conventional method. This paper proposes an improved method to compensate the nonlinear AP. Here, the conventional method is first used to compensate all the phase interferograms. By calculating the standard deviation of the phase sequence of every PS and setting a proper threshold, a large number of stable PSs are selected. Then these stable PSs are divided into a certain number of sub-regions, and some control points are determined. With the inverse distance weighting interpolation, the APs of all the PSs are estimated and compensated. To verify the effectiveness of the proposed method, 460 radar images are processed, and the results are made compared with those of the conventional method. The nonlinear AP could be better compensated with the proposed method to avoid misunderstanding of the motional area. Several reference PSs are selected to make quantitative comparisons, and measurement error up to 1 rad could be reduced.

This paper presents the optimization of the inverse distance weighting method (IDW) in the process of creating a digital terrain model (DTM) of the seabed based on bathymetric data collected using a multibeam echosounder (MBES). There are many different methods for processing irregular measurement data into a grid-based DTM, and the most popular of these methods are inverse distance weighting (IDW), nearest neighbour (NN), moving average (MA) and kriging (K). Kriging is often considered one of the best methods in interpolation of heterogeneous spatial data, but its use is burdened by a significantly long calculation time. In contrast, the MA method is the fastest, but the calculated models are less accurate. Between them is the IDW method, which gives satisfactory accuracy with a reasonable calculation time. In this study, the author optimized the IDW method used in the process of creating a DTM seabed based on measurement points from MBES. The goal of this optimization was to significantly accelerate the calculations, with a possible additional increase in the accuracy of the created model. Several variants of IDW methods were analysed (dependent on the search radius, number of points in the interpolation, power of the interpolation and applied smoothing method). Finally, the author proposed an optimization of the IDW method, which uses a new technique of choosing the nearest points during the interpolation process (named the growing radius). The experiments presented in the paper and the results obtained show the true potential of the IDW optimized method in the case of DTM estimation. [ABSTRACT FROM AUTHOR]

The estimation of individual values (marks) in a finite population of units (e.g., trees) scattered onto a survey region is considered under 3P sampling. For each unit, the mark is estimated by means of an inverse distance weighting interpolator. Conditions ensuring the design‐based consistency of maps are considered under 3P sampling. A computationally simple mean squared error estimator is adopted. Because 3P sampling involves the prediction of marks for each unit in the population, prediction errors rather than marks can be interpolated. Then, marks are estimated by the predictions plus the interpolated errors. If predictions are good, prediction errors are more smoothed than raw marks so that the procedure is likely to better meet consistency requirements. The purpose of this paper is to provide theoretical and empirical evidence on the effectiveness of the interpolation based on prediction errors to prove that the proposed strategy is a tool of general validity for mapping forest stands. [ABSTRACT FROM AUTHOR]

In agricultural ecosystems, soil organic matter (SOM) is a major determinant and indicator of soil fertility and quality. The objectives of this study were to understand the spatial distribution of SOM and the accuracy of two interpolation methods evaluated: Kriging and inverse distance weighting (IDW) in a gravel-sand mulch of northwest China. We are measuring SOM in 256 soil samples collected from 0 to 10, 10–20, 20–30, and 30–50 cm layers at five sampling scales, 32 × 32, 28 × 28, 24 × 24, 20 × 20, and 16 × 16 m, and three sampling spacings, 4, 8, and 12 m. SOM content decreased with depth in each scale, varying from 2.41 to 5.75 g/kg. The SOM was weakly to moderately variable and has a strong spatial autocorrelation. The standard deviation was small for each soil layer, and the variability was low or weakly moderate, indicating that two interpolation methods were applicable to the entire data set. Kriging interpolation was more accurate than IDW. The distribution of SOM differed in the surface layers at the five sampling scales, which was more uniform as the sampling scale decreased. Eight meter is a reasonable sampling spacing. Through the scales effect and spacing change on SOM for fixed-point monitoring, combing the estimate of SOM to reduce the sampling workload will aid the supply of SOM in gravel-sand mulched fields in arid regions. [ABSTRACT FROM AUTHOR]

Inverse distance weighting (IDW) is a simple and practical interpolation method. Taking the global ionospheric map (GIM) product as a sample, the latitude and longitude anisotropy of the ionospheric total electron content (TEC) distribution is taken into account with an introduction of the latitude and longitude adjustment factor r. Six ionospheric distance calculation schemes are used for testing and results show that the correlation of the ionospheric TEC with the longitude direction is higher than the latitude direction and different ionospheric distance calculation schemes can effectively improve the IDW interpolation accuracy. Using the IDW interpolation based on an optimal scheme, a long-term interpolation accuracy is analyzed and results show that the precision of the optimal scheme interpolation is about 25% higher than the general IDW interpolation precision in the ionospheric activity area (20° north and south latitude) for GIM data before and after spring vernal and summer solstice, autumnal equinox and winter solstice in 12 consecutive years. When the ionospheric activity was active at 3-5 hours after 14 o'clock in the local time of 2014, the interpolation accuracy base on the optimal scheme was improved obviously with an interpolation error smaller than 4.0 TECU. [ABSTRACT FROM AUTHOR]

Surveys estimating chronic obstructive pulmonary disease (COPD) prevalence are unevenly distributed in the Americas, which make it difficult to estimate accurately its geographical distribution. The geographic information system inverse distance weighted (IDW) interpolation technique has proved to be an effective tool in spatial distribution estimation of epidemiological variables, even when real data are few or widely spread. We aimed to represent cartographically the COPD prevalence in the Americas by means of a blue to red scale representation of the prevalence data, where different values are represented as different colours, and a population density filtered IDW interpolation mapping, where areas with a population density <0.1 inhabitants/km2 are hidden. We systematically searched for prevalence rates from population surveys of individuals 40 years and older, and a COPD diagnosis confirmed by spirometry. Interpolation maps were obtained for the whole Americas, even from extensive areas lacking real data. Maps showed high prevalence values in the Southeast and Southwest regions of Canada bordering the United States; in several states of the Great Lakes region, and in the lower Missouri, Ohio and Mississippi basins of the United States; in the coastal regions of south-eastern and southern Brazil; Uruguay, and the Argentine Pampas. In general, most of the remaining American regions showed intermediate values of COPD prevalence. IDW interpolation seems to be a suitable tool to visually display estimates of COPD prevalence, and it may be a valuable help to draw attention about the worrying prevalence of this preventable and treatable disease. [ABSTRACT FROM AUTHOR]

The appropriate spatial interpolation methods must be selected to analyze the spatial distributions of Potentially Toxic Elements (PTEs), which is a precondition for evaluating PTE pollution. The accuracy and effect of different spatial interpolation methods, which include inverse distance weighting interpolation (IDW) (power = 1, 2, 3), radial basis function interpolation (RBF) (basis function: thin-plate spline (TPS), spline with tension (ST), completely regularized spline (CRS), multiquadric (MQ) and inverse multiquadric (IMQ)) and ordinary kriging interpolation (OK) (semivariogram model: spherical, exponential, gaussian and linear), were compared using 166 unevenly distributed soil PTE samples (As, Pb, Cu and Zn) in the Suxian District, Chenzhou City, Hunan Province as the study subject. The reasons for the accuracy differences of the interpolation methods and the uncertainties of the interpolation results are discussed, then several suggestions for improving the interpolation accuracy are proposed, and the direction of pollution control is determined. The results of this study are as follows: (i) RBF-ST and OK (exponential) are the optimal interpolation methods for As and Cu, and the optimal interpolation method for Pb and Zn is RBF-IMQ. (ii) The interpolation uncertainty is positively correlated with the PTE concentration, and higher uncertainties are primarily distributed around mines, which is related to the strong spatial variability of PTE concentrations caused by human interference. (iii) The interpolation accuracy can be improved by increasing the sample size around the mines, introducing auxiliary variables in the case of incomplete sampling and adopting the partition prediction method. (iv) It is necessary to strengthen the prevention and control of As and Pb pollution, particularly in the central and northern areas. The results of this study can provide an effective reference for the optimization of interpolation methods and parameters for unevenly distributed soil PTE data in mining areas. [ABSTRACT FROM AUTHOR]

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ABSTRACT As many cities are increasingly affected by heat waves, knowledge regarding those parts of cities most susceptible to heat exposure is essential for the implementation of directed adaptation measures. The frequency of heat waves is projected to increase in both German cities considered for this study: Karlsruhe and Berlin. By aggregating temperature data from meteorological stations within the two cities and their hinterlands, the local temperature distribution within the administrative city boundaries was assessed. A multiple regression approach was used to reveal the regional inter-relationship between non-meteorological factors such as altitude, population density and land use, on the one hand, and the heat distribution, on the other. This functional relationship was then applied at the city quarter level for the two cities. A model selection process was undertaken to find the most significant models describing the heat exposure of two heat indicators: heat wave days (HWDs) and tropical nights (TRNs). While altitude and population density were found to be the most significant explanatory variables for Karlsruhe, population density had a dominating influence on the distribution of heat at the city quarter level for Berlin. In Karlsruhe, models describing the daytime temperature performed best, whereas in Berlin those describing the night time temperature distribution had the highest statistical significance. This method could be used with relatively low financial and material expense to assess heat exposure in different city quarters even if there are insufficient meteorological stations within a city. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method to model non-deterministic quantities based on experimental measurement data. The focus of this work is on quantities that vary over a continuous domain, e.g., material properties, time-dependent strain rate effects, or stress–strain curves. These quantities are modelled by means of the recently introduced concept of interval fields. An interval field defines intervals that are defined throughout the continuous domain and have dependence in this domain by expanding them over a set of basis functions, describing the spatial nature of the non-determinism of the modelled quantities. One of the more intuitive concepts of defining basis functions in an interval field is through inverse distance weighting interpolation (IDW), which starts from known intervals at specific control points within the domain. For each of these control points, a corresponding basis function is defined, the relative weight of which is decreasing inversely with the distance. Through this definition, all intervals have non-vanishing basis functions throughout the model domain. This makes the application of standard IDW extremely challenging when the interval uncertainty varies inhomogeneously over the domain, i.e., when local effects are present in the model. Therefore, in this paper standard IDW is adapted by changing the distance measure. More specifically, the weight of intervals is increased locally, while diminishing the weight in other regions. For this purpose, a function is introduced that maps the domain to a higher dimension feature space, in which the distances that determine the weight are measured. This mapping function is based on either the size of the intervals at the control points or experimental data, which both yield additional control resulting in increased agreement with experimental data. This paper demonstrates that this method outperforms standard IDW in controllability, while limiting the number of control points. This is illustrated in three case studies: a first case concerning modelling local non-determinism; a second case where a mix of global and local effects is modelled; and the third case, where the interval field is based on experimental stress strain curves. In all these cases, multiple configurations demonstrate the effects of the parameters, and how the new technique is applied. The proposed technique outperforms standard IDW in all three case studies, with an increased coefficient of determination, R 2 , between 22% and 56%, in comparison to standard IDW. [ABSTRACT FROM AUTHOR]