Performance Of Interpolation Methods Research Articles

Simulation investigation of spatial interpolations in virtual rotating array beamforming with different array configurations for rotating sound source localization

Virtual rotating array (VRA) beamforming is a frequency domain rotating sound source localization algorithm, whose basic concept is to make the microphones stationary relative to the sound source. Previously, VRA beamforming was restricted to the array configuration of ring formation. Recently, scholars have successfully applied several spatial interpolation methods to an array with arbitrary microphone configuration for VRA beamforming. However, the performance of these interpolation methods in different array configurations has not been verified. In this paper, spatial interpolation methods in VRA beamforming are applied to several array configurations by simulation, to verify their Doppler shift compensation capability, spectrum reconstruction capability, sound source position precision and sound source strength accuracy. Meanwhile, comparing the results with those of a ring array. Results show that regardless of the interpolation method and array configuration applied, the Doppler effect can be compensated well. The performance of interpolation methods is affected by the array configuration, yet the inverse distance weighting class performs well in terms of position precision across all arbitrary array configuration. Although each arbitrary array configuration can better locate all sound source locations, it cannot accurately identify the sound intensity differences of each source. While the ring array can identify the position and sound intensity of each source more accurately.

Residual Interpolation Integrated Pixel-by-Pixel Adaptive Iterative Process for Division of Focal Plane Polarimeters.

Residual interpolations are effective methods to reduce the instantaneous field-of-view error of division of focal plane (DoFP) polarimeters. However, their guide-image selection strategies are improper, and do not consider the DoFP polarimeters’ spatial sampling modes. Thus, we propose a residual interpolation method with a new guide-image selection strategy based on the spatial layout of the pixeled polarizer array to improve the sampling rate of the guide image. The interpolation performance is also improved by the proposed pixel-by-pixel, adaptive iterative process and the weighted average fusion of the results of the minimized residual and minimized Laplacian energy guide filters. Visual and objective evaluations demonstrate the proposed method’s superiority to the existing state-of-the-art methods. The proposed method proves that considering the spatial layout of the pixeled polarizer array on the physical level is vital to improving the performance of interpolation methods for DoFP polarimeters.

Assessment of Ordinary Kriging and Inverse Distance Weighting Methods for Modeling Chromium and Cadmium Soil Pollution in E-Waste Sites in Douala, Cameroon.

Background.Several studies have demonstrated that chromium (Cr) and cadmium (Cd) have adverse impacts on the environment and human health. These elements are present in electronic waste (e-waste) recycling sites. Several interpolation methods have been used to evaluate geographical impacts on humans and the environment.Objectives.The aim of the present paper is to compare the accuracy of inverse distance weighting (IDW) and ordinary kriging (OK) in topsoil analysis of e-waste recycling sites in Douala, Cameroon.Methods.Selecting the proper spatial interpolation method is crucial for carrying out surface analysis. Ordinary kriging and IDW are interpolation methods used for spatial analysis and surface mapping. Two sets of samples were used and compared. The performances of interpolation methods were evaluated and compared using cross-validation.Results.The results showed that the OK method performed better than IDW prediction for the spatial distribution of Cr, but the two interpolation methods had the same result for Cd (in the first set of samples). Results from Kolmogorov-Smirnov and Shapiro-Wilk tests showed that the data were normally distributed in the study area. The p value (0.302 and 0.773) was greater than 0.05 for Cr and for Cd (0.267 and 0.712). In the second set of samples, the OK method results (for Cd and Cr) were greatly diminished and the concentrations dropped, looking more like an average on the maps. However, the IDW interpolation gave a better representation of the concentration of Cd and Cr on the maps of the study area. For the second set of samples, OK and IDW for Cd and Cr had more similar results, especially in terms of root mean square error (RMSE).Conclusions.Many parameters were better identified from the RMSE statistic obtained from cross-validation after exhaustive testing. Inverse distance weighting appeared more adequate in limited urban areas.Competing Interests. The authors declare no competing financial interests

Dataset characteristics influence the performance of different interpolation methods for soil salinity spatial mapping.

This study compared the performance of different interpolation methods for mapping soil salinity of three different agricultural fields having the same land use but different dataset characteristics. Four common spatial interpolation methods including global polynomial interpolation (GPI), inverse distance weighted (IDW), ordinary kriging (OK), and radial basis functions (RBF) were employed for mapping soil EC. The performance of interpolation methods in predicting soil EC was evaluated based on mean bias error, root mean square error, mean absolute percentage error, and coefficient of determinations criteria. Results showed that dataset characteristics, including central tendency and distribution, were significantly different among the studied fields. Experimental semivariogram and fitted model parameters indicated that three studied fields were also different in their spatial dependence strength. Considering all of the performance assessment measures used, the best interpolation method for fields A and C was OK and IDW for field B. The performance of interpolation methods was found to be affected by data characteristics of the studied fields, which were mostly ascribed to management practices. This study suggests in order to obtain accurate mapping of soil salinity in agricultural fields, it is essential to first find the best spatial interpolation method compatible with the characteristics of the collected data from the selected agricultural land.

Evaluating Different Interpolation Methods to Predict Copper and Nickel Concentrations in Surface Soil

Determining the spatial distribution of different contaminants in soil is essential for the pollution assessment and risk control. Interpolation methods are widely used to estimate the concentrations of the heavy metals in the unstudied sites. In this study, the performances of interpolation methods (inverse distance weighting, local polynomials and ordinary Kriging and radial basis functions) were evaluated to estimate the topsoil contamination with copper and nickel in Golestan Province. 216 surface soil samples were collected from Golestan province, and their Cu and Ni concentrations were measured. Soil contamination was determined using different interpolation methods. Cross validation was applied to compare the methods and estimate their accuracy. The results showed that all the tested interpolation methods have an acceptable prediction accuracy of the mean content for soil heavy metals. RBF-IMQ and IDW1 methods had the lowest RMSE, whereas RBF-TPS method with the largest RMSE estimated a larger size for the polluted area. The greater the weighting power, the larger the polluted area estimated by IDW. Compared with the ‘‘sample ratio over the pollution limits” method, the polluted areas of Cu and Ni were reduced by 8.38% and 6.14%, respectively.

Spatial distribution of soil heavy metal pollution estimated by different interpolation methods: Accuracy and uncertainty analysis

Mapping the spatial distribution of contaminants in soils is the basis of pollution evaluation and risk control. Interpolation methods are extensively applied in the mapping processes to estimate the heavy metal concentrations at unsampled sites. The performances of interpolation methods (inverse distance weighting, local polynomial, ordinary kriging and radial basis functions) were assessed and compared using the root mean square error for cross validation. The results indicated that all interpolation methods provided a high prediction accuracy of the mean concentration of soil heavy metals. However, the classic method based on percentages of polluted samples, gave a pollution area 23.54–41.92% larger than that estimated by interpolation methods. The difference in contaminated area estimation among the four methods reached 6.14%. According to the interpolation results, the spatial uncertainty of polluted areas was mainly located in three types of region: (a) the local maxima concentration region surrounded by low concentration (clean) sites, (b) the local minima concentration region surrounded with highly polluted samples; and (c) the boundaries of the contaminated areas.

Interpolation of animal tracking data in a fluid environment

Interpolation of geolocation or Argos tracking data is a necessity for habitat use analyses of marine vertebrates. In a fluid marine environment, characterized by curvilinear structures, linearly interpolated track data are not realistic. Based on these two facts, we interpolated tracking data from albatrosses, penguins, boobies, sea lions, fur seals and elephant seals using six mathematical algorithms. Given their popularity in mathematical computing, we chose Bézier, hermite and cubic splines, in addition to a commonly used linear algorithm to interpolate data. Performance of interpolation methods was compared with different temporal resolutions representative of the less-precise geolocation and the more-precise Argos tracking techniques. Parameters from interpolated sub-sampled tracks were compared with those obtained from intact tracks. Average accuracy of the interpolated location was not affected by the interpolation method and was always within the precision of the tracking technique used. However, depending on the species tested, some curvilinear interpolation algorithms produced greater occurrences of more accurate locations, compared with the linear interpolation method. Total track lengths were consistently underestimated but were always more accurate using curvilinear interpolation than linear interpolation. Curvilinear algorithms are safe to use because accuracy, shape and length of the tracks are either not different or are slightly enhanced and because analyses always remain conservative. The choice of the curvilinear algorithm does not affect the resulting track dramatically so it should not preclude their use. We thus recommend using curvilinear interpolation techniques because of the more realistic fluid movements of animals. We also provide some guidelines for choosing an algorithm that is most likely to maximize track quality for different types of marine vertebrates.