From electronic navigational chart data to sea-bottom models: Kriging approaches for the Bay of Pozzuoli

<p class="Abstract">Electronic Navigational Charts (ENCs), official databases created by a national hydrographic office and included in Electronic Chart Display and Information System (ECDIS), supply, among essential indications for safe navigation, data about sea-bottom morphology in terms of depth points and isolines. Those data are very useful to build bathymetric 3D models: applying interpolation methods, it is possible to produce a continuous representation of the seafloor for supporting studies concerning different aspects of a marine area, such as directions and intensity of currents, sensitivity of habitats and species, etc. Many interpolation methods are available in literature for bathymetric data modelling: among them kriging ones are extremely performing, but require deep analysis to define input parameters, i.e. semi-variogram models. This paper aims to analyze kriging approaches for depth data concerning the Bay of Pozzuoli. The attention is focused on the role of semi-variogram models for Ordinary and Universal kriging. Depth data included in two ENCs, namely IT400129 and IT400130, are processed using Geostatistical Analyst, an extension of ArcGIS 10.3.1 (ESRI). The results testify the relevance of the choice of the mathematical functions of the semi-variogram: Stable Model supplies, for this case study, the best performance in terms of depth accuracy for both Ordinary and Universal kriging.</p>

Aiming for the Optimum: Examining Complex Relationships Between Sampling Regime, Sampling Density and Landscape Complexity to Accurately Model Resource Availability

Context Obtaining accurate maps of landscape features often requires intensive spatial sampling and interpolation. The data required to generate reliable interpolated maps varies with spatial scale and landscape heterogeneity. However, there has been no rigorous examination of sampling density relative to landscape characteristics and interpolation methods.ObjectivesOur objective was to characterize the 3-way relationship among sampling density, interpolation method, and landscape heterogeneity on interpolation accuracy in simulated and in situ landscapes. MethodsWe simulated landscapes of variable heterogeneity and sampled at increasing densities using both systematic and random strategies. We applied each of three local interpolation methods: Inverse Distance Weighting, Universal Kriging, and Nearest Neighbor — to the sampled data and estimated accuracy (R2) between interpolated surfaces and the original surface. Finally, we applied these analyses to in situ data, using a normalized difference vegetation index raster collected from pasture with various resolutions.Results All interpolation methods and sampling strategies resulted in similar accuracy; however, low heterogeneity yielded the highest R2 values at high sampling densities. In situ results showed that Universal Kriging performed best with systematic sampling, and inverse distance weighting with random sampling. Heterogeneity decreased with resolution, which increased accuracy of all interpolation methods. Landscape heterogeneity had the greatest effect on accuracy.ConclusionsHeterogeneity of the original landscape is the most significant factor in determining the accuracy of interpolated maps. There is a need to create structured tools to aid in determining sampling design most appropriate for interpolation methods across landscapes of various heterogeneity.

Spatio-Temporal Dynamic Fields Estimating and Modeling of Missing Points in Data Sets Using a Flexible State-Space Model

Modelling and estimating spatio-temporal dynamic field are common challenges in much applied research. Most existing spatio-temporal interpolation methods require massive prior calculations and consistent observational data, resulting in low interpolation efficiency. This paper presents a flexible state-space model for iteratively fitting time-series from random missing points in data sets, namely Flexible Universal Kriging state-space model(FUKSS). In this work, a recursive method similar to Kalman filter is used to estimate the time-series, avoiding the problem of increasing data caused by Kriging space-time extension. Based on the statistical characteristics of Kriging, this method introduces a spatial selection matrix to make the different observation data and state vectors identical at different times, which solves the problem of missing data and reduces the calculation complexity. In addition, a dynamic linear autoregressive model is introduced to solve the problem that the universal Kriging state-space model cannot predict. We have demonstrated the superiority of our method by comparing it with different methods through experiments, and verified the effectiveness of this method through practical cases.

Coastal Depth Extraction from Satellites Images

The problems in bathymetry measurement often have gaps or ‘holes’ within the data. As a result, hydrographic surveyors often have sparse data, and even though the data is dense and equal distances, there is still a gap in time. This paper present coastal depth extraction from satellite images. The problem encountered during the bathymetry derivation process and the problem related to the space, distribution and quantity of the Single-beam echo sounder (SBES) data. Therefore, the idea of using spatial interpolation could be a suitable approach in solving the problems. This study intends to produce Satellite-Derived Bathymetry (SDB) from Landsat 8 images at Pantai Tok Jembal, Terengganu, Malaysia. The proposed method by first interpolating the SBES point in the calibration data using spatial predictors, i.e. Inverse Distance Weightage, Thin-Plate Spline, Spline with Tension, Universal Kriging, Natural Neighbor, and Topo to Raster. Second, the raster output created from the interpolation process then converts into the point shapefile. Third, intersect function use to eliminate the point whereby not in the domain. Finally, the newly generated SBES points in calibration data ready to apply at the SDB computation process, generating SDB. In continuation, a comparative analysis conducted between six SDB results generated using each different newly generated calibration data. The result indicates SDB utilizes with Universal Kriging-newly generated calibration data (RMSE: 0.718 m) was the best result. To summarise, this study has successfully attained the research objectives by utilizing the newly generated calibration data in generating SDB. The task of spatial interpolation recreates the SBES data from irregular space and short data to uniform space and long data, which facilitate in pixel to point value extraction and help refine the bathymetry derivation process. Furthermore, the proposed method suitable to be used when the data are not applicable or limited.

An Optimized Fingerprinting-Based Indoor Positioning with Kalman Filter and Universal Kriging for 5G Internet of Things

Fingerprinting technique for indoor positioning based on 5G system has attracted attention. Kalman filter (KF) is used as preprocessing of raw data to reduce the disturbance of Received Signal Strength (RSS) values. After preprocessing, Universal Kriging (UK) algorithm is adopted to reduce the efforts of establishing a fingerprinting database by Spatial Interpolation. A machine learning algorithm named K -Nearest Neighbour (KNN) is used to calculate user equipment’s position. Real experiments are setup with 5G signals over the air. Two indoor scenarios are considered depending whether the base station is located in the same room with user equipment or not. In test room A, the proposed KF and UK algorithms achieve 53% positioning accuracy improvement. In test room B, 43% performance improvement is obtained by the proposed algorithm. 1.44-meter positioning error is observed as the best case for 80% test samples.

On the drawback of local detrending in universal kriging in conditions of heterogeneously spaced regional TEC data, low-order trends and outlier occurrences

The study intercompares three stochastic interpolation methods originating from the same geostatistical family: least-squares collocation (LSC) known from geodesy, as well as ordinary kriging (OKR) and universal kriging (UKR) known from geology and other geosciences. The objective of this work is to assess advantages and drawbacks of fundamental differences in modeling between these methods in imperfect data conditions. These differences primarily refer to the treatment of the reference field, commonly called ‘mean value’ or ‘trend’ in geostatistical language. The trend in LSC is determined globally before the interpolation, whereas OKR and UKR detrend the observations during the modeling process. The approach to detrending leads to the evident differences between LSC, OKR and UKR, especially in severe conditions such as far from the optimal data distribution. The theoretical comparisons of LSC, OKR and UKR often miss the numerical proof, while numerical prediction examples do not apply cross-validation of the estimates, which is proven to be a reliable measure of the prediction precision and a validation of empirical covariances. Our study completes the investigations with precise parametrization of all these methods by leave-one-out validation. It finds the key importance of the detrending schemes and shows the advantage of LSC prior global detrending scheme in unfavorable conditions of sparse data, data gaps and outlier occurrence. The test case is the modeling of vertical total electron content (VTEC) derived from GNSS station data. This kind of data is a challenge for precise covariance modeling due to weak signal at higher frequencies and existing outliers. The computation of daily set of VTEC maps using the three techniques reveals the weakness of UKR solutions with a local detrending type in imperfect data conditions.