• Korean Journal of Remote Sensing
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• v.25 no.4
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• pp.321-338
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• 2009

The objective of this paper is to compare spatial prediction capabilities of univariate kriging algorithms for generating GIS-based thematic maps from ground survey data with asymmetric distributions. Four univariate kriging algorithms including traditional ordinary kriging, three non-linear transform-based kriging algorithms such as log-normal kriging, multi-Gaussian kriging and indicator kriging are applied for spatial interpolation of geochemical As and Pb elements. Cross validation based on a leave-one-out approach is applied and then prediction errors are computed. The impact of the sampling density of the ground survey data on the prediction errors are also investigated. Through the case study, indicator kriging showed the smallest prediction errors and superior prediction capabilities of very low and very high values. Other non-linear transform based kriging algorithms yielded better prediction capabilities than traditional ordinary kriging. Log-normal kriging which has been widely applied, however, produced biased estimation results (overall, overestimation). It is expected that such quantitative comparison results would be effectively used for the selection of an optimal kriging algorithm for spatial interpolation of ground survey data with asymmetric distributions.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2237-2242
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• 2005

The original RRT is iteratively expanded by applying control inputs that drive the system slightly toward randomly-selected states, as opposed to requiring point-to-point convergence, as in the probabilistic roadmap approach. It is generally known that the performance of RRTs can be improved depending on the selection of the metrics in choosing the nearest vertex and bias techniques in choosing random states. We designed a path planning algorithm based on the RRT method for a remote-controlled mobile robot. First, we considered a bias technique that is goal-biased Gaussian random distribution along the command directions. Secondly, we selected the metric based on a weighted Euclidean distance of random states and a weighted distance from the goal region. It can save the effort to explore the unnecessary regions and help the mobile robot to find a feasible trajectory as fast as possible. Finally, the constraints of the actuator should be considered to apply the algorithm to physical mobile robots, so we select control inputs distributed with commanded inputs and constrained by the maximum rate of input change instead of random inputs. Simulation results demonstrate that the proposed algorithm is significantly more efficient for planning than a basic RRT planner. It reduces the computational time needed to find a feasible trajectory and can be practically implemented in a remote-controlled mobile robot.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.1
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• pp.47.2-47.2
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• 2021

Focusing on both small separations and baryonic acoustic oscillation scales, the cosmic evolution of the clustering properties of peak, void, wall, and filament-type critical points is measured using two-point correlation functions in ΛCDM dark matter simulations as a function of their relative rarity. A qualitative comparison to the corresponding theory for Gaussian random fields allows us to understand the following observed features: (i) the appearance of an exclusion zone at small separation, whose size depends both on rarity and signature (i.e. the number of negative eigenvalues) of the critical points involved; (ii) the amplification of the baryonic acoustic oscillation bump with rarity and its reversal for cross-correlations involving negatively biased critical points; (iii) the orientation-dependent small-separation divergence of the cross-correlations of peaks and filaments (respectively voids and walls) that reflects the relative loci of such points in the filament's (respectively wall's) eigenframe. The (cross-) correlations involving the most non-linear critical points (peaks, voids) display significant variation with redshift, while those involving less non-linear critical points seem mostly insensitive to redshift evolution, which should prove advantageous to model. The ratios of distances to the maxima of the peak-to-wall and peak-to-void over that of the peak-to-filament cross-correlation are ~2-√~2 and ~3-√~3WJ, respectively, which could be interpreted as the cosmic crystal being on average close to a cubic lattice. The insensitivity to redshift evolution suggests that the absolute and relative clustering of critical points could become a topologically robust alternative to standard clustering techniques when analysing upcoming surveys such as Euclid or Large Synoptic Survey Telescope (LSST).