scholarly journals Normal Cloud Distribution probability density fast calculation

2013 ◽  
Author(s):  
Jingfang Wang
Keyword(s):  
Probability Density ◽  
Fast Calculation ◽  
Distribution Probability

The Movement Planning of Mobile Robots in Performing Search Task Based on Probability Theory

2019 ◽  
Vol 20 (9) ◽  
pp. 560-567
Author(s):  
S. L. Zenkevich ◽  
А. V. Nazarova ◽  
Meixin Zhai
Keyword(s):  
Probability Density ◽  
Target Detection ◽  
Continuous Distribution ◽  
Search Time ◽  
Target Position ◽  
Movement Planning ◽  
Probability Density Distribution ◽  
Optimal Distribution ◽  
Search Area ◽  
Distribution Probability

The article is devoted to the development of searching and covering task in different areas, for example, for extinguishing fires, during search operations in the air, on the ground, etc. Two probabilistic models were created based on the characteristics of the sensors and the search zone, that is, the probability density of the target position and the conditional probability of detecting the target by the sensor under the conditions that the target is at the point of observation (depending on the distance between the sensor and the point of observation). Based on these models, the parameters and the search procedure were analyzed; more precisely, the relationship and formulas between the target detection probability, the search time and other parameters were found. The main difference of the proposed research lies in the fact that by optimizing the obtained relations and formulas it is possible to obtain an optimal distribution of time in the search process, as a result, to increase the probability of target detection. In the research process, at first, the case where the distribution probability of target position in the search area represents a discrete form (network map) is investigated, then a formula for the probability of target detection in a discrete and continuous probe is obtained. Using the method of Lagrange multipliers and dynamic programming, the optimal distribution of search time in each cell was obtained. Further, according to the result obtained, the study was expanded to a continuous distribution probability of target position in the search area, the functional probability of detecting the target of search time, probability density of target and the search trajectory (velocity) was derivated. As a result of solving this functional, for a given search time and probability density distribution of target, optimal control (trajectory and speed) was obtained. The simulation confirmed the efficiency of the proposed search method. The simulation result shows that the greater the probability density of target and the slower the agent’s movement speed, the greater the probability of target detection, for some values of the search parameters, the difference in probabilities of target detection reaches 75.3 %.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

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