RESEARCH ABSTRACT CELLULAR AUTOMAT INDEPENDENT OF TIME
The relevance of the study is due to the increasing number of computing cores from a single computing device, and the total number of such devices. At the same time, many algorithms are designed to work in a strictly defined sequence, as a result, either part of the computing power is idle, or additional logic is added on top of the main calculations, which not only complicates the development, but also requires additional calculations, the only purpose of which is synchronization between nodes / cores / threads. In this regard, this article aims to identify how to perform calculations without the need for synchronization as such, using the example of the cellular automaton. The leading method for the study of this problem is the mathematical and computer simulation of the cellular automaton, which allows to comprehensively consider the root cause of the need to perform synchronization – time. The article presents a method of describing a cellular automaton, in which all unnecessary entities are excluded, one of which was time, as a result of which synchronization was no longer necessary. Key entities that are sufficient for a full description of the operation of an arbitrary cellular automaton are identified. The applicability of the minimum set of entities is justified by the example of an elementary one-dimensional cellular automaton. The materials of the article are of practical value for specialists in the field of mathematical modeling and information technology.
Keywords: :cellular automaton, rule, state, superposition, space, time, matrix.
SYNTHESIS OF LINEAR REGRESSION MODEL AND EIV-MODEL
M. P. Bazilevskiy
This paper is devoted to a synthesis of pair-wise linear regression model and simplest EiV-model (Errors-In-Variables model), better known as the Deming regression. The EIV model is a regression in which all variables contain random errors. Such models have a number of significant drawbacks, which makes it difficult to work with them. The synthesis proposed in the paper, called the two-factor model of a fully connected linear regression, is not only devoid of these shortcomings, but also has certain advantages. The main stages of the construction and analysis of two-factor models of fully connected linear regression are considered. The proposed fully connected linear regression model has much in common with the classical multiple regression model; however, these two types are based on completely different approaches. If multiple regression is based on the principle “independent variables affect the dependent one”, then the principle of fully connected regression is “all variables influence each other”. It is established that the approximation abilities of fully connected models do not exceed the capabilities of multiple regressions, but the former have a much more diverse interpretation. The developed synthesis can be used in the construction of multiple models as a tool for solving problems of reducing the dimensionality of data, eliminating multicollinearity and selecting informative regressors.
Keywords: :regression model, ordinary least squares, total least squares, Deming regression, EIV-model, fully connected linear regression model.
METHOD OF AUTONOMOUS CORRECTION OF INERTIAL NAVIGATION SYSTEM OF UNMANNED AIRCRAFT ON THE BASIS OF MODERN GEOINFORMATION TECHNOLOGIES
A.V. Sizov, S.V. Ippolitov, A.Y. Savchenko, V.A. Malyshev
The method of correction of inertial navigation system based on modern geoinformation technologies with the use of optical-electronic system and electronic terrain map, allowing determining the coordinates of the location of the unmanned aircraft in offline mode without the use of satellite and radio navigation, is developed. In this case, the current coordinates of the unmanned aircraft are determined with the help of inertial navigation system. Then these coordinates, taking into account the error accumulated after the last correction of the inertial navigation system, are entered into an electronic terrain map. Thus, the boundaries of the working area of the electronic terrain map are determined, which significantly reduces the computational cost. The correction of the current coordinates of the location of the unmanned aircraft from the optical-electronic system is carried out by two types of data – the geographical coordinates of the three known landmarks (identical points) of the area and the coordinates of the position of the unmanned aircraft relative to these landmarks (relative coordinates – range, height and lateral deviation). Determination of geographical coordinates of three identical points is made in the electronic terrain map on the basis of recognition of the received by the optical-electronic system image. The calculation of the relative coordinates of the unmanned aircraft is carried out by the triangle method with the circumscribed (inscribed) circle (sphere), the vertices of which are three identical points, with the determination of their coordinates in the associated coordinate system of the unmanned aircraft as a result of the corresponding image processing by the optical-electronic system.
Keywords: :inertial navigation system, optical-electronic system, electronic terrain map.
THE ALGORITHM OF CORRECTION OF THE INERTIAL NAVIGATION SYSTEM OF THE UNMANNED AIRCRAFT ON THE BASIS OF THE OPTICAL-ELECTRONIC SYSTEM AND THE ELECTRONIC TERRAIN MAP
A.V. Sizov, S.V. Ippolitov, A.Y. Savchenko, V.A. Malyshev
The paper presents an algorithm of correction of the inertial navigation system of an unmanned aircraft based on the usage of an optical-electronic system and an electronic terrain map, which will provide high accuracy of determining of the navigation parameters, the speed of the correction system, small size, cost and also autonomy of work. This algorithm implements a new method of correction of the inertial navigation system based on the developed mathematical model describing the procedures for solving navigation problems: determining the relative coordinates of three identical points (landmarks on the ground) in the coordinate system of the optical-electronic system associated with the unmanned aircraft; recalculating of the obtained relative coordinates with the help of the matrix of guide cosines into the geographic coordinate system; determining the geographical coordinates of identical points from the electronic terrain map; calculation of the current geographical coordinates of the unmanned aircraft on the basis of its relative coordinates and geographical coordinates of identical points. The solution of the described problems is carried out by the developed algorithm, the final step of which is the input of the current geographical coordinates of the unmanned aircraft into the inertial navigation system for its correction.
Keywords: :inertial navigation system, optical-electronic system, electronic terrain map, unmanned aircraft.
ALGORITHM FOR ADDING TURBOVINET EFFECT
The article discusses the occurrence of noise components from rotating structural elements of the aircraft or turboprop components and the effect of these components on the radio signal tracking aerodynamic object. The masking effect of signals from rotating elements affects the observation of the glider component, which interferes with the tracking of the object. The need to suppress the turboprop components in the radio signal is noted. To solve the problem, it is proposed to use fractal signal processing methods. An algorithm for suppressing turboprop spectral components in an echo signal of an aerodynamic object, based on the definition of the similarity function, is proposed. The article describes the steps of the algorithm and its block diagram. An example of a signal from a bank of temporal functions of micro-movements of an object’s structural elements, used as a basis for approximating the initial echo signal, is given. A simulation was performed for a single aerodynamic object, confirming the suppression of the turboprop component of the echo signal. The proposed algorithm is proposed to be used to classify the number of objects in a swarm of unmanned aerial vehicles. The necessity of decreasing the interval of discreteness of the parameters describing the kinematics of the object’s micro-movements is noted. The materials are of practical value in radiolocation when accompanied by unmanned aerial vehicles to eliminate interfering components in the far-Doppler portrait of the object, automatic coordination, navigation, and increased flight safety.
Keywords: :turboprop component, glider component, micromovement, echo signal, spectrum, radar, Doppler.
APPLICATION OF ANN IN HUMAN-MACHINE INTERFACES
The article continues the cycle of the author’s works on the subject of HIL-simulation. The article proposes an algorithm for the decomposition of any radio system and the subsequent coupling of its parts by adjusting only one of the two stabilizing parameters of the coupling scheme. In addition, the possibility of using a coupling scheme as a matching device between fragments of the system through the aspect of system stability was analyzed. All this makes it possible to significantly reduce the amount of debugging work performed in HIL-simulation of radio systems, both in the field of research of elementary systems and in working out options for creating complex multisystems. As a proof of the correctness of the proposed method, an analytical calculation was performed, in general, showing the possibility of adjusting only one stabilizing parameter in the coupling scheme of a decomposed system, while convergence of the parameters of the divided system to the parameters of the original system can be achieved in several iterations. In some cases, this convergence can be achieved in one iteration. In the conclusion of the article, the calculation was performed using a numerical example for practical confirmation of the proposed method. For clarity and correct understanding of the described actions, illustrations are given of both the operations performed and the results of the calculations..
Keywords: :stabilizing parameter, system decomposition, coupling scheme, HIL-modeling, radio system, Cramer’s rule, Schur complement.
MULTIOBJECTIVE OPTIMIZATION OF BAND-PASS FILTERS CHARACTERISTICS USING HEURISTIC ALGORITHM
The problem of multiobjective optimization of band pass filter (BPF) is investigated. There were three objectives considered: a nonuniformity of attenuation in the pass band, a minimum attenuation in the stop band and a nonuniformity of delay time in the pass band. The first method of solution was to derive Pareto-optimal approximations for BPF from such for low pass filter (LPF) by means of reactance frequency transform. The second method was to search optimal approximation for BPF directly. In the both methods the heuristic algorithm was applied. This algorithm searches out the set of Pareto optimal solutions and uses multistart for searching of global extreme for each point of Pareto front. The numerical experiments showed that for cases with wide pass band of BPF and comparatively poor-quality indexes of gain frequency response the second method can give lower nonuniformity of delay time than the first one when other objectives are the same. This result means that Pareto-optimality does not persist in the frequency transform in such cases. At once in the cases with narrow pass band of BPF or comparatively good quality indexes of gain frequency response the direct search provides no preferences.
Keywords: :transfer function, band pass filter, approximation, Pareto optimality, heuristic algorithm.
OPTIMAL DESING OF THE EXPERIMENT WITH THE ACTIVE IDENTIFICATION OF FUZZY LINEAR REGRESSION MODELS
The problem of constructing linear regression models with respect to parameters and factors for the case of sufficiently wide ranges of variable variation is considered. It is proposed to use fuzzy linear regression models to restore the dependencies. The problem of a priori optimal experiment planning for fuzzy linear regression model’s identification is considered. At the same time, the area of determining the acting factors is divided into 2-3 fuzzy partitions. This model representation provides the restoration of dependencies which differ in different parts of the region determination of the input variables. The problem of construction and optimal planning of the experiment is formulated. A numerical algorithm in the form of gradient descent is used to construct optimal plans. The effectiveness of the obtained solutions is controlled by the implementation of the necessary and sufficient conditions of optimality. The problem of constructing an optimal plan is considered for the case of one and two factors with the number of fuzzy partitions 2 and 3. The analysis of the characteristics of optimal plans depending on the width of the intersection zone of fuzzy partitions is carried out. It is noted that with a decrease in the zone of intersection of fuzzy partitions, the efficiency of optimal plans increases, which affects the reduction of the determinants of dispersion matrices and their trace. Other characteristic features of the synthesized-optimal plans are noted. The conclusion is made about the efficiency of active identification of fuzzy linear regression models.
Keywords: :fuzzy regression, membership function, optimal design of experiment, the criterion of optimality.
ACCOUNTING OF THE SET OF RANDOM FACTORS WHEN USING THE MINIMEX CRITERION IN THE PROBLEMS OF OBJECTS RECOGNITION
In modern pattern recognition systems, the source data is usually random values, and the results of statistical processing of such data can lead to significant recognition errors. This article discusses the possibility of taking into account the errors of the source data in the case of using the minimax criterion. It is assumed that the descriptions of objects are a priori probabilities of the appearance of objects and the conditional probability density distribution of feature values, the parametric form of which is known. To determine the estimates of the parametric model, taking into account the errors of the values of functions and arguments, the methods of confluent analysis were used, allowing one to obtain unbiased estimates of the parameters. It is shown that taking into account the errors of the parameters of conditional probability densities of the probability distribution leads to the need to take into account the error of the boundaries of the separation of classes and the need to correct the formulas for determining errors of the first and second kinds. The error of separation of the attribute space leads to the emergence of a zone of uncertainty, the width of which will depend on the errors of the parameters of conditional probability distribution densities. In the article, a method is proposed for estimating the boundaries of separation of a feature space for normally distributed conditional probability distribution densities, taking into account the errors of the source data, in which the errors of the parameters are determined based on the variances of parameter estimates. The developed approach can be used in the tasks of object recognition by a variety of random signs.
Keywords: : object recognition, random variables, minimax criterion, methods of confluent analysis, class separation boundary.
THE SIMULATION OF METAL-DIELECTRIC ANTENNA ON THE BASE OF COMBINED APPROACH
I. Y. Lvovich, A. P. Preobrazhenskiy, O. N. Choporov, E. Ruzhitsky
The structure of modern radio transmitting devices may include antennas formed of both metal and dielectric components-metal-dielectric antennas. They are compact enough and can be placed on various objects of equipment. The paper presents a simulation of a metal-dielectric antenna based on a combined approach. The scheme of antenna construction in different planes is given. The process of scattering of a plane electromagnetic wave on an antenna is considered. The combined algorithm including the method of the integral equation, parallel approach and genetic algorithm is developed. In this paper, the integral equation is used to determine the unknown surface electric currents on the antenna surface, it is solved on the basis of the method of moments. A parallel algorithm was used to speed up the calculations. The impedance matrix is represented as a block matrix. Each block has its own parallel stream. Taking into account the influence of a plane dielectric waveguide on the scattered field, a method associated with a generalized scattering matrix is used. To solve the problem of multi-alternative optimization associated with determining the linear dimensions of the antenna device at a given operating frequency of the antenna, a genetic algorithm is used. As a result, the dimensions of the designed antenna for the specified dimensions of its components are obtained.
Keywords: : antenna, integral equation, parallel approach, optimization, genetic algorithm.