
Main / Aleksei Vladimirovich Golubkov
Author: "Aleksei Vladimirovich Golubkov"
Aleksei Vladimirovich Golubkov, graduated from Ilya Ulyanov State Pedagogical University with the Master’s degree in the Methodology of Mathematical Education; Postgraduate Student at the Department of Higher Mathematics of the Faculty of Physics, Mathematics, and Technology Education of Ilya Ulyanov State Pedagogical University; an author of articles and certificates of software registration in the field of mathematical modeling and software engineering. email: kr8589@gmail.comA.V. Golubkov 

On algorithm for detecting changes in the object motion mode
The article deals with the solution to the problem of determining the motion mode of an object along a complex trajectory. A hybrid stochastic model is used to describe a complex trajectory. The solution of the problem is based on the application of a sequential decision rule about the choice at an unknown time of the hypothesis about the current mode of motion, with a limited size of the bank of competing Kalman filters. An algorithm is constructed for calculating the average size of the Kalman filter bank in the case of Mpossible motion modes. The algorithm is developed in a general form, therefore, it can be used not only for the four types of object motion models considered in this paper, but also for any linear discretetime models with Gaussian noise presented by equations in the state space. The algorithm for a priori estimation of the average size of a bank of competing Kalman filters for Mpossible modes of motion is implemented in MATLAB, the results of computer simulation are presented.
Stochastic discrete linear systems, hybrid stochastic model, Kalman filter bank, sequential decision rule.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksei Vladimirovich Golubkov, graduated from Ilya Ulyanov State Pedagogical University with the Master’s degree in the methodology of mathematical education; Postgraduate Student at the Department of Higher Mathematics of the Faculty of Physics, Mathematics, and Technology Education of UlSPU; an author of articles and certificates of software registration in the field of mathematical modeling and software engineering. email: kr8589@gmail.comA.V. Golubkov


A solution to the problem of the detection of changes in object motion mode with a limited size of the kalman filters bank
The paper presents a solution to the problem of detecting the changes in motion mode of an object along a complex trajectory. It is assumed that a complex trajectory can be presented by a sequence of pieces of finite length, at each of which the object moves uniformly and on a straight line, or makes a circular motion when turning to the right or to the left with constant velocity. To simulate a complex trajectory, a hybrid stochastic model is used. The task is to detect the change in the motion mode as soon as possible in order to calculate the optimal estimates of the object’s motion parameters in real time. The solution to the problem is based on a sequential decision rule about choosing the current motion mode at an unknown time instant, with a limited size of the bank of competitive Kalman filters. The algorithm for a priori estimate calculation of the size of the competitive filters bank is implemented in MATLAB, numerical experiments are carried out. The developed algorithm for estimating the size of the Kalman filter bank is used to solve the problem of early detection of changes in the motion mode of an object along a complex trajectory.
Stochastic discrete linear systems, hybrid stochastic model, a bank of Kalman filters, sequential decision making rule.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Andrei Vladimirovich Tsyganov, Ulyanovsk State Pedagogical University named after I.N. Ulyanov, Candidate of Physics and Mathematics, Associate Professor at Ulyanovsk State Pedagogical University named after I.N. Ulyanov; an author of papers, monographs, and textbooks; holds State Registration Certificates of computer programs; interested in metaheuristic and hybrid algorithms of stochastic and discrete minimization. [email: andrew.tsyganov@gmail.com]A. Tsyganov, Innokentiy Vasilyevich Semushin, Ulyanovsk State University, Doctor of Science in Engineering, Professor of Information Technologies Department at Ulyanovsk State University; an author of papers, monographs, and textbooks; holds patents for inventions; interested in filtering and control under uncertainty. [email: kentvsem@yandex.ru]I. Semushin, Iuliia Vladimirovna Tsyganova, Ulyanovsk State University, Candidate of Physics and Mathematics, Associate Professor of the Information Technologies Department at Ulyanovsk State University; an author of papers, a monograph, and textbooks; holds State Registration Certificates of computer programs; interested in parameter identification, adaptive filtering, and numerically efficient algorithms for stochastic systems. [email: tsyganovajv@gmail.com]I. Tsyganova, Aleksei Vladimirovich Golubkov, Ulyanovsk State Pedagogical University named after I.N. Ulyanov, Candidate for the Master’s Degree of Ulyanovsk State Pedagogical University named after I.N. Ulyanov; an author of papers; holds State Registration Certificates of computer programs; interested in mathematical modelling and programming. [email: kr8589@gmail.com]A. Golubkov, Stanislav Dmitriievich Vinokurov, Ulyanovsk State Pedagogical University named after I.N. Ulyanov, Postgraduate Student at Ulyanovsk State Pedagogical University named after I.N. Ulyanov; an author of papers; holds State Registration Certificates of computer programs; interested in mathematical modelling and programming. [email: phoenixdragonvista@ya.ru]S. Vinokurov


Metaheuristic Algorithms in the Issue of Identification of the Moving Object Mathematical Model Parameters
The article considers issues on the calculation of an aircraft range capability on the basis of tactical radius data within different altitude and speed ranges. In some cases, it is necessary to calculate the enemy’s aircraft range capability. As a rule, such calculations do not have any documents, parameters (fuel flow rate and consumption per kilometre), and methodologies for fuel consumption calculation. Usually, open information sources also do not have any information about the enemy’s aircraft flight distance and time. Due to this fact, the need in indirect and approximate estimation of the enemy’s aircraft range capability with the use of information from public and common data is driven. Information about tactical radiuses within the enemy’s aircraft different altitude and speed ranges is the example of such public data. The proposed methodology for calculation of the enemy’s aircraft range capability allows to estimate the enemy’s capabilities in target attacks with 10% ratio error and can be used in combat management systems of surface ships and shorebased complexes. The methodology is also of great interest for operational and approximate estimation of own forces capabilities in case of the operational loading choice. More accurate calculations should be carries out on the basis of manuals on flight operation and time if such opportunity exists.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
