### INFORMATICS AND INFORMATION PROCESSES

SETS OF QUINARY KASAMI-LIKE SEQUENCES FOR DIGITAL INFORMATION TRANSMISSION SYSTEMS
Victor G. Starodubtsev, Yan G. Morozov

637

For quinary basic M-sequences (MS) with the period N = 5S – 1 (S = 4, 6), sets of vectors of decimation indices IS,MK = (d1, d2, ..., dn) are presented, on the basis of which small sets of Kasami-like sequences (KLS) with the period N < 20 000 are formed in the finite fields GF(5S). It is shown that for values of S = 4, 6 the periodic cross-correlation function (PCCF) of a small set of KLS is four-level with a maximum value of the PCCF RmaxS,MK = (5S/2 + 1). The values of the volumes of small sets of quinary KLS are given.

EXPERIMENTAL STUDY OF CLUSTER PERFORMANCE WITH CONTAINER VIRTUALIZATION
Phung Van Quy , Bogatyrev Vladimir A

647

The intensity of query servicing during automatic division of computer system resources between active, i.e. currently used, containers is investigated experimentally. At the first stage of experiments, the formation and deployment of a service (web server) on a cluster is performed. At the second stage, a test program is launched with the results saved in a log file. Algorithms for conducting experiments at the first and second stages are proposed. The experiments are conducted in a laboratory environment of Proxmox cloud virtualization and Kubernetes cluster management tools. A program in the Python programming language is developed to automate the deployment and update of the service configuration on the Kubernetes cluster. The program uses the SCP and PARAMIKO libraries for remote deployment and update of the service. The influence of the distribution of limited system resource capabilities between active and deployed containers in the system (virtual machine) on the intensity of request servicing was revealed. The obtained results can be used in the development of an analytical model for servicing a system with container virtualization, including virtual cluster systems.

### SYSTEM ANALYSIS, CONTROL, AND INFORMATION PROCESSING

ANALYTICAL APPROACH TO THE STUDY OF HETEROGENEOUS MARKOV CHAINS WITH PIECEWISE
CONSTANT CHANGES IN TRANSITION PROBABILITIES
Alexey V. Zemskov

657

An analytical approach to the study of countable non-homogeneous Markov chains based on the z-transformation is proposed. Using two variants of the initial data for the transition probabilities of a Markov chain as an example, it is shown that estimates of the steady-state mode can significantly distort the understanding of the system behavior. Analytical procedures for obtaining probability functions for real and complex-conjugate eigenvalues of the transition probability matrix are described for the case when its elements change abruptly. Estimates are given for the boundaries of the onset of a steady-state mode in the clock time. The main calculations are illustrated by an assessment of the characteristics of Markov chains taking into account the influence of transition dynamics under variance of the state probabilities and the piecewise constant change in transition probabilities over the operating interval in clock time.

METHOD OF ESTIMATION OF PARAMETERS OF LINEAR REGRESSION MODEL
WITH LINEARLY DEPENDENT ELEMENTS
Alexey O. Ovcharov, Vedyakov Alexei A.

670

The problem of online estimation of parameters of linear regression models in the presence of linearly dependent elements in the regressor is considered. To solve the problem, a method is proposed that allows estimating the parameters corresponding to independent elements of the regressor. The method includes two stages. At the first stage, the original regression model with unknown vector parameters is transformed into a model with a new unknown vector method. Thus, the problem of measuring parameters leads to the problem of synthesizing an observer. At the second stage, an adaptive observer of the new vector of variables is synthesized, which allows simultaneously estimating the desired vector of parameters.

### NAVIGATIONAL INSTRUMENTS

APPLICATION OF CROSS-LINKED POSITIONAL CORRECTION IN A STRAPDOWN ORIENTATION SYSTEM
Valery V. Aleshkin, Roman A. Zdrazhevsky, Yurу M. Efremov, Sergeу A. Skibin

678

The quaternionic equations describing operation of strapdown inertial orientation system (BISO) consisting of an inertial measurement module (IMU) and an on-board computer, are considered. The IMU contains a three-component angular velocity meter, a linear acceleration sensor and a magnetometer. The aim of the work construction of a system of kinematic equations with asymptotically stable solutions configured for the Shuler period and a low-pass filter with a given bandwidth. This ensures compensation for errors in the initial exposure, tolerance to linear accelerations (ballistic errors), reduction of the noise level in the estimates of orientation parameters in relation to the signals of gyroscopes, accelerometers, and magnetometers and the absence of accumulation of orientation determination errors. The BISO algorithms are based on the Poisson equations in the Rodrigue-Hamilton parameters with additionally introduced terms of cross-positional correction, the signs of which are set based on the requirement of asymptotic stability, while the numerical values of the correction coefficients provide the remaining properties of the algorithms. The range of angular velocities of an object at which the properties of the algorithms are preserved is theoretically substantiated. The results of the work are confirmed by mathematical modeling of the work of the IMU and BISO and full-scale tests of a BISO model with a micromechanical IMU on a vehicle

### OPTICAL AND OPTO-ELECTRONIC INSTRUMENTS AND SYSTEMS

DETERMINING THE WAVELENGTH OF RADIATION IN AN OPTICAL FIBER
Andrej O. Zenevich, Evgeny V. Novikov, Tatiana A. Matkovskaia, Andreу V. Shvakov

689

Optical fibers are the basis of data transmission systems. However, during operation, the optical cable may be damaged, and to eliminate the damage that has occurred in the field, it is necessary to know the wavelength of optical radiation in this fiber and the radiation power for each of the wavelengths used. This determines the relevance of developing a method for recording the wavelength of radiation at the output of an optical fiber that is accessible for use in field conditions, without the use of complex and expensive equipment. A method for determining the wavelength of optical radiation propagating through an optical fiber based on the use of the fiber macrobending is proposed. An experimental setup for implementing the method is developed. It is shown that this method can be used for both singlemode and multimode optical fibers. It is established that for all the studied optical fibers, the deviation of the power values determined using the method from the real ones does not exceed 12.5 %. The results of the work can be used in fiberoptic communication systems to determine the wavelength and power of radiation propagating through an optical cable.

USING COUPLED MODE THEORY TO MODEL INTERMODE COUPLINGS IN CURVED WAVEGUIDES BASED ON THIN-FILM LITHIUM NIOBATE
Dmitry N. Moskalev , Eugene D. Voblikov, Viktor V. Krishtop, Vitaly A. Maksimenko, Anatoly B. Volyntsev

697

Thin-film lithium niobate, due to its unique properties and the possibility of manufacturing high-contrast waveguides based on it, is a promising material for the production of high-speed photonic integrated circuits with a large number of elements per chip. However, the process of designing and modeling elements of such circuits on thin-film lithium niobate is complicated by the presence of anisotropy. For example, on the X-cut of lithium niobate, the influence of anisotropy will manifest itself in a change in the mode propagation constant, as well as in the transfer of power between modes during the propagation of radiation in the plane of the plate. The coupling between fundamental TE and TM modes in curved single-mode waveguides on the X-cut of thin-film lithium niobate is considered. The intermode coupling is analyzed using the coupled-mode theory. The coupling coefficient is calculated using the formulas corresponding to the cases of arbitrary and small anisotropy. It is shown that if only the influence of the crystal anisotropy is considered, then the calculation of the coupling coefficients using the formulas for arbitrary and small anisotropy gives similar results. The volume of the transferred power between the fundamental TE and TM modes is determined by solving the coupled-mode equations taking into account the radius of curvature, the angle of rotation of the waveguide, and the coupling coefficient.

713

The influence of the reflectivity of objects on the accuracy of constructing a normalized depth map of space using an active-pulse television measuring system is considered. Brief information about the system, its structure, principles of measuring range and constructing depth maps with its help is given. Eight video files obtained as a result of experimental studies in a large aerosol chamber using an active-pulse television measuring system in the multi-zone range measurement mode and multi-zone range measurement with modulation are taken as material for the study. A method for subtracting coefficients is proposed, which ensures the elimination of the discrepancy in the relative brightness values on the normalized depth map between dark and light objects located at the same distance from the system. The method is experimentally tested. A comparison of the proposed method and the method of subtracting a dark frame is performed according to the criterion of minimizing the root-mean-square deviation of the depth measurement between dark and light objects. As a result of applying both methods, the mean square deviation was reduced by 1.3 to 20 times, depending on the minimization method and the range measurement method used in the system. The coefficient subtraction method can only be used in post-processing, but it shows better results than the dark frame subtraction method, which can be used in real time.

### METHODS AND INSTRUMENTS FOR ANALYSIS AND MONITORING OF THE NATURAL ENVIRONMENT, SUBSTANCES, MATERIALS AND PRODUCTS

STUDY OF THE DYNAMIC SURFACE OF AN AIRCRAFT BY THE INTERFERENCE METHOD
Majorov Evgeniy E., Gennady A. Kostin, Viktor V. Kurlov, Nikolay E. Baranov

722

The surfaces of the fin fragments of the Airbus A 320, Boeing 737-700 and Tu-214 are investigated using the interference method. The functional diagram of the measuring setup is given. The images of the surface microrelief are obtained and the distances to the surface are measured during its linear movement along the 0X axis relative to the optical pupil with a step of 100 μm, 20 measurements are performed at each point.