2017. № 96
Mechanics  
Deformable body mechanics  
Polymer composite materials are applied in a wide range of aviation and space technology products. A lot of such products’ components are curvilinear beams that work on bending. However, in connection with pronounced property anisotropy, composed materials’ behavior in such components differs significantly fr om metals. While developing design technique, information is required on material’s working in these or that conditions. For this purpose, samples with shapes close to typical structural elements are tested, in which course the stresseddeformed state of these elements is studied. Classical tensile, compression and shear tests cannot fully demonstrate the behavior of multilayered composite materials. Bending tests can provide additional information that fully describes the behavior of the material. ASTM D6415 Standard describes the samples testing of a typical structural element. The radial stresses in the sample are determined at the end of the test. Based on the experimental data listed in the ASTM Standards, a conclusion can be made that the destruction occurs in the curved zone of the sample due to delamination. While composite structures designing, the interlaminar stresses should be taken into account, since the contact zone between the layers has a low strength and destruction can be caused by the delamination of the material. Thus, determination of internal stresses caused by interlaminar interactions during stretching and compression of layers is an important task. The model determining the stress state in a layered curvilinear composite beam is suggested. The model correctness is verified by comparing the calculated stress values and the results obtained by finite element modeling. It is shown that the discrepancy between the results does not exceed 5%. Calculations for curvilinear beams with cylindrical anisotropy of properties and for layered beams were performed. It is shown that maximum stress values are determined by the bending moment and geometric parameters of the beam. The most effective stress reduction can be achieved by reducing the curvature of the laminated beam. It was determined that the central part of a composite beam, wh ere delamination is most possible, was the most dangerous zone. Optimum relationship of the beam’ material strength in circumferential and radial directions was determined. Recommendations to increase the bearing capacity of curved beams were elaborated. Keywords: bending, polymeric composite material, stresseddeformed state, curvilinear beam 

Fluid, gas and plasma mechanics  
The problem of evaluating maximum possible changes in the position of the pressure center at small angles of attack and specified constrains on surface distortions of hypersonic vehicles in the form of sharp cones with smallparameter linearization is reduced to the math problem of a linear functional norm. The developed integral expression of linear functional, evaluating changes in the position of the pressure center for the shape variations is based on a semianalytic method of differential locality hypothesis. The general integral expression of the preset functional norm in linear space of weak surface variations for the specified restrictive function is developed.
The validity of the developed analytical expressions being strictly in the class of sharp cones is confirmed by analyzing test examples for two possible types of linear surface variations and their linear combination. The first variation is related to a linear scale and the second one relates to a cone angle. The compliance of numerical results of analytical estimates of δx_{ƒ} to the exact result is taken as a criterion. The validity of the obtained analytical results for bodies close to a sharp cone shape is estimated by comparing with the results of numerical computations based on the solutions of inviscid Euler equations for models of perfect gas or equilibrium and dissociating air.
It is shown that the first variation of the sharp cone pressure center δx_{ƒ}
at the specified weak variation of its surface under supersonic and hypersonic flows at small angles of attack depends only on two dimensionless parameters: a cone angle θ_{k}
and relation of derivatives of its surface pressure coefficient. The integral dependence of the first variation norm δx_{ƒ} for a sharp cone on the surface variation δy(x) and the above parameters is developed. The integral dependence of the first variation norm δx_{ƒ} for a sharp cone is developed at the specified restrictive norming function ψ(x) for a set of admissible variations of the cone surface δy(x), which allows of estimating a scale of probable variations δx_{ƒ}
in indefinitetype conditions δy(x). The method to determine qualitative variation of the sharp cone surface, which is close to maximum possible variation δx_{ƒ} at the specified variation constrains δy(x), is pointed out.
Keywords: hypersonic vehicle, rotary body, sharp cone, small angles of attack, weak surface variations, pressure center 

Dynamics, strength of machines, instruments and equipment  
For the last years, energy efficiency is one of the main and important issues in developing fluid power technology. The discrete method of regulation is of particular interest while the development of such systems, in which the fluid stream is alternately supplied to the hydraulic drive actuator. For this purpose, discrete action valves are used. They are relatively simple, reliable, insensitive to contamination, and possess low cost. The paper presents the mathematical model of the hydraulic drive for loads lifting, containing discrete valve and switched inertia tube. Employing a switched inertia device (inertia tube and discrete valve) in the hydraulic drive system allows increase efficiency of such system by 2030% due to the inflow of additional liquid from the lowpressure line (socalled flow amplifier mode). As a result of dynamic processes simulation in MATLAB/Simulink package, transients occurring while hydraulic drive operation were calculated. The article analyzes the effect of the following parameters on the hydraulic drive efficiency: the discrete valve operation frequency in the pressure line, the pulse duty cycle, the diameter and length of the inertia tube. Regulation quality estimation is given in the movement of the output link of the hydraulic drive with a cargo on the set trajectory. It was established that for the hydraulic drive with the pressure in the pressure line of 15 MPa and a weight of the cargo up to 1000 kg, the use of a hydraulic drive scheme with discrete valve and switched inertia tube allows increase its efficiency by 17% compared to the throttle control. The recommended parameters for such system configuration are as follows: the discrete valve operating frequency is 40 Hz, the pulse duty cycle is 30 to 50%, the inertial tube diameter is 10 mm, its length is no more than 10 m. The diameter of the discrete valve hole in the pressure line should be sel ected fr om conditions for ensuring the required speed of the output link. The disadvantage is acoustic noise while using a switched inertia device. It is necessary to use a pulsation damper to eliminate it. The obtained results can be useful for selecting hydraulic drive schemes with a higher coefficient of energy efficiency. Keywords: discrete hydraulic drive, electrohydraulic valve, pulse ratio, duty cycle, inertia tube, mathematical model, efficiency 

Aeronautical and SpaceRocket Engineering  
Design, construction and manufacturing of flying vehicles  
The article analyzes virtues and shortcomings of the twinfuselage aircraft configuration as applied to a passenger and cargo aircraft. It notes specifics of aerodynamic and weight perfection of the twinfuselage aircraft. The peculiarities of aerodynamics and weight perfection of the twinfuselage aircraft are noted. The article also reveals the differences between twinfuselage aircraft configuration and the aircraft of traditional schemes. The main ones are the as follows. The aircraft increase of the moment of inertia relative to the longitudinal axis complicates the compliance with the Part 25 airworthiness for recovering the aircraft from a turn with the tilt of 30° and entering it into a turn of the opposite direction with the tilt of 30° within no more than 7 seconds. The emergence of specific natural modes of aircraft oscillations with the rotation of the fuselages in pitch plane with opposite phase. The advantages of unswept central part of the wing are asserted. Attention is drawn to the increase of the aircraft pivoting radius on the ground and the complication of aircraft control when the pilot’s line of vision is shifted from the axis of the runway. As twinfuselage aircraft configuration has no advantages over traditional aircraft configuration, its use is advisable only for solution of specific problems. For example, developing a passenger aircraft with a passenger capacity exceeding 500 seats, or a multifunctional heavy transport aircraft for the cargo placing in two fuselages, as well as a hard cargo on the external sling between the fuselages. Existence of the fuselage of certified donor aircraft will provide technical and economic efficiency of the twinfuselage aircraft. Keywords: aircraft layout diagram, doubledeck fuselage, twinfuselage aircraft configuration, airplane controllability, natural oscillations waveforms and frequencies, aircraft pivoting on the ground, technical perfection 

With significant increase of satellite structural components size specifics of their relative position adjustment occur, associated with singular masses separate by a certain distance and structural elements coupling them. All structural components are affected by various space factors, including temperature impact, which leads to satellite structure optimal geometric disposition changing due to deformations. The author suggests employing the sixdegreeoffreedom adjustment actuator to ensure fine adjustment. To control the adjustment device movement the author suggests the methodology based on implementation of measuring machine, three measuring spheres and an algorithm for measurement results processing. Contacting the spheres in at least four points, the measuring machine computes the coordinates of the position of each sphere’s center, which defines the spatial position of the adjustment device upper base. Data spheres’ centers position control is performed at the initial position (prior to spacial movement performing) and end position (after spacial movement performing). Position determining technique consists in the following. Using the obtained coordinates, we determine the values of the three linear and three angular movements of the plane, formed by the centers of the three spheres. To determine the movemeents one should compute coefficients of coordinates’ transformation matrix for the displacement from the initial position to the end position. Analyzing theoretical (defined by control block) and actual (computed from coordinate measuring device data) values of the adjustment actuator spatial movement allows evaluate transmission errors for every degreeoffreedom. Specified errors led to satellite structural components relative offset in an area, which depends on their distance from each other. The proposed final adjustment methodology of structural elements and mechanical devices allows account for interaction of separate actuators in adjustment devise and structure of satellite geometry changing to achieve the specified parameters during ground experimental tests and onorbit satellite functioning. Keywords: satellite, fine adjustment mechanism, reference point, six degreeoffreedom actuator 

Thermal engines, electric propulsion and power plants for flying vehicles  
There is an increasing need for low Earth orbiting satellites for various purposes. Such satellites are cheaper to put into orbit (for altitudes 160−300 km), and can ensure highresolution for Earth observation. However, lowering orbit altitude means that atmosphere gases concentration and the aerodynamic drag force increase causing decrease in the spacecraft orbit lifetime. Electric propulsion thrusters could be used to counteract the aerodynamic drag. For example, the European Space Agency spacecraft GOCE operating in a nearcircular orbit with altitudes of 250−280 km for more than four years used the ion thruster T5 of QinetiQ Company for aerodynamic drag compensation. This thruster used onboard xenon as propellant. When the whole amount of propellant was consumed, the vehicle began lowering and burnt in atmosphere. Application of atmosphere gases as propellant may substantially increase lifetime of low orbit spacecraft. This work focuses on the operation of highfrequency ion thrusters operating with atmosphere gases as propellant. Such thrusters may be used to counteract the aerodynamic drag of low Earth orbit spacecraft. Work processes in the ionization chamber of ion thruster were modeled. A mixture of atomic and molecular nitrogen and oxygen was considered as a propellant. During ionization each of these gases partially transforms in singly charged ions. The thruster characteristics, namely its thrust and consumed power were analyzed and compared to characteristics of the spacecraft from the viewpoint of its aerodynamic drag and solar panels power. The results of this work demonstrate the possibility of creation a low orbit spacecraft with highfrequency ion thruster operating with atmosphere gases as propellant to counteract the aerodynamic drag. Keywords: low Earth orbit spacecraft, aerodynamic braking, highfrequency ion thruster 

The article is devoted to the analysis of changes in characteristics of smallsized gas turbine engines with a twostage axialcentrifugal compressor instead of a singlestage centrifugal compressor, and analysis of the current level of cycle parameters of smallsized gas turbine engines. The work was performed by mathematical modeling, using empirical data. Initial stage of the work revealed that even a slight improvement of modern smallsized engines cycle parameters would lead to a significant improvement in the main characteristics of the engine. Models were developed with average parameters in their class: air flow of 650 g/s, gas temperature of 1100 °K. A number of assumptions was made: the efficiency was fixed for all units, except the compressor at the operation level of design mode; generalized characteristics of highspeed turbocharges and characteristics of singlerotor singleloop singlecascade jet engine compressors were adopted as the characteristics of compressors. For a singlestage centrifugal compressor, the compression ratio in the rated mode was adopted as 4 at the level of the leading serial analogues, and for an axialcentrifugal as 5.7. Analysis of the obtained altitudeairspeed performance revealed that by employing an axialcentrifugal compressor instead of a centrifugal one we can expect improvements of the main parameters (internal thrust, specific thrust, specific fuel consumption) of the engine up to 10−15% in the entire range of airspeeds and altitudes. Particularly, in the basic modes of flight of an unmanned aerial vehicle equipped with a similar engine, i. e. cruising (M = 0.8, H = 8000 m) and takeoff (M = 0, H = 0m), thrust grew by 8%, and fuel consumption reduced by 12%. This result allows concluding that it is reasonable to use a constructive scheme of a smallsized engine with a twostage axialcentrifugal compressor while developing new engines. Keywords: jet engine, compressor, smallsized 

Ground complexes, launching equipment, flying vehicle operation  
The article presents a mathematical model of a twolink object movement on the dirt road with periodic unevenness. This model may be useful for the suspension system development at the initial design stages. Mathematical models are presented for different viscoelastic characteristics of the coupling device. It studies the smoothness of the unit in resonant modes of motion of a twounit tractor. The study of smoothness is based on the intensity curves, which are constructed using the amplitudefrequency characteristics. These characteristics were obtained from the solving the systems of differential equations by analytical matching method or numerical RungeKutta method. Matching method is very effective for dynamic systems studying if a differential equation does not exceed the sixth order. It is an organic combination of operator method and the method of variation of constants. Operator method allows construct the equation authorization for the original system of differential equations, and find coefficients of dissipation and frequency of free oscillations of the system under study. As for the method of variation of constants based on the solutions obtained by the operator method, it allows determine a particular solution of the original system of differential equations in the form convenient for analysis. The obtained results can be applied to groundcar mobile and crawler units, a well as aircraft while studying its landing or emergency landing. According to the obtained results the authors concluded that the improvement of the smoothness of a twounit tractor when driving on dirt soil with periodic unevenness requires modification of the viscoelastic characteristics of the hitch mechanism, which, in its turn, alter geometric and weight parameters of the tractor. Keywords: twolink caterpillar tractor physical model, twolink caterpillar tractor design scheme, mathematical model, system of differential equations, smoothness of movement, dirt road periodic unevenness, hitch mechanism 

Dynamics, ballistics, movement control of flying vehicles  
A lot of tasks of unmanned aviation on observation of the objects, in the most general set up is reduced to route selection between the two benchmarks, which lead to mathematical problem of optimization on the graph. It is assumed herewith that the route is closed and passes through all ribs of the graph. The optimization task on the graph meant for calculating the set of closed routes of minimal length relates to the integer programming problem [1]. The goal of the work consists in solving the optimization problem on the graph leading to obtaining optimal closed routes (OCR). The authors suggest genetic algorithm (GA) as an optimization method. For its implementation the objective function of sevral variables was developed, which simplified significantly the program code and reduced the computation time. The objective function represents the sum of three functions. The first function depends on the edges of the graph, and penalizes edges and loops which do not belong to the graph. The second function depends on the Euler model of the original graph, i. e. the method of the graph reduction to the Euler type by adding multiple edges. The third addend depends on the vertices of the graph and accounts for their multiplicity. The minimum of the objective function is achieved on OCR only. The GA application allows obtain limited quantity of OCRs from a large variety of variants during finite time, which can be reproduced several times by using the group of the graph’s automorphisms. The presence of the OCRs variety allows planning the order of graphs flyoffs afield while solo and group flights, promptly regroup monitoring routes in consecutive and dispersed flight over various ribs and without intersection at vertices. Keywords: graph, reference point, optimal closed routes, automorphism, objective function, genetic algorithm 

The subject of this study is the problem of Venusian analoguesgroups simulation, which arises anew while planning the future spacecraft expeditions to new areas of Venus. Here, under the analogssoils, we imply mathematical models or purposefully made in terrestrial conditions artificial physical models of soils to substitute natural soils of Venus. These analogssoils are employed for landing dynamics calculation and testing of a spacecraft landing on soil. The goal of this work consists in analyzing the problems while developing new analogues and the experience of employing analogssoils in JSC “NGO Lavochkin” during the bygone Soviet spacecraft “Venus 914” and “Vega 12” development. At present, planetologists еtake interest in studying new areas of Venus, where tectonic processes occurred earlier. They expect to bump into ancient rock yield of the planet in these areas, which wlould help to elucidate the history of Venus evolution. On June 15 1985 the Vega2 spacecraft landing had completed a fifteenyear series of successful landings of ten Soviet spacecraft on the surface of Venus. Structurally, the landing mechanism was attached to a cushioning toroidal shell, which was deformed and absorbed the kinetic energy of the spacecraft, while hitting the surface. Analysis of radar images of the Venusian surface revealed that all Soviet spacecraft landed in the areas with predomination plain types of Venusian terrain. The terrain relief of this area differs from the one, with the new landing areas. The area with the new landing areas was called “tesserae”, which in Greek means “tile”. The “tessera” relief represents an aggregate of intersecting ridges and furrows, the ridges’ height herewith can reach up to 1–2 km, the ledges – up to 1 km, while slope angles of the surface can reach up to 30 degrees. The spacecraft landing practice was performed at the JSC “NPO Lavochkin” on both physical and mathematical test benches. The article lists the objectives of physical tests. Models of deformable and nondeformable soils were employed for landing practice. The article presents the description of the physical test bench, which was employed for developing mathematical model of a spacecraft penetration into deformable Venusian soil. It also presents the description of mathematical models of landing on various models of soil. The work lists the sequence of models simulating the spacecraft hit with the soil. These models are listed by the degree of their complication – from a flat impact on an nondeformed flat surface to a spatial impact on an elasticviscousplastic medium with a complex relief. Finally, the article drew conclusions that two most common basic problems exist for soilanalogue: – Selection of hypothetical soil of Venus in the “tesserae” area; – Selection of Earth soilanalogue, corresponding to the hypothetical Venusian soil. The relief in new regions of Venus is much more complicated than the terrain in which Soviet vehicles landed, so these problems are of particular importance for the safe landing of spacecraft. Keywords: landing on Venus, landing on soil, soilanalogues, test bench, landing simulation 

The existence of a steady and rapidly growing demand for remote probing data (RPD) stimulates organizations operating the domestic spacecraft grouping (RPD) and ground infrastructure to seek the ways to improve the system’s efficiency. Presently, the topical problem consists in the lack of multiobjective planning of intended use of aggregate information resource of diversified orbital grouping, insufficient level of automation, the lack of means for feasibility calculation of consumers’ applications, insufficient operative planning horizon, which does not allow rational employing of a spacecraft technical capabilities. The article considers the issues associated with formalization of uptodate task of target grouping operations planning for various types of remote probing spacecraft and development of a set of interrelated mathematical models necessary for specialized software developing that allows create optimal control programs for surveying in a realistic situation at a given planning interval. An approach to the solution of the planning problem for a spacecraft group of the one type is proposed. The initial set of surveying objects is being divided into subsets according to the type of shooting equipment specified in the consumer’s application, and by the geometric parameters of the survey areas. Models for changing the occupied volume of the onboard storing device and changing the orientation of the line of sight of the camera are presented in the form of discrete equations of state. The basic formulas necessary for determining the moments of possible shooting of point and area objects, determining the boundaries of possible radio communication intervals with ground receiving points of information, checking the conditions of shooting by illumination and the amount of clouds over the survey area are presented. A technique for calculating the area captured in a single survey of a specific spacecraft and the area captured by a spacecraft group in the planning interval is described. As a model of the plan, a pair of interrelated programs is considered: a time sequence of switching on and off the survey and radio transmitting equipment of the spacecraft of the group and a piecewise linear program for reorienting the line of sight of the camera. A criterion for the effectiveness of the plan is introduced in the form of a linear convolution of the normalized information efficiency and the relative costs of the onboard resource of a group of similar spacecraft. The solution of the task of planning the target functioning of a grouping of diverse types of spacecraft is reduced to the sequential solution of planning problems for groups of the same type of spacecraft that are part of the initial grouping. Keywords: earth operative monitoring, operational planning of survey, distribution of space vehicles’ information resources, optimization, efficiency 

The article analyzes an applied problem of area monitoring with a quadrotor group. The problem solves in two stages. At the first stage, the problem of searching an optimal route for each quadrotor is solving. This problem is the problem for travelling salesman group in 3D space, and related to the class of computation tasks of NPdifficulty. Variation genetic algorithm is applicable for such task solving. This genetic algorithm employs the principle small variations of basic solution. All genetic operations perform on the sets of basic solution variations. The rate of convergence of the genetic algorithm depends on the obtained basic solution. At the second stage, the problem of synthesis of quadrotors control to ensure their movement along the routs obtained at the first stage is solving. To solve the problem synthesis of control the numerical symbolic regression method was employed, i. e. method of variation analytical programming, which allows finding mathematical expression for a control function. The arguments of this function are contained in the quadrotor state vector. The control function ensures an optimal mode of quadrotor stability relative to the point in state space. An example of control problem solution for two quadrotors group is presented. Keywords: control system synthesis, method of variation analytical programming, a flying robot, routing task for group of quadrotors 

In this article servocontrol means the principle when control levers are coupled with their control tabs rather than main control surfaces. Control tab is a small surface located in control surface tail section. Its deflection causes the hinge moment occurrence, which moves the control surface. The purpose of the emergency servocontrol consists in ensuring redundancy of a mixed flight control system. The study was conducted for regional aircraft with two independent hydraulic systems and two elevators for longitudinal adjustment and control. Two conventional electrohydraulic servoactuators (EHSA) provide each elevator deflection in the main control mode. Each elevator has a control tab with electromechanical actuator (EMA) for emergency control in case of both hydraulic systems failure, when all the EHSAs switch to damping mode. The estimated value of control tab’s own hinge moment is significantly less than elevator’s hinge moment. Such smallsized EMA of low weight could be used to control tab deflection. The description of elevator deflection dynamics includes the nonlinear dependencies of both elevator’s and control tab’s hinge moments, damping force caused by EHSAs in damping mode, and elevator aerodynamic damping. After the loss of hydraulic power, the elevators move under the hinge moment. It could result inthe exceeding the operational values of angle of attack or normal gfactor of the aircraft. For smooth and safe transition between control modes, the control tabs in main mode should be controlled so as the elevator hinge moment close to zero. Furthermore, such deflection of control tabs allows reduce the EHSAs load during the flight. The handling quality of an aircraft being in servocontrol mode depends on a considerable degree on the actuator damping coefficient. In the course of the study the acceptable range of actuator damping coefficient values necessary to provide the required handling qualities in emergency control mode has been determined. Flight simulator study with test pilots involved proved that aircraft handling qualities in servocontrol mode ensured the safe flight continuation and landing. Keywords: longitudinal control channel, control tab, hinge moment, actuator damping coefficient 

Instrument making, metrology, information and measuring equipment and systems  
Instruments and control methods of environment, substances, materials and products  
The paper presents the results of application of multispectral images obtained from OrbView2 and Envisat missions to monitoring of vegetation activity annual dynamics at 12 test sites in VolgaAkhtuba floodplain based on conventional FAPAR index over a decade since 1997, including drought summer season of 2006, as a part of a project conducted by N.N. Zubov State Oceanographic Institute for monitoring of Lower Volga. The territory under consideration extends over 9000 square kilometers, thus making the use of satellite imagery to be the only source of assessing the overall ecosystem state. Time series of FAPAR values for regular (non anomalous) years are being approximated by a single harmonic model function. This function then serves as a reference to analyze deviations of particular FAPAR values from it. To introduce stronger physical relation between reference model function and parameters of the environment we consider using public annual temperature data from weather stations of World meteorological organization in addition to satellite images. The two models, one with temperature variations included and one without these, are then calibrated and compared against each other at all test sites. Mathematical and physical rationale for both types of models and some visual examples of their calibration are given. Our study concludes that despite of the fact that using the temperature data improves the accuracy of vegetation dynamics model, this effect does not prove to be significant, while yet increasing demands in the amount of input data for analysis. Quantitative statistical results support the case.
Keywords: vegetation activity, Earth remote sensing, multispectral imagery, FAPAR 

Radio engineering and communication  
Radio engineering, including TV systems and devices  
This paper is devoted to the issue of recognizing received encoded radio signal sequences. Traditionally, correlators or matched filters are used in communication systems to detect and process noiselike signals. These two models use a threshold detection parameter. The use of a neural network is proposed to improve the quality of signal recognition when the noise characteristics in an environment are unknown. The neural network is a nonlinear model with a relatively large number of parameters which tests proposed examples during the learning phase and attempts to reproduce the relationship between them using the responses. To use the neural network, it is necessary to reformulate the original issue in terms of optimization. That is, to enter a quality functional, which will be optimized, and choose a method of optimization for the given functionality. To select the neural network parameters that achieve the optimum of the quality functional, the back propagation algorithm will be used. The stochastic gradient descent algorithm determined by the quality functional will be used to calculate parameter updates of the neural network. For convenience, only digital signals will be considered in this paper. Nevertheless, the method described in this paper can be applied to a continuous signal. The digitizing of a continuous signal will transform the task into one of signal detecting, which has been formulated above. In each cycle of the receiver’s operation, a signal is generated at its input. The signal is a sequence of fixedlength and can either be similar to the protocoldefined signal, or be significantly different. Therefore, the task can be formulated as a task of binary classification of the received signal in each cycle of the receiver’s operation as a valid signal and noise. It is assumed that the quality of recognition will be better than with the traditional methods because, during training, the neural network is able to memorize the special features of the noise and, consequently, use the obtained model at the signal classification stage. A diagram for an experimental stand is also provided in this paper that would allow for the confirmation of this assumption.Keywords: neural network, signal processing, msequence, Barker's codes, correlator 

Antennas, SHFdevices and technologies  
The article analyzes the interaction of electromagnetic waves in radiopulse signals mode with the medium above hydrocarbon deposits. Tensor of the dielectric permittivity constant of an anisotropic medium over the deposit in the mode of radiopulse signals is derived by means of a quasihydrodynamic approach using multiparticle electronion currents. The study was carried out based on the solution of the electron motion equation. Hilbert transform was employed to find the envelope and instantaneous frequency of the two acting signals. The components of the medium’s dielectric permittivity constant above hydrocarbons were analyzed. Selection of the radiopulse signals’ frequencies was stipulated by determining characteristics of media over deposits at great depths compared to the earth surface. It is shown that the results of the study can be used to identify the environment over deposits by the nature and magnitude of the total and differential components of the dielectric permittivity constant of the anisotropic layer. The tensor of the dielectric constant of the anisotropic medium over the hydrocarbon deposit in the radiopulse signals mode can be used to determine the electrodynamic characteristics of the medium above the deposit in a wide range of probed signals’ frequencies, dielectric permittivity and conductivity of the media. The studies can be applied to determine characteristics of the medium over the deposit under the propagation of electromagnetic waves with right and lefthand circular polarizations, which increases the informative value of the methods of contouring and the hydrocarbon deposits allocation. The propagation of electromagnetic waves with lefthand polarization while changing the dielectric constant of the medium leads to the alteration in the combination component with a change in the sign of the differential component. Thus, it can be used to develop methods of electromagnetic exploration, search and identification of hydrocarbon deposits. Electromagnetic methods of hydrocarbon search and identification can be updated due to the received information on objects through not only one or two information channels but also using larger quantity of them, which enables their boundaries to be identified against the background of the underlying environment with a sufficiently high level of certainty. The results of the study can be applied in geophysics search. Keywords: radiopulse signal, anisotropic medium, hydrocarbon deposit, electromagnetic reconnaissance methods 

Systems, networks and telecommunication devices  
The article considers generation of msequences and Gold’s codes employed in spectrum spreading systems. The goal of the article consists in ensembles systematization and search for all pairs of polynomials, forming Gold’s codes. Gold’s codes have a low level of crosscorrelation between the sequences in the ensemble, which allows employ them for users’ separation in communication systems. Maximum number of users in the system depends on the number of sequences in the code ensemble. The classical method of esequences and Gold’s codes generation is representation of generator in the form of linearfeedback shift register (LFSR), since this approach ensures the simplicity of algorithm implementation to a digital unit. Employing the classical generation method (based on the generator representation in the form of LFSR) becomes nonoptimal while generating ensembles of long sequences (N > 2^{10} – 1). The generation time of all Gold’s code pairs grows significantly due to the number of all possible combinations increasing while sorting pairs of sequences. The Gold’s code generation method using the BerlekampMassey algorithm and decimations defined for the codes under consideration generation was selected. Based on this algorithm the authors developed the program for searching the preferable pairs returning the Gold’s code under addition modulo two. The main goal of the program is generation of all volume of the Gold’s code family. The obtained results were checked by evaluation of the value and number of crosscorrelation peaks of the two tested sequences. The obtained results can be implemented in the systems employing direct spectrum spreading, such as CDMA. The paper presents the number of binary polynomials and the list of the number of unique polynomial pairs for the code length up to m ≤ 16, forming Gold’s codes. The full list of primitive polynomials for the code length of N = 2^{10} – 1 is presented. The example of preferable pairs of primitive polynomials of mth degree (m = 5) is given. The number of pairs polynomials for generating Goldlike codes for the degrees of m = 8 and m = 12 of code seeds is given. The obtained results can be implemented while developing communication systems with users’ separation for obtaining overall Gold’s ensemble and studying the properties of the obtained sequences and their derivatives. Keywords: msequences, Gold’s codes, preferred pairs, decimation coefficients, binary polynomials, DSSS, linearfeedback shift register 

According to the «Digital Economy of Russian Federation» program, new requirements for wireless communication technologies, including technologies for remote sensing systems (RSS) are now being put forward. The share of Russian remote sensing data in the total amount of remote sensing data used in Russian geographic information systems will grow steadily and reach 90% by 2024 [1]. At the same time, it will be necessary to ensure complex implementation of the overall technical capabilities of the manifold of spacecraft and ground infrastructure in order to obtain the large amount of RSS data of the required quality [2]. The article considers technical characteristics of modern remote sensing spacecraft from the viewpoint of radio downlink organization. It presents the problem of the discrepancy between the current throughput rate of the satellite channel and the volume of transmitted information from the remote sensing. The existing radio RSS links keep on employing various frequency ranges depending on the requirements for the communication system. However, the Xband and Kband have the largest bandwidth for RS data transmission. It is shown that the standard transmission rates in the Xband are 150 Mbps and 300 Mbps employing standard modulation and coding methods, while maximum throughput rate of the satellite radio channel of some foreign satellite communication systems reaches 1 Gbps [3]. Future methods and modern trends for increasing throughput rate were determined based on the analysis of modern satellite transmitters for remote sensing systems: methods of modulation and error control coding in the Xband , as well as the possibility of transition to the Kband. The article shows that in practice the use of the Kband at the present time does not allow achieving the required advantage in radio link capacity. This, in particular, is caused by more stringent requirements for the implementation of onboard and groundbased equipment imposed on the transmitters in the Kband, as well as due to the higher losses in the propagation of radio waves in this range. As the main recommendations for the development of highspeed satellite radio links equipment, we should indicate implementation of modulation and coding schemes with high spectral efficiency, the use of several channels and the adaptability of the communication system. The authors propose a modulation scheme with high spectral efficiency [23] as well as the implementation of fourchannel transmitter scheme [24] allowing combine X and Kband transceivers to achieve larger total throughput rate of the radio link. Development prospects in this area should also include the development of an element base in the Kband of frequencies and an increase in the accuracy of antenna guidance for a polarization decoupling employing. Keywords: highspeed radio link, satellite radio link, remote Earth probing, throughput rate, signalcode sstructures 

Radiolocation and radio navigation  
One of the effective methods of noise immunity improving is implementation of integrated inertialsatellite systems. NAP GNSS with INS integration will allow eliminate the existing shortcomings of each system separately. Typically, integration involves the joint processing of pseudorange, pseudophase and pseudovelocities, obtained by the GNSS receiver, as well as vectors of angular velocities and accelerations derived with nonstationary Kalman filter, which will be called the Kalman filter type (KFT). Highly dynamic object is characterized by the presence of jerking while moving. The jerking is customarily understood as the discontinuous change of the third derivative of a coordinate with respect to time. To ensure this requirement it is necessary to employ navigation receiver with signal phase tracking system with the third order astatism. Employing a navigation receiver with conventional second order filter within the system of signal envelope tracking just enough for delay tracking. Since the exact model for integrating equations of orientation is based on the model proposed by Bartram, it complicates the use KFT, as it requires rather complex notation of derivatives in analytical form. The state vector of the filter should include accelerometers’ instrumental error, namely the rate of zero drift and scale factor error of each, which expands the state vector, and thus reduces the potential accuracy. Besides, the use of highspeed gyroscopes requires a priori orientation setting. In this regard, we suggest using no gyroscopes, positioning accelerometers to the phase center of navigation receiver antenna, and rotating herewith the frame with mounted antenna and accelerometers in a prescribed manner. It is necessary for orientation determining in the event of uniform movement of the object, i.e. when the measurement of the accelerometers is close to zero. Integration of these devices, each of which possesses the ability to determine positioning, gives the system a new feature, namely orientation determining. In this case, the KFT formingup with this type of integration does not cause mathematical difficulties, and adaptive KFT element in use allows tracking course maneuvers of the object, while frames rotation allows orientation estimating even with rectilinear and uniform motion of the frame’s center. Keywords: global navigation satellite system receiver, strapdown inertial navigation system, Kalman filter type, accelerometer 

A promising trend for improving organization and management of air traffic is the implementation of the concept of communications, navigation, surveillance and air traffic management, developed by the international civil aviation organization. This concept is based on the principles of broadcasting automatic dependent surveillance (ADSB), which is a digital system for airborne transmission of flight path parameters by data of the global navigation satellite system (GNSS). To solve the problems of highprecision positioning and of flight safety, a groundbased augmentation system is used. When controlling the flight path, the aircraft position relative to the ADSB ground station changes, thus affecting the Position Dilution of Precision (PDOP). In addition, when the distance from a local area augmentation system (LAAS) increases, the effect of decorrelation factors on the compensation of systematic errors increases as well. Keywords: global navigation satellite system, trajectory, multicriterion optimization, augmentation, area navigation, optimal control, Kalman filter 

Informatics, computation engineering and management  
System analysis, control and data processing  
Solving problems of the competitive analysis refers to the modern theory of decisionmaking. Decision makers should have necessary and sufficient information on new technologies in the industry, key competitors, potential risks, etc., as well as have time to process it and take optimal decisions. The goal of this work is developing of competitive analysis tools that is methodical, mathematical and software systems for supporting decisionmaking based on global competition modeling on the major stages of the life cycle of aerospace industry hightech products. The article suggested for the first time an extension of the classical model of analysis of M. Porter’s five competitive forces, namely, a model of global competition. It also proposed methods for competitive strategy designing and forecasting the state of the industry markets based on of the behavior of intelligent agents, game theory and decisionmaking theory, methods of analysis of the competitiveness of hightech product. Among the obtained results are the following:
The developed models, algorithms and software are used for the analysis of global competition for existing businesses of the aerospace industry and has shown its effectiveness. Keywords: model of global competition, competitive analysis, intelligent agents, complementors and influentors, computer software complex 

Development of an algorithm of a group of unmanned aerial vehicles evolution for signature reduction
For a long time the work has been underway on the development of the systems defending from smallsized unmanned aerial vehicles (SUAV) [13]. Modern unmanned air systems are capable of successfully overcoming the enemy’s air defense systems when used singly, [5], but the use of SUAVs group significantly increases the probability of their detection, due to better group’s visibility and less maneuverability compared to a single SUAV. The complexity of SUAV detecting is associated with a small value of radar crosssection (RCS) in radar observation range. In the optical and infrared observation ranges, the small sizes of SUAV complicates their detection as well. However, there is information on developing the control system for enhancing RCS for a group of missiles or UAVs [4]. One of the current problems of multiple SUAV’s application consists in reducing the group’s visibility in optical range when passing the air defense systems. As it is noted in [6], the visibility can be reduced by «reducing of the aircraft size». In this case, regarding the multiple SUAV’s application, we should speak about reducing the total area occupied by SUAV’s group in the image. An appropriate SUAVs group regrouping to reduce its visibility can solve this problem. This paper demonstrates how various groups’ readjustments could reduce their visibility. Various scenarios of the group entry into the scope of the enemy’s air defense systems were considered. A comparative efficiency analysis of various staffed formations was carried out. An algorithm providing for the operational reconstruction of the drone’s group, oriented to implementation using the Pixhawk autopilot was developed. Computer simulation using the model of autopilot and drone, which showed the operability of the proposed algorithm, was performed. Keywords: unmanned aerial vehicle, visibility, group control 

Stabilization by rotation and stabilization of a spacecraft relative to the three axes are the main methods employed to maintain the exact solid body orientation. The idea of rotation stabilization is based on the application of a gyroscopic effect. The advantage of this method, compared to the other approaches, consists in simplicity and the lack of a prolonged active rotation period to maintain orientation in a certain direction. Rotational stabilization was being employed for a large number of foreign and Soviet/Russian spacecraft. Application of rotation stabilization for passive control is relevant for spacecraft with limited resources. However, the shortcomings of the passive stabilization method are also well known and are associated mainly with the problem of the exact reorientation of space antennas and optics. Thus, frequently used maneuvers for angular motion lead to the need to resort to solving problems of controlling the exact reorientation in threedimensional space. The article studies the problem of angular motion optimal control of a rigid body by stabilized rotation. The efficiency criterion of is a minimum of energy costs. Compared to the general problem of reorientation and rotation control, the problem of bodies with stabilized rotation from the mathematical viewpoint is somewhat simpler. It is explained by reduction of dimensionality and complexity of the corresponding nonlinear equations of the system. Nevertheless, the problem of controlling joint reorientation and rotation remains complex and nonlinear. This, in turn, does not allow obtaining the required analytical result at the given time. Therefore, the purpose of this article is to obtain a characterization of extremal trajectories. There is a possibility to study in detail the problem of zero stabilization by rotation, when the projection of the angular velocity on one of the axes is identically zero. Keywords: optimal control, reorientation, symmetric solid body, energy consumption, maximum principle 

Mathematical support and software for computers, complexes and networks  
The design of a modern aircraft gas turbine engine (GTE) is associated with numerous calculations of the stressstrain state, strength and dynamics of the engine components and parts. It involves several processes, including substantiation of the main components sources, certification, analysis of the defects origins detected while operation and implementation of measures that can prevent the defects occurrence. Thus, the design procedure requires a complete set of data on the structural strength (realized in the course of the design) of the materials used. This paper presents the results of the longterm work in CIAM on the development of the database (DB) for information storage on the structural strength of the metal alloys used in manufacturing of the main and critical parts of an aviation GTE. The DB contains characteristics of a large number of materials obtained from experiments on 10000 specimens (more than 120 titles). Knowing these characteristics is necessary to perform calculations of the static strength and cyclic durability, dynamic characteristics and life of the GTE parts in a wide range of loading and operation conditions. The DB is based on the “Granta MI platform” software and consists of several sections containing reference information, experimental results, statistical processing results and characteristics for calculations. A description of the database structure, its functional capabilities and user interaction features is provided. A structure has also been developed for the DB section designed for samples made by using additive manufacturing. The developed CIAM databank on the structural strength of materials corresponds to current global analogues and can be used by the aircraft engine industry to calculate strength and dynamics, as well as to examine defects. Keywords: data bank, metallic materials, structural strength, resource, aircraft gas turbine engines 

The article focuses on the algorithms of the event detection in contentbased video retrieval. Video has a complex structure and can express the same idea in different ways. This makes the task of searching for video more complicated. Video titles and text descriptions cannot give the whole information about objects and events in the video. This creates a need for contentbased video retrieval. There is a semantic gap between lowlevel video features, that can be extracted, and the users’ perception. The task of event detection is reduced to the task of video segmentation. Complex contentbased video retrieval can be regarded as the bridge between traditional retrieval and semanticbased video retrieval. The properties of video as a time series are described. The concept of anomalies in the video is introduced. A method for event detection based on comparing moving averages with windows of different sizes is proposed. According to the classification given at the beginning of this article, our method refers to statistical methods. It differs from other methods of low computational complexity and simplicity. The video stream processing language is proposed for functionbased description of video handling algorithms. So, our method is formulated in the form of a declarative description on an interpreted programming language. Unfortunately, most of the existing video processing methods use exclusively imperative approach, which often complicate its understanding. Examples of this language implementation are given. Its grammar is described either. As it was shown by the experiments, the implementation of the proposed video events retrieval method, unlike their counterparts, can work for video streams as well with a realtime and potentially infinite frame sequences. Such advantages within low computational requirements make implementation of the method helpful in aviation and space technology. The algorithm has some disadvantages due to necessity of parameter selection for particular task classes. The theorem on nearduplicates of video is formulated at the end of the article. It asserts the nearduplicate videos express the same sequence of phenomena. Keywords: discord detection, video segmentation, video duplicates, moving average score, video streaming 

The paper analyses the problem of a small multirotor UAV control in various flight modes. The modern tendencies of control systems design for selfsupporting UAVs assume employing methods allowing decrease the level of the spacial position uncertainty and surrounding conditions of the UAV itself without external pilot’s (operator) engagement. With this, the standard technological solution for a certain number of critical flight phases, requiring precise spatial positioning and control (such as takeoff, hovering over landing site, and landing) does not exist. These phases require more precise UAV’s control, due to the necessity of holding it in a specified point in space. The presented article analyses principles of autotakeoffautolanding systems design, based on computer vision (CV) methods implementation, and considers specifics of markers employing. The article analyses the existing autotakeoffautolanding systems without global positioning implementation. It suggests an approach to the autotakeoffautolanding system design based on computer vision, for an UAV of a multi rotor or a helicopter type. Three types of the system components mutual arrangement were considered and analyzed, and merits and demerits of each configuration were formulated. The article shows that with any cameras positioning within the autotakeoffautolanding system, it is necessary to employ markers to facilitate localization of the key points the UAV or a landing site by the CV systems. Various methods of markers’ positioning and realization of marker labels, depending on marker’s position were analyzed. Markers on the landing site can be realized by the following methods: contrast image of some pattern, liable to identification by the CV methods; lights, remotely controlled by the processor; colored or infrared LEDs, operating in continuous or pulse mode. Variants of marker labels on an UAV are as follows: colored or infrared LEDs, operating in continuous or pulse mode; lights, remotely controlled by the processor; the system of angle reflectors and illuminator; contrast imagepattern (including a fuselage shape). The studies revealed that the controlled markers mode was preferable in all cases, when formation of a control channel between an UAV and landing system was possible. Further research will be devoted to development of software for autolanding system based on obtained marker implementation recommendations. Keywords: unmanned aerial vehicles, UAV, multi copters, markers, computer vision, CV, autolanding 

CAD systems  
Liquids and gases are widely used in aircrafts structures as energy carriers for propulsion systems, in hydraulic actuators and pneumatic boosters, and as coolants, lubricants or in pneumatic actuators to ensure vital activity of a crew and passengers. The presence of liquid and gaseous media onboard an aircraft leads to the necessity of employing piping systems. One could hardly imagine fuel and pneumatic systems of modern aircraft without pipelines and automatic equipment, regulating their delivery. At present, aircraft and helicopter pipeline systems count thousands of tubular structures joints. The aggregate length pipelines herewith is hundreds plus meters. There are various pipelines with diameters sized from units to several tens of millimeters from various materials – aluminum, titanium, steel and other alloys. The great majority of them herewith are various fixed junctions with tips, flanges or pipes between each other. The presented article is devoted to methodology development of automated design of both aircraft pipelines structures in 3D space, including various complex pipeline structures, and modeling the process of magneticpulse deformation and formation of fixed junctions of pipelines between each other from homogenous and heterogeneous materials using CAD system. For this purpose a computer solidstate simulation is used together with solving the dynamic problem of junction formation while varying various structure parameters, characteristics of materials and parameters of magnetopulse deformation. On creating pipelines parts and further modeling of the magneticpulse deformation the Autodesk Invertor design environment was used. To model 3D objects which axisymmetric tubular workpieces of junction structures can be related to, various tools for geometry creation were used. While modeling the process of high speed deformation by pulsing magnetic field and formation of junctions the Autodesk Simulation Mechanical 2015 program, allowing effectively try out tubular workpieces assembly with the required surface shapes, parts sizes and specified characteristics of materials, was used. This simulation of the process of connecting tubular workpieces by pressure of pulse magnetic field allows select effective modes of deformation in terms of junction quality to form the required parameters of welding in cold state in contact zones of tubular structures. Keywords: aircraft pipelines, permanent connection of heterogeneous pipes, magneticpulse welding, computeraided design system, simulation of pipelines, simulation of connection formation 

The article considers the solution of a problem of the instruments automating layout design in the aircraft technical compartments. An additional requirement to the layout is the ensuring of service areas, which is understood as assembling or servicing ease of the equipment. The purpose of this study consists in developing methods and algorithms, providing access to assembly tools and the workspace while installation and maintenance of the already installed equipment. The gist of methodological approach employed in this study consists in modeling of spatial movements of the equipment necessary for performing maintenance work on this equipment. The set of equipment necessary for its assembling and dismantling (screwdrivers, wrenches, special installation tools etc) is determined for each unit. On its basis the geometry model of this equipment is formed. Further, all necessary movements for both the assembly process itself (such as a wrench rotational motion) and the process of installation tools delivery to the work point are determined. Thus, modeling of this process is rather complicated task of geometric modeling. Solving method is geometric modeling of both placed objects, and mounting hardware and the trajectory of its motion. Thus, both the mounting hardware and motion trajectory are considered as assembling objects. Intersection with other objects is unallowable. Geometric receptor models, discretizing the installation area, are used a modeling method. Selection of receptor models is stipulated by the fact that a solidstate model of the entire positions of the assembling tools in the course of their delivery and operation is utterly geometrically complex. Based on heuristic algorithms the possible trajectory of assembling tools delivery to its point of use is used. This trajectory represents a solidstate model of the instantaneous movements of the installation tool along the sel ected path. Based on the receptor computational model the authors developed the procedure for determining the movement trajectory of the installation tools, or the finding of fact of impossibility to service the concrete object, which indicates the poor (lowtech) design decision. The disadvantage of the receptor geometric model is that it is not a initial model for a design engineer. The initial information for the designer is parametric model containing of the primitive's description and its main parameters values, which can easily determine fr om the drawing. Therefore, the necessity in extra program module “Parametric model”↔“Receptor model” arises. Thus, we can consider receptor model as an “intrаcomputer model”. The advantage of the receptor model, determining its selection for our studies, is the ease of determining the condition of intersection of geometric objects described by this method, which cannot be described analytically. For instruments in need of servicing three receptor models are being developed: geometric shape of assembling tool, its delivery trajectory to the point of use, and working space where this tool would be used. With this, the database is used, determining the necessary installation tool for each type of the object in servicing. The type of the assembling tool is determined by the type of attachment this object in aircraft structure. The installation tools acceptable for the specified operation are ranked also according to productivity and operational comfort. Thus, the installation tools are checked on workability by preferability. The preferability is determined by productivity and operational comfort of installation tools acceptable for work. Thus, a solid state geometric object of extremely complex shape lacking analytical description is developed. If this object can be accommodated among the already installed aircraft instrumentation, this equipment can be serviced, otherwise– it cannot be serviced. The possibility of rather easily determining the fact of intersection of all objects of the scene described by receptor models, is the substantiation of selection in our studies of receptor method of geometric modeling. The authors developed the software in C# implementing the described receptor geometric models allowing evaluate the possibility of servicing the already installed equipment in the aircraft technical bay. Keywords: 

The study relates to the field of design automation and technological preparation of production in aircraft construction. The authors propose a technique for a product emodel objects’ structure identification by formalized parameters. For this purpose, the technique for contour pattern recognition, allowing identify geometric primitives bounding the surfaces, that form contours of each structural element, is employed. Thus, the necessity to develop structural geometric model of a product arises. It is necessary to identify hereafter the formal parameters of a part structure objects. The article considers the sequence of work with part’s emodel, which employs production rules, theory of sets elements, and apparatus of mathematical logic. The obtained structural and technological parameters of a part allow qualify it to a certain type, i. e. identify. Identification of a part, its structure and data on its coupling face allows define technological parameters, which structural form sets the geometrical requirements to basing. The article presents several basic rules for establishing the relation between individual parts, which can be used while a part processability evaluation, development of routes of producing and assembling, as well as technological equipment design. Thus, recognition systems implementation will significantly increase production efficiency by structural and technological problems solution unification. It will serve as a platform for intelligent systems of decision making of various directionality within the industry, which will allow decrease the effect of human factor while decision making due to formal criteria employing. Recognition systems implementation will allow ensure competitive products’ manufacturing with product’s structure with high target manufacturing and operating processability indices. The project is based on idea of technologist’s knowledge formalization, and developing on its basis the system of decisionmaking support. It will allow reduce the number of errors while performing technical control of the product while production startup, and decrease production costs due to analyzing several design solutions and selection of compositionoptimal structural elements with the specified level of processability and cost. The project is flexible while adjusting, with the possibility of implementation at various machinebuilding enterprises. Keywords: 

Mathematica modeling, numerical technique and program complexes  
At present, there are contradictions in the formulation of the indicators of resolving power of synthetic aperture radar (SAR). Developers of SAR equipment usually suggest evaluate the resolution through the width of the profile of the scattering functions (hardware function). This definition simplifies the commissioning of the target equipment, but does not take into account the resolution relationship with the radiometric characteristics of the Xray diffraction pattern, the background signal of the underlying surface, and random synthesizing errors. The inflated expectations of the consumers of radar information quality come into conflict with the requirements of the design specifications formulated by the developer of the target equipment based on their parochial interests. As a result, to formulate the requirements of the design specifications, it is necessary to develop methods for evaluating the quality of the radar image (SAR) that account for the characteristics of SAR. The article suggests an improved method for estimating the spatial resolution of a synthesized aperture radar, based on the condition that the modulation amplitude exceeds the signal equivalent to noise. The modulation difference is evaluated with account for attenuation of the spatial frequencies of the complex scattering coefficient on the SAR information path. To evaluate the resolution, the author suggested to employ two types of test objects with harmonic amplitude and phase modulation. Mathematical relationships determining the resolution equation through the spatial function of amplitude modulation transmission by the radar information path are considered. Analysis of the image formation specifics in radar complexes compared to optoelectronic ones was carried out. The article shows that the SAR provides spatial resolution about twice as low as the limiting value determined by the halfwidth of the hardware function. An improved method for determining the space radar’s resolution capability with account for the synthesized aperture formation specifics and random errors, is suggested. The proposed model of a test object with harmonic change in the complex amplitude or phase of the reflected signal allows relate the resolution capability of the SAR with its radiometric characteristics and reflection from the underlying surface. The function of modulation transmission of the amplitude and phase of the information path of the PCA for harmonic test objects was obtained. The properties of the amplitude modulation transfer function dependence on the spatial frequency made it possible to explain certain characteristic properties of the radar compared to optical images. The article shows that the SAR ensures approximately the same spatial resolution for the amplitude and phase harmonic modulation of the object scattering function, which is approximately two times worse than the limiting one. Increasing the contrast of the object to absolute values slightly improves the resolution up to 1.6 times. In case of lowcontrast objects, the amplitude modulation is transmitted without distortion; the resolution capability is determined only by the realized signaltonoise ratio with a resolution of 2.5 times worse. If an object is observed against speckle noise, the resolution of the SAR drops three or more times. Keywords: quality indicators, space radar with synthesized aperture, linear ground resolution, radiometric resolution, modulation transfer function, radar image quality 