rus
Issue #5/2023
Yu. I. Yakimenko, S. P. Astakhov, I. V. Yakymenko
Estimation Method for the Spatial Radiation Structure of Unmanned Aerial Vehicles
Estimation Method for the Spatial Radiation Structure of Unmanned Aerial Vehicles
DOI: 10.22184/1993-7296.FRos.2023.17.5.356.364
The estimation method for the spatial radiation structures of unmanned aerial vehicles is proposed that allows obtaining the approximate mathematical models of their spatial radiation structure. Such models can be used as the initial data for efficiency evaluation of problem solution related to the detection of unmanned aerial vehicles using the passive optoelectronic systems.
The estimation method for the spatial radiation structures of unmanned aerial vehicles is proposed that allows obtaining the approximate mathematical models of their spatial radiation structure. Such models can be used as the initial data for efficiency evaluation of problem solution related to the detection of unmanned aerial vehicles using the passive optoelectronic systems.
Теги: atmospheric background field of view passive optoelectronic system unmanned aerial vehicle атмосферный фон беспилотное воздушное судно пассивная оптико-электронная система поле зрения
Estimation Method for the Spatial Radiation Structure of Unmanned Aerial Vehicles
Yu. I. Yakimenko, S. P. Astakhov, I. V. Yakymenko
Branch of the Federal State Budgetary Educational Institution of Higher Education “National Research University “Moscow Power Engineering Institute”, Smolensk, Russia
The estimation method for the spatial radiation structures of unmanned aerial vehicles is proposed that allows obtaining the approximate mathematical models of their spatial radiation structure. Such models can be used as the initial data for efficiency evaluation of problem solution related to the detection of unmanned aerial vehicles using the passive optoelectronic systems.
Keywords: unmanned aerial vehicle, passive optoelectronic system, atmospheric background, field of view
Article received: 30.05.2023
Article accepted: 10.07.2023
Introduction
The up-to-date unmanned aerial vehicles (UAVs) perform a wide range of tasks: surveillance (reconnaissance), strikes, transportation of goods, target designation for weapons, data broadcasting, etc. As a result, there is a need to arrange the countering activities against the UAVs that potentially create threats to the military, industrial and man-made facilities. To ensure this, it is necessary, first of all, to increase the detection efficiency. Since the small values of the UAV scattering cross-sections (SCS) make it impossible to use the active radar equipment for its detection, the use of passive optoelectronic systems (POES) can become an alternative option.
It is proposed to assess the POES application efficiency by the detection range value of UAVs for a given detection probability. To assess the performance indicators of POES functioning for UAV detection, information is required related to the UAV features as the source (boosters) of optical radiation and nature of the spatial radiation distribution from various atmospheric backgrounds (AB). The estimation methods and results for the spatial AB radiation specifications are provided in detail in a number of sources, for example, [1–3], while information about the features of UAVs as the sources (boosters) of optical radiation.
Available evaluation methods for the spatial radiation structures of aerial vehicles
There are several methods to determine the spatial radiation structure of aerial vehicles (AVs), including the UAVs:
radiance measurement of the aircraft during its flight along the specified trajectories. This method makes it possible to obtain information about the AV radiation parameters mainly to the lower hemisphere and limited sectors. Moreover, such studies require the comprehensive and expensive equipment.
radiance measurement of a stationary AV with an active propulsion system placed on the bench [4]. In this case, the radiance measurement is performed in such a way that the measuring equipment is moving around the aircraft in a circular motion. The disadvantages of the method include the fact that the radiation effect due to the aerodynamic heating (or cooling) of the aircraft airframe elements is almost completely eliminated. In addition, in this case, it is possible to obtain the indicatrix of the AV radiation only in the horizontal plane, while the AV observer requires information relating to the radiation type into the lower hemisphere.
determination of the spatial structure of the AV radiation based on calculations [5]. The disadvantages of this method include approximation and the limited scope of the results obtained.
Developed evaluation method for the spatial radiation structure of unmanned aerial vehicles
The main feature of the developed method for estimating the spatial radiation structure is that the UAV under study is fixed in a specially designed rotary device with two degrees of freedom (Fig. 1) that provides a change in the UAV angular position in terms of the yaw angle (ψ) and roll angle (γ) in various operating modes of the propulsion system. Measurements of the UAV radiation strength are made using a measuring and computing complex (MCC) at various times of the day and year under various weather conditions to be recorded using a portable meteorologic station.
The radiometer from the MCC is mounted on a tripod that makes it possible to direct the radiometer optical axis to the UAV (Fig. 1), and the distance D between the radiometer and the UAV is selected so that all possible UAV views correspond to the field of view of the radiometer that is controlled using an optical viewer.
The diameter of circle d (field of view of the radiometer) depends on the distance D between the radiometer and the UAV and is determined by the following formula:
(1)
where D are the distances D between the radiometer and the UAV,
d is the diameter of the field of view of the radiometer,
δθ is the angle of the field of view of the radiometer.
The multichannel radiometer has the following parameters:
working spectral ranges: 1.5–2 microns, 3–5 microns and 8–13 microns,
field of view width δθ = 24′.
Since the radiometer receives a mixture of background and UAV radiation BfUAV(γ, ψ), the useful information, i. e., the radiance value BUAV(γ, ψ) is obtained in accordance with the algorithm by subtracting from BfUAV(γ, ψ) any radiance values of the background area screened by the UAV glider: Bf(γ, ψ) ∙ kp(γ, ψ) (Fig. 2).
The current background parameters are determined immediately after the UAV radiance measurements using the same radiometer.
The UAS overlap factor of the radiometer field of view is determined on the basis of the following formula:
, (2)
where Spr (γ, ψ) is the UAV projection area on the image plane that is perpendicular to the direction of sighting, at different observation angles.
Sp is the area of the radiometer field of view at a distance D, determined by the following formula:
(3)
The background radiance (in the presence of an UAV) in the radiometer field of view B'f(γ, ψ) is calculated by the following formula:
B'f(γ, ψ) = Bf(γ, ψ) ∙ kp(γ, ψ), (4)
where Bf(γ, ψ) is the radiance of the current background (in the absence of UAV).
With a well-known background component of the radiation, the UAV radiance in relation to the background is as follows:
BUAV(γ, ψ) = BfUAV(γ, ψ) – B'f(γ, ψ). (5)
In the case of UAV observation at a long distance (in the form of a point source of radiation), it should be specified not by the radiance, but by the radiation intensity.
The radiation flux (luminous flux) generated by the UAV radiation F(γ, ψ) is related to the radiance BUAV(γ, ψ) measured at the point of observance with the following dependence:
F(γ, ψ) = BUAV(γ, ψ) ∙ Sp(γ, ψ) ∙ Ω, (6)
where Ω is the solid angle occupied by the radiometer field of view, av.
In addition, the luminous flux can be shown in terms of the radiation intensity:
(7)
where JUAV(γ, ψ) is the UAV radiation intensity depending on the observation angle,
τa is the atmospheric transmissivity for the meteorological situation relevant to the measurement conditions,
Sav is the area of the input aperture of the radiometer.
By equating the expressions (6) and (7), we can indicate the UAV radiation intensity through the results of the observed radiance:
(8)
Thus, in order to implement the calculation procedure using the formulas (4–8), it is necessary to determine the background overlap factor and the area of projection onto the UAV image plane as the functions of its spatial position from ψ and from γ. Since the UAVs of various types have different configurations, this issue should be solved for each case separately.
The value of the UAS overlap factor of the radiometer field of view kp (γ, ψ) is determined by the full-scale modeling for the UAV class under study, using a rotary device and a digital camera:
the UAV is fixed in the rotary device with two degrees of freedom (Fig. 3),
a digital camera is placed at a fixed distance from the rotary device with UAV,
photographic fixation of the UAV is performed against a white screen with the dimensions of Lh × Ld when the values of ψ are changed from 0 to 360° every 10° at a fixed value of γ, the value of which is changed from –180° to 180° at an increment of 10° after a full rotation ψ,
the frames obtained during the photographic fixation process are processed (the background is removed in the image editor in order to increase the UAV image contrast),
the obtained images are binarized based on the thresholding (Fig. 4).
Thresholding allows to divide the set of image pixels into two subsets: one containing the background image and one containing the UAV image. The background-cleared frames of the UAV images are used to determine the UAV overlap factor of the radiometer field of view kp(γ, ψ) at different angles.
Counting of the number of pixels with a unit value N1(γ, ψ) (background pixels) and with a zero value N0(γ, ψ) (target pixels) makes it possible to calculate the overlap factor for a given target angle. For thi purpose, in the expression (2) the value Sp is replaced by the number of pixels in the binary image N:
N = N1(γ, ψ) + N0(γ, ψ).
Then:
(9)
where kc(γ, ψ) is the coefficient of participation in the target radiation.
An example of the dependence of the overlap factor on the UAV angle kp(γ, ψ) is shown in Fig. 5.
The UAV projection area Spr(γ, ψ) onto the image plane, at different angles, was determined by the following formula:
Spr(γ, ψ) = Skp ∙ kUAV(γ, ψ), (10)
Skp = Ld ∙ Lh,
KUAV(γ, ψ) = 1 – kp(γ, ψ),
where Ld – the horizontal size of the screen in the image plane when the UAV is projected onto it;
Lh – the vertical size of the screen in the image plane when the UAV is projected onto it.
An example of dependence of the UAV projection area on the image plane at different angles is shown in Fig. 6. The examples of values of JUAV(γ, ψ) obtained using the formula (8) in the form of normalized indicatrices are shown in Fig. 7–9.
Conclusion
A method is proposed for obtaining the approximate mathematical models of the spatial UAV radiation structure that can be used as the input data for efficiency evaluation of solving the UAV detection issues using the POES.
An analysis of the normalized indicatrix shapes of the UAV radiation demonstrates the following:
in the spectral range of 1.5–2 μm at fixed roll angles, the fluctuations in the levels of radiation intensity are noted (Fig. 7), due to the changes in the brightness of the reflected solar radiation from the UAV glider and, possibly, occurrence in some cases of a “negative” contrast as a result of screening of the reflected solar radiation from the clouds. The observed asymmetry of the radiation indicatrix shapes is shown as an increase in the radiation intensity from the left that is explained by the solar radiation influence during measurements,
in the spectral ranges of 3–5 µm and 8–13 µm (Fig. 8, 9), the fluctuations in the radiation intensity levels are insignificant, since they mainly contain the UAV own radiation. The observed asymmetry of the UAV radiation indicatrix shapes is due to the design peculiarities of its propulsion system.
AUTHORS
Yakimenko Igor Vladimirovich, Dr.of Sc.(Engin.), associate professor, branch of the Federal State Budgetary Educational Institution of Higher Education “National Research University “Moscow Power Engineering Institute” in Smolensk, Smolensk, Russia.
ORCID 0000-0002-1003-8403
Astakhov Sergey Petrovich, Cand.of Sc.(Engin.), associate professor, branch of the Federal State Budgetary Educational Institution of Higher Education “National Research University “Moscow Power Engineering Institute” in Smolensk, Smolensk, Russia.
Yakimenko Yury Igorevich, post-graduate student, branch of the Federal State Budgetary Educational Institution of Higher Education “National Research University “Moscow Power Engineering Institute” in Smolensk, Smolensk, Russia.
ORCID 0009-0001-2631-5997
Conflict of interest
The authors confirm the absence of a conflict of interest, all the authors have reviewed the final version of the manuscript and agreed on it after making some corrections.
Yu. I. Yakimenko, S. P. Astakhov, I. V. Yakymenko
Branch of the Federal State Budgetary Educational Institution of Higher Education “National Research University “Moscow Power Engineering Institute”, Smolensk, Russia
The estimation method for the spatial radiation structures of unmanned aerial vehicles is proposed that allows obtaining the approximate mathematical models of their spatial radiation structure. Such models can be used as the initial data for efficiency evaluation of problem solution related to the detection of unmanned aerial vehicles using the passive optoelectronic systems.
Keywords: unmanned aerial vehicle, passive optoelectronic system, atmospheric background, field of view
Article received: 30.05.2023
Article accepted: 10.07.2023
Introduction
The up-to-date unmanned aerial vehicles (UAVs) perform a wide range of tasks: surveillance (reconnaissance), strikes, transportation of goods, target designation for weapons, data broadcasting, etc. As a result, there is a need to arrange the countering activities against the UAVs that potentially create threats to the military, industrial and man-made facilities. To ensure this, it is necessary, first of all, to increase the detection efficiency. Since the small values of the UAV scattering cross-sections (SCS) make it impossible to use the active radar equipment for its detection, the use of passive optoelectronic systems (POES) can become an alternative option.
It is proposed to assess the POES application efficiency by the detection range value of UAVs for a given detection probability. To assess the performance indicators of POES functioning for UAV detection, information is required related to the UAV features as the source (boosters) of optical radiation and nature of the spatial radiation distribution from various atmospheric backgrounds (AB). The estimation methods and results for the spatial AB radiation specifications are provided in detail in a number of sources, for example, [1–3], while information about the features of UAVs as the sources (boosters) of optical radiation.
Available evaluation methods for the spatial radiation structures of aerial vehicles
There are several methods to determine the spatial radiation structure of aerial vehicles (AVs), including the UAVs:
radiance measurement of the aircraft during its flight along the specified trajectories. This method makes it possible to obtain information about the AV radiation parameters mainly to the lower hemisphere and limited sectors. Moreover, such studies require the comprehensive and expensive equipment.
radiance measurement of a stationary AV with an active propulsion system placed on the bench [4]. In this case, the radiance measurement is performed in such a way that the measuring equipment is moving around the aircraft in a circular motion. The disadvantages of the method include the fact that the radiation effect due to the aerodynamic heating (or cooling) of the aircraft airframe elements is almost completely eliminated. In addition, in this case, it is possible to obtain the indicatrix of the AV radiation only in the horizontal plane, while the AV observer requires information relating to the radiation type into the lower hemisphere.
determination of the spatial structure of the AV radiation based on calculations [5]. The disadvantages of this method include approximation and the limited scope of the results obtained.
Developed evaluation method for the spatial radiation structure of unmanned aerial vehicles
The main feature of the developed method for estimating the spatial radiation structure is that the UAV under study is fixed in a specially designed rotary device with two degrees of freedom (Fig. 1) that provides a change in the UAV angular position in terms of the yaw angle (ψ) and roll angle (γ) in various operating modes of the propulsion system. Measurements of the UAV radiation strength are made using a measuring and computing complex (MCC) at various times of the day and year under various weather conditions to be recorded using a portable meteorologic station.
The radiometer from the MCC is mounted on a tripod that makes it possible to direct the radiometer optical axis to the UAV (Fig. 1), and the distance D between the radiometer and the UAV is selected so that all possible UAV views correspond to the field of view of the radiometer that is controlled using an optical viewer.
The diameter of circle d (field of view of the radiometer) depends on the distance D between the radiometer and the UAV and is determined by the following formula:
(1)
where D are the distances D between the radiometer and the UAV,
d is the diameter of the field of view of the radiometer,
δθ is the angle of the field of view of the radiometer.
The multichannel radiometer has the following parameters:
working spectral ranges: 1.5–2 microns, 3–5 microns and 8–13 microns,
field of view width δθ = 24′.
Since the radiometer receives a mixture of background and UAV radiation BfUAV(γ, ψ), the useful information, i. e., the radiance value BUAV(γ, ψ) is obtained in accordance with the algorithm by subtracting from BfUAV(γ, ψ) any radiance values of the background area screened by the UAV glider: Bf(γ, ψ) ∙ kp(γ, ψ) (Fig. 2).
The current background parameters are determined immediately after the UAV radiance measurements using the same radiometer.
The UAS overlap factor of the radiometer field of view is determined on the basis of the following formula:
, (2)
where Spr (γ, ψ) is the UAV projection area on the image plane that is perpendicular to the direction of sighting, at different observation angles.
Sp is the area of the radiometer field of view at a distance D, determined by the following formula:
(3)
The background radiance (in the presence of an UAV) in the radiometer field of view B'f(γ, ψ) is calculated by the following formula:
B'f(γ, ψ) = Bf(γ, ψ) ∙ kp(γ, ψ), (4)
where Bf(γ, ψ) is the radiance of the current background (in the absence of UAV).
With a well-known background component of the radiation, the UAV radiance in relation to the background is as follows:
BUAV(γ, ψ) = BfUAV(γ, ψ) – B'f(γ, ψ). (5)
In the case of UAV observation at a long distance (in the form of a point source of radiation), it should be specified not by the radiance, but by the radiation intensity.
The radiation flux (luminous flux) generated by the UAV radiation F(γ, ψ) is related to the radiance BUAV(γ, ψ) measured at the point of observance with the following dependence:
F(γ, ψ) = BUAV(γ, ψ) ∙ Sp(γ, ψ) ∙ Ω, (6)
where Ω is the solid angle occupied by the radiometer field of view, av.
In addition, the luminous flux can be shown in terms of the radiation intensity:
(7)
where JUAV(γ, ψ) is the UAV radiation intensity depending on the observation angle,
τa is the atmospheric transmissivity for the meteorological situation relevant to the measurement conditions,
Sav is the area of the input aperture of the radiometer.
By equating the expressions (6) and (7), we can indicate the UAV radiation intensity through the results of the observed radiance:
(8)
Thus, in order to implement the calculation procedure using the formulas (4–8), it is necessary to determine the background overlap factor and the area of projection onto the UAV image plane as the functions of its spatial position from ψ and from γ. Since the UAVs of various types have different configurations, this issue should be solved for each case separately.
The value of the UAS overlap factor of the radiometer field of view kp (γ, ψ) is determined by the full-scale modeling for the UAV class under study, using a rotary device and a digital camera:
the UAV is fixed in the rotary device with two degrees of freedom (Fig. 3),
a digital camera is placed at a fixed distance from the rotary device with UAV,
photographic fixation of the UAV is performed against a white screen with the dimensions of Lh × Ld when the values of ψ are changed from 0 to 360° every 10° at a fixed value of γ, the value of which is changed from –180° to 180° at an increment of 10° after a full rotation ψ,
the frames obtained during the photographic fixation process are processed (the background is removed in the image editor in order to increase the UAV image contrast),
the obtained images are binarized based on the thresholding (Fig. 4).
Thresholding allows to divide the set of image pixels into two subsets: one containing the background image and one containing the UAV image. The background-cleared frames of the UAV images are used to determine the UAV overlap factor of the radiometer field of view kp(γ, ψ) at different angles.
Counting of the number of pixels with a unit value N1(γ, ψ) (background pixels) and with a zero value N0(γ, ψ) (target pixels) makes it possible to calculate the overlap factor for a given target angle. For thi purpose, in the expression (2) the value Sp is replaced by the number of pixels in the binary image N:
N = N1(γ, ψ) + N0(γ, ψ).
Then:
(9)
where kc(γ, ψ) is the coefficient of participation in the target radiation.
An example of the dependence of the overlap factor on the UAV angle kp(γ, ψ) is shown in Fig. 5.
The UAV projection area Spr(γ, ψ) onto the image plane, at different angles, was determined by the following formula:
Spr(γ, ψ) = Skp ∙ kUAV(γ, ψ), (10)
Skp = Ld ∙ Lh,
KUAV(γ, ψ) = 1 – kp(γ, ψ),
where Ld – the horizontal size of the screen in the image plane when the UAV is projected onto it;
Lh – the vertical size of the screen in the image plane when the UAV is projected onto it.
An example of dependence of the UAV projection area on the image plane at different angles is shown in Fig. 6. The examples of values of JUAV(γ, ψ) obtained using the formula (8) in the form of normalized indicatrices are shown in Fig. 7–9.
Conclusion
A method is proposed for obtaining the approximate mathematical models of the spatial UAV radiation structure that can be used as the input data for efficiency evaluation of solving the UAV detection issues using the POES.
An analysis of the normalized indicatrix shapes of the UAV radiation demonstrates the following:
in the spectral range of 1.5–2 μm at fixed roll angles, the fluctuations in the levels of radiation intensity are noted (Fig. 7), due to the changes in the brightness of the reflected solar radiation from the UAV glider and, possibly, occurrence in some cases of a “negative” contrast as a result of screening of the reflected solar radiation from the clouds. The observed asymmetry of the radiation indicatrix shapes is shown as an increase in the radiation intensity from the left that is explained by the solar radiation influence during measurements,
in the spectral ranges of 3–5 µm and 8–13 µm (Fig. 8, 9), the fluctuations in the radiation intensity levels are insignificant, since they mainly contain the UAV own radiation. The observed asymmetry of the UAV radiation indicatrix shapes is due to the design peculiarities of its propulsion system.
AUTHORS
Yakimenko Igor Vladimirovich, Dr.of Sc.(Engin.), associate professor, branch of the Federal State Budgetary Educational Institution of Higher Education “National Research University “Moscow Power Engineering Institute” in Smolensk, Smolensk, Russia.
ORCID 0000-0002-1003-8403
Astakhov Sergey Petrovich, Cand.of Sc.(Engin.), associate professor, branch of the Federal State Budgetary Educational Institution of Higher Education “National Research University “Moscow Power Engineering Institute” in Smolensk, Smolensk, Russia.
Yakimenko Yury Igorevich, post-graduate student, branch of the Federal State Budgetary Educational Institution of Higher Education “National Research University “Moscow Power Engineering Institute” in Smolensk, Smolensk, Russia.
ORCID 0009-0001-2631-5997
Conflict of interest
The authors confirm the absence of a conflict of interest, all the authors have reviewed the final version of the manuscript and agreed on it after making some corrections.
Readers feedback
