Method for flight testing of unmanned aerial systems based on extrapolation of dynamics of growth of spatial resolution from flight altitude
The method extrapolates spatial resolution of UAV infrared video systems by using thermal targets and polynomial trends to predict spatial resolution at any altitude, enhancing accuracy and reducing flight requirements.
Patent Information
- Authority / Receiving Office
- RU · RU
- Patent Type
- Patents
- Current Assignee / Owner
- МОЛЧАНОВ АНДРЕЙ СЕРГЕЕВИЧ
- Filing Date
- 2026-02-01
- Publication Date
- 2026-07-07
AI Technical Summary
Existing methods for determining the spatial resolution of infrared video systems on unmanned aerial vehicles (UAVs) are limited, as they do not allow for determining spatial resolution at different flight altitudes and do not establish a trend in the dependence of spatial resolution on flight altitude, necessitating flights at required altitudes for prediction.
A method involving the extrapolation of spatial resolution dynamics from flight altitude, using thermal line targets with thermal contrast, multiple aerial photographs, and decoder operators to calculate spatial resolution, followed by a polynomial trend equation for accurate prediction without actual flights at the required altitudes.
Accurately predicts spatial resolution at any flight altitude by extrapolating estimates from lower altitudes, increasing accuracy by 29.3% and reducing the need for flights, while maintaining high reliability with 98.0% convergence to experimental values.
Smart Images
Figure 00000090_ABST
Abstract
Description
[0001] The invention relates to technical physics and can be used for qualimetry of unmanned aerial systems (UAS) of infrared video shooting (IRS) during flight tests.
[0002] A known method from the prior art is for qualimetry of an unmanned aerial vehicle (UAV) of a copter type with an optoelectronic system (OES), which involves assessing the spatial resolution of the OES by determining the linear resolution on the ground (LRT) of the OES (patent for invention RU 2838121), which consists of placing a line target on the ground, performing aerial photography of the target using an unmanned aerial vehicle of a copter type equipped with an OES observation with a varifocal lens (a lens with a variable focal length), with given values of the focal length changed at equal intervals, and a constant altitude of aerial photography, decoding the obtained aerial photographs, calculating the linear resolution on the ground (LRT) using a conversion formula that relates the LRT to the width of a line in a group of lines recognized by the operator-decipherer, the geometric altitude of the aerial photography and the focal length.The disadvantage of this method is that it does not allow determining spatial resolution at different UAV flight altitudes, since it assumes that flights are carried out at one constant altitude.
[0003] The closest analogue is the method for estimating the spatial resolution of infrared systems (IRS) of aerial reconnaissance by determining the LRM (patents for invention RU 2836103), according to which, with a priori specified values of the altitude and flight course of an aircraft, an aerial survey of areas of the terrain with placed line targets is carried out, which are sheets of sheet material made of iron, then, with a priori specified values of the altitude and flight course of the aircraft, an aerial survey of areas of the terrain with placed line targets is carried out, the images are processed and the LRM of the IRS is calculated as the arithmetic mean of the values of the estimates obtained by all decoder operators for all images of the targets, each of which is the minimum width of a line in the recognized groups of lines, in which all lines are observed separately along their entire length,In this case, simultaneously with the aerial photography, as the aircraft flies over the line target, the temperature difference between the line target and the background is measured, and the value of the linear resolution on the ground of the infrared system is calculated taking into account the temperature of the line target. The disadvantage of this method is that, due to its limited capabilities, it does not allow for determining the spatial resolution without performing flights at the required altitudes, and establishing a trend in the dependence of spatial resolution on flight altitude in order to predict the spatial resolution at the required flight altitudes by extrapolating the trend, without performing flights at these altitudes.
[0004] The technical objective of the claimed invention is to develop an arsenal of methods for qualimetry of unmanned aerial systems for infrared video filming during their flight tests.
[0005] The solution to the technical problem is achieved due to the fact that the method of flight testing of unmanned aerial systems of infrared video filming based on the extrapolation of the dynamics of growth of spatial resolution from the height of video filming is characterized by the fact that
[0006] Determine the required flight altitudes H i an unmanned aerial system for infrared video filming to create an extrapolation base, which is a set of m pairs of flight altitude values and corresponding spatial resolution values, which form a series of the dynamics of the change in spatial resolution from flight altitude, where the flight altitude changes with a lead step Δ, calculated in accordance with the expression: , Where - the altitude at which it is necessary to perform a spatial resolution forecast, H0 is the initial flight altitude, m is the number of members of the series that constitute the extrapolation base, where m≥5, then the value of the required flight altitudes is determined in accordance with the expression: , where i=0, 1, 2, …, m-1,
[0007] place thermal line targets on the ground, consisting of warm and cold lines and providing thermal contrast, taking into account the location of the lines along and across the direction of flight of the unmanned aerial system of infrared video filming, and the absence of objects shading the surface of the area on which the targets are located,
[0008] carry out infrared aerial survey of thermal streak worlds using an unmanned aerial system of infrared video survey at flight altitudes of H i for given flight course values, so as to obtain at each flight altitude H iat least 20 aerial photographs obtained with angular oscillations of the unmanned aerial system of infrared video filming not exceeding the permissible values, with the location of thermal line targets in the center of the aerial photograph or removed from the center in the direction of the horizontal and vertical sides of the aerial photograph at distances not exceeding 20% of the transverse and longitudinal dimensions of the aerial photograph, respectively, while during the flight, the flight altitude H is monitored i by measuring the geometric flight altitude of an unmanned aerial system for infrared video surveillance using a laser altimeter or a radio altimeter,
[0009] Determine the thermal contrast ΔT0 of thermal line targets on the ground by measuring the radiation temperatures of warm and cold lines simultaneously with aerial photography at the time of flight of an unmanned aerial system of infrared video shooting over the line targets, and performing further calculations in accordance with the formula: , where T m and T с - results of brightness measurements of warm and cold strokes, respectively,
[0010] display the received aerial photographs on the screen of the automated interpretation workstation,
[0011] the decoding of thermal line target images on the obtained aerial photographs is performed by at least three decoder operators, as a result of which each decoder operator determines the value of the spatial resolution, which corresponds to the width of a warm dark or cold light line of the smallest group of lines, in which the lines are observed separately along their entire length in such a way that there is a visual perception of the difference in the level of gray tone between each warm dark line and the cold light lines adjacent to it along their entire length, and it is possible to count the number of lines in the group on the screen of the automated decoding workstation,
[0012] determine the final value of spatial resolution for each i-th flight altitude of the unmanned aerial system of infrared video filming, as a result of averaging the spatial resolution estimates for all operator-decipherers and all aerial photographs obtained at the i-th altitude, in accordance with the expression: , Where - average value of spatial resolution for flight altitude H i ; - the value of spatial resolution obtained by the r-th operator-decoder as a result of decoding the s-th image of thermal line targets obtained at flight altitude H i , r=1, ..., R; s=1, ..., S; R is the number of decoder operators, where R≥3; S is the number of thermal line target images obtained at flight altitude H i and subjected to decryption, with S≥20,
[0013] Calculate the threshold thermal contrast transfer coefficients , corresponding to the found values of spatial resolution , by determining the temperatures of pixels in the images of warm dark and cold light strokes of the smallest recognized group of thermal strokes in tone gradations from 0 to 65535 using the graphical editor of the automated decryption workstation, and performing further calculations in accordance with the formulas: , , , Where - the average value of the threshold thermal contrast obtained from images obtained at flight altitude H i ; - the value of the threshold thermal contrast obtained by the r-th operator-decoder from the s-th image obtained at flight altitude H i ; , - average values of the temperatures of the warm dark and cold light strokes of the smallest recognized group of strokes in tone gradations from 0 to 65535, respectively, measured at the automated decoding workstation by the r-th operator-decoder using the s-th image obtained at flight altitude H i ,
[0014] plot a graph of L(H) dependence of spatial resolution on height, taking into account the obtained coefficients of transmission of threshold contrasts at points with coordinates ( ;H i ) and determine the equation trend of the dependence of spatial resolution on height by approximating the constructed graph L(H) by a third-order polynomial function of the form , where a0, a1, a2, a3 are the values of the parameters for approximating the line of the graph L(H) using the least squares method,
[0015] perform trend validation by evaluating the forecast accuracy using the mean relative forecast error indicator according to the expression: , Where - calculated value of spatial resolution for height H i , calculated as a result of substitution into the trend equation H values i , however, if the validation results are obtained >5%, then the parameters of the trend equation approximation are refined and selected in such a way as to obtain a trend equation , ensuring the forecast accuracy corresponding to ≤5%,
[0016] Calculate the predicted value of spatial resolution for flight altitude by extrapolating the trend, for which a substitution is made into the trend equation height values .
[0017] The technical result achieved by the combination of features of the claimed invention consists in increasing the accuracy of estimating the spatial resolution of infrared video filming systems of unmanned aerial systems for a given flight altitude without performing flights at that altitude by extrapolating the spatial resolution estimates obtained when performing flights at other, lower altitudes, and determining the coefficients of transfer of threshold thermal contrasts, which make it possible to take into account the temperature properties of aerial filming objects.
[0018] The implementation of the claimed invention is illustrated by the figures:
[0019] Figure 1 - Fragment of an aerial photograph showing thermal streaks.
[0020] Figure 2 - Graphs of the dependence of spatial resolution on flight altitude.
[0021] The essence of the invention consists in the following sequence of operations.
[0022] 1. Determination of required flight altitudes H iUAS IKV for the formation of an extrapolation base, which is a set of m pairs of flight altitude values and the corresponding spatial resolution values, which form a series of the dynamics of the change in spatial resolution from the flight altitude, where the flight altitude changes with a lead step Δ, calculated in accordance with the expression: , Where - the altitude at which the spatial resolution forecast must be performed, H0 is the initial flight altitude, m is the number of members of the series constituting the extrapolation base, where m≥5. Then the required flight altitudes are determined in accordance with the expression: , where i=0, 1, 2, …, m-1.
[0023] 2. Placement of thermal target charts on the ground, consisting of warm and cold charts and providing thermal contrast, taking into account the location of the charts along and across the direction of flight of the UAV IKV, and the absence of objects shading the surface of the area on which the charts are located.
[0024] 3. Infrared aerial photography of thermal streaks of the world using UAV IKV at flight altitudes H i for given values of the UAV IKV flight course, so as to obtain at each flight altitude H i at least 20 aerial photographs obtained with angular oscillations of the UAV IKV not exceeding the permissible values, with the location of thermal line targets in the center of the aerial photograph or removed from the center in the direction of the horizontal and vertical sides of the aerial photograph at distances not exceeding 20% of the transverse and longitudinal dimensions of the aerial photograph, respectively, while during the flight, monitoring of flight altitudes H is carried out i by measuring the geometric flight altitude of the UAV using a laser altimeter or radio altimeter.
[0025] The flight course of the UAV IKV is selected in such a way that the longitudinal and transverse axes of the thermal dash lines of the target are within ±10° of the lines perpendicular and parallel to the flight direction, respectively.
[0026] The lateral distance of the UAS IKV path line from the location of the thermal line targets is selected in such a way that the images of the line targets fall in the center of the aerial photograph.
[0027] Flights are carried out at a meteorological visibility range of at least 10 km, and also in the absence of clouds or the height of the cloud base exceeding the flight altitude H m -1 by 5%.
[0028] 4. Determining the thermal contrast ΔT0 of thermal line targets on the ground by measuring the radiation temperatures of warm and cold lines simultaneously with aerial photography at the moments of the IKV UAV flight over the thermal line targets, and performing further calculations in accordance with the formula: , where T m and T с - results of brightness measurements of warm and cold strokes, respectively.
[0029] 5. Displaying the obtained aerial photographs on the screen of the automated workstation (AWS) for interpretation.
[0030] 6. Interpretation of thermal line chart images on the obtained aerial photographs by at least three operator-interpreters, as a result of which each operator-interpreter determines the value of spatial resolution, which corresponds to the width of a warm dark or cold light line of the smallest group of lines, in which the lines are observed separately along their entire length in such a way that there is a visual perception of the difference in the level of gray tone between each warm dark line and the neighboring cold light lines along their entire length, and it is possible to count the number of lines in the group on the screen of the automated workstation.
[0031] 7. Determination of the final value of spatial resolution for each i-th flight altitude of the UAV IKV, as a result of averaging the spatial resolution estimates for all operator-decipherers and all aerial photographs obtained at the i-th altitude, in accordance with the expression: , Where - average value of spatial resolution for flight altitude H i ; - the value of spatial resolution obtained by the r-th operator-decoder as a result of decoding the s-th image of thermal line targets obtained at flight altitude H i , r=1, ..., R; s=1, ..., S; R is the number of decoder operators, where R≥3; S is the number of thermal line target images obtained at flight altitude H i and subjected to decryption, with S≥20.
[0032] 8. Determination of threshold thermal contrast transfer coefficients , corresponding to the found values of spatial resolution , by determining the temperatures of pixels in the images of warm dark and cold light strokes of the smallest recognized group of thermal strokes in tone gradations from 0 to 65535 using the graphical editor of the ARM decryption, and performing further calculations in accordance with the formulas: , , , Where - the average value of the threshold thermal contrast obtained from images obtained at flight altitude H i ; - the value of the threshold thermal contrast obtained by the r-th operator-decoder from the s-th image obtained at flight altitude H i ; , - average values of the temperatures of the warm dark and cold light strokes of the smallest recognized group of strokes in tone gradations from 0 to 65535, respectively, measured at the automated decoding workstation by the r-th operator-decoder using the s-th image obtained at flight altitude H i .
[0033] 9. Plotting the L(H) graph of the spatial resolution dependence on height, taking into account the obtained threshold contrast transfer coefficients for points with coordinates ( ;H i ) and the definition of the equation trend of the dependence of spatial resolution on height by approximating the constructed graph L(H) by a third-order polynomial function of the form , where a0, a1, a2, a3 are the values of the parameters for approximating the line of the graph L(H) using the least squares method,
[0034] 10. Perform trend validation by evaluating the forecast accuracy using the average relative forecast error indicator according to the expression: , Where - calculated value of spatial resolution for height H i , calculated as a result of substitution into the trend equation H values i .
[0035] If the validation results are >5%, then the parameters of the trend equation approximation are refined and selected in such a way as to obtain a trend equation , ensuring the forecast accuracy corresponding to ≤5%.
[0036] 11. Calculating the predicted value of spatial resolution for flight altitude by extrapolating the trend, for which a substitution is made into the trend equation height values .
[0037] The technical result achieved by the set of features of the claimed invention consists in increasing the accuracy of estimating the spatial resolution of UAS IRS systems for a given flight altitude without performing flights at this altitude by extrapolating the spatial resolution estimates obtained when performing flights at other, lower altitudes, and determining the coefficients of transfer of threshold thermal contrasts, which make it possible to take into account the temperature properties of aerial photography objects.
[0038] Example 1. The effect of the claimed method was confirmed during flight tests of a quadcopter-type UAS with an infrared video camera (IRVC).
[0039] It is required to determine the spatial resolution of the ICVK at flight altitudes H ТЗ1 =500 m and H ТЗ2=2000 m. UAS flights in the flight zone are permitted at altitudes of H<H ТЗ2 , as a result of which on H ТЗ2 It is not possible to carry out flight experiments.
[0040] As a result of implementing the developed methodology, the following results were obtained:
[0041] 1. Before the UAS flight, the required flight altitudes were calculated to obtain an extrapolation base consisting of 5 spatial resolution values at 5 flight altitudes, i.e. m=5. For simplicity, the notation H0=H was introduced. ТЗ1 =500 m and =N ТЗ2 =2000 m.
[0042] Calculated lead step: m.
[0043] The required flight altitudes have been calculated:
[0044] m;
[0045] m;
[0046] m;
[0047] m.
[0048] 2. The UAS completed a flight at the designated altitudes H0, H1, H2, H3, and H4, during which the IKVK conducted an infrared aerial survey of thermal line targets, obtaining 20 aerial photographs at each altitude. Figure 1 shows a fragment of an aerial photograph obtained at flight altitude H1.
[0049] During the UAS flight, measurements were taken of the radiation temperatures of warm and cold streaks of thermal streaks on the ground and their thermal contrast was determined, which amounted to ΔT0=12.5°C.
[0050] 3. After the UAS flight, the images of thermal line charts were decoded on the decoding workstation, during which the spatial resolution values were determined. , , , , , measurements of the pixel temperatures of warm dark and cold light strokes in images of the smallest groups of strokes were carried out, and the values of threshold thermal contrasts were calculated , , , , and coefficients of transmission of threshold thermal contrasts , , , , for flight altitudes H0, H1, H2, H3, H4, respectively. The decoding results are presented in Table 1.
[0051] Table 1 - Results of decoding images of thermal line patterns
[0052]
[0053] 3. A graph of the L(H) dependence was plotted based on points with coordinates ( ;Н0), ( ;Н1), ( ;Н2), ( ;Н3), ( ;H4), a trend line was added using a third-order polynomial approximation function (Figure 2) and the trend equation was determined : .
[0054] 4. Trend validation completed , according to the results of which it was determined that the accuracy of the approximation was =2.3%, which indicates the possibility of using the trend equation for extrapolation.
[0055] 5. The predicted value of spatial resolution for flight altitude has been calculated. =2000, which amounted to =0.363 m by extrapolating the trend, for which a substitution was made into the equation height values =2000 m.
[0056] To check the reliability of the obtained predicted value of spatial resolution =0.363 m, a test flight of a flying laboratory based on the An-2 aircraft was carried out, during which an infrared aerial survey of thermal streak images was carried out using an infrared infrared camera at an altitude of =2000 m and then the spatial resolution was determined based on the results of interpretation of the obtained aerial photographs. The spatial resolution value in this case was =0.356 m, which indicates a high reliability of the calculated spatial resolution forecast: the convergence of the predicted value of spatial resolution for flight altitude with true spatial resolution at flight altitude amounted to 98.0%.
[0057] An alternative method for determining spatial resolution without flying at the required altitude involves using the formula for calculating the pixel projection onto the earth's surface (Ground Sampling Distance (GSD)) taking into account the Nyquist-Shannon-Kotelnikov theorem: , where L GSD_N - spatial resolution according to the GSD criterion taking into account the Nyquist-Shannon-Kotelnikov theorem; a - linear size of a pixel of the IKVK matrix photodetector; ƒ' - focal length of the IKVK lens.
[0058] Calculated value of the spatial resolution of the ICVK for the flight altitude =2000 m was L GSD_N =0.303 m (calculated taking into account the values of the TPS parameters: a=2.5 µm, ƒ'=33 mm).
[0059] The results of the comparison of the obtained estimates of the spatial resolution of the IKVK are presented in the table.
[0060] Table - Comparison of predicted, calculated and experimental estimates of the spatial resolution of the IKVK
[0061] Method for estimating spatial resolution Spatial resolution, m Number of flights at altitude Convergence of estimates, % Experimental evaluation of spatial resolution based on the results of a flight at the required altitude 0,356 1 Predictive assessment of spatial resolution when implementing the claimed method without performing a flight at the required altitude 0,363 0 98,0 Estimated spatial resolution LGSD_N 0,303 0 68,7 Increase in the accuracy of the forecast estimate relative to the calculated estimate LGSD_N, % 29,3
[0062] The table data demonstrates the effectiveness of the proposed method for predictive spatial resolution estimation using the example of a quadcopter-type UAS ICVC. Specifically, the proposed method improves the accuracy of spatial resolution determination for a given flight altitude without the need to fly at that altitude. The accuracy of the predictive spatial resolution estimate increased by 29.3% compared to the calculated one. Furthermore, the predictive estimation method reduces the number of flights required to estimate spatial resolution by eliminating the need to fly at the required altitude. At the same time, the high reliability of the predictions is maintained: predictive spatial resolution estimates obtained without flying at the required altitude demonstrate 98.0% convergence with experimental estimates obtained at that altitude.
Claims
1. A method for flight testing unmanned aerial systems for infrared video filming based on extrapolation of the dynamics of growth of spatial resolution from the height of video filming, characterized by the fact that determine the required flight altitudes H i an unmanned aerial system for infrared video filming to create an extrapolation base, which is a set of m pairs of flight altitude values and corresponding spatial resolution values, which form a series of the dynamics of the change in spatial resolution from flight altitude, where the flight altitude changes with a lead step Δ, calculated in accordance with the expression: , Where - the altitude at which it is necessary to perform a spatial resolution forecast, H0 is the initial flight altitude, m is the number of members of the series that constitute the extrapolation base, where m≥5, then the value of the required flight altitudes is determined in accordance with the expression: , where i=0, 1, 2, …, m–1, thermal line targets are placed on the ground, consisting of warm and cold lines and providing thermal contrast, taking into account the location of the lines along and across the direction of flight of the unmanned aerial system of infrared video filming, and the absence of objects shading the surface of the area on which the targets are located, perform infrared aerial photography of thermal streaks using an unmanned aerial system for infrared video shooting at flight altitudes of H i for given flight course values, so as to obtain at each flight altitude H iat least 20 aerial photographs obtained with angular oscillations of the unmanned aerial system of infrared video filming not exceeding the permissible values, with the location of thermal line targets in the center of the aerial photograph or removed from the center in the direction of the horizontal and vertical sides of the aerial photograph at distances not exceeding 20% of the transverse and longitudinal dimensions of the aerial photograph, respectively, while during the flight, the flight altitude H is monitored i by measuring the geometric flight altitude of an unmanned aerial system for infrared video surveillance using a laser altimeter or a radio altimeter, The thermal contrast ΔT0 of thermal line targets on the ground is determined by measuring the radiation temperatures of warm and cold lines simultaneously with aerial photography at the moment of flight of an unmanned aerial system of infrared video photography over the line targets, and performing further calculations in accordance with the formula: , where Tm and T с - results of brightness measurements of warm and cold strokes, respectively, display the obtained aerial photographs on the screen of the automated interpretation workstation, deciphering of thermal line chart images on the obtained aerial photographs is performed by at least three operator-decipherers, as a result of which each operator-decipherer determines the value of the spatial resolution, which corresponds to the width of a warm dark or cold light line of the smallest group of lines, in which the lines are observed separately along their entire length in such a way that there is a visual perception of the difference in the level of gray tone between each warm dark line and the cold light lines adjacent to it along their entire length, and it is possible to count the number of lines in the group on the screen of the automated deciphering workstation, determine the final value of the spatial resolution for each i-th flight altitude of the unmanned aerial system for infrared video filming, as a result of averaging the spatial resolution estimates for all operator-decipherers and all aerial photographs obtained at the i-th altitude, in accordance with the expression: , Where - average value of spatial resolution for flight altitude H i ; - the value of spatial resolution obtained by the r-th operator-decoder as a result of decoding the s-th image of thermal line targets obtained at flight altitude H i , r=1, ..., R; s=1, ..., S; R is the number of decoder operators, where R≥3; S is the number of thermal line target images obtained at flight altitude H i and subjected to decryption, with S≥20, calculate the coefficients of transmission of threshold thermal contrasts , corresponding to the found values of spatial resolution , by determining the temperatures of pixels in the images of warm dark and cold light strokes of the smallest recognized group of thermal strokes in tone gradations from 0 to 65535 using the graphical editor of the automated decryption workstation, and performing further calculations in accordance with the formulas: , , , Where - the average value of the threshold thermal contrast obtained from images obtained at flight altitude H i ; - the value of the threshold thermal contrast obtained by the r-th operator-decoder from the s-th image obtained at flight altitude H i ; , - average values of the temperatures of the warm dark and cold light strokes of the smallest recognized group of strokes in tone gradations from 0 to 65535, respectively, measured at the automated decoding workstation by the r-th operator-decoder using the s-th image obtained at flight altitude H i , construct a graph of L(H) dependence of spatial resolution on height, taking into account the obtained coefficients of transmission of threshold contrasts at points with coordinates ( ; N i ) and determine the equation trend of the dependence of spatial resolution on height by approximating the constructed graph L(H) by a third-order polynomial function of the form , where a0, a1, a2, a3 are the values of the parameters for approximating the line of the graph L(H) using the least squares method, perform trend validation by assessing the forecast accuracy using the mean relative forecast error in accordance with the expression: , Where - calculated value of spatial resolution for height H i , calculated as a result of substitution into the trend equation H values i , however, if the validation results are obtained >5%, then the parameters of the trend equation approximation are refined and selected in such a way as to obtain a trend equation , ensuring the accuracy of the forecast corresponding to ≤5%, calculate the predicted value of spatial resolution for flight altitude by extrapolating the trend, for which a substitution is made into the trend equation height values .
2. The method according to paragraph 1, characterized in that a Raynger radiation thermometer is used as a means for measuring the radiation temperatures of warm and cold lines of thermal line charts on the ground.
3. The method according to paragraph 1, characterized in that the warm strokes of the thermal worlds are made of aluminum plates painted black.
4. The method according to paragraph 1, characterized in that the thermal line chart consists of warm lines, made in the form of metal plates laid out on the earth's surface at specified distances, and cold lines, which are areas of the earth's surface between the laid out metal plates.
5. The method according to paragraph 1, characterized in that the cold strokes of the thermal worlds are made of polished aluminum plates.
6. The method according to paragraph 1, characterized in that a satellite navigation system is used as a means for measuring the geometric flight altitude of the aircraft.