Ground object detection refraction error compensation modeling method and system

Abstract

The invention relates to a ground object detection refraction error compensation modeling method and system, and belongs to the technical field of earth remote sensing detection and space remote sensing. The atmosphere between the aircraft and the ground surface is divided into N layers, the distance between every two adjacent layers is calculated, and then the light refraction angle of each atmosphere layer is obtained through solving according to the Snell law; in combination with a Hopfield model of the atmospheric refractive index and an e index joint model, analog calculation of an atmospheric refractive index profile is realized, and then a horizontal distance between two adjacent atmospheric layers on a light propagation path is solved; and finally, combining the vertical distance from the aircraft to the earth surface to calculate an included angle between a connecting line from the aircraft to the real position of the ground object and a geocentric vertical line, namely a real elevation angle, thereby analyzing the real elevation angle to solve an elevation angle error and a distance error. According to the invention, the elevation angle error and distance error of the aircraft caused by atmospheric refraction can be corrected, so that the method can be applied to accurate identification and positioning of an observed target.

Description

Technical Field

[0001] The present invention relates to a modeling method and system for compensating refraction errors in ground object detection, belonging to the technical fields of earth remote sensing detection and space remote sensing. Background Art

[0002] The density of the earth's atmosphere is a continuous curve that varies with altitude. The difference in the light propagation speed in different substances is the cause of refraction. The closer to the earth's surface, the greater the atmospheric density, the slower the light propagation speed, and the larger the refractive index. The farther from the earth's surface, the smaller the atmospheric density, the faster the light propagation speed, and the smaller the refractive index. When observing ground object targets from an aircraft, because light has to pass through different concentrations of the atmosphere, the light is bent due to refraction, which ultimately leads to a difference between the observed position of the ground object and the actual situation, thus affecting the detection and positioning of distant targets and the research on the shape and surface characteristics of the targets. This difference is particularly prominent in high-altitude observations (such as satellites and high-altitude aircraft) or large-angle detections, seriously restricting the reliability and application value of remote sensing data.

[0003] Problems of the existing technologies are as follows: Insufficient accuracy of the layered model: Traditional methods simplify the atmosphere into a finite number of layers (usually N = 1 - 200 layers) and calculate the refraction angle layer by layer through Snell's law. However, too few layers will lead to an increase in the cumulative error of the refraction path, and the calculation results show large fluctuations, which cannot meet the high-precision positioning requirements.

[0004] Simplification of the refractive index model: Existing methods use a single model (such as the Hopfield model or the e-exponential model) to describe the variation of atmospheric refractive index with height. However, there are significant differences in the distribution laws of atmospheric refractive index in the near-surface area and the high-altitude area: the existing technologies do not effectively combine the advantages of the two models, resulting in systematic deviations in the refractive index calculation in the cross-elevation area. For example, in the existing patent publication number CN118707452A, a method and device for correcting atmospheric refraction errors in a low-dimensional area are disclosed, which combines Snell's theorem and an iterative optimization algorithm to achieve error correction through integral operation and interpolation method. Its core is to improve the correction efficiency in low-dimensional areas (such as flat terrain) by layering and segmentation, but it does not involve joint modeling in the full elevation range.

[0005] Insufficient dynamic coupling of environmental parameters: Existing methods do not fully consider the dynamic influence of real-time environmental parameters (such as temperature, pressure, wavelength λ) at the ground object position on the refractive index, resulting in unreliable correction results. Summary of the Invention

[0006] The object of the present invention is to propose a method and system for compensating and modeling the refraction error of ground object detection. According to information such as the line-of-sight direction, flight altitude, and wavelength of the ground object observation target by the aircraft, an algorithm for compensating the apparent direction error of atmospheric refraction is established. During the construction process, the Hopfield model and the e-exponential model of the atmospheric refractive index are combined to realize the simulation of the atmospheric refractive index profile. Finally, by calculating the difference between the apparent elevation angle and the true elevation angle of the aircraft, an elevation angle error model is constructed to correct the elevation angle error of the aircraft caused by atmospheric refraction, so as to be applied to the precise identification and positioning of the observed target. The problems in the prior art are solved.

[0007] The method for compensating and modeling the refraction error of ground object detection according to the present invention includes the following steps: S1: Divide the atmosphere between the aircraft and the ground surface into N layers, and calculate the distance between adjacent layers; S2: Solve the refraction angle of the light at each atmospheric layer according to Snell's law; S3: Calculate the horizontal distance between two adjacent atmospheric layers on the light propagation path; S4: Calculate the distance between the projection of the aircraft on the ground surface and the true position of the ground object according to the result of step S3; S5: Combine the vertical distance from the aircraft to the earth's surface and the distance obtained in step S4 to calculate the angle between the line connecting the aircraft to the true position of the ground object and the vertical line of the earth's center, that is, the true elevation angle; S6: Calculate the elevation angle error and the distance error according to the true elevation angle in step S5 and the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the earth's center, that is, the apparent elevation angle.

[0008] Preferably, when the atmosphere is divided into N layers in step S1, the distance between adjacent layers is , where h is the distance from the aircraft to the earth's surface.

[0009] Preferably, in step S2, the earth's atmosphere is stratified. Assuming that the atmospheric density is the same within the same layer and different between different layers, Snell's law is satisfied between adjacent layers. By analogy, the following relational expressions hold:

[0010] Thus, the refraction angle of each layer can be calculated:

[0011] Where: is the refractive index of the 0th layer of the atmosphere, is the incident angle of the 0th layer, is the refractive index of the 1st layer of the atmosphere, is the refraction angle of the 1st layer, and so on. is the atmospheric refractive index of the (N - 1)th layer, is the incident angle of the (N - 1)th layer, is the atmospheric refractive index of the Nth layer, is the refraction angle of the Nth layer; according to the alternate interior angle theorem, the calculated refraction angle is the incident angle of the next layer.

[0012] Preferably, the calculation of the atmospheric refractive index includes: where represents the atmospheric refractive index at the apparent position of the ground object, which is expressed by the following formula,

[0013] In the formula, , t, P, e, λ respectively refer to the atmospheric temperature, pressure, water vapor pressure, and wavelength at the ground object position; The atmospheric refractive index on the light propagation path is expressed by the following formula,

[0014] Among them, represents the elevation, which is calculated by 40136 + 148.72× t , the unit is m. Below the elevation, the atmospheric refractive index at each altitude position is given by the Hopfield model. Above the elevation, the atmospheric refractive index at each altitude position is given by the e exponential model, where represents the atmospheric refractive index at the elevation, β is the piecewise fitting exponent.

[0015] Preferably, the horizontal distance between two adjacent layers in step S3 is calculated by the following formula: .

[0016] Preferably, in step four, according to the result obtained in step three, calculate the distance between the projection of the aircraft and the ground to the true position of the ground object :

[0017] Preferably, in step S6, according to the true elevation angle calculated in step S5, combined with the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the earth's center, that is, the apparent elevation angle, calculate the elevation angle error, which is expressed as:

[0018] Among them, Z0 is the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the earth's center, that is, the apparent elevation angle, and this value is a known quantity, θIt is the angle between the line connecting the aircraft to the true position of the ground object and the vertical line of the earth's center, that is, the true elevation angle, which is obtained through step S5.

[0019] Preferably, in step S6, the distance error represents the distance between the true position of the ground object and the apparent position of the ground object, and is represented by and is solved by the following formula

[0020] where h is the distance from the aircraft to the earth's surface, which is a known quantity, is the distance from the projection of the aircraft on the earth's surface to the true position of the ground object, and Z0 is the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the earth's center, that is, the apparent elevation angle.

[0021] The ground object detection refraction error compensation modeling system described in the present invention includes: Stratification module: used to divide the atmosphere between the aircraft and the ground surface into N layers and calculate the distance between adjacent layers; Refraction angle calculation module: iteratively solve the refraction angle of each atmosphere layer based on Snell's law; Horizontal distance calculation module: calculate the horizontal distance between adjacent layers according to the refraction angle and the stratification distance; Projection distance module: accumulate the horizontal distances of all layers to obtain the distance from the projection of the aircraft on the ground surface to the true position of the ground object; True elevation angle calculation module: calculate the true elevation angle in combination with the vertical distance and the projection distance of the aircraft; Error calculation module: calculate the elevation angle error and the distance error according to the difference between the true elevation angle and the apparent elevation angle.

[0022] Preferably, the value range of N in the stratification module is 900 to 1000, and the distance between adjacent layers is fixed at 100 meters.

[0023] Compared with the existing technology, a ground object detection refraction error compensation modeling method and system of the present invention can correct the elevation angle error and the distance error of the aircraft caused by atmospheric refraction, so as to be applied to the accurate identification and positioning of the observed target. It has the following beneficial effects: ① High-precision error correction: Combining the Hopfield model and the e-index piecewise refractive index model, the optimal model is adopted respectively in the area below the elevation (near the ground surface) and above the elevation (high altitude) areas, so as to reduce the cross-layer refractive index calculation error.

[0024] By optimizing the number of atmosphere layers to 900 - 1000 layers and fixing the layer distance at 100 meters, the calculation efficiency and accuracy are effectively balanced, and the fluctuation of the elevation angle error is controlled within ±0.5 arcseconds.

[0025] ② Multi-band adaptability: By introducing the wavelength parameter λ to dynamically correct the refractive index calculation formula, it supports unified correction for multiple bands such as visible light, near-infrared, mid-wave infrared, and long-wave infrared.

[0026] ③ Dynamic environmental parameter coupling: Integrate the real-time temperature (t), pressure (P), water vapor pressure (e), and wavelength (λ) parameters at the location of the ground object to improve the adaptability of the model in extreme climates and complex geographical environments.

[0027] ④ Full altitude and global applicability: Cover the altitude range from 40 to 120 km, and verify the applicability in different geographical regions. The standard deviation of the elevation angle error is less than 0.3 arcseconds, meeting the requirements of global remote sensing monitoring. Brief Description of the Drawings

[0028] Figure 1 It is a flowchart of the ground object detection refraction error compensation modeling method described in Embodiment 1 of the present invention; Figure 2 It is a schematic diagram of the observation geometry of the ground object detection refraction error compensation modeling method described in Embodiment 1 of the present invention; Figure 3 It is the corresponding relationship between the elevation angle error and the height within the range of 1 - 80 km in Embodiment 1 of the present invention; Figure 4 It is an observation schematic diagram of the variation law of the elevation angle error within the range of 1 - 80 km with a zenith distance of 45° in Embodiment 1 of the present invention; Figure 5 It is a corresponding relationship diagram between the distance error and the altitude in Embodiment 1 of the present invention; Figure 6 It is a corresponding relationship diagram between the elevation angle error and the altitude under the condition of a zenith distance of 45° in Embodiment 1 of the present invention; Figure 7 It is a comparison effect diagram of the results of the present invention and the existing SIDNEY BERTRAM in Embodiment 1 of the present invention. Detailed Embodiment

[0029] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0030] Embodiment 1: As Figure 1 - Figure 2 shown, this embodiment discloses a ground object detection refraction error compensation modeling method, including the following steps: Step 1: Divide the atmosphere between the aircraft and the ground surface into N layers, and calculate the distance between adjacent layers; In Step 1, when the atmosphere between the aircraft and the ground surface is divided into N layers, the distance between adjacent layers is , h is the distance from the aircraft to the Earth's surface. In theory, the larger the stratification N, the better. However, if N is too large, the calculation speed will be relatively slow. Through calculation, it is found that when N is small (1 - 200), the calculation results have large fluctuations. When N is in the range of 900 - 1000, the fluctuations of the calculation results are small. In order to ensure the accuracy of the calculation results and the operation speed of the program, the distance between the atmospheres is fixed at 100 meters. After verification, when the altitude resolution is 100 meters, the fluctuations of the elevation angle error are small.

[0031] Step 2: Solve the refraction angle of the light at each atmospheric layer according to Snell's law; In the said Step 2, according to the stratification result of the Earth's atmosphere in Step 1, assuming that the atmospheric density is the same within the same layer and different between different layers, then Snell's law is satisfied between adjacent layers. For example, the refractive index of the 0th layer of the atmosphere is , the incident angle is , the refractive index of the 1st layer of the atmosphere is , the refraction angle is , then according to Snell's law between the two layers, we can get . According to the alternate interior angle theorem, the calculated refraction angle is the incident angle of the next layer. Therefore, for the 1st and 2nd layers, there is a relational expression . By analogy, the following relational expressions hold,

[0032] Thus, the refraction angle of each layer can be calculated.

[0033] The solution of the atmospheric refractive index in the said Step 2 is a key point, which is related to the calculation of the refraction angle of each layer of the atmosphere. Among them, represents the atmospheric refractive index at the apparent position of the ground object, which can be expressed by the following formula,

[0034] where, , t, P, e, λ respectively refer to the atmospheric temperature, pressure, water vapor pressure, and wavelength at the ground object position; The atmospheric refractive index on the light propagation path can be expressed by the following formula,

[0035] where, represents the scale height, which can be calculated by 40136 + 148.72× t , and the unit is m. Below the scale height, at each altitude position The atmospheric refractive index at [location] is given by the Hopfield model. Above the elevation, at each altitude position the atmospheric refractive index at e is given by the exponential model, where represents the atmospheric refractive index at the elevation, β is the piecewise-fitted exponent.

[0036] Step 3: Calculate the horizontal distance between two adjacent atmospheric layers along the light propagation path; In Step 3 for calculating the horizontal distance between two adjacent atmospheric layers along the light propagation path, the horizontal distance between two adjacent atmospheric layers can be expressed as

[0037] Step 4: According to the result obtained in Step 3, calculate the distance between the projection of the aircraft and the ground surface to the true position of the ground object; In Step 4, according to the result obtained in Step 3, calculate the distance between the projection of the aircraft and the ground surface to the true position of the ground object :

[0038] Step 5: According to the conclusion of Step 4, combined with the vertical distance from the aircraft to the Earth's surface, calculate the angle between the line connecting the aircraft to the true position of the ground object and the vertical line from the center of the Earth, i.e., the true elevation angle; In Step 5, according to the conclusion of Step 4, combined with the vertical distance from the aircraft to the Earth's surface, calculate the angle between the line connecting the aircraft to the true position of the ground object and the vertical line from the center of the Earth, i.e., the true elevation angle. The calculation formula is as follows:

[0039] where, h is the distance from the aircraft to the Earth's surface, which is a known quantity, is the distance from the projection of the aircraft on the Earth's surface to the true position of the ground object.

[0040] Step 6: According to the true elevation angle calculated in Step 5, combined with the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line from the center of the Earth, i.e., the apparent elevation angle, and then calculate the elevation angle error and the distance error.

[0041] In Step 6, according to the true elevation angle calculated in Step 5, combined with the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line from the center of the Earth, i.e., the apparent elevation angle, calculate the elevation angle error, which can be expressed as:

[0042] where, Z0 is the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line from the center of the Earth, i.e., the apparent elevation angle, and this value is a known quantity, θIt is the angle between the line connecting the aircraft to the true position of the ground object and the vertical line of the earth's center, that is, the true elevation angle, which is obtained through Step Five.

[0043] The distance error represents the distance between the true position and the apparent position of the ground object, and is represented by and is solved by the following formula

[0044] where h is the distance from the aircraft to the earth's surface, which is a known quantity, is the distance from the projection of the aircraft on the earth's surface to the true position of the ground object, and Z0 is the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the earth's center, that is, the apparent elevation angle.

[0045] To verify the accuracy and reliability of the calculation results, the elevation angle error is calculated by selecting the following environmental parameters: Time (UTC): 2023-04-15; T 12:00:00, the aircraft is flying over Beijing, the solar activity index F107 is 60 sfu, the geomagnetic activity index Ap is 10 nT, the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the earth's center is between 0-30°, and the aircraft is flying at an altitude of 40-120 km. The elevation angle errors in the visible light, near-infrared, mid-wave, and long-wave bands are calculated respectively in the range of 0-30° of the deviation angle from the vertical line of the earth's center and the altitude of 40-120 km, as shown in Table 1, Table 2, Table 3, and Table 4 respectively, and the unit of the elevation angle error is arcseconds.

[0046] Table 1 Elevation Angle Error (Unit: Arcseconds) in the Visible Light Wavelength Range of 0.39~0.78μm (Select 0.58μm)

[0047] Table 2 Elevation Angle Error in the Near-Infrared Band of 0.78-2.5μm (Select 1.64μm)

[0048] Table 3 Elevation Angle Error in the Mid-Wave Band of 3-5μm (Select 4μm)

[0049] Table 4 Elevation Angle Error in the Long-Wave Band of 8–14μm (Select 11μm)

[0050] From the calculation results in Tables 1, 2, 3, and 4, it is found that the atmospheric refraction angle (elevation error) shows a decreasing trend with the increase of wavelength. The formula for the absolute refractive index is \(n = \sin i / \sin r = c / v\), where \(c\) is the speed of light in vacuum, \(v\) is the speed in the medium. From \(v=\lambda*f\), in the same medium, the longer the \(\lambda\), the greater the \(v\). And since the speed of light \(c\) is a constant, it can be concluded that in the same medium, the longer the \(\lambda\), the smaller the refractive index \(n\). Therefore, as the wavelength decreases, the refraction effect becomes more significant, the atmospheric refraction angle increases, and as the wavelength increases, the atmospheric refraction angle gradually decreases.

[0051] From the above calculation results, it is found that the atmospheric refraction angle increases with the increase of the observation angle. This is because as the observation angle increases, the transmission distance of the light in the atmosphere increases. Since the transmission distance of the light increases, a longer transmission distance will cause the refraction effect of the light to be more significant, resulting in an increase in the atmospheric refraction angle. At the same time, it is also found that in the altitude range of 40 - 120 km, as the altitude increases, the atmospheric refraction angle decreases. In order to obtain the variation law of the atmospheric refraction angle and altitude, the corresponding relationship between the atmospheric refraction angle and altitude in the range of 1 - 80 km is drawn.

[0052] By calculating the variation law of the elevation error with altitude in the altitude range of 1 - 80 km under the conditions of the apparent zenith distance being 25°, 30°, 35°, and 45° respectively, it is found that the elevation error first increases and then decreases with altitude, as Figure 3 shown, and the elevation error is the largest at about the altitude of 15 km.

[0053] Cause analysis: Taking the variation law of the elevation error in the range of 1 - 80 km with the apparent zenith distance of 45° as an example, Figure 4 as the observation schematic diagram, \(S\) represents the distance from the aircraft to the apparent position of the ground object, γ represents the elevation error, \(h\) represents the altitude of the aircraft, \(\Delta\) represents the distance error between the true position and the apparent position of the ground object. In order to show the variation law between the elevation error γ and the flight altitude \(h\), a relational expression between the two needs to be established. Based on the sine theorem, there is the following relational expression,

[0054] where , then the above formula can be transformed into,

[0055] Further simplifying the above formula, it can be obtained that,

[0056] Thus, it can be obtained that γThe relationship between h and

[0057] In the above formula, △ represents the distance error between the true position and the apparent position of different h corresponding ground objects, and this value has been calculated by the refraction compensation system. Figure 5 is the corresponding relationship diagram between △ and h under the condition of apparent zenith distance of 45° and within the altitude range of 1 - 80 km.

[0058] There is a complex arctangent relationship between the elevation angle error γ and the altitude h. Figure 6 shows the corresponding relationship between the elevation angle error γ and the height h under the condition of apparent zenith distance of 45°. Because there is a formula such a relationship between γ and h, which indicates that the elevation angle error first increases and then decreases as the altitude increases.

[0059] The density of the earth's atmosphere is a continuous curve that changes with altitude. The difference in the light propagation speed in different substances is the cause of refraction. The closer to the earth's surface, the greater the atmospheric density, the slower the light propagation speed, and the larger the refractive index. The farther from the earth's surface, the smaller the atmospheric density, the faster the light propagation speed, and the smaller the refractive index. When observing ground object targets from an aircraft, because the light has to pass through the atmosphere with different concentrations, the light is bent due to refraction, which ultimately leads to a difference between the observed position of the ground object and the actual situation, thus affecting the detection and positioning of distant targets and the study of target shape and surface characteristics.

[0060] Accuracy verification experiment: (1) Influence of water vapor pressure on elevation angle error Although the water vapor content in the atmosphere is not much, it also affects the refractive index, thereby affecting the elevation angle error. The water vapor pressure has obvious latitude distribution characteristics, with the maximum at the equator being about 30 hPa and gradually decreasing towards the poles. The variation range of the water vapor pressure on the land surface is between 0 - 30 hPa, and it is larger near the ground and then decreases rapidly with the increase in height. Assuming the vertical distribution of the water vapor pressure is as shown in the following formula,

[0061] where, represents the water vapor pressure at the earth's surface, represents the distance above the earth's surface, with the unit of km.

[0062] In order to analyze the influence of water vapor pressure on elevation angle error, the elevation angle errors are calculated respectively under the conditions of considering and not considering water vapor pressure, and finally the difference between the two is calculated. The environmental parameters are: the latitude and longitude of Beijing area (39.56°, 116.20°), time 12:00:00 on September 1, 2022 (UTC), and wavelength 0.58μm.

[0063] Calculate respectively = 30hPa and = 0, the elevation angle errors (unit: arcseconds) of the aircraft at flight altitudes of 40km, 70km, and 100km are calculated, and the difference error between the two is calculated. The definition of error is The difference between the elevation angle error under the condition of = 0 and The elevation angle error under the condition of = 30hPa. The calculation results are shown in Tables 5, 6, and 7 respectively.

[0064] Table 5 Elevation Angle Error of the Aircraft at 40km Flight Altitude

[0065] Table 6 Elevation Angle Error of the Aircraft at 70km Flight Altitude

[0066] Table 7 Elevation Angle Error of the Aircraft at 100km Flight Altitude

[0067] From the above calculation results, it is found that the influence of water vapor pressure on elevation angle error is within 10 -4 –10 -3 arcseconds, and the influence on the accuracy of elevation angle error is about 0.005%. Therefore, under general weather conditions, the influence of water vapor pressure on the elevation angle error of ground object refraction can be ignored.

[0068] Under other weather conditions with large water vapor such as rain, snow, cloudy days, and overcast days, the water vapor pressure on land can reach 45hPa. In order to analyze the change of elevation angle error under bad weather conditions such as rain, snow, and cloudy days, the initial values of water vapor pressure are calculated respectively = 35hPa, 40hPa, 45hPa, the elevation angle errors (unit: arcseconds) of the aircraft at flight altitudes of 40km, 70km, and 100km are calculated, and compared with the elevation angle error under the condition of the initial value of water vapor pressure = 0. The calculation results are shown in Table 8.

[0069] Table 8 Influence of Water Vapor Pressure on Elevation Angle Error under Extreme Conditions

[0070] As can be seen from the above table, in weather with more water vapor such as rain, snow, and cloudy days, the change in the elevation angle error caused by water vapor pressure is within 5×10 -3 –5×10 -3 arcseconds, and the maximum impact on the elevation angle error accuracy is approximately 0.0068%. Therefore, whether in weather such as rain, snow, cloudy, or overcast days, or under normal circumstances, the impact of water vapor pressure on the elevation angle error accuracy is very small.

[0071] By analyzing the influence of water vapor pressure on the elevation angle error of ground object refraction in general weather conditions ( ≤30 hPa) and weather with more water vapor such as rain, snow, cloudy, and overcast days ( ≤30 hPa), it is found that the influence of water vapor pressure on the elevation angle error accuracy is less than 0.0068%. This value is a very small amount. In summary, the influence of water vapor pressure on ground object refraction can be ignored.

[0072] (2) Influence of temperature on elevation angle error The temperature of the Earth's atmosphere does not change uniformly. In the troposphere and mesosphere, the atmospheric temperature decreases with increasing altitude. Among them, in the troposphere, for every 1 km increase in altitude, the temperature drops by about 6°C. In the stratosphere, an inversion layer will appear, that is, the temperature increases with increasing altitude. In the thermosphere, the temperature also increases with increasing altitude. To analyze the influence of temperature on the elevation angle error, in actual operation, assuming that the pressure remains unchanged and the water vapor pressure e = 0, the change in the elevation angle error is calculated under the condition of temperature change ΔT.

[0073] The environmental parameters are: latitude and longitude of Beijing area (39.56°, 116.20°), time 12:00:00 (UTC) on September 1, 2022, solar activity index F107 is 60 sfu, geomagnetic activity index Ap is 10 nT, and wavelength is 0.58 μm. Based on these environmental parameters, the initial values of temperature and pressure at the ground object position are calculated using the NRLMSIS2.0 model. These values can also be given by other models or measured data.

[0074] The elevation angle errors (unit: arcseconds) of the aircraft at flight altitudes of 40 km, 70 km, and 100 km are calculated respectively under the conditions of temperature changes ΔT (±1 K, ±5 K, ±10 K), as shown in Tables 9, 10, and 11. Table 9 Elevation angle error of the aircraft at a flight altitude of 40 km with temperature change ΔT

[0075] Table 10 Elevation angle error of the aircraft at a flight altitude of 70 km with temperature change ΔT

[0076] Table 11 Elevation Angle Error of Temperature Change ΔT for Aircraft at a Flight Altitude of 100 km

[0077] Based on the ground object refraction elevation angle error values in Table 9, Table 10, and Table 11, calculate the difference error between the elevation angle errors under the conditions of ΔT changing by ±1K, ±5K, ±10K and the elevation angle error when ΔT = 0. Here, it is defined that: the difference between the elevation angle error when ΔT changes by ±1K and the elevation angle error when ΔT = 0 is error1, the difference between the elevation angle error when ΔT changes by ±5K and the elevation angle error when ΔT = 0 is error5, and the difference between the elevation angle error when ΔT changes by ±10K and the elevation angle error when ΔT = 0 is error10. Then, the absolute values of the ranges of error1, error5, and error10 within the 5–30° apparent elevation angle range for the aircraft at flight altitudes of 40 km, 70 km, and 100 km are shown in Table 12.

[0078] Table 12 Absolute Values of the Ranges of error1, error5, and error10 within the Apparent Elevation Angle Range (unit: arcseconds)

[0079] It can be seen from Table 12 that as the altitude of the aircraft increases, the change in the elevation angle error caused by temperature decreases, and as the apparent direction of the aircraft and the deviation angle from the vertical line of the earth's center increase, the change in the elevation angle error caused by temperature increases. For every 1K change in temperature, the elevation angle error changes by approximately 10 -3 –10 -2 arcseconds, and for every 10K change in temperature, the elevation angle error can change by 10 -1 arcseconds. Through calculation, it is found that even when the temperature change is 10K, the impact on the elevation angle error accuracy is still less than 5%.

[0080] (3)Effect of Pressure on Elevation Angle Error Atmospheric pressure is the atmospheric pressure acting on a unit area, which numerically equals the gravity of the vertical air column extending upward to the upper boundary of the atmosphere on a unit area. The atmosphere is divided into different layers in the vertical direction, and each layer has a different air pressure. The air pressure at sea level is approximately 1013.25 hPa, but as the altitude increases, the air pressure gradually decreases. At a place about 5.5 km above sea level, the air pressure is only about half of that at sea level.

[0081] To analyze the effect of pressure on the elevation angle error, in actual operation, assuming the temperature remains constant and the water vapor pressure e = 0, calculate the change in the elevation angle error under the condition of pressure change ΔP.

[0082] Calculate the elevation angle errors (unit: arcseconds) of the aircraft at flight altitudes of 40 km, 70 km, and 100 km under pressure changes ΔP (~1 hPa, ~5 hPa, ~10 hPa, ~50 hPa) respectively, as shown in Tables 13, 14, and 15.

[0083] Table 13 Elevation Angle Errors of the Aircraft at a Flight Altitude of 40 km under Pressure Change ΔP

[0084] Table 14 Elevation Angle Errors of the Aircraft at a Flight Altitude of 70 km under Pressure Change ΔP

[0085] Table 15 Elevation Angle Errors of the Aircraft at a Flight Altitude of 100 km under Pressure Change ΔP

[0086] From the elevation angle error values in Tables 13, 14, and 15, calculate the elevation angle errors under the conditions of ΔP changes of 1‰, 5‰, 1%, and 5% respectively. (Among them, a ΔP change of 1‰ is equivalent to a change in surface pressure of about 1 hPa, a ΔP change of 5‰ is equivalent to a change in surface pressure of about 5 hPa, a ΔP change of 1% is equivalent to a change in surface pressure of about 1 kPa, and a ΔP change of 5% is equivalent to a change in surface pressure of about 5 kPa). Then subtract the elevation angle error under the condition of ΔP = 0. Here, it is defined that: the difference between the elevation angle error of ΔP change of 1‰ and the elevation angle error under the condition of ΔP = 0 is error1‰, the difference between the elevation angle error of ΔP change of 5‰ and the elevation angle error under the condition of ΔP = 0 is error5‰, the difference between the elevation angle error of ΔP change of 1% and the elevation angle error under the condition of ΔP = 0 is error1%, and the difference between the elevation angle error of ΔP change of 5% and the elevation angle error under the condition of ΔP = 0 is error5%. Then the ranges of error1‰, error5‰, error1%, and error5% within the 5–30° apparent elevation angle range of the aircraft at flight altitudes of 40 km, 70 km, and 100 km are shown in Table 16.

[0087] Table 16 Ranges of error1‰, error5‰, error1%, and error5% within the Apparent Elevation Angle Range (unit: arcseconds)

[0088] It can be seen from Table 16 that as the altitude of the aircraft increases, the change in the elevation angle error caused by pressure decreases. As the apparent direction of the aircraft and the deviation angle from the vertical line of the earth's center increase, the change in the elevation angle error caused by pressure increases. For every 1 kPa change in pressure, the elevation angle error changes by about 10 -3 –10 -2Arcsecond level. When the pressure changes by 5 kPa, the change in elevation angle error is within 10 -1 arcseconds. When the pressure at the ground object location changes by 5 kPa, the influence on the elevation angle error accuracy is less than 5%.

[0089] (4)Influence of latitude on elevation angle error One representative area is selected from low-latitude, mid-latitude, and high-latitude land areas in the Northern Hemisphere of the Earth to calculate the elevation angle error. The specific information is as follows: The low-latitude area selects East Kalimantan Province, Indonesia (1°N, 115°E), the mid-latitude area selects Beijing (40°N, 116°E), and the high-latitude area selects Yakutia, Russia (70°N, 116°E). The elevation angle errors of the aircraft at flight altitudes of 40 km, 70 km, and 100 km are calculated under the condition of apparent elevation angles of 5–30°, as shown in Table 16. Except for geographical longitude and latitude, other environmental parameters are: time 12:00:00 on September 1, 2022 (UTC), solar activity index F107 is 60 sfu, geomagnetic activity index Ap is 10 nT, and wavelength is 0.58 μm. It can be seen from Table 17 that the elevation angle error decreases with the increase of latitude. This is because in areas with high latitudes, the air pressure is high, the temperature is low, and the air is thin. Compared with mid- and low-latitude areas, the refraction effect is not particularly significant.

[0090] Table 17 Calculation of elevation angle error in low, mid, and high latitude areas

[0091] (5)Influence of season on elevation angle error To analyze the influence of season on elevation angle error, the elevation angle errors in Beijing on April 15, 2021 (spring), July 15, 2021 (summer), October 15, 2021 (autumn), and January 15, 2022 (winter) are discussed. It is found that the elevation angle error is the largest in winter, the smallest in summer, and the elevation angle error in spring and autumn is in the middle. However, as the altitude increases, the elevation angle error in summer gradually becomes larger, and the elevation angle error in winter gradually becomes smaller, as shown in Table 18. This is because in winter, the temperature is low and the atmosphere shrinks. At lower altitude positions, the atmospheric density in winter is relatively larger than that in summer, and the refraction effect is more obvious. However, as the altitude increases, the atmospheric density in winter decreases rapidly relative to that in summer, resulting in the elevation angle error in winter gradually becoming smaller relative to that in summer as the altitude increases.

[0092] Table 18 Seasonal variation of elevation angle error

[0093] Table 19 Comparison of the results of the present invention with those of SIDNEY BERTRAM

[0094] As shown in Table 19, by comparing with the calculation results of SIDNEY BERTRAM, it is found that the maximum relative error between the two is 25.6%, and the minimum relative error is 5.9%, as Figure 7 shown in the comparison chart.

[0095] Difference analysis: Significance of accuracy improvement: The error of the present invention in the low altitude area (1 km) is 13.82 micro-radians, which is 25.6% higher than that of SIDNEY BERTRAM (11 micro-radians), but the error is significantly reduced to 5.9% in the high altitude area (9 km).

[0096] Key progress: The error systematically decreases with the increase of altitude (from 25.6% to 5.9%), indicating that the present invention has stronger adaptability to the vertical structure of the atmosphere.

[0097] Adaptability to modern atmospheric conditions: SIDNEY BERTRAM is modeled based on the 1966 atmospheric data, without considering the long-term changes in atmospheric parameters (such as the global increase in density, temperature, and pressure) caused by the greenhouse effect.

[0098] The present invention more closely fits the current atmospheric state through dynamic integration of real-time environmental parameters (temperature, pressure, humidity) and a multi-band correction mechanism, and the calculation results reflect the actual physical change trend, as Figure 7 shown in the comparison chart.

[0099] Limitations of the prior art: Due to the outdated data, the error of SIDNEY BERTRAM's model is as high as 25.6% in the low altitude area, which cannot meet the requirements of modern high-precision remote sensing (such as satellite earth observation requires an error < 1%).

[0100] The present invention compresses the error to less than 10% in the high altitude area (>5 km) by optimizing the layering strategy (900 - 1000 layers) and dual-model fusion (Hopfield + e-index), breaking through the accuracy bottleneck of traditional models.

[0101] Innovation of technical effects: Error convergence characteristics: The error of the present invention at 9 km (5.9%) is less than one-fourth of the error at 1 km (25.6%), highlighting the inhibitory effect of layering optimization on cumulative errors.

[0102] Practical application value: Compared with static historical models, the present invention supports precise correction under the background of global warming and provides a reliable data basis for high-altitude remote sensing (such as satellite positioning, disaster monitoring).

[0103] By integrating modern atmospheric parameters and hierarchical optimization, the present invention significantly reduces the error gap with the classical model (especially in high-altitude regions), solves the systematic deviation problem caused by outdated data in SIDNEY BERTRAM, and provides a more reliable error compensation scheme for earth observation. During the construction process, the Hopfield model and the e-index model of atmospheric refractive index are combined to simulate the atmospheric refractive index profile. Finally, by calculating the difference between the apparent elevation angle and the true elevation angle of the aircraft, the elevation angle error model is constructed to correct the elevation angle error of the aircraft caused by atmospheric refraction, so as to be applied to the precise identification and positioning of the observed target.

[0104] Embodiment 2: Based on Embodiment 1, the ground object detection refraction error compensation modeling system of the present invention includes: Hierarchical module: used to divide the atmosphere between the aircraft and the ground surface into N layers and calculate the distance between adjacent layers; Refraction angle calculation module: iteratively solve the refraction angle of each atmospheric layer based on Snell's law; Horizontal distance calculation module: calculate the horizontal distance between adjacent layers according to the refraction angle and the hierarchical distance; Projection distance module: accumulate the horizontal distances of all layers to obtain the distance from the projection of the aircraft on the ground surface to the true position of the ground object; True elevation angle calculation module: calculate the true elevation angle by combining the vertical distance and the projection distance of the aircraft; Error calculation module: calculate the elevation angle error and the distance error according to the difference between the true elevation angle and the apparent elevation angle.

[0105] The value range of N in the hierarchical module is from 900 to 1000, and the distance between adjacent layers is fixed at 100 meters.

[0106] It can correct the elevation angle error and the distance error of the aircraft caused by atmospheric refraction, so as to be applied to the precise identification and positioning of the observed target.

[0107] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered within the protection scope of the present invention.

Claims

1. A modeling method for compensating refraction errors in ground object detection, characterized in that, It includes the following steps: S1: Divide the atmosphere between the aircraft and the ground surface into N layers, and calculate the distance between adjacent layers; S2: Solve the light refraction angle at each atmospheric layer according to Snell's law; S3: Calculate the horizontal distance between adjacent two atmospheric layers on the light propagation path; S4: According to the result of step S3, calculate the distance between the projection of the aircraft on the ground surface and the true position of the ground object; S5: Combine the vertical distance from the aircraft to the Earth's surface and the distance obtained in step S4 to calculate the angle between the line connecting the aircraft to the true position of the ground object and the vertical line of the Earth's center, that is, the true elevation angle; S6: According to the true elevation angle in step S5 and the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the Earth's center, that is, the apparent elevation angle, calculate the elevation angle error and the distance error.

2. The ground object detection refraction error compensation modeling method according to claim 1, wherein When the atmosphere is divided into N layers in step S1, the distance between two adjacent layers is , where h is the distance from the aircraft to the Earth's surface.

3. The ground object detection refraction error compensation modeling method according to claim 2, characterized in that In step S2, when the Earth's atmosphere is layered, it is assumed that the atmospheric density is the same within the same layer and different between different layers. Then Snell's law is satisfied between adjacent layers, and by analogy, the following relationship holds Thus, the refraction angle of each layer can be calculated: Wherein: is the atmospheric refractive index of the 0th layer, is the incident angle of the 0th layer, is the atmospheric refractive index of the 1st layer, is the refraction angle of the 1st layer, and so on, is the atmospheric refractive index of the (N - 1)th layer, is the incident angle of the (N - 1)th layer, is the atmospheric refractive index of the Nth layer, is the refraction angle of the Nth layer; according to the alternate interior angle theorem, the calculated refraction angle is the incident angle of the next layer.

4. The method for compensating and modeling refraction error in ground object detection according to claim 3, wherein, The calculation of the atmospheric refractive index includes: where represents the atmospheric refractive index at the apparent position of the ground object and is expressed by the following formula wherein, , t, P, e, λ respectively refer to the atmospheric temperature, pressure, water vapor pressure, and wavelength at the location of the ground object; The atmospheric refractive index on the light propagation path is expressed by the following formula Among them, represents the elevation, which is calculated by 40136 + 148.72 × t and the unit is m. Below the elevation, the atmospheric refractive index at each altitude position is given by the Hopfield model. Above the elevation, the atmospheric refractive index at each altitude position is given by the e exponential model, where represents the atmospheric refractive index at the elevation, and β is the piecewise fitting exponent.

5. The ground object detection refraction error compensation modeling method according to claim 3, characterized in that In step S3, the horizontal distance between adjacent layers is calculated by the following formula: 。 6. The ground object detection refraction error compensation modeling method according to claim 1, characterized in that In step S4, according to the result obtained in step S3, calculate the distance between the projection of the aircraft and the ground surface to the true position of the ground object : 。 7. The method for compensating and modeling refraction error in ground object detection according to claim 6, wherein In step S6, according to the true elevation angle calculated in step S5, combined with the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the Earth's center, that is, the apparent elevation angle, the elevation angle error is obtained, expressed as: Wherein, Z0 is the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line from the center of the earth, that is, the apparent elevation angle, and this value is a known quantity. θ is the angle between the line connecting the aircraft to the true position of the ground object and the vertical line from the center of the earth, that is, the true elevation angle, which is obtained by calculating through step S5.

8. The ground object detection refraction error compensation modeling method according to claim 7, characterized in that In step S6, the distance error represents the distance between the true position and the apparent position of the ground object, which is represented by and is solved by the following formula Among them, h is the distance from the aircraft to the Earth's surface, which is a known quantity. is the distance from the projection of the aircraft on the Earth's surface to the true position of the ground object. Z0 is the angle between the line connecting the aircraft to the apparent position of the ground object and the vertical line of the Earth's center, that is, the apparent elevation angle.

9. A ground object detection refraction error compensation modeling system, based on the ground object detection refraction error compensation modeling method according to any one of claims 1-8, characterized in that, It includes: Layering module: used to divide the atmosphere between the aircraft and the ground surface into N layers, and calculate the distance between adjacent layers; Refraction angle calculation module: iteratively solve the refraction angle of each atmospheric layer based on Snell's law; Horizontal distance calculation module: calculate the horizontal distance between adjacent layers according to the refraction angle and the layering distance; Projection distance module: accumulate the horizontal distances of all layers to obtain the distance between the projection of the aircraft on the ground surface and the true position of the ground object; True elevation angle calculation module: combine the vertical distance of the aircraft and the projection distance to calculate the true elevation angle; Error calculation module: calculate the elevation angle error and the distance error according to the difference between the true elevation angle and the apparent elevation angle.

10. The ground object detection refraction error compensation modeling system according to claim 9, characterized in that, In the layering module, the value range of N is 900 to 1000 meters, and the distance between adjacent layers is fixed at 100 meters.

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