Ground-based space object monitoring radar atmospheric refraction error correction method

Abstract

The application discloses a ground-based space target monitoring radar atmospheric refraction error correction method. The ground-based space target monitoring radar atmospheric refraction error correction method comprises the following steps: based on the vertical distribution of atmospheric refraction index and the radar elevation angle measurement value, the signal propagation path is accurately recursively calculated by using the refraction theorem and geometric relationship, the corresponding elevation angle, geocentric angle and target apparent distance of different heights are calculated, and a one-to-one corresponding relationship between the apparent distance and the distance, the elevation angle measurement error is established; then, according to the radar distance measurement value, the radar distance and the elevation angle measurement error are calculated by interpolation, and finally, the distance and the elevation angle measurement error caused by the atmospheric refraction of the space target monitoring radar are corrected. The ground-based space target monitoring radar atmospheric refraction error correction method has higher error calculation precision under the condition of given layer interval, has more stable error correction performance, and can more accurately correct the atmospheric refraction error of the space target monitoring radar.

Description

Technical Field

[0001] This invention relates to the field of radar detection and atmospheric radio wave propagation, specifically to a method for correcting atmospheric refraction errors in ground-based space target surveillance radar. Background Technology

[0002] As an important component of the space target surveillance system, the main task of ground-based space target surveillance radar is to detect, locate and track important space targets, so as to achieve all-round and dynamic perception of the space situation. When ground-based space target surveillance radar detects space targets, the radar signal will be refracted twice as it passes through the atmosphere. The atmospheric refraction generated by the troposphere and ionosphere is the most significant, which can lead to errors in the measurement of radar slant range and elevation angle. For example, for a P-band ground-based space target surveillance radar with a carrier frequency of 500MHz (assuming the radar is located in the mid-latitude region), when detecting a space target at an altitude of 1000 km and an elevation angle measurement value of 3°, the elevation angle measurement error can reach 0.3° and the range measurement error can reach 150 meters in the year of peak solar activity. Therefore, it is necessary to correct the radar slant range and elevation angle measurement errors. The literature [1] "Atmospheric refraction correction of radio wave propagation for airborne and spaceborne radar" (Science in China Series E, 2001, 31(1):19-27) reported a traditional method for atmospheric refraction correction of radio wave propagation. However, it has the problems of insufficient robustness of error correction performance and insufficient accuracy of error correction. Furthermore, with the increase of the layer interval, it exhibits greater range and angle measurement errors. Summary of the Invention

[0003] To address the aforementioned problems, the present invention aims to provide a method for correcting atmospheric refraction errors in ground-based space target surveillance radar. This method overcomes the technical issues of existing atmospheric refraction error correction methods, such as insufficient robustness and accuracy, and the resulting larger ranging and angle measurement errors as the layering interval increases. It avoids the approximation processes in the derivation of traditional methods, achieving higher error calculation accuracy and more robust error correction performance under given layering intervals. Its performance advantages are particularly evident at low elevation angles, enabling more accurate correction of atmospheric refraction errors in space target surveillance radar.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] This invention provides a method for correcting atmospheric refraction errors in ground-based space target surveillance radar, comprising the following steps:

[0006] S1. Based on the vertical distribution of atmospheric refractive index and radar elevation angle measurements, calculate the elevation angle, geocentric angle and apparent target range at different altitudes, and establish a one-to-one correspondence between apparent range and range and elevation angle measurement errors;

[0007] S2. Based on the radar range measurement values, interpolate and calculate the radar range and elevation angle measurement errors;

[0008] S3. Correct the radar range and elevation angle measurement errors by atmospheric refraction of the space target surveillance radar.

[0009] As one aspect of the atmospheric refraction error correction method for a ground-based space target surveillance radar of the present invention, S1 includes the following steps:

[0010] S11. Obtain the vertical distribution characteristic curve of the atmospheric refractive index;

[0011] S12. Calculate the elevation angle change along the signal propagation path using a recursive method;

[0012] S13. Calculate the geocentric angle between the radar station and the target;

[0013] S14. Calculate the apparent distance of targets at different altitudes.

[0014] As one aspect of the atmospheric refraction error correction method for a ground-based space target surveillance radar of the present invention, S11 includes the following steps:

[0015] S111. Obtain the vertical distribution of the tropospheric refractive index: Using the Hopfield model, the tropospheric refractive index Nt is divided into dry and wet terms, and fitted with a fourth power function of altitude h.

[0016]

[0017] Where h≤60km, N d N w The dry and wet refractive indices are respectively, H d H w Equivalent heights for dry and wet conditions, and H d =40136+148.72(T0-273.16)m, H w =11000m, T0 is the Kelvin temperature, N d0 N w0 These represent the dry and wet terms of the refractive index of the ground at the station, where N d0 =77.6P0 / T0, N w0 =3.73×10 5 ×e0 / T0 2 , The refractive index and refractive index n of the troposphere t The relationship is: N t =(n t -1)×10 6 ;

[0018] S112. Obtain the vertical distribution of the ionospheric refractive index: Read the ionospheric electron density profile N using the international reference ionospheric model. e (h) For electromagnetic wave signals in the VHF band and above, neglecting the ionospheric birefringence effect, the relationship between the ionospheric refractive index and electron density is established:

[0019]

[0020] Where, r e It is the classical electron radius, and k0 = 2π / λ is the wave number corresponding to the radar signal.

[0021] As one aspect of the atmospheric refraction error correction method for a ground-based space target surveillance radar of the present invention, S12 includes the following steps:

[0022] S121. Define the pitch angle θ of the j-th layer. j Let θ be the angle between the radar signal propagation path and the tangent of the spherical layer, and let θ be the incident angle of the j-th layer. j * Let be the angle between the signal propagation path within the j-th layer and the normal to the spherical layer. Then, the refraction formula applies to two adjacent layers:

[0023]

[0024] S122. According to the Law of Sines:

[0025]

[0026] Where, r j Let r be the distance between the signal propagation path and the puncture point in the j-th atmospheric layer and the Earth's center, and r j+1 =r j +Δh, where Δh is the vertical layer interval, calculates the change in pitch angle between two adjacent layers:

[0027]

[0028] S123. Establish the pitch angle θ of the j-th layer through recursion. j Theoretical relationship between radar-measured elevation angle and:

[0029]

[0030] As one aspect of the atmospheric refraction error correction method for a ground-based space target surveillance radar of the present invention, the method for calculating the geocentric angle between the radar station and the target in S13 is as follows: Based on the sine theorem, the following relationship is obtained:

[0031]

[0032] And calculated

[0033]

[0034] As one aspect of the atmospheric refraction error correction method for a ground-based space target surveillance radar of the present invention, wherein the apparent range R of targets at different altitudes in S14 e The formula is as follows:

[0035]

[0036] With 60 kilometers as the dividing line, the first term in the formula represents the apparent distance in the troposphere, and the second term represents the apparent distance in the ionosphere.

[0037] As one aspect of the atmospheric refraction error correction method for a ground-based space target surveillance radar of the present invention, S2 includes the following steps:

[0038] S21. Radar measurement range;

[0039] S22. Establish a one-to-one correspondence between apparent range and radar measured range and elevation angle measurement errors;

[0040] S23. Interpolate to calculate the measurement errors of radar range and elevation angle.

[0041] As one aspect of the atmospheric refraction error correction method for a ground-based space target surveillance radar of the present invention, S22 includes the following steps:

[0042] S221. Within the triangle formed by the geocenter, the radar station, and the target, calculate the corrected target elevation angle α0 using the law of sines:

[0043]

[0044] Where, r m Let m be the distance between the target located at layer m and the Earth's center; then we can obtain:

[0045]

[0046] The pitch angle measurement error is ε0 = θ1 - α0;

[0047] S222. The corrected distance between the target and the measuring station is calculated as follows:

[0048]

[0049] Therefore, the distance measurement error is ΔR = R e -R0;

[0050] S223. Based on the vertical distribution characteristic curve of the refractive index and the radar measured elevation angle θ1, following the approach of ray tracing, establish the apparent range R. e The one-to-one correspondence between distance measurement error ΔR and pitch angle measurement error ε0.

[0051] By adopting the above technical solution, the present invention has the following advantages:

[0052] This invention provides a method for correcting atmospheric refraction errors in ground-based space target surveillance radar. Based on the vertical distribution of the atmospheric refractive index, the method uses the radar measurement point as the starting point to progressively invert the trajectory ray of the radar signal propagation and recursively calculates the angles and path changes along the propagation path. This allows for further calculation of the measurement errors of target points at different altitudes. Finally, a parameter-correspondence interpolation method is used to correct the refraction error. Compared to traditional methods, this method can improve the accuracy of radar atmospheric refraction error correction (including range and elevation angle measurement errors) given a vertical distribution characteristic curve of the atmospheric refractive index. This method offers higher error calculation accuracy and more robust error correction performance under given layer intervals, especially at low elevation angles, where its performance advantages are more pronounced. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the atmospheric refraction error correction process for the ground-based space target surveillance radar of the present invention.

[0054] Figure 2 The atmospheric refraction indicator in this embodiment of the invention is the vertical distribution curve.

[0055] Figure 3 This is a schematic diagram of the atmospheric propagation geometric model of the ground-based space target surveillance radar signal according to the present invention;

[0056] Figure 4 The calculation results for the atmospheric refraction error of the space target surveillance radar of the present invention are shown below.

[0057] Figure 5 The curves show a comparison of radar range and elevation angle measurement errors between the method of this invention and the conventional method.

[0058] Figure 6 The curves show the comparison of residual errors in radar range and elevation angle between the method of this invention and the conventional method. Detailed Implementation

[0059] The technical solution of the present invention will be specifically described below with reference to the accompanying drawings. It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0060] Figure 1 A flowchart illustrating the atmospheric refraction error correction process for the ground-based space target surveillance radar of the present invention is shown.

[0061] Given the radar station's altitude h0, transmitted electromagnetic wave wavelength λ, measurement elevation angle θ1, and measurement distance R... M .

[0062] A method for correcting atmospheric refraction errors in a ground-based space target surveillance radar is as follows: Figure 1 As shown, it includes the following steps:

[0063] S1. Based on the vertical distribution of atmospheric refractive index and radar elevation angle measurements, the signal propagation path is accurately deduced using the refraction theorem and geometric relationships. The elevation angle, geocentric angle and apparent target range at different altitudes are calculated, and a one-to-one correspondence is established between apparent range and range and elevation angle measurement errors.

[0064] S1 includes the following specific steps:

[0065] S11. Obtain the vertical distribution characteristic curve of the atmospheric refractive index;

[0066] S11 includes the following specific steps:

[0067] S111. To obtain the vertical distribution of the tropospheric refractive index, a combination of meteorological measurements and models is typically used. Given temperature T0, air pressure P0, and relative humidity f0, the Hopfield model is used to calculate the tropospheric refractive index N. t It is divided into dry and wet components, and fitted using a fourth power function of altitude h, where h ≤ 60 km:

[0068]

[0069] In the formula N d N w The dry and wet refractive indices are respectively, H d H wThe equivalent heights for dry and wet terms are the heights at which the refractive index decays to zero in both dry and wet conditions, and H... d =40136+148.72(T0-273.16)m, H w =11000m, where T0 is the Kelvin temperature, N d0 N w0 These represent the dry and wet terms of the refractive index of the ground at the station, where N d0 =77.6P0 / T0, N w0 =3.73×10 5 ×e0 / T0 2 , The refractive index and refractive index n of the troposphere t The relationship is:

[0070] N t =(n t -1)×10 6

[0071] S112. To obtain the vertical distribution of the ionospheric refractive index, it is necessary to accurately and in real-time acquire the characteristic curve of the vertical distribution of ionospheric electron density. The most recent accurate approach is to conduct on-site measurements using ionospheric vertical measurement equipment. Considering cost factors, the total vertical electron content (TEC) can also be measured using a navigation satellite receiving and processing system, and this can be used to correct the vertical distribution of electron density generated by the ionospheric model. The focus of this invention is on the radar measurement error model, and therefore does not involve the accurate acquisition of the refractive index. Therefore, the ionospheric electron density profile N is directly read from the International Reference Ionosphere (IRI) model. e (h) For electromagnetic wave signals in the VHF band and above, neglecting the ionospheric birefringence effect, the relationship between the ionospheric refractive index and electron density is established:

[0072]

[0073] In the formula, r e It is the classical electron radius, and k0 = 2π / λ is the wave number corresponding to the radar signal.

[0074] Combining the above two factors, we can obtain the vertical distribution curve of the atmospheric refractive index above the radar station.

[0075] S12. Calculate the elevation angle change along the signal propagation path using a recursive method;

[0076] S12 includes the following specific steps:

[0077] S121. Since the atmospheric refractive index changes gradually with altitude, it can be assumed that the refractive index remains constant within a certain altitude range. Therefore, the atmosphere is divided into several layers vertically, and the refractive index of the j-th layer is set to n. j When a ground-based space target surveillance radar detects a space target, the transmitted signal is transmitted at a refractive index of n. j Within the atmosphere, the signal propagates in a straight line, but due to the difference in refractive index between adjacent layers, refraction occurs at the layer boundaries. This forms a set of approximately zigzag propagation paths. The signal then propagates to the target point and is reflected by the target point, eventually being received by the radar receiver along the same path. Therefore, starting with the radar measurement of the elevation angle θ1, based on the refractive index n of each layer... j By gradually reversing the changes in the propagation paths at each layer, the true location of the target point can be deduced.

[0078] Define the pitch angle θ of the j-th layer. j Let θ be the angle between the radar signal propagation path and the tangent of the spherical layer, and let θ be the incident angle of the j-th layer. j * Let be the angle between the signal propagation path within the j-th layer and the normal to the spherical layer. Then, the refraction formula applies to two adjacent layers:

[0079]

[0080] S122. According to the Law of Sines:

[0081]

[0082] Where, r j Let r be the distance between the signal propagation path and the puncture point in the j-th atmospheric layer and the Earth's center, and r j+1 =r j +Δh, where Δh is the vertical layer interval, allows us to calculate the change in pitch angle between two adjacent layers:

[0083]

[0084] S123. The pitch angle θ of the j-th layer can be established through recursion. j Theoretical relationship between radar-measured elevation angle and:

[0085]

[0086] S13. Calculate the geocentric angle between the radar station and the target;

[0087] Define the angle between the puncture point at layer j, the puncture point at layer j+1, and the geocentric line as the geocentric angle at layer j. Traditional methods hold that:

[0088]

[0089] In this invention, the geocentric angle between the radar station and the target is calculated using precise geometric modeling, and the following relationship is obtained based on the sine theorem:

[0090]

[0091] And calculated

[0092]

[0093] S14. Calculate the apparent distance of targets at different altitudes.

[0094] Electromagnetic waves in a refractive index of n j In the troposphere, the velocity is v j =c / n j Propagation occurs in the ionosphere at a group velocity v j =c·n j Propagation, where c = 3 × 10 8 m / s is the speed of light in a vacuum. Traditional methods assume the signal propagation path length Δl in the j-th layer is... j It can be approximated as:

[0095]

[0096] In this invention, the pitch angle and geocentric angle of layer j obtained above are used for precise derivation, and the propagation path length Δl is calculated. j It can be calculated as:

[0097]

[0098] Then the time required for the signal to propagate in the j-th layer is Δt. j =Δl j / v j The total time required for propagation is:

[0099]

[0100] If a radar mistakenly interprets a received electromagnetic wave signal as traveling at the speed of light in a vacuum, then the calculated distance, or apparent distance, will be R. e =c·t, the traditional method ultimately derives as:

[0101]

[0102] After model optimization, the calculated apparent distance of this invention is:

[0103]

[0104] With an altitude of 60 kilometers as the boundary, the first term of the formula represents the apparent distance in the troposphere, and the second term represents the apparent distance in the ionosphere.

[0105] S2. Based on the radar range measurement values, interpolate and calculate the radar range and elevation angle measurement errors;

[0106] S2 includes the following specific steps:

[0107] S21. Radar measurement range;

[0108] S22. Establish a one-to-one correspondence between apparent range and radar measured range and elevation angle measurement errors;

[0109] S221. Within the triangle formed by the geocenter, the radar station, and the target, calculate the corrected target elevation angle α0 using the law of sines:

[0110]

[0111] Where, r m Let the distance between the target located at layer m and the Earth's center be denoted as . Then we can obtain:

[0112]

[0113] The pitch angle measurement error is ε0 = θ1 - α0.

[0114] S222. The corrected distance between the target and the measuring station is calculated as follows:

[0115]

[0116] Therefore, the distance measurement error is ΔR = R e -R0;

[0117] Based on the vertical distribution characteristic curve of the refractive index and the radar-measured elevation angle θ1, following the approach of ray tracing, the apparent range R can be established. e The one-to-one correspondence between distance measurement error ΔR and pitch angle measurement error ε0.

[0118] S23. Interpolate to calculate the measurement errors of radar range and elevation angle.

[0119] After establishing a one-to-one correspondence between the apparent distances of targets at different altitudes and their corresponding distance measurement errors and elevation angle measurement errors, if the radar measurement distance of a target is obtained, the corresponding radar distance and elevation angle measurement errors can be obtained through interpolation calculation, and finally, error correction can be performed.

[0120] S3. Correct the radar range and elevation angle measurement errors by atmospheric refraction of the space target surveillance radar.

[0121] Figure 2 The vertical distribution curve of the atmospheric refractive index in an embodiment of the present invention is shown. In a specific embodiment, the vertical distribution characteristic curve of the atmospheric refractive index at 14:00 local time in Chengdu on March 9, 2009 is shown as follows. Figure 2 As shown, the vertical distribution of the refractive index in the troposphere is calculated using the Hopfield model based on local altitude, temperature, humidity, and pressure, while the vertical distribution of the refractive index in the ionosphere is calculated using the electron density read from the IRI model.

[0122] Figure 3 A schematic diagram of the atmospheric propagation geometric model of the ground-based space target surveillance radar signal of the present invention is shown; as follows: Figure 3 As shown, the radar is located at point A1 and transmits electromagnetic wave signals. Under the assumption of atmospheric stratification, the signal will be emitted at a refractive index of n. j The radio wave propagates in a straight line within the j-th layer of the atmosphere, but at the puncture points (such as A2 and A3) of each sub-layer, refraction occurs due to changes in the refractive index, forming a coarse broken propagation path as shown in the figure. The propagation continues until it reaches the target point T and is reflected. The radio wave returns along the original path and is received by the radar antenna, but the radar will interpret the target as being at point P, which extends along the direction of the measured elevation angle.

[0123] Figure 4 The results of atmospheric refraction error calculation for ground-based space target surveillance radar are shown. Among them, Figure 4 (a) shows the distance measurement error curve; Figure 4 (b) shows the pitch angle measurement error curve. According to... Figure 2 The provided vertical distribution of atmospheric refractive index is used to calculate the variation curves of target range (a) and elevation angle (b) measurement errors with target altitude for a P-band radar with a carrier frequency of 500MHz under different measurement elevation angles. Figure 4 It can be observed that the lower the elevation angle, the greater the measurement error in both elevation angle and distance. This is because the lower the elevation angle, the longer the electromagnetic wave propagation path, and the more pronounced the effect of atmospheric refraction.

[0124] The apparent distance R formed by targets at different altitudes e The relationship between distance measurement error ΔR and pitch angle measurement error ε0 is shown in Table 1 below:

[0125] Table 1: Apparent Distance R e —Relationship between distance measurement error ΔR and pitch angle measurement error ε0 (list of relationships)

[0126]

[0127] according to Figure 2The provided vertical distribution of atmospheric refractive index, for a P-band radar with a carrier frequency of 500MHz, under the conditions of a measurement elevation angle of 3° and a layering interval of 10m, establishes the corresponding apparent range R. e The relationship between distance measurement error ΔR and pitch angle measurement error ε0 is shown in Table 1, with a partial excerpt. If the target's measured distance R... M The distance is 2285910m. Through interpolation, the distance measurement error ΔR is 132.505589m and the pitch angle measurement error ε0 is 0.26467290°. Therefore, the corrected target distance is 2285777.494411m and the pitch angle is 2.73532710°.

[0128] Figure 5 The comparison curves of radar range and elevation angle measurement errors between the method of this invention and the traditional method {Reference [1] "Atmospheric Refraction Correction for Radio Wave Propagation of Airborne and Spaceborne Radars" (Science in China: Series E, 2001, 31(1):19-27)} are shown; among them, Figure 5 (a) shows the curve of distance measurement error as a function of stratification interval; Figure 5 (b) is the curve showing the change of pitch angle measurement error with the stratification interval.

[0129] The atmospheric refraction error correction method of the ground-based space target surveillance radar of the present invention is compared and analyzed with the traditional method described in reference [1]. Here, the measurement elevation angle is set to 3°, and the target is located at an altitude of 1000km. The curves of the change of distance measurement error, elevation angle measurement error and layer interval Δh are calculated as follows. Figure 5 As shown, as the layer interval decreases, the distance and elevation angle measurement errors calculated by the two methods gradually converge, and both converge to the same value, indicating that as the layer interval decreases, the propagation path tracked by the two methods tends to the true path, which also verifies the effectiveness of the method of the present invention. For a given target, the increase of the layer interval will inevitably lead to a decrease in model accuracy, thereby causing correction deviation. Compared with the correction amount when the layer interval Δh is 1m, the correction amount of the traditional method described in reference [1] deteriorates sharply with the increase of the layer interval, while the atmospheric refraction error correction method of the ground-based space target surveillance radar of the present invention has a distance correction amount that differs by less than 2.3m and an angle correction amount that differs by less than 0.006° when the layer interval is 1m and 1000m, indicating that even with a large layer interval, the atmospheric refraction error correction method of the ground-based space target surveillance radar of the present invention can still maintain high stability.

[0130] Figure 6The comparison curves of residual errors in radar range and elevation angle between the method of this invention and the traditional method {reference [1] "Atmospheric Refraction Correction for Radio Wave Propagation of Airborne and Spaceborne Radars" (Science in China: Series E, 2001, 31(1):19-27)} are shown. Figure 6 (a) Comparison of residual distance errors between the two methods; Figure 6 (b) Comparison of residual pitch angle errors between the two methods.

[0131] When the layer spacing is small enough, the inverted signal propagation path is the actual propagation path, and the target position can be regarded as the actual target position. We can take the distance measurement error ΔR (Δh = 1) and the elevation angle measurement error ε0 (Δh = 1) calculated when the layer spacing Δh is 1m as the true values. Then, we can calculate the residual distance error ΔR (Δh) - ΔR (Δh = 1) and the residual elevation angle error ε0 (Δh) - ε0 (Δh = 1) under different layer spacing conditions. Figure 6 The figures show the comparison curves of residual radar range and elevation angle errors for the two methods. The results show that, under the same layering interval, the method of the present invention has smaller residual correction error and higher error correction accuracy. As the layering interval increases, the method of the present invention becomes more robust, while the traditional method described in reference [1] exhibits larger range and angle measurement errors. Therefore, in practical applications, the method of the present invention can achieve the given atmospheric error correction accuracy requirements using a sparser layering interval.

[0132] Finally, it should be noted that although the present invention has been described with reference to specific embodiments, those skilled in the art should recognize that the above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Various equivalent changes or substitutions can be made without departing from the concept of the present invention. Therefore, any changes or modifications to the above embodiments within the essential spirit of the present invention will fall within the scope of the claims of the present invention.

Claims

1. A method for correcting atmospheric refraction errors in a ground-based space target surveillance radar, characterized in that, Includes the following steps: S1. Based on the vertical distribution of atmospheric refractive index and radar elevation angle measurements, calculate the elevation angle, geocentric angle and apparent target range at different altitudes, and establish a one-to-one correspondence between apparent range and range and elevation angle measurement errors; S1 includes the following steps: S11. Obtain the vertical distribution characteristic curve of the atmospheric refractive index; S11 includes the following steps: S111. Obtain the vertical distribution of the tropospheric refractive index: Use the Hopfield model to calculate the tropospheric refractive index N. t The study is divided into dry and wet components, and the data is fitted using a fourth-power function of altitude h. in, , , These are the dry and wet refractive indices, respectively. , Equivalent heights for dry and wet conditions, and , , Kelvin temperature, , These represent the dry and wet terms of the refractive index of the ground at the station, respectively. , , The tropospheric refractive index and refractive index n t The relationship is: ; S112. Obtain the vertical distribution of the ionospheric refractive index: Read the electron density profile of the ionosphere using the international reference ionospheric model. For electromagnetic wave signals in the VHF band and above, neglecting the ionospheric birefringence effect, the relationship between the ionospheric refractive index and electron density is established: in, It is the classical electron radius. The wave number corresponding to the radar signal; S12. Calculate the elevation angle change along the signal propagation path using a recursive method; S12 includes the following steps: S121. Definition of the first j Pitch angle Let be the angle between the radar signal propagation path and the tangent of the spherical layer, and be the angle between the radar signal propagation path and the tangent of the spherical layer. j Layer incident angle For the first j The angle between the signal propagation path within a layer and the normal to the spherical layer is given by the refraction formula between two adjacent layers: ； S122. According to the Law of Sines: in, For the signal propagation path and the first j The distance between the puncture point in the atmosphere and the Earth's center, and , To determine the vertical layer spacing, calculate the change in pitch angle between adjacent layers: ； S123. Establish the first... through recursion j Pitch angle Theoretical relationship between radar-measured elevation angle and: ； S13. Calculate the geocentric angle between the radar station and the target; The method for calculating the geocentric angle between the radar station and the target in S13 is as follows: Based on the law of sines, the following relation is obtained: And calculated ； S14. Calculate the apparent distance of targets at different altitudes; The apparent distance R of targets at different altitudes in S14 e The formula is as follows: With 60 kilometers as the boundary, the first term of the formula is the apparent distance in the troposphere, and the second term is the apparent distance in the ionosphere. S2. Based on the radar range measurement values, interpolate and calculate the radar range and elevation angle measurement errors; S3. Correct the radar range and elevation angle measurement errors by atmospheric refraction of the space target surveillance radar.

2. The atmospheric refraction error correction method for a ground-based space target surveillance radar according to claim 1, characterized in that, S2 includes the following steps: S21. Radar measurement range; S22. Establish a one-to-one correspondence between apparent range and radar measured range and elevation angle measurement errors; S23. Interpolate to calculate the measurement errors of radar range and elevation angle.

3. The atmospheric refraction error correction method for a ground-based space target surveillance radar according to claim 2, characterized in that, S22 includes the following steps: S221. Within the triangle formed by the geocenter, the radar station, and the target, calculate the corrected target elevation angle using the law of sine. : in, For the position located at the m The distance between the target layer and the Earth's center; therefore, we can obtain: The pitch angle measurement error is ; S222. The corrected distance between the target and the measuring station is calculated as follows: Then the distance measurement error is ; S223. Based on the vertical distribution characteristic curve of the refractive index and the radar measurement elevation angle... Following the principles of ray tracing, establish apparent distance... Distance measurement error Pitch angle measurement error A one-to-one correspondence between them.

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