A method for estimating aerial target height using spaceborne radar based on multipath measurement

Abstract

The present invention discloses a method for estimating the height of an aerial target using a spaceborne radar based on multipath measurement. The method comprises: obtaining a signal transmission path when the spaceborne radar illuminates the aerial target; the signal transmission path comprises a transmission path, a reflection path and a scattering path obtained under a micro-multipath phenomenon; extracting key point information in the signal transmission path; and solving the height of the aerial target using the key point information. When a micro-multipath phenomenon occurs to the aerial target caused by the spaceborne radar, the present invention constructs a geometric relationship model using the signal transmission path in the micro-multipath phenomenon, and solves the height of the aerial target using a geometric method based on the geometric relationship model, thereby solving the problem of large errors in the pitch angle measurement of the aerial target by a single spaceborne radar.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite-borne radar target tracking, and in particular relates to a satellite-borne radar aerial target height estimation method based on multipath measurement. Background Art

[0002] Spaceborne radar has all-weather, all-day strategic and tactical early warning capabilities, and is not restricted by the curvature of the earth and is not vulnerable to attack. It occupies a very important position in the early warning and defense system.

[0003] Typically, when tracking and locating an aerial target, a single satellite-borne radar's elevation angle measurement error is greater than the target's radial range and azimuth angle errors, resulting in a single satellite-borne radar's inability to estimate the target's altitude. This lack of altitude information significantly amplifies the target's positioning error and hinders target attribute identification and threat assessment. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for estimating the altitude of an aerial target using a spaceborne radar based on multipath measurement, so as to reduce the error in the pitch angle measurement of an aerial target by a single spaceborne radar.

[0005] The present invention adopts the following technical solutions:

[0006] A method for estimating the height of an aerial target using a spaceborne radar based on multipath measurement comprises the following steps:

[0007] Obtain the signal transmission path when the spaceborne radar illuminates the aerial target; the signal transmission path includes the transmission path, reflection path and scattering path obtained under the micro-multipath phenomenon;

[0008] Extract key point information in the signal transmission path;

[0009] The altitude of aerial targets is solved using key point information.

[0010] Furthermore, the key point information includes: the position of the spaceborne radar, the position of the aerial target, the position where the signal is reflected or scattered, the projection point of the aerial target on the ground, the symmetrical point of the aerial target about the projection point, the position of the center of the earth, the first auxiliary point and the second auxiliary point;

[0011] The first auxiliary point is on the line connecting the position of the satellite-borne radar and the center of the earth, and is on the same horizontal plane as the position of the aerial target;

[0012] The second auxiliary point is on the line connecting the position of the satellite-borne radar and the center of the earth, and is in the same horizontal plane as the symmetrical point.

[0013] Furthermore, using key point information to solve the height of the aerial target includes:

[0014] The equation for the height of the aerial target is established as:

[0015] (2|GT| 3 +(-|ST'| 2 +2|OS| 2 -2|OG| 2 -|ST| 2 )|GT|-|OG||ST'| 2 +|OG||ST| 2 ) / (|OG|-|GT|)=0

[0016] Among them, |GT| represents the distance from the position of the aerial target to the projection point, that is, the height of the aerial target, |ST'| represents the distance from the position of the spaceborne radar to the symmetry point, |OS| represents the distance from the position of the spaceborne radar to the center of the earth, |OG| represents the distance from the projection point to the center of the earth, and |ST| represents the radial distance from the position of the spaceborne radar to the position of the aerial target.

[0017] Furthermore, using key point information to solve the height of the aerial target also includes:

[0018] The equation of the target height in the air is converted into a cubic equation, which is expressed as:

[0019]

[0020] Furthermore, an equation for the altitude of the aerial target is established based on the first geometric relationship, the second geometric relationship, and the third geometric relationship;

[0021] The first geometric relationship is the proportional geometric relationship between the position of the aerial target, the position of the center of the earth, the first auxiliary point, the second auxiliary point and the symmetrical point, which can be expressed as:

[0022]

[0023] Wherein, |MT| represents the distance from the position of the aerial target to the first auxiliary point, |NT'| represents the distance from the second auxiliary point to the symmetrical point, |OM| represents the distance from the center of the earth to the first auxiliary point, |ON| represents the distance from the center of the earth to the second auxiliary point, |SM| represents the distance from the position of the spaceborne radar to the first auxiliary point, and |SN| represents the distance from the position of the spaceborne radar to the second auxiliary point.

[0024] The second geometric relationship is the geometric relationship between the position of the aerial target, the position of the center of the earth, the first auxiliary point, the second auxiliary point and the symmetrical point, which can be expressed as:

[0025] |MT| 2 +|SM| 2 =|ST| 2

[0026] |NT′| 2 +|SN| 2 =|ST′| 2 ,

[0027] The third geometric relationship is the geometric relationship between the position of the spaceborne radar, the position of the aerial target, the first auxiliary point, the second auxiliary point and the symmetrical point, which can be expressed as:

[0028] |MT| 2 +|OM| 2 =|OT| 2

[0029] |NT′| 2 +|ON| 2 =|OT′| 2 ,

[0030] Among them, |OT| represents the distance from the position of the aerial target to the center of the earth, and |OT'| represents the distance from the center of the earth to the symmetrical point.

[0031] Furthermore, before establishing the equation for the height of the aerial target, the Gaussian distribution of the distance from the satellite-borne radar to the center of the earth, the Gaussian distribution of the radial distance from the position of the satellite-borne radar to the position of the aerial target, the Gaussian distribution of the distance from the position of the satellite-borne radar to the symmetric point, and the Gaussian distribution of the distance from the projection point to the center of the earth are obtained, which can be expressed as:

[0032]

[0033] in, represents the Gaussian distribution of the distance from the satellite-borne radar to the center of the Earth, μ S represents the semi-major axis of the spaceborne radar, represents the error of the semi-major axis of the spaceborne radar, represents the Gaussian distribution of the radial distance between the satellite-borne radar and the aerial target, μ T Indicates the radial distance from the position of the spaceborne radar to the position of the aerial target, It represents the measurement error of the radial distance from the position of the spaceborne radar to the position of the aerial target. represents the Gaussian distribution of the distance from the satellite-borne radar to the symmetric point, μ T′ represents the distance from the position of the spaceborne radar to the symmetric point, It represents the measurement error of the distance from the position of the spaceborne radar to the symmetric point, Represents the Gaussian distribution of the distance from the projection point to the center of the earth, μ G Represents the distance from the projection point to the center of the earth. Indicates the error in the distance from the projected point to the center of the earth.

[0034] Furthermore, the process of solving the cubic equation includes:

[0035] Using the Cardinal formula to solve the cubic equation, we can get the roots of the equation, which are expressed as:

[0036]

[0037] in,

[0038] make Calculation shows that Δ≥0, so the cubic equation has 1 real root and 2 complex roots, among which the real root is the height value of the aerial target.

[0039] Furthermore, the satellite-borne radar is a single satellite-borne radar.

[0040] An electronic device, comprising:

[0041] at least one processor;

[0042] and, a memory communicatively coupled to the at least one processor;

[0043] The memory stores instructions that can be executed by at least one processor, and the instructions are executed by at least one processor so that the at least one processor can execute any one of the above-mentioned methods for estimating the altitude of aerial targets using a space-borne radar based on multipath measurement.

[0044] The beneficial effect of the present invention is that when a satellite-borne radar generates micro-multipath phenomenon to an aerial target, the present invention utilizes the signal transmission path in the micro-multipath phenomenon to construct a geometric relationship model, and uses a geometric method based on the geometric relationship model to solve the height of the aerial target, thereby solving the problem that a single satellite-borne radar does not have the ability to estimate the height of the aerial target. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2 Schematic diagram of micro-multipath path of spaceborne radar to aerial targets;

[0047] Figure 3 A geometric relationship model diagram of the spaceborne radar and the aerial target in the present invention;

[0048] Figure 4 This is the 2D real trajectory diagram of the spaceborne radar tracking the aerial target in STK;

[0049] Figure 5 This is a 3D image of an aerial target. DETAILED DESCRIPTION

[0050] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Spaceborne radar aerial target tracking uses nonlinear filtering methods to achieve high-precision tracking of aerial targets based on the target's motion model and radar measurements. However, there are two main errors associated with spaceborne radar observation of aerial targets: measurement error and positioning error of the detection platform itself. Both of these errors affect aerial target tracking. To address the issue of excessive pitch angle measurement error, the tracking error is typically reduced by assuming a target altitude and then estimating the pitch angle using geometric or other methods. However, the lack of target altitude information leads to inaccurate pitch angle estimation methods.

[0052] Because spaceborne radars use electromagnetic wave reflection to detect aerial targets, they typically obtain micro-multipath measurements when the area they detect includes specular reflections, such as in the ocean. Specifically, when a spaceborne radar transmits electromagnetic waves toward an aerial target, it not only detects electromagnetic waves directly reflected from the target but also waves reflected from the target back to the ground / ocean. This multipath measurement allows for altitude estimation of aerial targets using a single spaceborne radar. However, no research has yet been conducted on altitude estimation of aerial targets using a single spaceborne radar.

[0053] A method for estimating the height of aerial targets using spaceborne radar based on multipath measurement, such as Figure 1 shown.

[0054] S110, obtaining a signal transmission path when the spaceborne radar illuminates an aerial target; the signal transmission path includes a transmission path, a reflection path, and a scattering path obtained under a micro-multipath phenomenon;

[0055] Specifically:

[0056] Micro-multipath measurement of aerial targets by spaceborne radar Figure 2 As shown in the figure, the solid line represents the transmitted ray (i.e., the ray emitted from the spaceborne radar and then irradiated by the aerial target), while the dashed line represents the received ray (i.e., the ray scattered from the aerial target and then received by the spaceborne radar). Considering the ground as a mirror-reflecting surface, after the spaceborne radar transmits a ray, one ray directly irradiates the aerial target, while another ray reflects off the ground or sea surface and then irradiates the aerial target. Similarly, for the backscattered echo signal from the aerial target, the received ray can be reflected directly by the spaceborne radar, while another ray reflects off the ground or sea surface and then reaches the spaceborne radar.

[0057] Therefore, there are four path combinations for electromagnetic waves emitted from the spaceborne radar to the aerial target and then scattered from the aerial target to the spaceborne radar. Figure 2As shown, the four paths are: from the satellite-borne radar to the aerial target, and then scattered from the aerial target back to the satellite-borne radar, that is, the ①-②-③ path; from the satellite-borne radar to the aerial target, and then scattered from the aerial target to the sea surface / ground to the satellite-borne radar, that is, the ①-②-④-⑥ path; from the satellite-borne radar to the sea surface / ground, and then reflected to the aerial target and then returned to the satellite-borne radar, that is, the ⑦-⑤-②-③ path; from the satellite-borne radar to the sea surface / ground, and then reflected to the aerial target, and finally scattered from the aerial target to the sea surface / ground to the satellite-borne radar, that is, ⑦-⑤-②-④-⑥. Generally speaking, this situation (i.e., ⑦-⑤-②-④-⑥) rarely occurs because the energy decays quickly and the signal level cannot be detected. Therefore, the measurement of this path is not considered in the present invention.

[0058] Spaceborne radar measurements typically include radial range, azimuth, elevation, and Doppler frequency. When micro-multipath occurs, the radial range reflected by the ground / sea surface becomes larger, while other measurements remain unchanged. Generally speaking, within a sub-beam emitted by a spaceborne radar at an aerial target, if only the radial range shows significant variation, while the azimuth and Doppler frequency show minimal variation, the measurement with the larger radial range is considered micro-multipath.

[0059] The calculation formula for the radial distance between a satellite-borne radar and an aerial target is generally:

[0060]

[0061] Where τ is the time delay of signal propagation and c is the speed of light.

[0062] For radial distances that are not micro-multipath measurements, i.e., the ①-②-③ path, (0.1) can accurately calculate the radial distance. However, for micro-multipath measurements, i.e., the ①-②-④-⑥ path and the ⑦-⑤-②-③ path, corrections are required when calculating the radial distance. The calculation formula is:

[0063] R′ mp =2R mp -R (0.2)

[0064] Among them, R mp Indicates the radial distance of micro multipath measurement, R represents the radial distance measured by direct path,

[0065] S120, extracting key point information in the signal transmission path; the key point information includes: the position of the satellite-borne radar, the position of the aerial target, the position where the signal is reflected or scattered, the projection point of the aerial target on the ground, the symmetrical point of the aerial target about the projection point, the position of the center of the earth, the first auxiliary point, and the second auxiliary point;

[0066] The first auxiliary point is on the line connecting the position of the satellite-borne radar and the center of the earth, and is on the same horizontal plane as the position of the aerial target;

[0067] The second auxiliary point is on the line connecting the position of the satellite-borne radar and the center of the earth, and is in the same horizontal plane as the symmetrical point.

[0068] Specifically:

[0069] According to the signal transmission path, the geometric relationship between the spaceborne radar and the aerial target is further established. Figure 3 As shown in the figure, point O represents the center of the Earth, point S represents the position of the spaceborne radar, point T represents the position of the aerial target, point P is the position where the signal is reflected or scattered, that is, the position where the micro-multipath measurement intersects the ground / sea surface, point G is the projection point of the aerial target on the ground, point T′ is the symmetrical point of the aerial target about the projection point G, point M is the first auxiliary point, located on the line connecting the position of the spaceborne radar and the center of the Earth, and is in the same horizontal plane as the position of the aerial target, and point N is the second auxiliary point, located on the line connecting the position of the spaceborne radar and the center of the Earth, and is in the same horizontal plane as the symmetrical point.

[0070] |ST| represents the radial distance from the spaceborne radar to the aerial target, while |SP| + |PT| represents the radial distance measurement due to the micro-multipath phenomenon generated when the spaceborne radar illuminates the aerial target. |OS| represents the distance from the spaceborne radar to the center of the Earth, and |OT| represents the distance from the aerial target to the center of the Earth. Based on symmetry, the altitude of the aerial target, |GT| = |GT′|, and |PT| = |PT′|, thus making the micro-multipath measurement |SP| + |PT| equivalent to |ST′|. |ST′| is the distance from the spaceborne radar to the symmetric point T′, and |OG| is the distance from the projected point G to the center of the Earth.

[0071] The distance from the satellite-borne radar to the center of the Earth, the radial distance from the satellite-borne radar to the aerial target, and the distance from the projection point to the center of the Earth are relatively easy to obtain with minimal error. The distance from the satellite-borne radar to the symmetric point can be approximated as the radial distance measured by micro-multipath. To utilize this measurement, the present invention approximates it to the distance from the satellite-borne radar to the symmetric point when solving the geometric relationship. This approximation not only has a minimal error but can also be used for altitude estimation. Therefore, selecting the above distances and reference points facilitates calculation and measurement, and the calculation results are highly accurate.

[0072] S130, using key point information to calculate the height of the aerial target;

[0073] Specifically:

[0074] Obtain the Gaussian distribution of known quantities (i.e., the Gaussian distribution of the distance from the satellite-borne radar to the center of the earth, the Gaussian distribution of the radial distance from the position of the satellite-borne radar to the position of the aerial target, the Gaussian distribution of the distance from the position of the satellite-borne radar to the symmetric point, and the Gaussian distribution of the distance from the projection point to the center of the earth), expressed as:

[0075]

[0076] in, represents the Gaussian distribution of the distance from the satellite-borne radar to the center of the Earth, μ S represents the semi-major axis of the spaceborne radar, represents the error of the semi-major axis of the spaceborne radar, represents the Gaussian distribution of the radial distance between the satellite-borne radar and the aerial target, μ T Indicates the radial distance from the position of the spaceborne radar to the position of the aerial target, It represents the measurement error of the radial distance from the position of the spaceborne radar to the position of the aerial target. represents the Gaussian distribution of the distance from the satellite-borne radar to the symmetric point, μ T′ represents the distance from the position of the spaceborne radar to the symmetric point, It represents the measurement error of the distance from the position of the spaceborne radar to the symmetric point, Represents the Gaussian distribution of the distance from the projection point to the center of the earth, μ G Represents the distance from the projection point to the center of the earth. Indicates the error in the distance from the projected point to the center of the earth.

[0077] The area detected by the spaceborne radar is generally known, and |OG| can be approximately calculated by the latitude of the center of the detection area, where the mean μ G can be calculated as:

[0078]

[0079] Among them, a = 6378.137 km is the equatorial radius of the Earth, b = 63563.752 km is the polar radius of the Earth, and φ is the latitude of the center of the detection area.

[0080] Next, the expression of the aerial target height |GT| is derived based on the geometric relationship.

[0081] According to the proportional geometric relationship between triangle OMT and triangle ONT′ (i.e., the proportional geometric relationship between the position of the aerial target, the position of the center of the earth, the first auxiliary point, the second auxiliary point and the symmetrical point), we can get:

[0082]

[0083] And according to the geometric relationship between triangle OMT and triangle ONT′ (i.e., the geometric relationship between the position of the aerial target, the position of the center of the earth, the first auxiliary point, the second auxiliary point and the symmetrical point), we have:

[0084]

[0085] According to the geometric relationship between triangle SMT and triangle SNT′ (i.e., the geometric relationship between the position of the spaceborne radar, the position of the aerial target, the first auxiliary point, the second auxiliary point and the symmetrical point), we have:

[0086]

[0087] Combining formulas (0.5), (0.6) and (0.7), we finally get the equation for the height of the aerial target:

[0088] (2|GT| 3 +(-|ST'| 2 +2|OS| 2 -2|OG| 2 -|ST| 2 )|GT|-|OG||ST'| 2 +|OG||ST| 2 ) / (|OG|-|GT|)=0

[0089] For the convenience of representation, the following symbols are used for simplified representation:

[0090] x=|GT|, a=|ST′|, b=|OS|, c=|OG|, d=|ST| (0.8)

[0091] Then the equation for the height of the aerial target is simplified to:

[0092] (2x 3 +(-a 2 +2b 2 -2c 2 -d 2 )x-ca 2 +cd 2 ) / (cx)=0 (0.9)

[0093] In the above formula, since the height of the aerial target will not be equal to |OG|, that is, (cx)≠0, the cubic equation for the height x of the aerial target is obtained:

[0094]

[0095] Simplified to:

[0096]

[0097] This equation is a standard cubic equation and can be solved by applying the Cardinal formula. Let:

[0098]

[0099] For equation (0.10), we can apply the Cardinal formula to solve it, and the roots we get are:

[0100]

[0101] From this equation, we obtain three solutions. When Δ ≥ 0, the equation has one real root and two complex roots; when Δ < 0, the equation has three real roots. Let's analyze the sign of Δ.

[0102] first, and Depends on the sign of p. Since the orbital altitude of the spaceborne radar is very high, and the altitude of the aerial target is usually within 30km, Figure 3 The OSG of the middle triangle can get b 2 -c 2 >d 2 The radial distance of the micro-multipath of the aerial target is generally only a dozen kilometers larger than the radial distance of the direct path, and it can also have b 2 -c 2 >a 2 , so p>0, then Δ>0. Therefore, this equation can only get one real root and two complex roots, among which the real root is the required solution, that is, the height value of the aerial target.

[0103] In the simulation test, if the height of the aerial target is known, the micro-multipath measurement a can be solved according to the equation in formula (0.10), and the expression is:

[0104]

[0105] The satellite-borne radar used in the present invention is a single satellite-borne radar. Compared to altitude estimation using multiple radars, the geometric model constructed when estimating altitude using a single radar is simpler, reducing the amount of computation and complexity while also ensuring accuracy. Furthermore, the method overcomes the difficulty of altitude estimation with a single satellite-borne radar, and can also be used to estimate the altitude of the same aerial target using multiple satellite-borne radars.

[0106] The present invention utilizes the micro-multipath phenomenon to estimate the altitude of aerial targets. Currently, there is no method for using micro-multipath measurements for altitude estimation on spaceborne radars, nor is there any other effective method for altitude estimation on a single spaceborne radar. Secondly, micro-multipath measurements are very common and supplement radar measurements of direct paths to the same target point, thus providing more information about the target. Finally, the present invention uses radial distance measurements of direct paths and micro-multipath, which have very small ranging errors and can therefore estimate target altitude more accurately.

[0107] Example 1

[0108] Case 1 (Estimating the Altitude of an Aerial Target Using Micro-Multipath Measurement with a Single Satellite-borne Radar)

[0109] Using STK software, the orbital parameters of the spaceborne radar satellite are set as shown in Table 1.

[0110] Table 1 Number of satellite orbits

[0111]

[0112] The attitude angle of the radar body coordinate system relative to the orbit coordinate system is: rolling angle r c =75°, pitch angle Yaw angle φ c =5°. Assume that the latitude and longitude of the center of the detection area are 116.5° and 21.5° respectively, add an aerial simulation target to make a straight line movement, and its altitude climbs from 0.1km to 11km. Figure 4 and Figure 5 shown. Figure 4 This is the 2D real trajectory diagram of the spaceborne radar tracking the aerial target in STK. The blue part is the sea surface, the purple arc is the projection of the satellite-borne radar's orbit on the 2D plane, the purple fan-shaped part is the detection field of view of the satellite-borne radar, the purple box part is the aerial target, and the orange line is the trajectory projection of the aerial target that the satellite-borne radar can detect. Figure 5 This is a 3D image of an aerial target, where the blue part is the sea surface, the brown part is the sky, the yellow dots are aerial targets, and the yellow lines are the 3D trajectory of the aerial target.

[0113] First, the simulation generates the true values ​​of |OS|, |ST|, |ST′|, and |OG| for an aerial target within the field of view of a spaceborne radar over a 180-second period with a sampling interval of 3 seconds. |OS| is obtained from the semi-major axis of the spaceborne radar in STK, |ST| is obtained from the ECEF coordinate system positions of the spaceborne radar and the aerial target; |ST′| is obtained by substituting the aerial target's true altitude |GT| into Equation (0.13); and |OG| is calculated by substituting the aerial target's true latitude into Equation (0.4).

[0114] The following is the simulation content.

[0115] Simulation 1: Uncertainty estimation of a single aerial target's altitude. This involves sampling the Gaussian variables |OS|, |ST|, |ST′|, and |OG| at a single moment in time and then estimating the target's altitude. Using Monte Carlo simulation, the mean and variance of the estimated altitude are obtained.

[0116] We analyze a sampling moment of an aerial target, whose longitude is 116.3844°, latitude is 21.4349°, and altitude is 5.5197 km. We set |OS|, |ST|, |ST′|, and |OG| to follow the following distribution:

[0117]

[0118] Then, 1000 Monte Carlo simulations (MCMC) are performed. In each MCMC, |OS|, |ST|, |ST′|, and |OG| are sampled and substituted into equation (0.12) to calculate the altitude of the aerial target. For the altitude of the aerial target calculated from 1000 Monte Carlo simulations, the root mean square error (RMSE) of the altitude estimate is calculated as follows:

[0119]

[0120] Where N is the number of simulations calculated, is the estimated value of the aerial target height from the i-th Monte Carlo solution, x true It is the true altitude value of the aerial target.

[0121] Estimated altitude of aerial targets obtained from 1000 Monte Carlo simulations The mean of the aerial target height estimates is calculated as follows:

[0122]

[0123] in, is the mean of the Monte Carlo aerial target height estimates.

[0124] The final results are shown in Table 2:

[0125] Table 2 Target height estimation results of 1000 Monte Carlo simulations

[0126]

[0127]

[0128] Simulation 2: Estimate the height of an aerial target at multiple sampling moments. The altitude of the aerial target varies from 0.1 km to 11 km. Finally, compare the RMSE of the estimated altitude of the aerial target.

[0129] Set the standard deviations of |OS|, |ST|, |ST′|, and |OG| as follows:

[0130]

[0131] Appropriate noise was added to the true values ​​of |OS|, |ST|, |ST′|, and |OG| to simulate 360 ​​sampling points as the target altitude varied from 0.1 km to 11 km. The RMSE of the target altitude estimate was calculated to be 0.0639 km, a relatively low RMSE. This indicates that the altitude estimate obtained using the method of the present invention has a small error and is relatively accurate.

Claims

1. A method for estimating the height of an aerial target using a spaceborne radar based on multipath measurement, characterized in that: The following steps are involved: Obtaining a signal transmission path when a spaceborne radar illuminates an aerial target; the signal transmission path includes a transmission path, a reflection path, and a scattering path obtained under a micro-multipath phenomenon; Extract key point information in the signal transmission path; Use key point information to solve the height of aerial targets; The key point information includes: the position of the spaceborne radar, the position of the aerial target, the position where the signal is reflected or scattered, the projection point of the aerial target on the ground, the symmetrical point of the aerial target about the projection point, the center of the earth, the first auxiliary point and the second auxiliary point; The first auxiliary point is on the line connecting the position of the spaceborne radar and the center of the earth, and is in the same horizontal plane as the position of the aerial target; The second auxiliary point is on the line connecting the position of the spaceborne radar and the center of the earth, and is in the same horizontal plane as the symmetrical point; Using key point information to solve the height of aerial targets includes: The equation for the height of the aerial target is established as: (2|GT| 3 +(-|ST'| 2 +2|US| 2 -2|AND| 2 -|ST| 2 )|GT|-|OG||ST'| 2 +|AND||ST| 2 ) / (|OG|-|GT|)=0 Among them, |GT| represents the distance from the position of the aerial target to the projection point, that is, the height of the aerial target, |ST'| represents the distance from the position of the spaceborne radar to the symmetric point, |OS| represents the distance from the position of the spaceborne radar to the center of the earth, |OG| represents the distance from the projection point to the center of the earth, and |ST| represents the radial distance from the position of the spaceborne radar to the position of the aerial target.

2. The method for estimating the height of an aerial target using a spaceborne radar based on multipath measurement according to claim 1, wherein: Using key point information to solve the height of aerial targets also includes: The equation of the target height in the air is converted into a cubic equation, which is expressed as:

3. The method for estimating the height of an aerial target using a spaceborne radar based on multipath measurement according to claim 2, wherein: The equation for the height of the aerial target is established based on the first geometric relationship, the second geometric relationship and the third geometric relationship; The first geometric relationship is an equiproportional geometric relationship between the position of the aerial target, the position of the center of the earth, the first auxiliary point, the second auxiliary point, and the symmetrical point, which is expressed as: Wherein, |MT| represents the distance from the position of the aerial target to the first auxiliary point, |NT'| represents the distance from the second auxiliary point to the symmetrical point, |OM| represents the distance from the center of the earth to the first auxiliary point, |ON| represents the distance from the center of the earth to the second auxiliary point, |SM| represents the distance from the position of the spaceborne radar to the first auxiliary point, and |SN| represents the distance from the position of the spaceborne radar to the second auxiliary point. The second geometric relationship is the geometric relationship between the position of the aerial target, the position of the center of the earth, the first auxiliary point, the second auxiliary point and the symmetrical point, which is expressed as: |MT| 2 +|SM 2 =|ST| 2 |NT′| 2 +|SN| 2 =|ST′| 2 , The third geometric relationship is the geometric relationship between the position of the spaceborne radar, the position of the aerial target, the first auxiliary point, the second auxiliary point and the symmetrical point, which is expressed as: |MT| 2 +|OM| 2 =|OT| 2 |NT′| 2 +|ON| 2 =|OT′| 2 , Wherein, |OT| represents the distance from the position of the aerial target to the center of the earth, and |OT'| represents the distance from the center of the earth to the symmetrical point.

4. The method for estimating the height of an aerial target using a spaceborne radar based on multipath measurement according to claim 3, wherein: Before establishing the equation for the height of the aerial target, the Gaussian distribution of the distance from the satellite-borne radar to the center of the earth, the Gaussian distribution of the radial distance from the position of the satellite-borne radar to the position of the aerial target, the Gaussian distribution of the distance from the position of the satellite-borne radar to the symmetrical point, and the Gaussian distribution of the distance from the projection point to the center of the earth are obtained, which are expressed as: in, represents the Gaussian distribution of the distance from the satellite-borne radar to the center of the Earth, μ S represents the semi-major axis of the spaceborne radar, represents the error of the semi-major axis of the spaceborne radar, represents the Gaussian distribution of the radial distance between the satellite-borne radar and the aerial target, μ T Indicates the radial distance from the position of the spaceborne radar to the position of the aerial target, It represents the measurement error of the radial distance from the position of the spaceborne radar to the position of the aerial target. represents the Gaussian distribution of the distance from the satellite-borne radar to the symmetric point, μ T′ represents the distance from the position of the spaceborne radar to the symmetric point, represents the measurement error of the distance from the position of the spaceborne radar to the symmetric point, Represents the Gaussian distribution of the distance from the projection point to the center of the earth, μ G Indicates the distance from the projection point to the center of the earth, Indicates the error in the distance from the projection point to the center of the earth.

5. The method for estimating the height of an aerial target using a spaceborne radar based on multipath measurement according to claim 4, wherein: The process of solving the cubic equation includes: Using the Cardinal formula to solve the cubic equation, we can get the roots of the equation, which are expressed as: in, make Calculation shows that Δ≥0, so the cubic equation has 1 real root and 2 complex roots, among which the real root is the height value of the aerial target.

6. The method for estimating the height of an aerial target using a spaceborne radar based on multipath measurement according to claim 5, wherein: The satellite-borne radar is a single satellite-borne radar.

7. An electronic device, characterized in that: include: at least one processor; and, a memory communicatively coupled to at least one of the processors; The memory stores instructions that can be executed by at least one of the processors, and the instructions are executed by at least one of the processors so that at least one of the processors can execute a method for estimating the height of aerial targets using a spaceborne radar based on multipath measurement as described in any one of claims 1 to 6.

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