SAR (Synthetic Aperture Radar) three-dimensional reconstruction method based on bistatic differential distance
Through the SAR three-dimensional reconstruction method based on dual-base difference-segment distance, the problem that traditional SAR technology cannot obtain the target height is solved, efficient three-dimensional reconstruction is achieved, and the depth of information acquisition and processing is improved.
Patent Information
- Application Number
- CN202411473765.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-22
- Publication Date
- 2025-02-18
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Traditional SAR technology cannot obtain high-level information of the target, limiting the depth of subsequent information acquisition and processing.
The SAR three-dimensional reconstruction method based on the dual-basis difference distance is adopted to deduce the projection matrix of the three-dimensional target through the first-order approximation of the dual-basis difference difference distance, and establish the connection between the offset and height of the target in different SAR images to achieve high recovery and reconstruction.
The three-dimensional information of the target is restored from the dual-based SAR image, which improves the depth of information acquisition and processing, and has a low error rate.
Smart Images
Figure CN119478205A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of synthetic aperture radar, in particular to a SAR three-dimensional reconstruction method based on bistatic differential distance. Background Art
[0002] Since the concept of Synthetic Aperture Radar (SAR) was proposed in the 1950s, it has played an extremely important role in military reconnaissance and civilian fields. SAR obtains high-resolution radar images by emitting highly penetrating electromagnetic waves, overcoming the shortcomings of traditional optical imaging that is easily affected by the environment. It is not affected by weather and can work and be used normally regardless of day or night, and can detect, classify and locate distant targets. However, traditional SAR images are projections of three-dimensional scenes onto a plane, and cannot obtain the height information of the target, which is not conducive to subsequent information acquisition and processing. Summary of the invention
[0003] The present invention provides a SAR three-dimensional reconstruction method based on bistatic differential distance, so as to solve the defects in the prior art.
[0004] The present invention is achieved through the following technical solutions:
[0005] A SAR three-dimensional reconstruction method based on bi-basic differential distance includes the following steps:
[0006] Step 1: Dual-base differential distance
[0007] The position vectors of the transmitting station and the receiving station center at the same time are denoted as r t0 =(x t ,y t , z t ) and r r0 =(x r ,y r , z r ), the velocity vectors are v t =(V xt , V yt , 0) and v r =(V xr , V yr , 0), the position vector is denoted as r t (η) and r r (η). The target P is located at Rp = (x, y, z). After receiving the echo, the receiving station demodulates it and performs a range-to-Fourier transform.
[0008] Step 2: Target 3D projection matrix
[0009] Expand the double base difference distance to first order;
[0010] Step 3: Target height recovery algorithm
[0011] The position of the transmitting platform at the beam center is r t0 =(x t ,y t , z t ), the position of the i-th receiving platform is r r0 (i) =(x ri ,y ri , z ri ), i = 1, 2, the velocity vector of the launch platform is v t =(V xt , V yt , 0), the velocity vector of the receiving platform is v ri =(V xi , V yi , 0), i = 1, 2; without considering the error, when the target (x, y, z) is projected onto the two bistatic SAR images and At the position, the first bistatic SAR image is used as the reference image; according to the obtained bistatic SAR image, the height of the point can be obtained by utilizing the offset of the corresponding scattering point, thereby realizing the three-dimensional reconstruction of the point.
[0012] In the above-mentioned SAR three-dimensional reconstruction method based on dual-base differential distance, the signal obtained by performing range Fourier transform after demodulation in step 1 is:
[0013]
[0014] In the formula, f τ represents the distance frequency variable; T a is the synthetic aperture time, R(η) is the sum of the distances from the transmitting and receiving platforms to the target;
[0015] Then, matched filtering and motion compensation are performed, and (Equation 1) is multiplied by the following reference function:
[0016]
[0017] Where R0(η) is the sum of the distances from the transmitting and receiving platforms to the center of the scene;
[0018] The imaging result can be obtained by performing phase compensation according to Formula 1, which is expressed as:
[0019]
[0020] Where, 1≤i≤M and 1≤k≤N, where M and N represent the frequency range and time range respectively; ΔR(η k) is the sum of the distances from the transceiver station to the target minus the sum of the distances from the transceiver station to the center of the scene, that is, the differential distance of the bistatic SAR can be expressed as:
[0021] ΔR(η k )=ΔR t (η k )+ΔR r (η k )
[0022] Among them, ΔR t (η k )=|r t (η k )-r p |-|r t (η k )|;ΔR r (η k )=|r r (η k )-r p |-|r r (η k )|.
[0023] In the above-mentioned SAR 3D reconstruction method based on dual-base differential distance, the expression of R(η) is: R(η)=R t (η)+R r (η)=|r t (η)-r p |+|r r (η)-r p |.
[0024] In the above-mentioned SAR 3D reconstruction method based on dual-base differential distance, the expression of R0(η) is: R0(η)=R t0 (η)+R r0 (η)=|r t (η)|+|r r (η)|.
[0025] In the above-mentioned SAR 3D reconstruction method based on dual-base differential distance, the ΔR t and ΔR r Expand to first order at (x, y, z) = (0, 0, 0) and substitute ΔR (η k ), under far-field conditions, the azimuths of the transmitting platform and the receiving platform relative to the center of the scene are introduced, and the double-base differential distance is obtained by using polar coordinates:
[0026]
[0027] In the formula, and θt (η k ) are the azimuth and elevation of the launch platform, and θ r (η k ) represent the azimuth and elevation of the receiving platform respectively.
[0028] In the above-mentioned SAR 3D reconstruction method based on dual-base differential distance, when the distances from the transmitting platform and the receiving platform to the origin are large enough (i.e., the distances from the origin to the transmitting and receiving platforms are much larger than the distances between the transmitting and receiving platforms), the distances can be regarded as the distances about η. k constant, then, according to the geometric relationship, Can be used Approximately, cosθ t (η k ) can be used Approximately, the double base difference distance can be simplified to:
[0029] ΔR(η k )≈-β0+β1η k
[0030] Among them, β0 and β1 are functions of x, y, and z. It can be expressed as a matrix:
[0031] Recorded as
[0032] In imaging processing, it is assumed that all scatterers are located on the ground, that is, z = 0, and the transformation is defined as:
[0033] Recorded as
[0034] Combining equations 4 and 5, the motion trajectories of the bistatic SAR receiving platform and the transmitting platform can be used to establish the real scattering point position (x, y, z) and the projection position in the SAR image. The relationship is as follows:
[0035]
[0036] In the above-mentioned SAR 3D reconstruction method based on dual-base differential distance, U i With V i The expressions are:
[0037]
[0038] in, i=1,2.
[0039] In the above-mentioned SAR 3D reconstruction method based on bistatic differential distance, in the step 3, without considering the error, when the target (x, y, z) is projected onto the two bistatic SAR images, and At position, taking the first bistatic SAR image as the reference image, we have:
[0040]
[0041]
[0042] Denoted as U z Z
[0043] According to Equation 6, when the first bistatic SAR image is used as the reference image, the estimated value of the height is calculated as follows:
[0044]
[0045] According to the obtained bistatic SAR image, the height of the point can be obtained by utilizing the offset of the corresponding scattering point, thereby realizing the three-dimensional reconstruction of the point.
[0046] In the above-mentioned SAR 3D reconstruction method based on bistatic differential distance, in order to improve the accuracy in the step 3, the second bistatic SAR image can be used as a reference image, and Z21 can be obtained using the same method, and finally the average value is calculated;
[0047] For the two bistatic SAR images obtained, we have:
[0048]
[0049] In the formula, Target R p = The projection position of (x, y, z) in the two bistatic SAR images.
[0050] In the above-mentioned SAR 3D reconstruction method based on bistatic differential distance, when the target is at a height of 1m in step 3, the offset of the target position in the bistatic SAR image is:
[0051]
[0052] When the projection position and height of the target are known, the following formula can be used to achieve three-dimensional reconstruction:
[0053]
[0054] In the formula, is the target R recovered when the first bistatic SAR image is the reference image p= x and y in (x, y, z).
[0055] The advantages of the present invention are as follows: the present invention firstly derives the projection matrix of the three-dimensional target by using the first-order approximation of the dual-base differential distance, and then establishes the connection between the offset and the height of the target in different SAR images, thereby realizing the height recovery and reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS
[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.
[0057] Figure 1 A schematic diagram of two-dimensional imaging verified by a simulation experiment of the present invention;
[0058] Figure 2 It is a schematic diagram of three-dimensional imaging verified by the simulation experiment of the present invention. DETAILED DESCRIPTION
[0059] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0060] A SAR three-dimensional reconstruction method based on bi-basic differential distance includes the following steps:
[0061] Step 1: Dual-base differential distance
[0062] The position vectors of the transmitting station and the receiving station center at the same time are denoted as r t0 =(x t ,y t , z t ) and r r0 =(x r ,y r , z r ), the velocity vectors are v t =(V xt , V yt , 0) and v r =(V xr , V yr , 0), the position vector is denoted as r t (η) and rr (η). The target P is located at Rp = (x, y, z). After receiving the echo, the receiving station demodulates it and performs a range-to-Fourier transform.
[0063] Step 2: Target 3D projection matrix
[0064] Expand the double base difference distance to first order;
[0065] Step 3: Target height recovery algorithm
[0066] The position of the transmitting platform at the beam center is r t0 =(x t ,y t , z t ), the position of the i-th receiving platform is r r0 (i) =(x ri ,y ri , z ri ), i = 1, 2, the velocity vector of the launch platform is v t =(V xt , V yt , 0), the velocity vector of the receiving platform is v ri =(V xi , V yi , 0), i = 1, 2; without considering the error, when the target (x, y, z) is projected onto the two bistatic SAR images and At the position, the first bistatic SAR image is used as the reference image; according to the obtained bistatic SAR image, the height of the point can be obtained by utilizing the offset of the corresponding scattering point, thereby realizing the three-dimensional reconstruction of the point.
[0067] Specifically, the signal obtained by performing distance Fourier transform after demodulation in step 1 of this embodiment is:
[0068]
[0069] In the formula, f τ represents the distance frequency variable; T a is the synthetic aperture time, R(η) is the sum of the distances from the transmitting and receiving platforms to the target;
[0070] Then, matched filtering and motion compensation are performed, and (Equation 1) is multiplied by the following reference function:
[0071]
[0072] Where R0(η) is the sum of the distances from the transmitting and receiving platforms to the center of the scene;
[0073] The imaging result can be obtained by performing phase compensation according to Formula 1, which is expressed as:
[0074]
[0075] Where, 1≤i≤M and 1≤k≤N, where M and N represent the frequency range and time range respectively; ΔR(η k ) is the sum of the distances from the transceiver station to the target minus the sum of the distances from the transceiver station to the center of the scene, that is, the differential distance of the bistatic SAR can be expressed as:
[0076] ΔR(η k )=ΔR t (η k )+ΔR r (η k )
[0077] Among them, ΔR t (η k )=|r t (η k )-r p |-|r t (η k )|;ΔR r (η k )=|r r (η k )-r p |-|r r (η k )|.
[0078] Specifically, the expression of R(η) described in this embodiment is: R(η)=R t (η)+R r (η)=|r t (η)-r p |+|r r (η)-r p |.
[0079] More specifically, the expression of R0(η) described in this embodiment is: R0(η)=R t0 (η)+R r0 (η)=|r t (η)|+|r r (η)|.
[0080] More specifically, in step 2 of this embodiment, ΔR in the dual-base differential distance t and ΔR r Expand to first order at (x, y, z) = (0, 0, 0) and substitute ΔR (η k ), under far-field conditions, the azimuths of the transmitting platform and the receiving platform relative to the center of the scene are introduced, and the double-base differential distance is obtained by using polar coordinates:
[0081]
[0082] In the formula, and θ t (η k ) are the azimuth and elevation of the launch platform, and θ r (η k ) represent the azimuth and elevation of the receiving platform respectively.
[0083] More specifically, when the distance from the transmitting platform and the receiving platform to the origin is large enough (that is, the distance from the origin to the transmitting and receiving platforms is much larger than the distance between the transmitting and receiving platforms), the distance can be regarded as a function of η. k constant, then, according to the geometric relationship, Can be used Approximately, cosθ t (η k ) can be used Approximately, the double base difference distance can be simplified to:
[0084] ΔR(η k )≈-β0+β1η k
[0085] Among them, β0 and β1 are functions of x, y, and z. It can be expressed as a matrix:
[0086] Recorded as
[0087] In imaging processing, it is assumed that all scatterers are located on the ground, that is, z = 0, and the transformation is defined as:
[0088] Recorded as
[0089] Combining equations 4 and 5, the motion trajectories of the bistatic SAR receiving platform and the transmitting platform can be used to establish the real scattering point position (x, y, z) and the projection position in the SAR image. The relationship is as follows:
[0090]
[0091] Furthermore, in step 3 of this embodiment, i With V i The expressions are:
[0092]
[0093] in, i=1,2.
[0094] Furthermore, in step 3 of this embodiment, without considering the error, when the target (x, y, z) is projected onto the two bistatic SAR images, and At position, taking the first bistatic SAR image as the reference image, we have:
[0095]
[0096]
[0097] Denoted as U z Z
[0098] According to Equation 6, when the first bistatic SAR image is used as the reference image, the estimated value of the height is calculated as follows:
[0099]
[0100] According to the obtained bistatic SAR image, the height of the point can be obtained by utilizing the offset of the corresponding scattering point, thereby realizing the three-dimensional reconstruction of the point.
[0101] Furthermore, in order to improve the accuracy in step 3 of this embodiment, the second bistatic SAR image can be used as a reference image, and Z21 can be obtained using the same method, and finally the average value is calculated;
[0102] For the two bistatic SAR images obtained, we have:
[0103]
[0104] In the formula, Target R p = The projection position of (x, y, z) in the two bistatic SAR images.
[0105] Furthermore, in step 3 of this embodiment, when the target is at a height of 1 m, the offset of the target position in the bistatic SAR image is:
[0106]
[0107] When the projection position and height of the target are known, the following formula can be used to achieve three-dimensional reconstruction:
[0108]
[0109] In the formula, is the target R recovered when the first bistatic SAR image is the reference image p = x and y in (x, y, z).
[0110] Simulation experiment verification
[0111] The simulation parameters of the 3D reconstruction system are shown in Table 1, and the simulation parameters of the multi-base SAR are shown in Table 2. The scene targets consist of multiple point targets with a spacing of 4m. In the simulation experiment, the scattering coefficients of the targets are the same.
[0112] Parameter name Parameter Symbols Numeric Carrier frequency <![CDATA[f c ]]> 10GHz Transmit signal bandwidth B 400MHz Synthetic Aperture Time <![CDATA[T s ]]> 1s Pulse Width <![CDATA[T p ]]> 5μs Pulse repetition frequency PRF 2000Hz Pulse sampling frequency <![CDATA[f s ]]> 500MHz
[0113] Table 1
[0114] Parameter name Parameter Symbols Numeric Initial location of the transmitter <![CDATA[r t ]]> (35, 0, 10) km Transmitter station speed <![CDATA[V t ]]> (100, 100, 0) m / s Initial position of the first receiving station <![CDATA[r r1 ]]> (7.5, -2.7, 3) km The first receiving station speed <![CDATA[V r1 ]]> (50, 150, 0) m / s Initial position of the second receiving station <![CDATA[r r2 ]]> (8, -1, 3) km The second receiving station speed <![CDATA[V r2 ]]> (20, 180, 0) m / s Imaging Network (dx,dy) (0.01，0.01)m
[0115] Table 2
[0116] The error of 3D reconstruction is defined as follows:
[0117] Wherein: Δx=x-x'; Δy=y-y'; Δz=z-z', (x', y', z') is the result of three-dimensional reconstruction.
[0118] After obtaining two bistatic SAR images, the method of the present invention is used to perform SAR three-dimensional reconstruction ( Figure 1 is a schematic diagram of two-dimensional imaging. Figure 2 ( ) is a schematic diagram of 3D imaging. The comparison between the original position information and the restored results of some point targets is shown in Table III.
[0119]
[0120]
[0121] Table 3
[0122] Depend on Figure 1 and Figure 2 It can be seen that the position of the scattering point has been effectively restored. From the data in Table 3, it can be seen that the maximum error between the 3D reconstruction result and the real data does not exceed 0.3m. The error rate is low and the main source of the error is the first-order approximation of the dual-base differential distance and the approximation of the origin slant distance of the transceiver station when establishing the projection matrix, as well as the error of the scattering point position information, so that the SAR 3D reconstruction can be completed more accurately.
[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A SAR 3D reconstruction method based on bistatic differential distance, characterized in that: The steps include: Step 1: Dual-base differential distance The position vectors of the transmitting station and the receiving station center at the same time are denoted as r t0 =(x t ,y t , z t ) and r r0 =(x r ,y r , z r ), the velocity vectors are v t =(V xt , V yt , 0) and v r =(V xr , V yr , 0), the position vector is denoted as r t (η) and r r (η). The target P is located at Rp = (x, y, z). After receiving the echo, the receiving station demodulates it and performs a range-to-Fourier transform. Step 2: Target 3D projection matrix Expand the double base difference distance to first order; Step 3: Target height recovery algorithm The position of the transmitting platform at the beam center is r t0 =(x t ,y t , z t ), the position of the i-th receiving platform is r r0 (i) =(x ri ,y ri , z ri ), i = 1, 2, the velocity vector of the launch platform is v t =(V xt , V yt , 0), the velocity vector of the receiving platform is v ri =(V xi , V yi , 0), i = 1, 2; without considering the error, when the target (x, y, z) is projected onto the two bistatic SAR images and At the position, the first bistatic SAR image is used as the reference image; according to the obtained bistatic SAR image, the height of the point can be obtained by utilizing the offset of the corresponding scattering point, thereby realizing the three-dimensional reconstruction of the point.
2. The SAR 3D reconstruction method based on bistatic differential distance according to claim 1, characterized in that: The signal obtained by performing distance Fourier transform after demodulation in step 1 is: In the formula, f τ represents the distance frequency variable; T a is the synthetic aperture time, R(η) is the sum of the distances from the transmitting and receiving platforms to the target; Then, matched filtering and motion compensation are performed, and (Equation 1) is multiplied by the following reference function: Where R0(η) is the sum of the distances from the transmitting and receiving platforms to the center of the scene; The imaging result can be obtained by performing phase compensation according to Formula 1, which is expressed as: Where, 1≤i≤M and 1≤k≤N, where M and N represent the frequency range and time range respectively; ΔR(η k ) is the sum of the distances from the transceiver station to the target minus the sum of the distances from the transceiver station to the center of the scene, that is, the differential distance of the bistatic SAR can be expressed as: ΔR(η k )=ΔR t (or k )+ΔR r (or k ) Among them, ΔR t (or k )=|r t (or k )-r p |-|r t (or k )|;ΔR r (or k )=|r r (or k )-r p |-|r r (or k )|。 3. The SAR 3D reconstruction method based on bistatic differential distance according to claim 2, characterized in that: The expression of R(η) is: R(η)=R t (η)+R r (η)=|r t (η)-r p |+|r r (η)-r p |。 4. The SAR 3D reconstruction method based on bistatic differential distance according to claim 2, characterized in that: The expression of R0(η) is: R0(η)=R t0 (η)+R r0 (η)=|r t (η)|+|r r (η)|.
5. The SAR 3D reconstruction method based on bistatic differential distance according to claim 1, characterized in that: In the step 2, ΔR in the double base differential distance t and ΔR r Expand to first order at (x, y, z) = (0, 0, 0) and substitute ΔR (η k ), under far-field conditions, the azimuths of the transmitting platform and the receiving platform relative to the center of the scene are introduced, and the double-base differential distance is obtained by using polar coordinates: In the formula, and θ t (η k ) are the azimuth and elevation of the launch platform, and θ r (η k ) represent the azimuth and elevation of the receiving platform respectively.
6. The SAR 3D reconstruction method based on bistatic differential distance according to claim 5, characterized in that: When the distance from the transmitting platform and the receiving platform to the origin is large enough (i.e., the distance from the origin to the transmitting and receiving platforms is much larger than the distance between the transmitting and receiving platforms), the distance can be regarded as a function of η. k constant, then, according to the geometric relationship, Can be used Approximately, cosθ t (η k ) can be used Approximately, the double base difference distance can be simplified to: ΔR(η k )≈-β0+β1η k Among them, β0 and β1 are functions of x, y, and z. It can be expressed as a matrix: In imaging processing, it is assumed that all scatterers are located on the ground, that is, z = 0, and the transformation is defined as: Combining equations 4 and 5, the motion trajectories of the bistatic SAR receiving platform and the transmitting platform can be used to establish the real scattering point position (x, y, z) and the projection position in the SAR image. The relationship is as follows:
7. The SAR 3D reconstruction method based on bistatic differential distance according to claim 1, characterized in that: In step 3, U i With V i The expressions are: in, 8. The SAR 3D reconstruction method based on bistatic differential distance according to claim 1, characterized in that: In the step 3, without considering the error, when the target (x, y, z) is projected onto the two bistatic SAR images, and At position, taking the first bistatic SAR image as the reference image, we have: By using Equation 6, when the first bistatic SAR image is used as the reference image, the estimated value of the height is calculated as follows: According to the obtained bistatic SAR image, the height of the point can be obtained by utilizing the offset of the corresponding scattering point, thereby realizing the three-dimensional reconstruction of the point.
9. The SAR 3D reconstruction method based on bistatic differential distance according to claim 1, characterized in that: In order to improve the accuracy in the step 3, the second bistatic SAR image can be used as a reference image, and Z21 can be obtained using the same method, and finally the average value is calculated; For the two bistatic SAR images obtained, we have: In the formula, Target R p = The projection position of (x, y, z) in the two bistatic SAR images.
10. The SAR 3D reconstruction method based on bistatic differential distance according to claim 1, characterized in that: In step 3, when the target is at a height of 1 m, the offset of the target position in the bistatic SAR image is: When the projection position and height of the target are known, the following formula can be used to achieve three-dimensional reconstruction: In the formula, is the target R recovered when the first bistatic SAR image is the reference image p = x and y in (x, y, z).