A method for eliminating multipath effects based on airborne circular SAR

Abstract

The present invention discloses a method for eliminating multipath effects based on airborne circular SAR, comprising the following steps: step 1, analyzing a classic four-path reflection model, and constructing a radar multipath echo signal model according to the four-path reflection model; step 2, constructing a system function projection matrix for different echo paths; step 3, constructing a method based on dictionary sparse representation, realizing separation and imaging of mixed received echo data, and suppressing false targets and sidelobe energy in the estimation results; step 4, through experimental simulation, the echo data of multiple paths are mixed to verify the effectiveness of steps 1 to 3. The present invention can not only effectively suppress clutter by constructing an imaging method based on dictionary sparse representation, but also ensure the algorithm performance in a non-uniform environment.

Description

Technical Field

[0001] The invention belongs to the technical field of radar image processing, in particular to a method for eliminating multipath effects based on airborne circular track SAR. Background Art

[0002] With the expansion of SAR application scope and the rapid change of digital signal processing technology, the impact of multipath effect on SAR imaging has received more and more attention. Traditional radar detection is usually carried out in an open environment, and it is usually assumed that the reflected echo of the signal emitted by the radar can directly return to the radar's receiving antenna, but this assumption may not be true in an environment with rich scattering. For example, objects with complex shapes in nature, such as jungles and mountains, have complex reflection paths. In these scenes, it is usually difficult to directly distinguish multipath scattering from real echoes in SAR images, resulting in the inability to utilize the multipath information. In contrast, buildings with regular shapes in urban areas usually produce more regular multipath scattering paths, so their multipath scattering information is easier to capture and utilize, providing more valuable information. Multipath scattering in urban areas causes great trouble to radar detection of targets, which is usually manifested in the following aspects: 1. Interference from a large amount of clutter in the city; 2. The target is blocked by other buildings; 3. Radar electromagnetic waves are reflected back and forth in buildings to form a large number of multipath echo signals. Among the above interferences, indistinguishable multipath interference will cause a significant deviation in the accuracy of target positioning, while distinguishable multipath signals will also cause a large number of ghost images and artifacts to appear in SAR images, which will cause distortion of the real target. Summary of the invention

[0003] In order to solve the above problem, the present invention provides a multipath effect elimination method applicable to circular SAR.

[0004] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0005] The present invention is a method for eliminating multipath effects based on airborne circular SAR, comprising the following steps:

[0006] Step 1, constructing a radar multipath echo signal model according to a four-path reflection model;

[0007] Step 2, constructing a four-path joint system function projection matrix for different echo paths;

[0008] Step 3: construct a dictionary-based sparse representation method to transform the SAR image reconstruction problem into an optimization problem, and obtain image data from different paths through iteration;

[0009] Step 4: Mix the echo data of multiple paths through experimental simulation to verify the effectiveness of steps 1 to 3.

[0010] A further improvement of the present invention is that: in step 1, if the radar transmits and receives a linear frequency modulation signal during the radar imaging process, then the single echo returned by the radar from the target is:

[0011]

[0012] Where rect(g) represents the rectangular window function, T is the pulse width of the linear frequency modulation signal, τ is the fast time variable, and f c is the center frequency of the transmitted signal, k is the linear frequency modulation slope, σ p is the scattering characteristic function, which is used to represent the scattering characteristics of the target. is the instantaneous distance from the radar to the target, and c is the speed of light.

[0013] The further improvement of the present invention is that: the specific steps of step 1 are: according to the four-path reflection model and the radar single echo signal expression, and when the distances of the second and third paths are the same, a radar multipath echo signal model is constructed, and the model expression is:

[0014] s total (τ,τ a )=s 1 (τ,τ a )+2s 2 (τ,τ a )+s 4 (τ,τ a )

[0015] s 1 (τ,τ a )=s(τ,τ a )

[0016]

[0017]

[0018] Where: 1 , 2 is the reflection coefficient, ΔR 2 =R 2 -R 1 , ΔR 4 =R 4 -R 1 , R 1 , R 2 , R 4 , are the lengths of path 1, path 2, and path 4 respectively.

[0019] A further improvement of the present invention is that the multipath joint signal model in step 2 is expressed as:

[0020] Y=F I X+n 0

[0021] Among them, Y is the column vector data obtained after the pulse compression and accumulation and rearrangement of the SAR echo signals of the four paths, and the SAR joint projection matrix is ​​F I =[F 1 ,F 2 ,F 3 ,F 4 ], where F 1 to F 4 Represents the radar projection matrices of four different paths, X=[X 1 ,X 2 ,X 3 ,X 4 ] T , [·] T represents the matrix transpose, X 1 , X 2 , X 3 , X 4 They represent the four refocused path data obtained after separation, n 0 For noise.

[0022] The further improvement of the present invention is that: the specific operation of step 3 is: the cost function of converting the SAR image reconstruction problem into an optimization problem is:

[0023]

[0024] in Representative k Norm, λ 1 is the regularization parameter;

[0025] l k The norm is expressed using the following smooth approximation:

[0026]

[0027] where ε>0 is a small constant, K is the length of the complex vector z, and z i represents the i-th element of the complex vector z; the corrected cost function is:

[0028]

[0029] For X and Y, the minimum cost function is solved by using the quasi-Newton method based on the Hessian matrix, and image data of different paths are obtained through iteration.

[0030] A further improvement of the present invention is that the iteration termination condition in step 3 is:

[0031]

[0032] Among them, δ>0.

[0033] The beneficial effects of the present invention are as follows: 1. The present invention constructs a dictionary-based sparse representation imaging method, which can not only effectively suppress clutter, but also ensure the algorithm performance in a non-uniform environment.

[0034] 2. The method of the present invention can achieve accurate positioning of the target and avoid distortion of the target in the image. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is based on the multipath effect elimination method of airborne circular SAR

[0036] Figure 2 It is the geometric model of circular SAR imaging

[0037] Figure 3 This is a schematic diagram of the four-path model.

[0038] Figure 4(a) shows the BP imaging result without considering the multipath effect.

[0039] Figure 4(b) shows the result after considering the multipath effect.

[0040] FIG5(a) is a range profile of the direct echo without considering the multipath effect.

[0041] Figure 5(b) is the range profile after considering the multipath effect.

[0042] FIG6( a ) is a diagram showing the result of path 1 after removing the multipath effect.

[0043] FIG6( b ) is a diagram showing the result of path 2 after removing the multipath effect.

[0044] FIG6(c) is a diagram showing the result of path 4 after removing the multipath effect.

[0045] FIG7( a ) is a distance cross-sectional view of path 1 after multipath removal.

[0046] FIG7( b ) is a distance cross-sectional view of path 2 after multipath removal.

[0047] FIG7( c ) is a distance cross-sectional view of path 4 after multipath removal.

[0048] Figure 8 It is a spatial distribution map of multiple point targets.

[0049] Figure 9(a) shows the BP imaging results of multiple point targets without multipath effects.

[0050] Figure 9(b) shows the BP imaging results of multiple point targets after considering the multipath effect.

[0051] FIG10( a ) is a diagram showing the result of path 1 after removing the multipath effects of multiple point targets.

[0052] FIG10( b ) is a diagram showing the result of path 2 after removing the multipath effects of multiple point targets.

[0053] FIG10( c ) is a diagram showing the result of path 3 after removing the multipath effects of multiple point targets. DETAILED DESCRIPTION

[0054] The following will disclose the embodiments of the present invention with drawings. For the purpose of clear description, many practical details will be described together in the following description. However, it should be understood that these practical details should not be used to limit the present invention. That is to say, in some embodiments of the present invention, these practical details are not necessary.

[0055] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0056] like Figure 1 As shown, the present invention is a method for eliminating multipath effects based on airborne circular SAR, comprising the following steps:

[0057] Step 1, constructing a radar multipath echo signal model according to a four-path reflection model;

[0058] Step 2, constructing a four-path joint system function projection matrix for different echo paths;

[0059] Step 3: construct a dictionary-based sparse representation method to transform the SAR image reconstruction problem into an optimization problem, and obtain image data from different paths through iteration;

[0060] Step 4: Mix the echo data of multiple paths through experimental simulation to verify the effectiveness of steps 1 to 3.

[0061] The four-path reflection model in step 1 adopts a typical electromagnetic wave multipath propagation model, such as Figure 3 As shown in the figure, we can intuitively see how electromagnetic waves propagate. Path 1 represents the direct echo, path 2 and path 3 are single-reflection echoes, and path 4 is double-reflection echoes. Assuming the radar position is A, the target position is B, and the ground reflection position is C, the four path lengths can be expressed as follows:

[0062] R 1 =2R AB (1)

[0063] R 2 =R AB +R BC +R CA (2)

[0064] R 3 =R AC +R CB +R BA (3)

[0065] R 4 =2R AC +2R BC (4)

[0066] When studying the SAR multipath effect, the plane of electromagnetic wave reflection is usually considered to be a horizontal plane with a certain reflection coefficient. Therefore, according to the principle of mirror reflection, the multipath reflection delay can be considered to be only related to the height of the target and the radar pitch angle. Assuming that the mirror position of the radar relative to the target is A′, the four paths can be calculated as follows:

[0067] R 1 =2R AB (5)

[0068] R 2 =R A′C +R CA (6)

[0069] R 3 =R 2 =R A′C +R CA (7)

[0070] R 4 =2R A′C (8)

[0071] Circular SAR imaging geometry Figure 2 As shown in the figure, assuming that during the radar imaging process, the radar transmits and receives a linear frequency modulation signal, then the single echo returned by the radar from the target can be expressed as:

[0072]

[0073] Where rect(g) represents the rectangular window function, T is the pulse width of the linear frequency modulation signal, τ is the fast time variable, and f c is the center frequency of the transmitted signal, k is the linear frequency modulation slope, σ p is the scattering characteristic function, which is used to represent the scattering characteristics of the target, R τm is the instantaneous distance from the radar to the target, and c is the speed of light.

[0074] According to the above multipath model and the single echo signal expression of the radar, and the distances of the second and third paths are the same, we can obtain the radar at τ a The mixed echo at the time is:

[0075] s total (τ,τ a )=s 1 (τ,τ a )+2s 2 (τ,τ a )+s 4 (τ,τ a ) (10)

[0076] s 1 (τ,τ a )=s(τ,τ a ) (11)

[0077]

[0078]

[0079] where ρ 1 , 2 is the reflection coefficient. In the simulation, it is assumed that the reflection is specular reflection, so ρ 1 , 2 Take 1, ΔR 2 =R 2 -R 1 , ΔR 4 =R 4 -R 1 is the delay of multipath reflection relative to the direct echo. Equation (11) is the direct echo, (12) is the first reflection echo, and (13) is the second reflection echo.

[0080] The specific operations of step 2 are:

[0081] This step is mainly to construct the target multipath radar projection matrix. According to the four-path model in step 1, the target echo contains direct echo and multipath echo. Each path is represented by an observation matrix. The SAR joint projection matrix is ​​defined as F I =[F 1 ,F 2 ,F 3 ,F 4 ], where F 1 to F 4 Represents the radar projection matrices of four different paths. 1 , X 2 , X 3 , X 4 Then they represent the four refocused path data obtained after separation. Then the data of the four-path combination can be represented by the following signal model:

[0082] Y=F I X+n 0 (14)

[0083] Where Y is the column vector data obtained after the pulse compression and accumulation and rearrangement of the SAR echo signals of the four paths in step 1. 1 ,X 2 ,X 3 ,X 4 ] T , [·] T represents matrix transpose, n 0 For noise.

[0084] Step 3 is based on the multipath joint signal model obtained in step 2. To solve the separated X, based on the non-quadratic regularization framework, an equivalent regularization scheme with the following optimization problem is used to transform the SAR image reconstruction problem into an optimization problem. The cost function is as follows:

[0085]

[0086] here Representative k Norm, λ 1 is the regularization parameter. For X and Y, the minimum cost function is solved by using the quasi-Newton method based on the Hessian matrix. Finally, the image data of different paths are obtained through iteration. In formula (15), the first term is the data fidelity term, which includes the SAR projection matrix and the radar scattering coefficient of the observed scene, thus including the information of different observed paths. The second term l k The norm represents a priori constraints on X, which is usually used to constrain the sparsity of the reconstruction results. Here, we use l k The norm constrains the solution results through the sparse constraint method, which not only separates the results of mixed multipath, but also effectively suppresses the false targets and sidelobe energy in the estimation results.

[0087] In order to facilitate the solution, l in formula (15) k The norm can be expressed using the following smooth approximation:

[0088]

[0089] where ε>0 is a small constant, K is the length of the complex vector z, and z i represents the ith element of the complex vector z. For the convenience of calculation, substitute (16) into (15) to obtain the following modified cost function:

[0090]

[0091] In order to solve the gradient of the real and imaginary parts of formula (17), the quasi-Newton method based on the Hessian matrix is ​​used to obtain the following iterative formula:

[0092]

[0093] Among them, γ represents the iteration step, is the result after n iterations, and:

[0094]

[0095] Assume that F = (F I ) H F I , (·) H represents the matrix conjugate transpose, diag{·} represents the diagonal matrix, then:

[0096]

[0097] The iteration termination conditions are as follows:

[0098]

[0099] Usually δ>0 and is a very small real number, usually 0.001.

[0100] Step 4 verifies the effectiveness of steps 1 to 3 by simulating multipath mixed echo data experimentally. The verification process is as follows:

[0101] The radar simulation parameters are shown in Table 1:

[0102] Table 1 Radar simulation parameters

[0103] parameter Parameter Value Transmit signal bandwidth / GHz 0.5 Sampling frequency / GHz 1 Platform height / m 1000 Platform radius / m 300 Observation angle / ° -10～10

[0104] According to the multipath effect model analyzed in step 1, the second path and the third path are actually equivalent to one path. Therefore, in the simulation experiment, we only consider the direct echo path and the second and fourth echo paths. The following simulation experiments are conducted for the case of one point target and multiple point targets. First, consider the existence of a point target with a height of 1m in space, where Figure 4(a) is the BP imaging result without considering the multipath effect, and Figure 4(b) is the result with the multipath effect considered. It can be seen that after considering the multipath effect, two artifacts appear above the real target. The bottom of Figure 4(b) is the real image, the middle is the artifact generated by the second path, and the top is the artifact generated by the fourth path. Figure 5(a) is the distance profile of the direct echo without considering the multipath effect, and Figure 5(b) is the distance profile after considering the multipath effect, where peak 1 is the direct echo, peak 2 is the second path echo, and peak 3 is the fourth path echo. Select the iteration parameter λ 1=0.2, k=0.7. Figures 6(a), 6(b), and 6(c) are the final results of removing the multipath effect, and Figures 7(a), 7(b), and 7(c) are the distance profiles of each path after separation. It can be seen that not only the artifacts caused by the multipath effect are eliminated, but also the image quality is improved to a certain extent, and the energy is more concentrated.

[0105] The following simulation is performed on multiple point targets. Assume that there are 33 point targets with a height of 2 in the space. The distribution of the point targets is as follows: Figure 8 As shown, the radar parameters are shown in Table 1. BP imaging is performed on the scene with an imaging resolution of 0.5m×0.5m. Figure 9(a) is the imaging result without multipath effect, and Figure 9(b) is the imaging result after considering the multipath effect. In Figure 9(b), the A frame is the direct echo image, the B frame is the artifact generated by the second path echo, and the C frame is the artifact generated by the fourth path echo. After considering the multipath effect, the iteration parameter λ is selected. 1 = 0.2, k = 0.7. The final multipath elimination result is shown in FIG10 , and path 1 with a better multipath elimination effect is selected as the final result of multipath elimination.

[0106] The above description is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technology can understand and think of any changes or substitutions within the technical scope disclosed by the present invention, which should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for eliminating multipath effects based on airborne circular SAR, characterized in that: The following steps are involved: Step 1, constructing a radar multipath echo signal model according to a four-path reflection model; According to the four-path reflection model and the expression of the radar single echo signal, and when the distances of the second and third paths are the same, a radar multipath echo signal model is constructed. The model expression is: s total (t,t a )=s1(τ,τ a )+2s2(τ,τ a )+s4(τ,τ a ); s1(τ,τ a )=s(τ,τ a ); Where: ρ1, ρ2 are reflection coefficients, ΔR2=R2-R1, ΔR4=R4-R1, R1, R2, R4 are the lengths of path 1, path 2, and path 4 respectively; Step 2, constructing a four-path joint system function projection matrix for different echo paths to obtain a multipath joint signal model; The multipath joint signal model is expressed as: Y=F I X+n0; Among them, Y is the column vector data obtained after the pulse compression and accumulation and rearrangement of the SAR echo signals of the four paths, and the SAR joint projection matrix is ​​F I =[F1,F2,F3,F4], where F1 to F4 represent the radar projection matrices of four different paths, X = [X1,X2,X3,X4] T , [] T represents matrix transpose, X1, X2, X3, and X4 represent the four refocused path data obtained after separation, and n0 is noise; Step 3: construct a dictionary-based sparse representation method to transform the SAR image reconstruction problem into an optimization problem, and obtain image data from different paths through iteration; The iteration termination condition in step 3 is: Among them, δ>0; Step 4: The echo data of multiple paths are mixed through experimental simulation to verify the effectiveness of steps 1 to 3.

2. According to claim 1, a method for eliminating multipath effects based on airborne circular SAR is characterized in that: In step 1, if the radar transmits and receives a linear frequency modulation signal during the radar imaging process, then the single echo returned by the radar from the target is: Where rect(·) represents the rectangular window function, T is the pulse width of the linear frequency modulation signal, τ is the fast time variable, and f c is the center frequency of the transmitted signal, k is the linear frequency modulation slope, σ p is the scattering characteristic function, which is used to represent the scattering characteristics of the target. is the instantaneous distance from the radar to the target, and c is the speed of light.

3. The method for eliminating multipath effects based on airborne circular SAR according to claim 1, characterized in that: The specific operation of step 3 is: the cost function of converting the SAR image reconstruction problem into an optimization problem is: in Representative k norm, λ1 is the regularization parameter; l k The norm is expressed using the following smooth approximation: where ε>0 is a constant, K is the length of the complex vector z, i represents the i-th element of the complex vector z; The corrected cost function is: For X and Y, the minimum cost function is solved by using the quasi-Newton method based on the Hessian matrix, and image data of different paths are obtained through iteration.

Images