Motion compensation method for BiSAR polar coordinate format image of any configuration

Abstract

The invention discloses a motion compensation method for any-configuration BiSAR polar coordinate format images, solves the problem that the existing motion compensation method is difficult to solve the defocusing problem of general configuration at a squint angle, and belongs to the field of microwave remote sensing imaging. The method comprises the following steps: establishing an echo model of any-configuration BiSAR with a motion error, and obtaining a phase error caused by a two-dimensional motion error in a wavenumber domain according to the established echo model; a dimensionality reduction operation function is presented. Through the operation, QPE and coupling errors are reduced to one dimension. Then, a weighted maximum likelihood phase gradient automatic focusing algorithm WPGA is used to correct the one-dimensional motion error, and compared with a PGA, the algorithm uses fewer samples to realize more accurate phase estimation. Finally, the superiority of the method is verified through point target simulation and actual experiments.

Description

Technical Field

[0001] The invention relates to a motion compensation method for an image in a BiSAR polar coordinate format with arbitrary configuration, and belongs to the field of microwave remote sensing imaging. Background Art

[0002] Bistatic synthetic aperture radar (BiSAR) has many advantages over monostatic SAR, including high concealment, low cost and anti-interference ability. Therefore, BiSAR has attracted widespread attention from scholars in civil and military applications. In practical applications, due to the atmosphere, wind resistance and the vibration of the SAR platform itself, the BiSAR transceiver platform deviates from the ideal flight trajectory, introducing unknown motion errors and causing the SAR image to be out of focus. Therefore, motion compensation is crucial to the BiSAR system. Due to its high computational efficiency and applicability to BiSAR of any trajectory, the Polar format algorithm (PFA) is considered to be an ideal imaging algorithm for BiSAR of arbitrary configuration. However, accurately compensating for the unknown motion errors in BiSAR PFA images remains a challenge. The polar formatting process makes the expression of phase error more complicated. In addition, as the squint angle increases, the quadratic phase error (QPE) in the PFA image will also increase, making the unknown motion error more difficult to compensate. Existing motion compensation methods have difficulty in solving the defocus problem of general configurations under squint angles. Summary of the invention

[0003] In view of the fact that existing motion compensation methods are difficult to solve the defocus problem of general configuration under oblique viewing angles, the present invention provides a motion compensation method for BiSAR polar coordinate format images of arbitrary configuration.

[0004] A motion compensation method for an image in a BiSAR polar coordinate format with arbitrary configuration according to the present invention comprises:

[0005] S1. Establish an echo model of BiSAR with arbitrary configuration and motion error, and obtain the phase error caused by the two-dimensional motion error in the wave number domain according to the established echo model;

[0006] S2. Obtain the BiSAR polar coordinate format image S1(x,y) of arbitrary configuration with motion error, perform FFT transformation on the image S1(x,y) in the Y direction, and obtain the image S1(x,k y ), x represents the coordinate of the image domain in the X direction, k x , k y are the sum of the spatial frequencies of the image domain in the X and Y directions respectively;

[0007] S3, based on the phase error caused by the two-dimensional motion error in the wave number domain, the image S1(x,k y ) performs FFT transformation and dimensionality reduction processing in the X direction to obtain image S2(k x ,k y );

[0008] S4, for image S2(k x ,k y ) performs motion compensation to obtain the image represents the operator of WPGA algorithm;

[0009] S5, for image S3(k x ,k y ) performs IFFT transformation in the X direction to obtain image S3(x,k y );

[0010] S6, for image S3(x,k y ) is used to perform distortion correction to eliminate the influence of the dimensionality reduction function on the image phase, and an IFFT transform is performed in the Y direction to obtain image S3(x,y) to complete the refocusing.

[0011] Preferably, S3 includes:

[0012] The image S1(x,ky) is combined with the dimension reduction function H d (x,k y ) to obtain the image S2(x,ky):

[0013] S2(xk y )=S1(x,k y )·H d (x,k y )

[0014] in, t a Indicates the time of position, used to indicate k x and k y The functional relationship, f r is the distance axis frequency;

[0015] For image S2(x,k y ) performs FFT transformation in the X direction to obtain image S2(k x ,k y ).

[0016] Preferably, S3 includes:

[0017] For image S1(x,k y ) performs FFT transformation in the X direction to obtain image S1(k x,k y );

[0018] The image S1(k x ,k y ) to reduce the dimension and obtain image S2(k x ,k y ):

[0019]

[0020] in, t a Indicates the position time, used to indicate k x and k y The functional relationship, f r is the distance axis frequency.

[0021] As a preference, the operator for:

[0022]

[0023] Among them, S2(k,h) represents the image S2(k x ,k y ) is the discrete result after circular shift and window filtering, K represents the total number of samples obtained during the sample collection process, w k is the weight value of the kth distance unit, and h represents different circular shift units.

[0024] Preferably, in S6, the function For image S3(x,k y ) to perform distortion correction and eliminate the influence of dimensionality reduction function on image phase. for:

[0025]

[0026] Preferably, in S1, an echo model of BiSAR with arbitrary configuration and motion error is established:

[0027] S1=Aexp(j(k x x p +k y y p +K r Δe(t a )))

[0028] Among them, S1 represents the echo data in the wave number domain, A represents the product of the range-azimuth window, and the coordinates of the echo data are (x p ,y p ), Δe(t a ) is the sum of the non-ideal motion error and the plane wave error, k x, k y are the sum of the spatial frequencies of the image domain in the x and y directions, K r Represents the two-dimensional spatial frequency of a signal.

[0029] As a preference, the phase error caused by the two-dimensional motion error in the wavenumber domain is:

[0030]

[0031] in, Γ(k x0 ,k y0 ) is an intermediate variable, Indicates k x and k y The functional relationship of .

[0032] Beneficial effects of the present invention: The present invention is used for motion compensation and refocusing of polar coordinate format image imaging in BiSAR under arbitrary configurations. First, the structural characteristics of the two-dimensional phase error are revealed. Using these properties, a dimensionality reduction operation function is proposed. Through this operation, the QPE and coupling errors are reduced to one dimension. Then, the one-dimensional motion error is corrected using the weighted maximum likelihood phase gradient autofocus algorithm (Weighted maximum likelihood phase gradient autofocus, WPGA), which achieves more accurate phase estimation using fewer samples compared to PGA. Finally, the superiority of this method is verified through point target simulation and actual experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is the principle diagram of error dimension reduction operation;

[0034] Figure 2 is the target distribution map of the simulation scenario;

[0035] Figure 3 It is a point target BiSAR polar coordinate format image with motion error;

[0036] Figure 4 It is the point target BiSAR polar coordinate format image after WPGA algorithm correction;

[0037] Figure 5 The point target BiSAR polar coordinate format image after correction by the error dimension reduction compensation method of the present invention;

[0038] Figure 6 It is the contour map of the center point target after correction by WPGA algorithm;

[0039] Figure 7is a contour map of the center point target after correction by the compensation method for error dimension reduction of the present invention;

[0040] Figure 8 It is the contour map of the edge point target after correction by WPGA algorithm;

[0041] Fig. 9 is a contour map of the edge point target after correction by the compensation method for error dimension reduction of the present invention;

[0042] Fig.10 It is an azimuth profile of the center point target without compensation, WPGA compensation, and the compensation method of error dimension reduction of the present invention;

[0043] Fig.11 It is an azimuth profile diagram of an edge point target without compensation, WPGA compensation, and the compensation method of error dimension reduction described in the present invention. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0045] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0046] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0047] After matched filtering and space-invariant motion compensation relative to the center of the scene, at any point P(x p ,y p ) can be accurately modeled in the wavenumber domain as:

[0048] S1=Aexp(j(k x x p +k y y p +K r Δe(t a ))) (1)

[0049] Where A represents the product of the range-azimuth window, Δe(t a ) is the sum of the error of the non-ideal motion error and the plane wave error, f r and f c are the distance axis frequency and the carrier frequency, k x and k yis the sum of the spatial frequencies in the X and Y directions, expressed as:

[0050]

[0051] K r Represents the two-dimensional spatial frequency of the signal, f1(t a ) represents the coefficient of spatial frequency in the X direction, which is related to the azimuth time. f2(t a ) represents the coefficient of spatial frequency in the Y direction, which is related to the azimuth time, and c represents the speed of light;

[0052] Since the polar coordinate format image imaging results have a direct FFT relationship with the wavenumber domain, the structural characteristics of the two-dimensional error in the wavenumber domain are analyzed, and the law of two-dimensional error defocusing in the wavenumber domain is established. The azimuth time t is obtained by combining (2) a Explicit Expressions Regarding Spatial Frequency

[0053]

[0054] η represents k x and k y There is a functional relationship;

[0055] According to (1) and (3), the expression of Δφ in the wave number domain can be obtained:

[0056]

[0057] Δφ represents the phase error, f and υ represent functional relationships;

[0058] According to (4), the phase error in the two-dimensional wavenumber domain remains coupled in the wavenumber domain and has a complex form. In order to analyze the components of the remaining two-dimensional phase error, the two-dimensional phase error shown in (4) is x0 , k y0 Performing Taylor series expansion at

[0059]

[0060] In formula (5), the linear phase term a 10 and a 01 The coefficient of is related to the position displacement in the SAR imaging result, and the second-order coefficient a 20 and a 02 are respectively related to the two-dimensional defocus. 11 Indicates that in k x and k y Since linear phase shift does not affect focusing, the main analysis is the impact of quadratic terms and coupling terms on image defocus. The second-order coefficients are sorted to

[0061]

[0062]

[0063] Therefore, the phase error caused by the two-dimensional motion error in the wavenumber domain is

[0064]

[0065] According to the derivation of equation (8), the law of defocusing of two-dimensional error in wave number domain can be obtained. The two-dimensional error in wave number domain is reduced to one dimension, making the defocusing characteristics of two-dimensional phase error simpler and easier to compensate. The specific process is as follows:

[0066] According to the derivation of equation (8), the QPE and coupling terms show similar patterns. Using this feature, we perform dimensionality reduction on the echo signal in the two-dimensional wavenumber domain:

[0067]

[0068] According to the properties of Fourier transform, this operation is equivalent to multiplying (x, k y ) domain. The expression is as follows

[0069]

[0070] H d (x,k y ) represents the function for dimensionality reduction operation, and x represents the X-direction coordinate of the image domain.

[0071] Its schematic diagram is as follows Figure 1 As shown in the figure, after the spectrum operation in the wavenumber domain, the two-dimensional defocus in the polar coordinate format image imaging result is also reduced to one dimension. After the dimension reduction operation, the motion error is

[0072]

[0073] According to the above derivation process, the motion compensation method of the BiSAR polar coordinate format image of any configuration in this embodiment includes:

[0074] Step 1: Obtain an arbitrary configuration BiSAR polar coordinate format image S1(x,y) with motion error, perform FFT transformation on the image S1(x,y) in the Y direction, and obtain the image S1(x,k y ), x represents the coordinate of the image domain in the X direction, k x , k y are the sum of the spatial frequencies of the image domain in the X and Y directions respectively;

[0075] Step 2: Based on the phase error caused by the two-dimensional motion error in the wavenumber domain, the image S1(x, ky ) performs FFT transformation and dimensionality reduction processing in the X direction to obtain image S2(k x ,k y );

[0076] Step 2 can be achieved in two ways, one is:

[0077] The image S1(x,ky) is compared with the dimension reduction function H of formula (10) d (x,k y ) to obtain the image S2(x,ky):

[0078] S2(xk y )=S1(x,k y )·H d (x,k y )

[0079] For image S2(x,k y ) performs FFT transformation in the X direction to obtain image S2(k x ,k y ).

[0080] Another one is:

[0081] For image S1(x,k y ) performs FFT transformation in the X direction to obtain image S1(k x ,k y );

[0082] Using formula (9), image S1(k x ,k y ) to reduce the dimension and obtain image S2(k x ,k y ):

[0083] Step 3: For image S2(k x ,k y ) performs motion compensation to obtain the image represents the operator of WPGA algorithm;

[0084] The WPGA algorithm is used to compensate the one-dimensional error after processing. From formula (11), it can be seen that after dimensionality reduction, the phase error only affects k x direction, from two-dimensional defocusing to one-dimensional defocusing, in addition, the k x and k y The phase error coupling between them is then corrected using the WPGA algorithm. Compared with the PGA algorithm, the WPGA algorithm uses fewer samples to achieve more accurate phase estimation. The operator of WPGA is

[0085]

[0086] Among them, S2(k,h) represents the image S2(k x ,k y ) is the discrete result after circular shift and window filtering, K represents the total number of samples obtained during the sample collection process, w k is the weight value of the kth distance unit, and h represents different circular shift units. After the above process, the motion error is completely eliminated.

[0087] Step 4: For image S3(k x ,k y ) performs IFFT transformation in the X direction to obtain image S3(x,k y );

[0088] The effect of the dimensionality reduction operation on the echo is compensated, and finally the FFT is used to refocus the motion compensated data; Step 5: y ) to perform distortion correction, eliminate the influence of the dimensionality reduction function on the image phase, and perform IFFT transformation in the Y direction to obtain image S3(x,y) and complete refocusing. The specific process is as follows:

[0089] The dimensionality reduction operation will cause the echo phase to change, resulting in distortion of the final imaging result. To correct image distortion, the expression is as follows

[0090]

[0091] After the image distortion is corrected, the echo is subjected to IFFT transformation in the Y direction to obtain an image after error correction.

[0092] In order to verify the practicality and effectiveness of the proposed motion compensation method in arbitrary configuration BiSAR, a point target simulation was performed. In this simulation, the proposed algorithm and the WPGA algorithm were used to compensate for the bistatic PFA SAR image with motion error. The imaging geometry was specified as an arbitrary configuration, and the motion error was set to a third-order error, including acceleration and jerk errors. The transmitter was performing a dive curve motion, while the receiver was performing a dive motion with three-dimensional velocity and acceleration at a large oblique angle. The simulation scenario of the point target is as follows Figure 2 The complex structure and high oblique viewing angle make the motion error structure more complex. The results of the images without compensation, WPGA compensation and the proposed method compensation are shown in Figure 3 , Figure 4 , Figure 5 As shown, from Figure 3 It can be seen that under the influence of motion error, the point target defocus appears as obvious two-dimensional defocus. Figure 4 and Figure 5 It can be seen that the WPGA method cannot eliminate the motion error in the PFA image, while the proposed dimensionality reduction compensation algorithm can correct the motion error well. This is because the "dimensionality reduction" operation changes the defocus from two dimensions to one dimension, which is the core of this method.

[0093] In addition, in order to further verify the performance of the proposed method, the Figure 2 The points marked in the figure are used for imaging quality assessment. The contour lines of the center point and edge point after WPGA algorithm compensation are shown in the figure below. Figure 6 , Figure 8 As shown in Figure 2, it can be clearly seen that the PFA imaging result after WPGA compensation still has serious defocusing phenomenon. The contour lines of the center point and edge point after compensation using the proposed algorithm are shown in Figure 2. Figure 7 , Fig. 9 It can be seen that, through the method of this embodiment, both the central target and the edge target are well focused, indicating that the motion error is effectively corrected. Fig.10 , Fig.11 The comparison of the azimuth profiles of the marked points without compensation, WPGA compensation and the proposed method shows that this method eliminates the main lobe widening and side lobe elevation caused by motion errors of the marked target, and achieves accurate motion compensation.

[0094] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A motion compensation method for BiSAR polar coordinate format images of arbitrary configuration, characterized in that: The method comprises: S1. Establish an echo model of BiSAR with arbitrary configuration and motion error, and obtain the phase error caused by the two-dimensional motion error in the wave number domain according to the established echo model; S2. Obtain the BiSAR polar coordinate format image S1(x,y) of arbitrary configuration with motion error, perform FFT transformation on the image S1(x,y) in the Y direction, and obtain the image S1(x,k y ), x represents the coordinate of the image domain in the X direction, k x , k y are the sum of the spatial frequencies of the image domain in the X and Y directions respectively; S3, based on the phase error caused by the two-dimensional motion error in the wave number domain, the image S1(x,k y ) performs FFT transformation and dimensionality reduction processing in the X direction to obtain image S2(k x ,k y ); S4, for image S2(k x ,k y ) performs motion compensation to obtain the image represents the operator of WPGA algorithm; S5, for image S3(k x ,k y ) performs IFFT transformation in the X direction to obtain image S3(x,k y ); S6, for image S3(x,k y ) is used to perform distortion correction to eliminate the influence of the dimensionality reduction function on the image phase, and an IFFT transform is performed in the Y direction to obtain image S3(x,y) to complete the refocusing.

2. The motion compensation method for BiSAR polar coordinate format images of arbitrary configuration according to claim 1, characterized in that S3 include: The image S1(x,ky) is combined with the dimension reduction function H d (x,k y ) to obtain the image S2(x,ky): S2(x.k y )=S1(x,k y )·H d (x,k y ) in, t a Indicates the position time, used to indicate k x and k y The functional relationship, f r is the distance axis frequency; For image S2(x,k y ) performs FFT transformation in the X direction to obtain image S2(k x ,k y ).

3. The motion compensation method for BiSAR polar coordinate format images of arbitrary configuration according to claim 1, characterized in that S3 include: For image S1(x,k y ) performs FFT transformation in the X direction to obtain image S1(k x ,k y ); The image S1(k x ,k y ) to reduce the dimension and obtain image S2(k x ,k y ): in, t a Indicates the position time, used to indicate k x and k y The functional relationship, f r is the distance axis frequency.

4. The motion compensation method for BiSAR polar coordinate format images of arbitrary configuration according to claim 1, characterized in that: Operator for: Among them, S2(k,h) represents the image S2(k x ,k y ) is the discrete result after circular shift and window filtering, K represents the total number of samples obtained during the sample collection process, w k is the weight value of the kth distance unit, and h represents different circular shift units.

5. The motion compensation method for BiSAR polar coordinate format images of arbitrary configuration according to claim 1, characterized in that: In S6, using the function For image S3(x,k y ) to perform distortion correction and eliminate the influence of dimensionality reduction function on image phase. for:

6. The motion compensation method for BiSAR polar coordinate format images of arbitrary configuration according to claim 1, characterized in that: In S1, the echo model of BiSAR with arbitrary configuration and motion error is established: S1=Aexp(j(k x x p +k y y p +K r Δe(t a ))) Among them, S1 represents the echo data in the wave number domain, A represents the product of the range-azimuth window, and the coordinates of the echo data are (x p ,y p ), Δe(t a ) is the sum of the non-ideal motion error and the plane wave error, k x , k y are the sum of the spatial frequencies of the image domain in the x and y directions, K r Represents the two-dimensional spatial frequency of a signal.

7. The motion compensation method for BiSAR polar coordinate format images of arbitrary configuration according to claim 6, characterized in that: Phase error caused by two-dimensional motion error in the wavenumber domain: in, Γ(k x0 ,k y0 ) is an intermediate variable, Indicates k x and k y The functional relationship of .

8. A computer-readable storage device storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the motion compensation method of any configuration BiSAR polar coordinate format image as claimed in any one of claims 1 to 7 are implemented.

9. A motion compensation device for BiSAR polar coordinate format images of arbitrary configuration, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that: The processor executes the computer program to implement the steps of the motion compensation method for BiSAR polar coordinate format images of any configuration according to any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the motion compensation method of any configuration BiSAR polar coordinate format image as claimed in any one of claims 1 to 7 are implemented.

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