Motion compensation method for arbitrary configuration bi-sar polar format image

Abstract

The motion compensation method of arbitrary configuration BiSAR polar format image solves the defocusing problem of general configuration under the oblique angle which cannot be solved by the existing motion compensation method, and belongs to the field of microwave remote sensing imaging.The present application comprises: establishing the echo model of arbitrary configuration BiSAR with motion error, obtaining the phase error caused by two-dimensional motion error in the wave number domain according to the established echo model; a dimension reduction operation function is proposed. Through this operation, QPE and coupling error are reduced to one dimension. Then, the one-dimensional motion error is corrected by using the weighted maximum likelihood phase gradient autofocus algorithm WPGA, compared with 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 experiment.

Description

TECHNICAL FIELD

[0001] The application relates to a motion compensation method for an arbitrary configuration BiSAR polar format image and belongs to the field of microwave remote sensing imaging. BACKGROUND

[0002] Compared with monostatic SAR, bistatic synthetic aperture radar (BiSAR) has many advantages, including high concealment, low cost and anti-interference capability. Therefore, BiSAR has attracted wide attention of scholars in civil and military applications. In practical applications, due to the atmosphere, wind resistance and vibration of the SAR platform itself, the transmitting and receiving platforms of the BiSAR deviate from the ideal flight trajectory, introducing unknown motion errors, resulting in defocusing of the SAR image. Therefore, motion compensation is crucial to the BiSAR system. Because of its high computational efficiency and suitability for any trajectory of BiSAR, the polar format algorithm (PFA) is considered as an ideal imaging algorithm for arbitrary configuration BiSAR. However, accurately compensating unknown motion errors in BiSAR PFA images is still a challenge. The polar format algorithm process makes the expression of phase errors more complex. In addition, with the increase of squint angle, the quadratic phase error (QPE) in the PFA image also increases, making it more difficult to compensate for unknown motion errors. The existing motion compensation methods are difficult to solve the defocusing problem of general configuration at squint angle. SUMMARY

[0003] In view of the fact that the existing motion compensation methods are difficult to solve the defocusing problem of general configuration at squint angle, the application provides a motion compensation method for an arbitrary configuration BiSAR polar format image.

[0004] The motion compensation method for an arbitrary configuration BiSAR polar format image provided by the application comprises the following steps:

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

[0006] S2, an arbitrary configuration BiSAR polar format image S1(x,y) with motion errors is obtained, and an FFT transformation in the Y direction is performed on the image S1(x,y) to obtain an image S1(x,k y ), x represents the coordinate of the image domain in the X direction, k x and k y are the sum of the spatial frequencies of the image domain in the X direction and the Y direction, 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 an 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 in the Y direction is performed to obtain image S3(x,y) to complete the refocusing.

[0011] Preferably, S3 includes:

[0012] Combine the image S1(x,ky) with the dimensionality reduction function H d (x,k y ) and multiply them to get 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 bearing, 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 ) is reduced in dimension to obtain an image S2(k x ,k y ):

[0019]

[0020] wherein, t a represents an azimuth time, and is used to represent a function relationship of k x and k y , and f r is a distance axis frequency.

[0021] As a preferred, the operator is:

[0022]

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

[0024] As a preferred, in S6, a function is used to perform distortion correction on the image S3(x, k y ) to eliminate the influence of the dimension reduction function on the image phase, is:

[0025]

[0026] As a preferred, in S1, an echo model of an arbitrary configuration BiSAR with motion error is established:

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

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

[0029] As a preference, the two-dimensional motion error causes a phase error in the wave number domain:

[0030]

[0031] wherein, Γ(k x0 ,k y0 ) is an intermediate variable, denotes a functional relationship of k x and k y .

[0032] The application is used for motion compensation and refocusing of polar format image imaging in BiSAR with any configuration. Firstly, the structural characteristics of two-dimensional phase error are disclosed. By using these properties, a dimension reduction operation function is proposed. Through this operation, the QPE and coupling error are reduced to one dimension. Then, the one-dimensional motion error is corrected by using the weighted maximum likelihood phase gradient autofocus algorithm (WPGA), which realizes more accurate phase estimation with fewer samples compared with PGA. Finally, the superiority of the method is verified by point target simulation and actual experiment. BRIEF DESCRIPTION OF DRAWINGS

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

[0034] Figure 2 is the simulation scene target distribution diagram;

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

[0036] Figure 4 is the point target BiSAR polar format image corrected by the WPGA algorithm;

[0037] Figure 5 is the point target BiSAR polar format image corrected by the error dimension reduction compensation method described in the application;

[0038] Figure 6 is the contour map of the central point target corrected by the WPGA algorithm;

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

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

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

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

[0043] Figure 11 It is an azimuth profile 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 clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making any creative efforts shall fall 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 therein may be combined with each other.

[0046] The present invention will be further described below with reference to 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 non-ideal motion error and the plane wave error, f r and f c are the distance axis frequency and carrier frequency, k x and k yis the sum of spatial frequencies in X and Y directions, and the expression is

[0050]

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

[0052] Since the imaging result of the polar coordinate format image has a direct FFT relationship with the wave number domain, the structural characteristics of the two-dimensional error wave number domain are analyzed, the law of defocusing of the two-dimensional error in the wave number domain is established, and the azimuth time t a The display expression of the spatial frequency

[0053]

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

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

[0056]

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

[0058] According to (4), the phase error in the two-dimensional wave number domain remains coupled in the wave number domain, and the form is complex. In order to analyze the components of the remaining two-dimensional phase error, the Taylor series expansion is performed on the two-dimensional phase error shown in (4) at k x0 , k y0 , and the following is obtained

[0059]

[0060] In formula (5), the coefficients of the linear phase terms a 10 and a 01 are related to the position displacement in the SAR imaging result, and the second-order coefficients a 20 and a 02 are related to the two-dimensional defocusing, respectively. a 11 represents the coupled phase error in the k x and k y directions. Since the linear phase shift does not affect the focusing, the effects of the quadratic term and the coupling term on the image defocusing are mainly analyzed. The second-order coefficients are arranged as

[0061]

[0062]

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

[0064]

[0065] According to the derivation of equation (8), the law of defocusing of two-dimensional error in the wave number domain can be obtained. The defocusing characteristics of two-dimensional phase error are reduced to one dimension by dimension reduction processing of the two-dimensional error in the wave number domain, and the form is more simple and easy to compensate. The specific process is as follows:

[0066] According to the derivation of equation (8), QPE and the coupling term show similar patterns. Using this characteristic, we perform dimension reduction operation on the echo signal in the two-dimensional wave number domain

[0067]

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

[0069]

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

[0071] The principle diagram is shown in Figure 1 After the spectrum operation on the wave number domain, the two-dimensional defocusing in the imaging result of the polar format image 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 arbitrary configuration BiSAR polar format image of the embodiment includes:

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

[0075] Step 2, based on the phase error caused by the two-dimensional motion error in the wave number domain, the image S1(x, ky ) and dimension reduction processing to obtain an image S2(k x ,k y );

[0076] Step 2 can be implemented in two ways, one of which is:

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

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

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

[0080] The other is:

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

[0082] The image S1(k x ,k y ) is subjected to dimension reduction using formula (9) to obtain the image S2(k x ,k y ):

[0083] Step 3, the image S2(k x ,k y ) is subjected to motion compensation to obtain the image denotes the operator of the WPGA algorithm;

[0084] The WPGA algorithm is used to compensate for the processed one-dimensional error. As can be seen from formula (11), after dimension reduction processing, the phase error only affects the k x direction, and the two-dimensional defocus becomes one-dimensional defocus, and in addition, the phase error coupling between k x and k y is eliminated. Then the WPGA algorithm is used for correction. Compared with the PGA algorithm, the WPGA algorithm uses fewer samples to achieve more accurate phase estimation. The operator of the WPGA is

[0085]

[0086] where S2(k, h) represents the discrete result of image S2(k x ,k y ) after circular shift and window filtering processing, K represents the total number of samples obtained in 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, performing IFFT transformation on the image S3(k x ,k y ) in the X direction to obtain the image S3(x, k y );

[0088] The effect of the dimension reduction operation on the echo is compensated, and finally the data after motion compensation is re-focused by using FFT; Step 5, performing distortion correction on the image S3(x, k y ) to eliminate the effect of the dimension reduction function on the image phase, and performing IFFT transformation in the Y direction to obtain the image S3(x, y), and completing re-focusing, the specific process is as follows:

[0089] The dimension reduction operation will cause the echo phase to change, resulting in distortion of the final imaging result. Therefore, the designed function is used to correct the image distortion, and the expression is as follows

[0090]

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

[0092] In order to verify the practicability and effectiveness of the proposed motion compensation method in arbitrary configuration BiSAR, a point target is simulated. In this simulation, the algorithm and the WPGA algorithm are used to compensate the dual-base PFA SAR image with motion error. The imaging geometry is specified as an arbitrary configuration, and the motion error is set to a third-order error, including acceleration and jerk error. The transmitter makes a diving curve motion, while the receiver makes a diving motion with three-dimensional velocity and acceleration at a large squint angle. The simulation scene of the point target is as shown in Figure 2 . The complex structure and high squint 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 It can be seen from Figure 3 that under the influence of motion error, the point target defocuses as obvious two-dimensional defocus. Comparing Figure 4 andFigure 5 It can be seen that the WPGA method cannot eliminate the motion error in the PFA image, while the proposed dimension reduction compensation algorithm can well correct the motion error. This is because the "dimension reduction" operation changes the defocus from two-dimensional to one-dimensional, which is the core of the method.

[0093] In addition, in order to further verify the performance of the proposed method, the points marked in Figure 2 are extracted. The imaging quality is evaluated. The contour maps of the center points and the edge points after compensation by the WPGA algorithm are shown in Figure 6 、 Figure 8 It can be seen that the PFA imaging result after WPGA compensation still has serious defocus phenomenon. The contour maps of the center points and the edge points after compensation by the proposed algorithm are shown in Figure 7 、 Figure 9 It can be seen that through the method of the embodiment, the center target and the edge target are well focused, indicating that the motion error is effectively corrected. Figure 10 、 Figure 11 The comparison of the azimuth profiles of the marked points without compensation, WPGA compensation and the proposed method shows that the method eliminates the main lobe widening and side lobe lifting of the marked target caused by motion error, and realizes accurate motion compensation.

[0094] Although the present application is described herein with reference to particular embodiments, it is to be understood that these examples are merely illustrative of the principles and applications of the present application. It is therefore to be understood that numerous modifications can be made to the illustrative embodiments and that other arrangements can be devised without departing from the spirit and scope of the present application as defined by the appended claims. It is to be understood that the features of the dependent claims can be combined with those of the parent application in the alternative. It is also to be understood that features described with respect to one embodiment can be used in other embodiments.

Claims

1. A motion compensation method for BiSAR polar coordinate images of arbitrary configuration, characterized in that: The method comprises: S1. Establish an echo model for an arbitrary configuration BiSAR with motion error, and obtain the phase error caused by the two-dimensional motion error in the wavenumber domain based on 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 ) to perform motion compensation and obtain the image represents the operator of the 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 ) performs distortion correction to eliminate the influence of the dimensionality reduction function on the image phase, and performs IFFT transformation in the Y direction to obtain image S3(x,y) to complete refocusing; 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.

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,k y ) and the dimensionality reduction function H d (x,k y ) and multiply them to get the image S2(x,k y ): S2(x.k y )=S1(x,k y )·H d (x,k y ) in, t a Indicates the direction 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 the image S2(k x ,k y ): in, t a Indicates the direction time, used to indicate k x and k y 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 2, 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:

5. The motion compensation method for BiSAR polar coordinate format images of arbitrary configuration according to claim 2, 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 the signal.

6. The motion compensation method for BiSAR polar coordinate format images of arbitrary configuration according to claim 5, 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, represents k x and k y Functional relationship.

7. 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 for BiSAR polar coordinate format images of any configuration as claimed in any one of claims 1 to 6 are implemented.

8. 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 6.

9. 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 6 are implemented.

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