Method and apparatus for motion error compensation of video synthetic aperture radar interframe images

Abstract

The application discloses a kind of video synthetic aperture radar interframe image motion error compensation method and device, the method includes: obtaining the expression of two sub-aperture images corresponding to the original echo data of video synthetic aperture radar (SAR) acquisition;Analyze the correlation between the expression of two sub-aperture images;With correlation as objective function, analyze the gradient expression of objective function;Based on a plurality of initial points and the gradient expression, the global optimal value of quadratic term coefficient is obtained by optimizing and estimating objective function;The global optimal value of quadratic term coefficient is substituted into the approximate expression of azimuth direction motion error compensation, the approximate expression of azimuth direction motion error compensation is intercepted according to different frame pulse starting position and end position, and the approximate expression of azimuth direction motion compensation corresponding to each frame is obtained, to carry out phase error compensation to the corresponding frame of two sub-aperture images.The application can realize phase error compensation to full-aperture video SAR interframe image.

Description

Technical Field

[0001] This invention relates to the field of inter-frame imaging in video synthetic aperture radar, and more particularly to a method and apparatus for motion error compensation of inter-frame images in video synthetic aperture radar. Background Technology

[0002] This section is intended to provide background or context for the embodiments of the invention set forth in the claims. The description herein is not an admission that it is prior art simply because it is included in this section.

[0003] During the movement of the radar payload carried by the flight platform, motion errors exist in the radar echo due to engine vibration and atmospheric airflow. Because high-band radar is sensitive to motion errors, under conditions of limited inertial navigation accuracy, the quadratic coefficient of the error slant range causes drift along the azimuth direction in each frame of the image. This drift accumulates as the number of frames increases. For high-frame-rate video SAR systems, the number of frames can typically reach hundreds. With the increase in the number of imaging frames, the phenomenon of inter-frame drift becomes increasingly severe, seriously affecting the scene stability of multi-frame imaging.

[0004] Therefore, in order to achieve inter-frame image stabilization in video synthetic aperture radar (SAR) under inertial navigation-constrained conditions and generate highly stable "video stream" images, it is necessary to compensate for inter-frame motion error phase. For video SAR imaging, inter-frame phase discontinuity affects the consistency of inter-frame imaging; therefore, a solution is needed to ensure the continuity of inter-frame motion error compensation. Summary of the Invention

[0005] This invention provides a motion error compensation method for inter-frame images of video synthetic aperture radar (SAR) to achieve phase error compensation for inter-frame images of full-aperture video SAR. The method includes:

[0006] The representation of two sub-aperture images corresponding to the raw echo data acquired by video synthetic aperture radar (SAR) is obtained, wherein the sub-aperture images are video SAR inter-frame images;

[0007] The correlation between the representations of two sub-aperture images is analyzed. The correlation is a function of the coefficient of the quadratic term in the approximate representation of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode.

[0008] Using the correlation as the objective function, analyze the gradient expression of the objective function;

[0009] Based on multiple initial points and the gradient expression, the objective function is optimized and estimated to obtain the global optimal value of the quadratic term coefficient;

[0010] Substitute the global optimal value of the quadratic term coefficient into the approximate expression of azimuth motion error compensation. Based on the start and end positions of the pulses in different frames, truncate the approximate expression of azimuth motion error compensation to obtain the approximate expression of azimuth motion compensation for each frame.

[0011] Based on the approximate expression of the azimuth motion compensation corresponding to each frame, phase error compensation is performed on corresponding frames of two sub-aperture images.

[0012] This invention also provides a motion error compensation device for inter-frame images of video synthetic aperture radar (SAR) to achieve phase error compensation for inter-frame images of full-aperture video SAR. The device includes:

[0013] The image representation acquisition module is used to obtain the representation of two sub-aperture images corresponding to the original echo data acquired by video synthetic aperture radar SAR, wherein the sub-aperture images are video SAR inter-frame images;

[0014] The correlation analysis module is used to analyze the correlation between the representations of two sub-aperture images. The correlation is a function of the coefficient of the quadratic term in the approximate representation of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode.

[0015] The gradient expression analysis module is used to analyze the gradient expression of the objective function, taking the correlation as the objective function.

[0016] The optimization estimation module is used to optimize and estimate the objective function based on multiple initial points and the gradient expression to obtain the global optimal value of the quadratic term coefficient;

[0017] The motion error compensation module is used to substitute the global optimal value of the quadratic term coefficient into the approximate expression of azimuth motion error compensation. Based on the start and end positions of the pulses in different frames, the approximate expression of azimuth motion error compensation is truncated to obtain the approximate expression of azimuth motion compensation for each frame. Based on the approximate expression of azimuth motion compensation for each frame, phase error compensation is performed on corresponding frames of two sub-aperture images.

[0018] This invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-described motion error compensation method for inter-frame images of video synthetic aperture radar.

[0019] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described motion error compensation method for inter-frame images of video synthetic aperture radar.

[0020] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-described motion error compensation method for inter-frame images of synthetic aperture radar.

[0021] In this embodiment of the invention, the representations of two sub-aperture images corresponding to the raw echo data acquired by video synthetic aperture radar (SAR) are obtained, wherein the sub-aperture images are inter-frame images of video SAR; the correlation between the representations of the two sub-aperture images is analyzed, wherein the correlation is a function of the quadratic term coefficient in the approximate representation of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode; the gradient representation of the objective function is analyzed using the correlation as the objective function; based on multiple initial points and the gradient representation, the objective function is optimized and estimated to obtain the global optimal value of the quadratic term coefficient; the global optimal value of the quadratic term coefficient is substituted into the approximate representation of azimuth motion error compensation, and the approximate representation of azimuth motion error compensation is truncated according to the pulse start and end positions of different frames to obtain the approximate representation of azimuth motion compensation for each frame; phase error compensation is performed on the corresponding frames of the two sub-aperture images according to the approximate representation of azimuth motion compensation for each frame. Compared with existing solutions, the method of this invention uses the correlation between the expressions of sub-aperture images to construct an objective function. The correlation is a function of the quadratic term coefficient in the approximate expression of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode. Therefore, by performing optimization estimation, the global optimal value of the quadratic term coefficient is obtained. The global optimal value can be used to construct an approximate expression for azimuth motion error compensation, so as to realize phase error compensation for inter-frame images of full-aperture video SAR. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0023] Figure 1 This is a flowchart of the motion error compensation method for inter-frame images of video synthetic aperture radar in an embodiment of the present invention;

[0024] Figure 2 This is a flowchart illustrating the construction of a video SAR motion error model in an embodiment of the present invention;

[0025] Figure 3 This is a schematic diagram of airborne SAR motion with motion errors on a video SAR platform in an embodiment of the present invention;

[0026] Figure 4 This is a flowchart illustrating an approximate expression of azimuth motion error compensation in an embodiment of the present invention;

[0027] Figure 5 This is a schematic diagram of the azimuth time period of the video SAR inter-frame image in an embodiment of the present invention;

[0028] Figure 6 This is a flowchart illustrating the representation of two sub-aperture images corresponding to the original echo data acquired by video synthetic aperture radar (SAR) in an embodiment of the present invention.

[0029] Figure 7 This is a flowchart of the global optimization algorithm based on multi-point BFGS search in an embodiment of the present invention;

[0030] Figure 8 This is a schematic diagram of the motion error compensation device for inter-frame images of video synthetic aperture radar in an embodiment of the present invention;

[0031] Figure 9 This is a schematic diagram of a computer device in an embodiment of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0033] To address the problems existing in current technologies, it is necessary to theoretically derive motion errors, model and analyze motion feature models, construct corresponding motion error compensation functions, and compensate for the error phase that causes inter-frame image drift.

[0034] Furthermore, in processing real-world data, the more accurate the motion error estimation, the better the image stability after motion phase compensation. When estimating motion error using an optimization algorithm by establishing an objective function, multiple local optima may appear. In such cases, the optimization algorithm may get stuck in local optima and fail to find the global optimum. Further research is needed on how to establish the objective function for motion error estimation. If the designed objective function is too complex, the computational load of the search may be too large, significantly impacting the efficiency of parameter search. Moreover, the performance of optimization algorithms is often very sensitive to the initial point; selecting inappropriate initial points may lead to a slow search process or even failure. Therefore, it is necessary to establish a low-complexity objective function, constrain the initial points of the search, and employ a robust optimization algorithm to estimate inter-frame motion errors in video SAR.

[0035] Therefore, this invention proposes a motion error compensation method for inter-frame images of video synthetic aperture radar, such as... Figure 1 This is a flowchart of a motion error compensation method for inter-frame images of video synthetic aperture radar in an embodiment of the present invention, including:

[0036] Step 101: Obtain the representation of two sub-aperture images corresponding to the original echo data acquired by video synthetic aperture radar SAR, wherein the sub-aperture images are video SAR inter-frame images.

[0037] Step 102: Analyze the correlation between the representations of the two sub-aperture images. The correlation is a function of the coefficient of the quadratic term in the approximate representation of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode.

[0038] Step 103: Using the correlation as the objective function, analyze the gradient expression of the objective function;

[0039] Step 104: Based on multiple initial points and the gradient expression, optimize and estimate the objective function to obtain the global optimal value of the quadratic term coefficient;

[0040] Step 105: Substitute the global optimal value of the quadratic term coefficient into the approximate expression of azimuth motion error compensation. Based on the start and end positions of the pulses in different frames, truncate the approximate expression of azimuth motion error compensation to obtain the approximate expression of azimuth motion compensation for each frame.

[0041] Step 106: Based on the approximate expression of the azimuth motion compensation corresponding to each frame, perform phase error compensation on the corresponding frames of the two sub-aperture images.

[0042] Compared with existing solutions, the method of this invention uses the correlation between the expressions of sub-aperture images to construct an objective function. The correlation is a function of the quadratic term coefficient in the approximate expression of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode. Therefore, by performing optimization estimation, the global optimal value of the quadratic term coefficient is obtained. The global optimal value can be used to construct an approximate expression for azimuth motion error compensation, so as to realize phase error compensation for inter-frame images of full-aperture video SAR.

[0043] As can be seen from steps 101-106, this embodiment of the invention requires the construction of an approximate expression for azimuth motion error compensation. After obtaining the global optimal value of the quadratic term coefficient, it can be directly substituted into the constructed approximate expression for azimuth motion error compensation. After truncating, the approximate expression for azimuth motion compensation corresponding to each frame is obtained, thereby realizing phase error compensation for corresponding frames of two sub-aperture images.

[0044] Before constructing an approximate expression for azimuth motion error compensation, a video SAR motion error model needs to be built.

[0045] See Figure 2 This is a flowchart of constructing a video SAR motion error model in an embodiment of the present invention. The specific steps include:

[0046] Step 201: In circular trajectory spotting mode, obtain the ideal instantaneous slant range expression and the actual instantaneous slant range expression during inter-frame motion of video SAR.

[0047] Step 202: Determine the error instantaneous slope distance based on the ideal instantaneous slope distance expression and the actual instantaneous slope distance expression;

[0048] Step 203: Based on the ideal instantaneous slant range expression, the actual instantaneous slant range expression, and the error instantaneous slant range, construct the point target echo signal expression after adding the inertial navigation error;

[0049] Step 204: Perform matched filtering along the range direction on the point target echo signal representation after adding inertial navigation error to obtain the matched filtered echo signal representation.

[0050] Figure 3 This is a schematic diagram of airborne SAR motion with motion errors on a video SAR platform in an embodiment of the present invention, specifically for circular trajectory spotting mode. Figure 3 In the diagram, the black trajectory represents the ideal flight path of the aircraft, while the red trajectory represents the actual flight path. Under ideal conditions, the video SAR platform operates at a constant speed V. s The aircraft moves along an ideal trajectory at a constant altitude H. However, atmospheric turbulence or other factors can cause the actual trajectory to deviate from uniform linear motion, resulting in positional errors in the radar's antenna phase center (APC). Figure 3 (As indicated by the purple arrow in the middle).

[0051] Assume the ideal carrier coordinates are: (X(t) a ),Y(t a ),H); The coordinates of the ideal point target are: (x0,y0,0); where t a The direction is slowed down by time.

[0052] The ideal instantaneous slant range R during inter-frame motion in video SAR is expressed as... t (t a )for:

[0053]

[0054] The point target coordinates after adding inertial navigation error are (x0+ΔX(t)). a ),y0+ΔY(t a ),ΔZ(t a (X,Y,Z).

[0055] The actual instantaneous slant range R during inter-frame motion in video SAR is expressed as... a (t a )for:

[0056]

[0057] Instantaneous slope distance R of error e (t a )for:

[0058]

[0059] Point target echo signal expression s(t) after adding inertial navigation error r ,t a )for:

[0060]

[0061] In the formula: A0 is a complex constant; λ is the carrier wavelength; t r For distance to fast time; t a For azimuth, time slows down; w r (·) represents the range envelope; w a (·) represents the azimuth envelope; t ac f0 is the center time of the Doppler signal; R(·) is the slant range of the radar from the target (subscript omitted); c is the speed of light; K r The frequency modulation of the distance-direction pulse.

[0062] The echo signal s after matched filtering along the range direction of equation (4) is expressed as s o (t r ,t a This can be represented as:

[0063]

[0064] The above-mentioned instantaneous slant range error and the echo signal expression after matched filtering constitute the video SAR motion error model.

[0065] The following describes the process of constructing an approximate expression for azimuth motion error compensation based on the video SAR motion error model. (See [link to relevant documentation]). Figure 4 This is a flowchart illustrating an approximate expression for azimuth motion error compensation in an embodiment of the present invention. The specific steps include:

[0066] Step 401: Construct a video SAR motion error model, which includes the instantaneous slant range error and the echo signal expression after matched filtering; Step 401 includes the aforementioned steps 201-204.

[0067] Step 402: Perform a Taylor expansion on the instantaneous slope distance of the error and retain it down to the second term to obtain an approximate expression of the instantaneous slope distance of the error. The approximate expression of the instantaneous slope distance of the error contains constant term coefficients, first term coefficients, and second term coefficients.

[0068] Step 403: Based on the constant term coefficient, the first term coefficient, and the second term coefficient, perform azimuth time period analysis on the echo signal expression after matched filtering to obtain the echo data expression corresponding to the kth frame.

[0069] Step 404: Based on the echo data representation corresponding to the k-th frame, determine the offset phase term corresponding to the first-order term coefficient, the defocus phase term corresponding to the second-order term coefficient, and the drift phase term.

[0070] Step 405: Based on the drift phase term, modify the approximate expression of the instantaneous error slant distance to obtain an approximate expression of the instantaneous error slant distance using only the quadratic term coefficients;

[0071] Step 406: Based on the approximate expression of the instantaneous slant range error expressed only by quadratic term coefficients, obtain the approximate expression of the azimuth motion error compensation.

[0072] For the echo signal, the required azimuth motion phase compensation expression f error (t a )for:

[0073]

[0074] For ease of calculation, let the instantaneous slope distance of the error in formula (3) be...

[0075]

[0076] R e (t a ) in t a Performing a Taylor expansion at the point = 0 and retaining up to the second-order terms yields an approximate expression for the instantaneous slope error. for:

[0077]

[0078] Where ζ c , ζ o , ζ q These are the constant term coefficients, linear term coefficients, and quadratic term coefficients corresponding to the Taylor expansion of the slant range error, respectively.

[0079] Figure 5 This is a schematic diagram of the azimuth time interval of the video SAR inter-frame image in an embodiment of the present invention, as shown below. Figure 5 As shown, let the total number of sub-apertures in the echo data of the video SAR inter-frame image be M, and the total duration in the azimuth direction be T.a Let N be the number of sub-aperture images in each frame, then the azimuth duration T corresponding to each sub-aperture is... s for:

[0080] T s =T a / M (9)

[0081] The azimuth duration corresponding to any frame of echo data is:

[0082] T f =N·T s (10)

[0083] The azimuth time corresponding to the Kth frame can be represented as:

[0084] t K =t a +(K-1)·N2·T s ;t a ′∈[0,T f (11)

[0085] Where N2 is the number of non-overlapping sub-apertures between frames.

[0086] Then the echo data corresponding to the Kth frame is expressed as s′ K (t r ,t K This can be represented as:

[0087]

[0088] In equation (12), s(·) and A K The expression is as follows:

[0089]

[0090] According to equation (13), the coefficient of the first-order term of the instantaneous slant distance error will cause a fixed offset in each frame of the image. The offset phase term is:

[0091]

[0092] The quadratic coefficient of the instantaneous slant range error will cause the image to defocus along the azimuth direction in each frame. The defocus phase term is:

[0093]

[0094] The quadratic coefficient of the instantaneous slant range error causes azimuth drift in each frame. This drift accumulates over multiple frames, resulting in inter-frame image drift. The drift phase term can be expressed as:

[0095]

[0096] Therefore, in order to achieve inter-frame image stabilization in video SAR, it is necessary to estimate and compensate for the inter-frame drift phase term corresponding to the quadratic coefficient of the instantaneous slant range error. At this point, the approximate expression of the instantaneous slant range error in equation (8) can be rewritten as:

[0097]

[0098] Equation (17) is an approximate expression of the instantaneous slant distance error using only the quadratic coefficients.

[0099] Substituting equation (17) into equation (6), we obtain an approximate expression for the azimuth motion phase compensation function required for the echo signal. for:

[0100]

[0101] After constructing an approximate expression for the azimuth motion phase compensation function, actual error compensation can be performed.

[0102] See Figure 6 This is a flowchart illustrating the representation of two sub-aperture images corresponding to the raw echo data acquired by video synthetic aperture radar (SAR) in an embodiment of the present invention. The specific steps include:

[0103] Step 601: Extract the raw echo data acquired by video SAR to obtain the extracted echo data;

[0104] Considering the large amount of raw echo data acquired by video SAR, a feasible approach is to truncate the raw echo data and use the truncated echo data to quickly estimate the coefficients of the quadratic term of the instantaneous slant range error.

[0105] Assuming that it is extracted from the raw echo data Each pulse is used for quadratic term coefficient estimation, and the truncated echo data can be expressed as:

[0106]

[0107] in, and These are the starting pulse number and the ending pulse number for capturing echo data, respectively.

[0108] Step 602: Obtain pixel echo data corresponding to the two sub-aperture images corresponding to the truncated echo data. The pixel echo data includes an approximate expression of the instantaneous slant distance error represented only by the quadratic term coefficient.

[0109] Divide the imaging space into x n ×y n A grid composed of pixels, at a certain slow moment At that time, the SAR antenna phase center (APC) is located at P(0,y). APC ,H), Where V s The speed of the carrier aircraft. SAR to pixel P ij (x i ,y j Two-way slope distance of ,0) for:

[0110]

[0111] In the formula: ||·||2 represents the 2-norm, i∈(0,x) n ],j∈(0,y n ].

[0112] Pixel P ij In terms of location and time Location index in SAR echo data for:

[0113]

[0114] In the formula: R min is the shortest slant distance; Fs is the sampling rate; ratio is the distance oversampling coefficient; round(·) indicates rounding operation.

[0115] As the above analysis shows, the quadratic coefficient of the instantaneous slant range error will cause drift and defocusing between multiple frames. Therefore, in order to achieve inter-frame image stabilization of video SAR, it is necessary to estimate the quadratic coefficient of the instantaneous slant range error. From equation (17), the instantaneous slant range error term at this time is:

[0116]

[0117] Where ζ q The coefficient values ​​of the quadratic term to be estimated are denoted as .

[0118] For the truncated echo data, if the final image corresponding to the echo data is obtained by summing two sub-aperture images IM1 and IM2, then the pixel echo of the sub-aperture image can be represented as:

[0119]

[0120] in Used to compensate pixel P ij Doppler frequency shift at different azimuth times.

[0121] Step 603: Obtain the representation of each sub-aperture image based on the pixel echo data corresponding to each sub-aperture image.

[0122] Sub-aperture images can be represented as follows:

[0123]

[0124] In step 102, it is necessary to analyze the correlation between the representations of the two sub-aperture images. The correlation can be calculated as follows:

[0125]

[0126] The average values ​​of the sub-aperture images are as follows:

[0127]

[0128] At this point, the problem of estimating the quadratic coefficient of the instantaneous slant distance error can be solved by minimizing the correlation between the two sub-aperture images. An effective method is to use the gradient descent algorithm to determine the optimal solution of this coefficient under the correlation minimization constraint.

[0129] In step 103, the gradient expression of the objective function F needs to be analyzed, using the correlation as the objective function F. as follows:

[0130]

[0131] in:

[0132] Find the correlation F with respect to The partial derivatives are obtained. for:

[0133]

[0134] Find the correlation F with respect to The partial derivatives are obtained. for:

[0135]

[0136] Find the partial derivative of the correlation F with respect to m1, and obtain for:

[0137]

[0138] Find the partial derivative of the correlation F with respect to m2, and obtain for:

[0139]

[0140] Find the grid point echo about The partial derivatives are obtained. for:

[0141]

[0142] Find the grid point echo about The partial derivatives are obtained.

[0143]

[0144] Find the average value m1 of the aperture image IM1 with respect to The partial derivatives are obtained. for:

[0145]

[0146] Find the average value of IM2 in the aperture image with respect to m2 The partial derivatives are obtained. for:

[0147]

[0148] beg about The partial derivatives are obtained. for:

[0149]

[0150] beg Regarding ζ q The partial derivatives are obtained. for:

[0151]

[0152] In step 104, the objective function needs to be optimized and estimated based on multiple initial points and the gradient expression to obtain the global optimal value of the quadratic term coefficient.

[0153] In one embodiment, based on multiple initial points and the gradient expression, the objective function is optimized and estimated to obtain the globally optimal value of the quadratic term coefficient, including:

[0154] Based on multiple initial points and the gradient expression, the objective function is optimized and estimated to obtain the local optimal solution set of the quadratic term coefficients corresponding to each initial point;

[0155] From the set of local optimal solutions corresponding to the quadratic coefficients of each initial point, determine the set of local optimal solutions that minimizes the objective function value as the global optimal value of the quadratic coefficients.

[0156] In practice, a global optimization algorithm based on multi-point BFGS search is used to estimate the quadratic coefficient of the instantaneous slope distance error. Figure 7 This is a flowchart of the global optimization algorithm based on multi-point BFGS search in an embodiment of the present invention. See also... Figure 7 Since the BFGS method is typically used to search for local optima, this embodiment of the invention sets multiple initial points for quadratic coefficients to achieve multi-point local search, and selects the optimal value with the smallest corresponding objective function value as the global optimum to construct an approximate expression for the required azimuth motion error compensation.

[0157] A set of points {ζ} with multiple initial points q1 ,ζ q2 ,...,ζ qm The selection of} can be randomly generated or set according to the inertial navigation parameters (IMU).

[0158]

[0159] Here, a local optimization operation is defined as L:

[0160]

[0161] Where L(F,ζ) qi ) indicates starting from the starting point ζ qi Initially, a local optimization algorithm L is used, where F represents the objective function. Starting from ζ qi The local optimal solution at that time.

[0162] In one embodiment, the method further includes:

[0163] Obtain the objective function with a penalty term and its corresponding gradient expression;

[0164] Based on multiple initial points and the gradient representation of the objective function with a penalty term, the objective function with a penalty term is optimized and estimated to obtain the local optimal solution set of the quadratic coefficients corresponding to each initial point.

[0165] First, determine the penalty term function p(ζ). q )for:

[0166]

[0167] Where lb and ub are respectively ζ q The upper and lower boundaries.

[0168] Penalty term function p(ζ) q Regarding ζ q gradient for:

[0169]

[0170] The objective function F′ with penalty term is:

[0171] F′=F+p(ζ q (44)

[0172] Gradient representation of objective function F′ with penalty term for:

[0173]

[0174] For the i-th quadratic error coefficient, the BFGS search algorithm with a penalty term includes the following steps:

[0175] (1) Let To express the gradient of the objective function with a penalty term, an initial point ζ is selected. qi (0) Let B0 be a positive definite symmetric matrix (usually the identity matrix), set k = 0, and require an accuracy of μ.

[0176] (2) Calculate g k =g(ζ qi (k) If ||g k If || < μ, then stop the calculation and obtain an approximate solution. Otherwise, proceed to step (3);

[0177] (3) By B k p k =-g k Find p k ;

[0178] (4) One-dimensional search: Finding λ k Make

[0179]

[0180] (5) Set ζ qi (k+1) =ζ qi (k) +λ k p k ;

[0181] (6) Calculate g k+1 =g(ζ qi (k+1) If ||g k+1 If || < μ, then stop the calculation and obtain an approximate solution. Otherwise, calculate B according to formula (47). k+1 :

[0182]

[0183] in:

[0184] y k =g k+1 -g k ;δ k =ζ qi (k+1) -ζ qi (k) (48)

[0185] (7) Set k = k + 1, then go to step (3).

[0186] For each initial point ζ qi The BFGS algorithm is executed in parallel. During the parallel search, each local optimum can be considered an independent computational unit. Therefore, the i-th parallel computational unit P... i It can be represented as:

[0187]

[0188] After completing the entire parallel search, different computing units P i The set of points formed by the obtained local optimal solutions can be represented as:

[0189]

[0190] Based on the set of local optima, the solution with the smallest corresponding objective function value is selected as the global optimum:

[0191]

[0192] In step 105, the global optimal value of the quadratic term coefficients is substituted into the approximate expression for azimuth motion error compensation, resulting in:

[0193]

[0194] Then, based on the start and end positions of the pulses in different frames, the approximate expression of the azimuth motion error compensation is extracted to obtain the approximate expression of the azimuth motion compensation for each frame. Taking the Kth frame as an example,

[0195] The approximate expression for the azimuth motion compensation corresponding to the Kth frame is:

[0196]

[0197] Among them, T f The azimuth duration corresponding to any frame of echo data.

[0198] Next, proceed to step 105, which involves performing phase error compensation on corresponding frames of two sub-aperture images based on the approximate expression of azimuth motion compensation for each frame, thereby realizing phase error compensation for inter-frame images of full-aperture video SAR.

[0199] This invention also proposes a motion error compensation device for inter-frame images of video synthetic aperture radar. Its principle is similar to that of the motion error compensation method for inter-frame images of video synthetic aperture radar, and will not be described in detail here.

[0200] Figure 8 This is a schematic diagram of a motion error compensation device for inter-frame images of video synthetic aperture radar in an embodiment of the present invention, comprising:

[0201] The image representation acquisition module 801 is used to obtain the representation of two sub-aperture images corresponding to the original echo data acquired by video synthetic aperture radar SAR, wherein the sub-aperture images are video SAR inter-frame images.

[0202] The correlation analysis module 802 is used to analyze the correlation between the expressions of two sub-aperture images. The correlation is a function of the coefficient of the quadratic term in the approximate expression of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode.

[0203] The gradient expression analysis module 803 is used to analyze the gradient expression of the objective function with the correlation as the objective function.

[0204] The optimization estimation module 804 is used to optimize and estimate the objective function based on multiple initial points and the gradient expression to obtain the global optimal value of the quadratic term coefficient;

[0205] The motion error compensation module 805 is used to substitute the global optimal value of the quadratic term coefficient into the approximate expression of azimuth motion error compensation. Based on the start and end positions of the pulses in different frames, the approximate expression of azimuth motion error compensation is truncated to obtain the approximate expression of azimuth motion compensation for each frame. Based on the approximate expression of azimuth motion compensation for each frame, phase error compensation is performed on corresponding frames of two sub-aperture images.

[0206] In one embodiment, the image representation acquisition module is used for:

[0207] The raw echo data acquired by video SAR is truncated to obtain the truncated echo data;

[0208] Obtain pixel echo data corresponding to two sub-aperture images corresponding to the truncated echo data. The pixel echo data includes an approximate expression of the instantaneous slant distance error represented only by quadratic term coefficients.

[0209] The representation of each sub-aperture image is obtained based on the pixel echo data corresponding to each sub-aperture image.

[0210] In one embodiment, the optimization estimation module is used to:

[0211] Based on multiple initial points and the gradient expression, the objective function is optimized and estimated to obtain the local optimal solution set of the quadratic term coefficients corresponding to each initial point;

[0212] From the set of local optimal solutions corresponding to the quadratic coefficients of each initial point, determine the set of local optimal solutions that minimizes the objective function value as the global optimal value of the quadratic coefficients.

[0213] In one embodiment, the optimization estimation module is further configured to:

[0214] Obtain the objective function with a penalty term and its corresponding gradient expression;

[0215] Based on multiple initial points and the gradient representation of the objective function with a penalty term, the objective function with a penalty term is optimized and estimated to obtain the local optimal solution set of the quadratic coefficients corresponding to each initial point.

[0216] In one embodiment, the device further includes an approximate expression construction module 806 for azimuth motion error compensation, used for:

[0217] A video SAR motion error model is constructed, which includes the instantaneous slant range of the error and the echo signal expression after matched filtering;

[0218] The instantaneous slope distance of the error is expanded using Taylor and retained down to the second degree to obtain an approximate expression for the instantaneous slope distance of the error. This approximate expression for the instantaneous slope distance of the error contains constant term coefficients, first-degree term coefficients, and second-degree term coefficients.

[0219] Based on the constant term coefficient, the first term coefficient, and the second term coefficient, the echo signal expression after matched filtering is analyzed in the azimuth time period of multiple frames to obtain the echo data expression corresponding to the k-th frame.

[0220] Based on the echo data representation corresponding to the kth frame, determine the offset phase term corresponding to the first term coefficient, the defocus phase term corresponding to the second term coefficient, and the drift phase term;

[0221] Based on the drift phase term, the approximate expression of the instantaneous slant distance error is modified to obtain an approximate expression of the instantaneous slant distance error using only the quadratic term coefficients;

[0222] Based on the approximate expression of the instantaneous slant range error represented only by the quadratic term coefficient, an approximate expression for the azimuth motion error compensation is obtained.

[0223] In one embodiment, the apparatus further includes a video SAR motion error model construction module 807, used for:

[0224] In circular trajectory spotting mode, the ideal instantaneous slant range expression and the actual instantaneous slant range expression for inter-frame motion in video SAR are obtained;

[0225] Based on the ideal instantaneous slope distance expression and the actual instantaneous slope distance expression, the error instantaneous slope distance is determined;

[0226] Based on the ideal instantaneous slant range expression, the actual instantaneous slant range expression, and the error instantaneous slant range, a point target echo signal expression after adding inertial navigation error is constructed;

[0227] Matched filtering is performed along the range direction on the echo signal representation of the point target after adding inertial navigation error to obtain the echo signal representation after matching filtering.

[0228] In summary, the method and apparatus proposed in the embodiments of the present invention have the following key points:

[0229] First, by constructing a video SAR motion error model, the mechanism of long-term differences between inter-frame images was analyzed in depth. By modeling the motion error, the causes of image defocusing and inter-frame drift due to motion errors were analyzed. It was found that the quadratic coefficient of the instantaneous slant range error causes image defocusing and leads to image drift between multiple frames. The amount of drift accumulates with increasing azimuth time.

[0230] Second, to achieve inter-frame image stabilization in video SAR under inertial navigation-constrained conditions and generate a highly stable "video stream" image, it is necessary to compensate for the inter-frame motion error phase. For video SAR imaging, inter-frame phase discontinuity affects the consistency of inter-frame imaging. To ensure the continuity of inter-frame motion error compensation, this embodiment of the invention constructs an approximate expression for azimuth motion error compensation across multiple frames with full aperture. Since the quadratic coefficient of the instantaneous slant range error is the cause of inter-frame image drift, this embodiment of the invention establishes a corresponding approximate expression for azimuth motion error compensation based on this quadratic coefficient to compensate for the error phase.

[0231] Third, considering the large amount of raw echo data acquired by video SAR, the echo data was first truncated. An approximate expression for azimuth motion error compensation was constructed by setting the initial value of the quadratic coefficient of the instantaneous slant range error, and corresponding phase compensation was performed on the truncated echo. If the final image corresponding to the echo data is obtained by summing two sub-aperture images, then the problem of estimating the quadratic coefficient of the instantaneous slant range error can be solved by minimizing the correlation between the two sub-images. In this embodiment of the invention, the quadratic coefficient of the instantaneous slant range error is used as the independent variable, and the correlation between the two compensated sub-aperture images is calculated as the objective function for subsequent searching for the optimal value of the error estimate.

[0232] Fourth, phase compensation is performed on the sub-aperture images by assigning initial values ​​to the quadratic coefficients of the motion compensation function. Then, the correlation between the two motion-compensated sub-aperture images is used as the objective function, and the initial values ​​are optimized using the BFGS method. Since the BFGS method is typically used to search for local optima, multiple initial value points for the quadratic coefficients are set to achieve multi-point local search. The optimal value with the smallest corresponding objective function value is selected as the global optimum to construct the approximate expression for the required inter-frame azimuth motion error compensation.

[0233] The above key points have yielded the following beneficial effects:

[0234] First, this invention addresses the lack of theoretical framework for motion error models in signal domain video SAR, which hinders phase compensation for inter-frame errors. The embodiments of this invention perform motion feature modeling and analysis on inter-frame errors, and based on the characteristics of motion errors, establish an approximate expression for azimuth motion error compensation in video SAR inter-frame models.

[0235] Specifically, the mechanism of long-term differences in inter-frame images was analyzed in depth. By modeling motion errors, the causes of image defocusing and inter-frame drift due to motion errors were analyzed. According to the established motion error model, the quadratic coefficient of the instantaneous slant range error causes image defocusing and leads to image drift between multiple frames. The amount of drift accumulates with the increase of azimuth time. For video SAR imaging, inter-frame phase discontinuity affects the consistency of inter-frame imaging. To ensure the continuity of inter-frame motion error compensation, this patent constructs an approximate expression for azimuth motion error compensation for multiple frames across the full aperture. Since the quadratic coefficient of the instantaneous slant range error is the cause of inter-frame image drift, this embodiment of the invention establishes a corresponding approximate expression for azimuth motion error compensation based on this quadratic coefficient to compensate for the error phase.

[0236] Second, it solves the problem of high-precision estimation of motion error in video SAR. Using the quadratic coefficient of the instantaneous slant range error as the independent variable and the correlation between two sub-images after operational compensation as the objective function, the BFGS algorithm is used to achieve accurate estimation of inter-frame motion error.

[0237] Specifically, the original echo data was first truncated. An approximate expression for azimuth motion error compensation was constructed by setting initial values ​​for the quadratic coefficients of the instantaneous slant range error, and corresponding phase compensation was performed on the truncated echoes. Next, using the quadratic coefficients of the instantaneous slant range error as independent variables and the correlation between the two motion-compensated sub-aperture images as the objective function, the values ​​of the quadratic coefficients were optimized using the BFGS method. Since the BFGS method is typically used to search for local optima, multiple initial points for the quadratic coefficients were set to achieve multi-point local search. The optimal value with the smallest corresponding objective function value was selected as the global optimum to construct the required approximate expression for inter-frame azimuth motion error compensation.

[0238] This invention also provides a computer device. Figure 9 This is a schematic diagram of a computer device in an embodiment of the present invention. The computer device 900 includes a memory 910, a processor 920, and a computer program 930 stored in the memory 910 and executable on the processor 920. When the processor 920 executes the computer program 930, it implements the above-mentioned motion error compensation method for inter-frame images of video synthetic aperture radar.

[0239] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described motion error compensation method for inter-frame images of video synthetic aperture radar.

[0240] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-described motion error compensation method for inter-frame images of synthetic aperture radar.

[0241] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0242] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0243] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0244] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0245] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for motion error compensation of inter-frame images in video synthetic aperture radar, characterized in that, include: The representation of two sub-aperture images corresponding to the raw echo data acquired by video synthetic aperture radar (SAR) is obtained, wherein the sub-aperture images are video SAR inter-frame images; The correlation between the representations of two sub-aperture images is analyzed. The correlation is a function of the coefficient of the quadratic term in the approximate representation of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode. Using the correlation as the objective function, analyze the gradient expression of the objective function; Based on multiple initial points and the gradient expression, the objective function is optimized and estimated to obtain the global optimal value of the quadratic term coefficient; Substitute the global optimal value of the quadratic term coefficient into the approximate expression of azimuth motion error compensation. Based on the start and end positions of the pulses in different frames, truncate the approximate expression of azimuth motion error compensation to obtain the approximate expression of azimuth motion compensation for each frame. Based on the approximate expression of the azimuth motion compensation corresponding to each frame, phase error compensation is performed on corresponding frames of two sub-aperture images. The steps for constructing an approximate expression for azimuth motion error compensation include: constructing a video SAR motion error model, which includes an instantaneous error slant range and a matched-filtered echo signal representation; performing a Taylor expansion on the instantaneous error slant range and retaining it down to the second-order term to obtain an approximate expression for the instantaneous error slant range, which contains constant term coefficients, first-order term coefficients, and second-order term coefficients; performing azimuth time interval analysis on the matched-filtered echo signal representation using the constant term coefficients, first-order term coefficients, and second-order term coefficients to obtain the echo data representation corresponding to the k-th frame; determining the offset phase term corresponding to the first-order term coefficients, the defocus phase term corresponding to the second-order term coefficients, and the drift phase term based on the drift phase term; modifying the approximate expression for the instantaneous error slant range using only the second-order term coefficients to obtain an approximate expression for the instantaneous error slant range; and obtaining an approximate expression for azimuth motion error compensation based on the approximate expression for the instantaneous error slant range using only the second-order term coefficients.

2. The method as described in claim 1, characterized in that, The representation of two sub-aperture images corresponding to the raw echo data acquired by video synthetic aperture radar (SAR) includes: The raw echo data acquired by video SAR is truncated to obtain the truncated echo data; Obtain pixel echo data corresponding to two sub-aperture images corresponding to the truncated echo data. The pixel echo data includes an approximate expression of the instantaneous slant distance error represented only by quadratic term coefficients. The representation of each sub-aperture image is obtained based on the pixel echo data corresponding to each sub-aperture image.

3. The method as described in claim 1, characterized in that, Based on multiple initial points and the gradient expression, the objective function is optimized and estimated to obtain the global optimal value of the quadratic term coefficient, including: Based on multiple initial points and the gradient expression, the objective function is optimized and estimated to obtain the local optimal solution set of the quadratic term coefficients corresponding to each initial point; From the set of local optimal solutions corresponding to the quadratic coefficients of each initial point, determine the set of local optimal solutions that minimizes the objective function value as the global optimal value of the quadratic coefficients.

4. The method as described in claim 3, characterized in that, Also includes: Obtain the objective function with a penalty term and its corresponding gradient expression; Based on multiple initial points and the gradient representation of the objective function with a penalty term, the objective function with a penalty term is optimized and estimated to obtain the local optimal solution set of the quadratic coefficients corresponding to each initial point.

5. The method as described in claim 1, characterized in that, Constructing a video SAR motion error model includes: In circular trajectory spotting mode, the ideal instantaneous slant range expression and the actual instantaneous slant range expression for inter-frame motion in video SAR are obtained; Based on the ideal instantaneous slope distance expression and the actual instantaneous slope distance expression, the error instantaneous slope distance is determined; Based on the ideal instantaneous slant range expression, the actual instantaneous slant range expression, and the error instantaneous slant range, a point target echo signal expression after adding inertial navigation error is constructed; Matched filtering is performed along the range direction on the echo signal representation of the point target after adding inertial navigation error to obtain the echo signal representation after matching filtering.

6. A motion error compensation device for inter-frame images of video synthetic aperture radar, characterized in that, include: The image representation acquisition module is used to obtain the representation of two sub-aperture images corresponding to the original echo data acquired by video synthetic aperture radar SAR, wherein the sub-aperture images are video SAR inter-frame images; The correlation analysis module is used to analyze the correlation between the representations of two sub-aperture images. The correlation is a function of the coefficient of the quadratic term in the approximate representation of the instantaneous slant range error of the video SAR platform motion in circular trajectory spotting mode. The gradient expression analysis module is used to analyze the gradient expression of the objective function, taking the correlation as the objective function. The optimization estimation module is used to optimize and estimate the objective function based on multiple initial points and the gradient expression to obtain the global optimal value of the quadratic term coefficient; The motion error compensation module is used to substitute the global optimal value of the quadratic term coefficient into the approximate expression of azimuth motion error compensation. Based on the start and end positions of the pulses in different frames, the approximate expression of azimuth motion error compensation is truncated to obtain the approximate expression of azimuth motion compensation for each frame. Based on the approximate expression of azimuth motion compensation for each frame, phase error compensation is performed on corresponding frames of two sub-aperture images. The steps for constructing an approximate expression for azimuth motion error compensation include: constructing a video SAR motion error model, which includes an instantaneous error slant range and a matched-filtered echo signal representation; performing a Taylor expansion on the instantaneous error slant range and retaining it down to the second-order term to obtain an approximate expression for the instantaneous error slant range, which contains constant term coefficients, first-order term coefficients, and second-order term coefficients; performing azimuth time interval analysis on the matched-filtered echo signal representation using the constant term coefficients, first-order term coefficients, and second-order term coefficients to obtain the echo data representation corresponding to the k-th frame; determining the offset phase term corresponding to the first-order term coefficients, the defocus phase term corresponding to the second-order term coefficients, and the drift phase term based on the drift phase term; modifying the approximate expression for the instantaneous error slant range using only the second-order term coefficients to obtain an approximate expression for the instantaneous error slant range; and obtaining an approximate expression for azimuth motion error compensation based on the approximate expression for the instantaneous error slant range using only the second-order term coefficients.

7. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 5.

9. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method of any one of claims 1 to 5.

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