Motion error compensation method and device for inter-frame images of video synthetic aperture radar

Abstract

The invention discloses a motion error compensation method and device for inter-frame images of a video synthetic aperture radar (SAR). The method comprises the following steps: obtaining expressions of two sub-aperture images corresponding to original echo data acquired by the SAR; analyzing the correlation between the expressions of the two sub-aperture images; the correlation is used as a target function, and gradient expression of the target function is analyzed; based on a plurality of initial points and the gradient expression, performing optimization estimation on a target function to obtain a global optimal value of a quadratic term coefficient; and substituting the global optimal value of the quadratic term coefficient into the approximate expression of azimuth motion error compensation, and intercepting the approximate expression of azimuth motion error compensation according to the initial positions and the termination positions of different frames of pulses to obtain the approximate expression of azimuth motion compensation corresponding to each frame. And phase error compensation is carried out on the corresponding frames of the two sub-aperture images. According to the invention, phase error compensation can be carried out on full-aperture video SAR inter-frame images.

Description

Technical Field

[0001] The present invention relates to the field of video synthetic aperture radar inter-frame imaging, and in particular to a method and device for compensating motion errors of video synthetic aperture radar inter-frame images. Background Art

[0002] This section is intended to provide a background or context to the embodiments of the invention recited in the claims. No admission is made that the description herein is prior art by inclusion in this section.

[0003] During the movement of the flying platform carrying the radar payload, there are motion errors in the radar echo due to the vibration of the engine and the atmospheric airflow. Since the high-band is sensitive to motion errors, under the condition of limited inertial navigation accuracy, the quadratic coefficient of the error slant range will cause each frame of the image to drift in azimuth, and the drift will accumulate as the number of frames increases. For high-frame-rate video SAR systems, the number of frames can usually reach hundreds. With the increase in the number of imaging frames, the phenomenon of drift between image frames will become more serious, which seriously affects the scene stability of multi-frame imaging.

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

[0005] The embodiment of the present invention provides a method for compensating motion errors of video synthetic aperture radar inter-frame images, which is used to implement phase error compensation for full-aperture video SAR inter-frame images. The method includes:

[0006] Obtaining the expression of two sub-aperture images corresponding to the original echo data collected by the video synthetic aperture radar SAR, wherein the sub-aperture images are the video SAR inter-frame images;

[0007] Analyzing the correlation between the expressions of the two sub-aperture images, the correlation being a function of the coefficient of the quadratic term in the approximate expression of the error instantaneous slant range of the video SAR platform motion in the circular spotlight mode;

[0008] Taking the correlation as the objective function, analyzing 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] Substituting the global optimal value of the quadratic term coefficient into the approximate expression of the azimuth motion error compensation, intercepting the approximate expression of the azimuth motion error compensation according to the starting position and the ending position of the pulse of different frames, and obtaining the approximate expression of the azimuth motion compensation corresponding to each frame;

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

[0012] The embodiment of the present invention further provides a motion error compensation device for video synthetic aperture radar inter-frame images, which is used to realize phase error compensation for full-aperture video SAR inter-frame images. The device includes:

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

[0014] A correlation analysis module, used to analyze the correlation between the expressions of the two sub-aperture images, wherein the correlation is a function of the coefficient of the quadratic term in the approximate expression of the error instantaneous slant range of the video SAR platform motion in the circular spotlight mode;

[0015] A gradient expression analysis module, used to analyze the gradient expression of the objective function by taking the correlation as the objective function;

[0016] An optimization estimation module, used to optimize and estimate the objective function based on multiple initial points and the gradient expression to obtain a 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 the azimuth motion error compensation, intercept the approximate expression of the azimuth motion error compensation according to the starting position and the ending position of different frame pulses, and obtain the approximate expression of the azimuth motion compensation corresponding to each frame; according to the approximate expression of the azimuth motion compensation corresponding to each frame, phase error compensation is performed on the corresponding frames of the two sub-aperture images.

[0018] An embodiment of the present invention further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method for compensating motion errors of video synthetic aperture radar inter-frame images when executing the computer program.

[0019] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the motion error compensation method for video synthetic aperture radar inter-frame images is implemented.

[0020] An embodiment of the present invention further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the motion error compensation method of the video synthetic aperture radar inter-frame image is implemented.

[0021] In an embodiment of the present invention, expressions of two sub-aperture images corresponding to original echo data collected by a video synthetic aperture radar SAR are obtained, wherein the sub-aperture images are video SAR inter-frame images; the correlation between the expressions of the two sub-aperture images is analyzed, wherein the correlation is a function of the quadratic term coefficient in the approximate expression of the error instantaneous slant range of the video SAR platform motion in a circular spotlight mode; the correlation is used as the objective function, and the gradient expression of the objective function is analyzed; 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; the global optimal value of the quadratic term coefficient is substituted into the approximate expression of azimuth motion error compensation, and the approximate expression of azimuth motion error compensation is intercepted according to the starting position and the ending position of different frame pulses to obtain the approximate expression of azimuth motion compensation corresponding to each frame; and phase error compensation is performed on the corresponding frames of the two sub-aperture images according to the approximate expression of azimuth motion compensation corresponding to each frame. Compared with the existing schemes, the method of the present invention adopts the correlation between the expressions of sub-aperture images to construct the objective function, and the correlation is a function of the quadratic term coefficient in the approximate expression of the error instantaneous slant range of the video SAR platform motion in the circular spotlight mode. Therefore, an optimization estimate is performed to obtain the global optimal value of the quadratic term coefficient. The global optimal value can be used to construct an approximate expression of azimuth motion error compensation to achieve phase error compensation for full-aperture video SAR inter-frame images. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0023] Figure 1 It is a flow chart of a method for compensating motion errors of video synthetic aperture radar inter-frame images in an embodiment of the present invention;

[0024] Figure 2 A flowchart of constructing a video SAR motion error model in an embodiment of the present invention;

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

[0026] Figure 4 A flowchart of constructing an approximate expression for azimuth motion error compensation in an embodiment of the present invention;

[0027] Figure 5 It 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 A flowchart of obtaining the expression of two sub-aperture images corresponding to the original echo data collected by the video synthetic aperture radar SAR in an embodiment of the present invention;

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

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

[0031] Fig. 9 Schematic diagram of a computer device in an embodiment of the present invention. DETAILED DESCRIPTION

[0032] To make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings. Here, the exemplary 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] In order to solve the problems existing in the prior art, it is necessary to derive the motion error theoretically, construct a corresponding motion error compensation function by modeling and analyzing the motion feature model, and compensate for the error phase that causes inter-frame image drift.

[0034] In addition, in the process of processing actual data, the more accurate the motion error estimation is, the better the image stability after motion phase compensation is. By establishing an objective function and using an optimization algorithm to estimate the motion error, there may be a situation with multiple local optimal solutions. At this time, the optimization algorithm may fall into the local optimum and fail to find the global optimum. At the same time, how to establish an objective function for estimating motion errors also requires further research. If the designed objective function is too complex, it may lead to a large amount of search calculations, which greatly affects the efficiency of parameter search. In addition, the performance of the optimization algorithm is often very sensitive to the initial point. Selecting an inappropriate initial value point for searching may cause the search process to be slow or even fail. Therefore, it is necessary to establish an objective function with low complexity, constrain the initial value point of the search, and use an optimization algorithm with good robustness to estimate the motion error between video SAR frames.

[0035] To this end, the embodiment of the present invention proposes a method for compensating motion errors of video synthetic aperture radar inter-frame images, such as Figure 1 The flowchart of the motion error compensation method of the video synthetic aperture radar inter-frame image in the embodiment of the present invention includes:

[0036] Step 101, obtaining expressions of two sub-aperture images corresponding to original echo data collected by a video synthetic aperture radar SAR, wherein the sub-aperture images are video SAR inter-frame images;

[0037] Step 102, analyzing the correlation between the expressions of the two sub-aperture images, wherein the correlation is a function of the coefficient of the quadratic term in the approximate expression of the error instantaneous slant range of the video SAR platform motion in the circular spotlight mode;

[0038] Step 103, taking the correlation as the objective function, analyzing the gradient expression of the objective function;

[0039] Step 104, based on the multiple initial points and the gradient expression, optimizing and estimating the objective function to obtain the global optimal value of the quadratic term coefficient;

[0040] Step 105, substituting the global optimal value of the quadratic term coefficient into the approximate expression of the azimuth motion error compensation, intercepting the approximate expression of the azimuth motion error compensation according to the starting position and the ending position of the pulse of different frames, and obtaining the approximate expression of the azimuth motion compensation corresponding to each frame;

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

[0042] Compared with the existing schemes, the method of the present invention adopts the correlation between the expressions of sub-aperture images to construct the objective function, and the correlation is a function of the quadratic term coefficient in the approximate expression of the error instantaneous slant range of the video SAR platform motion in the circular spotlight mode. Therefore, an optimization estimate is performed to obtain the global optimal value of the quadratic term coefficient. The global optimal value can be used to construct an approximate expression of azimuth motion error compensation to achieve phase error compensation for full-aperture video SAR inter-frame images.

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

[0044] Before constructing an approximate expression for azimuth motion error compensation, it is necessary to construct a video SAR motion error model.

[0045] See also Figure 2 This is a flow chart of constructing a video SAR motion error model in an embodiment of the present invention, and the specific steps include:

[0046] Step 201, in the circular spotlight mode, obtaining an ideal instantaneous slant range expression and an actual instantaneous slant range expression during inter-frame motion of the video SAR;

[0047] Step 202, determining an error instantaneous slant distance according to the ideal instantaneous slant distance expression and the actual instantaneous slant distance expression;

[0048] Step 203, constructing a point target echo signal expression after adding an inertial navigation error according to the ideal instantaneous slant range expression, the actual instantaneous slant range expression, and the error instantaneous slant range;

[0049] Step 204, performing matched filtering along the range direction on the point target echo signal expression after adding the inertial navigation error, to obtain the echo signal expression after matched filtering.

[0050] Figure 3 FIG. 1 is a schematic diagram of airborne SAR motion with motion error on a video SAR platform in an embodiment of the present invention, which is for a circular spotlight mode. Figure 3 In the figure, the black track is the ideal track of the carrier aircraft, and the red track is the actual track. In an ideal situation, the video SAR platform flies at a constant speed V s The aircraft moves along the ideal trajectory with a constant altitude H. However, due to the influence of atmospheric turbulence or other factors, the actual trajectory of the aircraft deviates from the uniform linear motion, thus causing the position error of the radar's antenna phase center (APC) ( Figure 3 (indicated by the purple arrow).

[0051] Assume that 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 It is the slow time in azimuth.

[0052] Then the ideal instantaneous slant range expression for video SAR frame motion is R t (t a )for:

[0053]

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

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

[0056]

[0057] Error instantaneous slope distance R e (t a )for:

[0058]

[0059] The point target echo signal after adding the inertial navigation error is expressed as s(t r ,t a )for:

[0060]

[0061] Where: A0 is a complex constant; λ is the carrier wavelength; t r is the distance to fast time; t a is the azimuth slow time; w r (·) is the distance envelope; w a (·) is the azimuthal envelope; t ac is the Doppler center time; f0 is the center frequency; R(·) is the slant range length of the radar to the target (subscript omitted); c is the speed of light; K r is the modulation frequency of the distance pulse.

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

[0063]

[0064] The above error instantaneous slant range 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. Figure 4 The flowchart of constructing an approximate expression of azimuth motion error compensation in an embodiment of the present invention includes the following specific steps:

[0066] Step 401, constructing a video SAR motion error model, wherein the video SAR motion error model includes an error instantaneous slant range and an echo signal expression after matched filtering; Step 401 includes the aforementioned steps 201 to 204;

[0067] Step 402, Taylor expansion is performed on the instantaneous slope distance of the error and retained to the second-order term to obtain an approximate expression of the instantaneous slope distance of the error, wherein the approximate expression of the instantaneous slope distance of the error contains a constant term coefficient, a first-order term coefficient, and a second-order term coefficient;

[0068] Step 403, performing azimuth time period analysis of multiple frames of images on the echo signal expression after matched filtering according to the constant term coefficient, the first-order term coefficient and the second-order term coefficient, to obtain the echo data expression corresponding to the kth frame;

[0069] Step 404, determining the offset phase term corresponding to the first-order term coefficient, the defocus phase term and the drift phase term corresponding to the second-order term coefficient according to the echo data expression corresponding to the k-th frame;

[0070] Step 405, modifying the approximate expression of the error instantaneous slant range according to the drift phase term, to obtain an approximate expression of the error instantaneous slant range represented by only quadratic term coefficients;

[0071] Step 406, obtaining an approximate expression for azimuth motion error compensation based on an approximate expression of the instantaneous slant range of the error represented by only quadratic term coefficients.

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

[0073]

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

[0075]

[0076] R e (t a ) at t a = 0, and Taylor expansion is performed and retained to the second-order term to obtain the approximate expression of the instantaneous slope distance of the error for:

[0077]

[0078] where ζ c , o , q They are the constant term coefficient, linear term coefficient, and quadratic term coefficient corresponding to the Taylor expansion of the slant range error.

[0079] Figure 5 FIG. 1 is a schematic diagram of the azimuth time period of the video SAR inter-frame image in an embodiment of the present invention, as shown in FIG. 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 azimuth be Ta Let N be the number of sub-aperture images in each frame, then the azimuth time length T corresponding to each sub-aperture is s for:

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

[0081] Then 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 expressed 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 ) can be expressed as:

[0087]

[0088] Where s(·) and A in formula (12) K The expression is as follows:

[0089]

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

[0091]

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

[0093]

[0094] The quadratic term coefficient of the instantaneous slant range error will cause azimuth drift in each frame of image. The drift will accumulate with the increase of azimuth time of multiple frames, thus causing drift of the image between frames. The drift phase term can be expressed as:

[0095]

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

[0097]

[0098] Formula (17) is an approximate expression of the instantaneous slant range of the error using only the coefficient of the quadratic term.

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

[0100]

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

[0102] See also Figure 6 The flowchart of obtaining the expression of two sub-aperture images corresponding to the original echo data collected by the video synthetic aperture radar SAR in an embodiment of the present invention includes the following specific steps:

[0103] Step 601, intercepting the original echo data collected by the video SAR to obtain intercepted echo data;

[0104] Considering that the amount of original echo data collected by video SAR is large, a feasible way is to intercept the original echo data and use the intercepted echo data to quickly estimate the coefficient of the quadratic term of the error instantaneous slant range.

[0105] Assume that the original echo data is intercepted pulses are used to estimate the coefficient of the quadratic term, and the intercepted echo data can be expressed as:

[0106]

[0107] in, and They are respectively the starting pulse number and the ending pulse number of the intercepted echo data.

[0108] Step 602, obtaining pixel point echo data corresponding to two sub-aperture images corresponding to the intercepted echo data, wherein the pixel point echo data includes an approximate expression of the error instantaneous slant range represented by only quadratic term coefficients;

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

[0110]

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

[0112] Pixel P ij At the moment of position The position index in the SAR echo data for:

[0113]

[0114] Where: R min is the shortest slant range length; Fs is the sampling rate; ratio is the range oversampling factor; round(·) indicates rounding operation.

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

[0116]

[0117] where ζ q is the coefficient of the quadratic term to be estimated.

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

[0119]

[0120] in To compensate pixel P ij Doppler shift at different azimuths and times.

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

[0122] The sub-aperture images can be expressed as:

[0123]

[0124] In step 102, the correlation between the expressions of the two sub-aperture images needs to be analyzed. The correlation can be calculated as follows:

[0125]

[0126] Among them, the average values ​​of the sub-aperture images are:

[0127]

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

[0129] In step 103, the correlation is used as the objective function F, and the gradient expression of the objective function F is analyzed. as follows:

[0130]

[0131] in:

[0132] Find the correlation F about The partial derivative of for:

[0133]

[0134] Find the correlation F about The partial derivative of for:

[0135]

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

[0137]

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

[0139]

[0140] Find the grid point echo about The partial derivative of for:

[0141]

[0142] Find the grid point echo about The partial derivative of

[0143]

[0144] Find the average value m1 of the sub-aperture image IM1 about The partial derivative of for:

[0145]

[0146] Find the average value m2 of the sub-aperture image IM2 about The partial derivative of for:

[0147]

[0148] beg about The partial derivative of for:

[0149]

[0150] beg About q The partial derivative of for:

[0151]

[0152] In step 104, it is necessary 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.

[0153] In one embodiment, 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:

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

[0155] From the local optimal solution point set of the quadratic term coefficient corresponding to each initial point, the local optimal solution point set with the minimum objective function value is determined as the global optimal value of the quadratic term coefficient.

[0156] In the specific implementation, a global optimization algorithm based on multi-point BFGS search is used to estimate the quadratic term coefficient of the instantaneous slant range error. Figure 7 Flow chart of the global optimization algorithm based on multi-point BFGS search in the embodiment of the present invention. Figure 7 Since the BFGS method is usually used to search for local optimal values, the embodiment of the present invention sets multiple initial points of quadratic term coefficients to implement multi-point local search, and selects the optimal value with the smallest corresponding objective function value as the global optimal value for constructing the required approximate expression of azimuth motion error compensation.

[0157] Multiple initial point sets {ζ q1 ,ζ q2 ,...,ζ qm The selection of} can be randomly generated or set according to the inertial navigation parameters IMU.

[0158]

[0159] Here we define a local optimization operation as L:

[0160]

[0161] Among them, L(F,ζ qi ) indicates that from the starting point ζ qi Initially, we use the local optimization algorithm L, where F represents the objective function. The starting point is ζ qi The local optimal solution when .

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

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

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

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

[0166]

[0167] Among them, lb and ub are respectively q The upper and lower bounds of .

[0168] The penalty function p(ζ q )About q Gradient for:

[0169]

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

[0171] F′=F+p(ζ q ) (44)

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

[0173]

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

[0175] (1) Set is the gradient expression of the objective function with penalty term, and the initial point ζ is selected qi (0) , take B0 as a positive definite symmetric matrix (usually the unit matrix), set k = 0, and require an accuracy of μ.

[0176] (2) Calculate g k =g(ζ qi (k) ), if || g k ||<μ, then stop the calculation and get the approximate solution Otherwise, go to step (3);

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

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

[0179]

[0180] (5) Set 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 ||<μ, then stop the calculation and get the 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 and go to step (3).

[0186] For each initial point ζ qi , execute the BFGS algorithm in parallel. In the parallel search process, each local optimization can be regarded as an independent computing unit. Therefore, the i-th parallel computing unit P i It can be expressed as:

[0187]

[0188] After completing the entire parallel search, different computing units P i The point set consisting of the obtained local optimal solution can be expressed as:

[0189]

[0190] According to the set of local optimal solutions, the solution with the smallest corresponding objective function value is selected as the global optimal solution:

[0191]

[0192] In step 105, the global optimal value of the quadratic term coefficient is substituted into the approximate expression of azimuth motion error compensation to obtain:

[0193]

[0194] Afterwards, according to the starting position and ending position of different frame pulses, the approximate expression of azimuth motion error compensation is intercepted to obtain the approximate expression of azimuth motion compensation corresponding to each frame. Taking the Kth frame as an example,

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

[0196]

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

[0198] Then, the process proceeds to step 105, that is, according to the approximate expression of the azimuth motion compensation corresponding to each frame, phase error compensation is performed on the corresponding frames of the two sub-aperture images, thereby realizing phase error compensation for the full-aperture video SAR inter-frame images.

[0199] The embodiment of the present invention further provides a motion error compensation device for video synthetic aperture radar inter-frame images, the principle of which is similar to the motion error compensation method for video synthetic aperture radar inter-frame images, which will not be described in detail here.

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

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

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

[0203] A gradient expression analysis module 803 is used to analyze the gradient expression of the objective function by taking the correlation as the objective function;

[0204] An optimization estimation module 804 is used to optimize and estimate the objective function based on multiple initial points and the gradient expression to obtain a 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 the azimuth motion error compensation, intercept the approximate expression of the azimuth motion error compensation according to the starting position and the ending position of different frame pulses, and obtain the approximate expression of the azimuth motion compensation corresponding to each frame; according to 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.

[0206] In one embodiment, the image expression obtaining module is used to:

[0207] The original echo data collected by the video SAR is intercepted to obtain intercepted echo data;

[0208] Obtaining pixel point echo data corresponding to two sub-aperture images corresponding to the intercepted echo data, wherein the pixel point echo data includes an approximate expression of the error instantaneous slant range represented by only quadratic term coefficients;

[0209] The expression of each sub-aperture image is obtained according to the pixel echo data corresponding to each sub-aperture image.

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

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

[0212] From the local optimal solution point set of the quadratic term coefficient corresponding to each initial point, the local optimal solution point set with the minimum objective function value is determined as the global optimal value of the quadratic term coefficient.

[0213] In one embodiment, the optimization estimation module is further used for:

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

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

[0216] In one embodiment, the apparatus further comprises an approximate expression construction module 806 for azimuth motion error compensation, which is used to:

[0217] Constructing a video SAR motion error model, wherein the video SAR motion error model includes an error instantaneous slant range and an echo signal expression after matched filtering;

[0218] Taylor expansion is performed on the instantaneous slope distance of the error and retained to the second-order term to obtain an approximate expression of the instantaneous slope distance of the error, wherein the approximate expression of the instantaneous slope distance of the error contains a constant term coefficient, a first-order term coefficient, and a second-order term coefficient;

[0219] According to the constant term coefficient, the first-order term coefficient and the second-order term coefficient, the echo signal expression after matched filtering is analyzed in the azimuth time period of multiple frames of images to obtain the echo data expression corresponding to the kth frame;

[0220] According to the echo data expression corresponding to the kth frame, an offset phase term corresponding to the first-order term coefficient, a defocus phase term and a drift phase term corresponding to the second-order term coefficient are determined;

[0221] Modifying the approximate expression of the instantaneous slant range of the error according to the drift phase term to obtain an approximate expression of the instantaneous slant range of the error represented by only quadratic term coefficients;

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

[0223] In one embodiment, the apparatus further includes a video SAR motion error model building module 807, which is used to:

[0224] In the circular spotlight mode, the ideal instantaneous slant range expression and the actual instantaneous slant range expression are obtained when the video SAR moves between frames;

[0225] Determining an error instantaneous slope distance according to the ideal instantaneous slope distance expression and the actual instantaneous slope distance expression;

[0226] According to the ideal instantaneous slant range expression, the actual instantaneous slant range expression, and the error instantaneous slant range, constructing a point target echo signal expression after adding the inertial navigation error;

[0227] The point target echo signal expression after adding the inertial navigation error is subjected to matched filtering along the range direction to obtain the echo signal expression after matched filtering.

[0228] In summary, the method and device 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 frames is deeply analyzed. By modeling the motion error, the reasons for the image defocus and inter-frame drift caused by the motion error are analyzed. It can be seen that the quadratic term coefficient of the instantaneous slant range of the error will cause image defocus and drift between multiple frames. The drift will accumulate with the increase of azimuth time.

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

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

[0232] Fourth, the sub-aperture image is phase compensated by assigning the initial value of the quadratic term coefficient of the motion compensation function. Then, the correlation between the two sub-aperture images after motion compensation is used as the objective function, and the initial value is optimized using the BFGS method. Since the BFGS method is usually used to search for local optimal values, multiple initial value points of the quadratic term coefficients are set to realize multi-point local search, and the optimal value corresponding to the minimum objective function value is selected as the global optimal value to construct the required approximate expression of the inter-frame azimuth motion error compensation.

[0233] Through the above key points, the following beneficial effects are produced:

[0234] First, the problem of lack of theoretical basis for the motion error model of signal domain video SAR and the lack of theoretical basis for phase compensation of inter-frame errors is solved. The embodiment of the present invention performs motion feature modeling and analysis on the inter-frame errors, and establishes an approximate expression for the azimuth motion error compensation of video SAR frames based on the characteristics of the motion error.

[0235] Specifically, the mechanism of long-term differences between images of frames is deeply analyzed. By modeling the motion error, the reasons why the motion error causes image defocus and drift between frames are analyzed. According to the established motion error model, it can be seen that the quadratic term coefficient of the error instantaneous slant range will cause image defocus and cause the image to drift between multiple frames. The drift amount will accumulate with the increase of azimuth time. For video SAR imaging, inter-frame phase discontinuity will affect the consistency of inter-frame imaging. In order to ensure the continuity of inter-frame motion error compensation, this patent constructs an approximate expression of full-aperture azimuth motion error compensation corresponding to multiple frames. Since the quadratic term coefficient of the error instantaneous slant range is the cause of the drift between image frames, the embodiment of the present invention establishes a corresponding approximate expression of azimuth motion error compensation based on the quadratic term coefficient for compensating the error phase.

[0236] Secondly, the problem of high-precision estimation of video SAR motion error was solved. The quadratic term coefficient of the error instantaneous slant range was taken as the independent variable and the correlation between the two sub-images after motion compensation was taken as the objective function. The BFGS algorithm was used to achieve accurate estimation of the inter-frame motion error.

[0237] Specifically, the original echo data was first truncated, and the approximate expression of azimuth motion error compensation was constructed by setting the initial value of the quadratic term coefficient of the error instantaneous slant range, and the corresponding phase compensation was performed on the truncated echo. Then, the quadratic term coefficient of the error instantaneous slant range was used as the independent variable, and the correlation between the two sub-aperture images after motion compensation was used as the objective function, and the value of the quadratic term coefficient was optimized using the BFGS method. Since the BFGS method is usually used to search for local optimal values, multiple initial value points of the quadratic term coefficient are set to realize multi-point local search, and the optimal value with the smallest corresponding objective function value is selected as the global optimal value to construct the required approximate expression of inter-frame azimuth motion error compensation.

[0238] An embodiment of the present invention further provides a computer device, Fig. 9 9 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, the motion error compensation method for inter-frame images of a video synthetic aperture radar is implemented.

[0239] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the motion error compensation method for video synthetic aperture radar inter-frame images is implemented.

[0240] An embodiment of the present invention further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the motion error compensation method of the video synthetic aperture radar inter-frame image is implemented.

[0241] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented 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] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0243] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0244] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0245] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is 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 in the scope of protection of the present invention.

Claims

1. A method for compensating motion errors of video synthetic aperture radar inter-frame images, characterized in that: include: Obtaining the expression of two sub-aperture images corresponding to the original echo data collected by the video synthetic aperture radar SAR, wherein the sub-aperture images are the video SAR inter-frame images; Analyzing the correlation between the expressions of the two sub-aperture images, the correlation being a function of the coefficient of the quadratic term in the approximate expression of the error instantaneous slant range of the video SAR platform motion in the circular spotlight mode; Taking the correlation as the objective function, analyzing 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; Substituting the global optimal value of the quadratic term coefficient into the approximate expression of the azimuth motion error compensation, intercepting the approximate expression of the azimuth motion error compensation according to the starting position and the ending position of the pulse of different frames, and obtaining the approximate expression of the azimuth motion compensation corresponding to each frame; According to the approximate expression of the azimuth motion compensation corresponding to each frame, phase error compensation is performed on the corresponding frames of the two sub-aperture images.

2. The method according to claim 1, characterized in that The expression of two sub-aperture images corresponding to the original echo data collected by the video synthetic aperture radar SAR is obtained, including: The original echo data collected by the video SAR is intercepted to obtain intercepted echo data; Obtaining pixel point echo data corresponding to two sub-aperture images corresponding to the intercepted echo data, wherein the pixel point echo data includes an approximate expression of the error instantaneous slant range represented by only quadratic term coefficients; The expression of each sub-aperture image is obtained according to the pixel echo data corresponding to each sub-aperture image.

3. The method according to 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 the multiple initial points and the gradient expression, the objective function is optimized and estimated to obtain a local optimal solution point set of the quadratic term coefficient corresponding to each initial point; From the local optimal solution point set of the quadratic term coefficient corresponding to each initial point, the local optimal solution point set with the minimum objective function value is determined as the global optimal value of the quadratic term coefficient.

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

5. The method according to claim 1, characterized in that The steps to construct an approximate expression for azimuth motion error compensation include: Constructing a video SAR motion error model, wherein the video SAR motion error model includes an error instantaneous slant range and an echo signal expression after matched filtering; Taylor expansion is performed on the instantaneous slope distance of the error and retained to the second-order term to obtain an approximate expression of the instantaneous slope distance of the error, wherein the approximate expression of the instantaneous slope distance of the error contains a constant term coefficient, a first-order term coefficient, and a second-order term coefficient; According to the constant term coefficient, the first-order term coefficient and the second-order term coefficient, the echo signal expression after matched filtering is analyzed in the azimuth time period of multiple frames of images to obtain the echo data expression corresponding to the kth frame; According to the echo data expression corresponding to the kth frame, an offset phase term corresponding to the first-order term coefficient, a defocus phase term and a drift phase term corresponding to the second-order term coefficient are determined; Modifying the approximate expression of the instantaneous slant range of the error according to the drift phase term to obtain an approximate expression of the instantaneous slant range of the error represented by only quadratic term coefficients; Based on the approximate expression of the instantaneous slant range of the error represented by only the coefficient of the quadratic term, an approximate expression of the azimuth motion error compensation is obtained.

6. The method according to claim 5, characterized in that Construct a video SAR motion error model, including: In the circular spotlight mode, the ideal instantaneous slant range expression and the actual instantaneous slant range expression are obtained when the video SAR moves between frames; Determining an error instantaneous slope distance according to the ideal instantaneous slope distance expression and the actual instantaneous slope distance expression; According to the ideal instantaneous slant range expression, the actual instantaneous slant range expression, and the error instantaneous slant range, constructing a point target echo signal expression after adding the inertial navigation error; The point target echo signal expression after adding the inertial navigation error is subjected to matched filtering along the range direction to obtain the echo signal expression after matched filtering.

7. A motion error compensation device for video synthetic aperture radar inter-frame images, characterized in that: include: An image expression acquisition module is used to obtain the expression of two sub-aperture images corresponding to the original echo data collected by the video synthetic aperture radar SAR, wherein the sub-aperture images are video SAR inter-frame images; A correlation analysis module, used to analyze the correlation between the expressions of the two sub-aperture images, wherein the correlation is a function of the coefficient of the quadratic term in the approximate expression of the error instantaneous slant range of the video SAR platform motion in the circular spotlight mode; A gradient expression analysis module, used to analyze the gradient expression of the objective function by taking the correlation as the objective function; An optimization estimation module, used to optimize and estimate the objective function based on multiple initial points and the gradient expression to obtain a 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 the azimuth motion error compensation, intercept the approximate expression of the azimuth motion error compensation according to the starting position and the ending position of different frame pulses, and obtain the approximate expression of the azimuth motion compensation corresponding to each frame; according to the approximate expression of the azimuth motion compensation corresponding to each frame, phase error compensation is performed on the corresponding frames of the two sub-aperture images.

8. 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, the method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

10. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

Images