Moving target imaging and repositioning method based on bistatic synthetic aperture radar

Abstract

The invention relates to the technical field of synthetic aperture radar imaging detection, in particular to a moving target imaging and repositioning method based on a bistatic synthetic aperture radar, and the method comprises the steps: obtaining an original echo signal of a moving target through the bistatic synthetic aperture radar, and correcting the original echo signal based on two-step transformation; extracting a first-order Doppler parameter estimation value of the echo signal after the two-step transformation and moving target distance information under different azimuth blocks; constructing a parameter estimation and relocation model, and solving a second-order Doppler parameter estimation value and relocation information according to the first-order Doppler parameter estimation value and the moving target distance information under different azimuth blocks; and according to the second-order Doppler parameter estimation value and the repositioning information, constructing a matching function to perform focusing imaging on the moving target. The objective of the invention is to synchronously realize parameter estimation and relocation of a moving target and improve the calculation efficiency.

Description

Technical Field

[0001] The invention relates to the technical field of synthetic aperture radar imaging detection, and in particular to a moving target imaging and relocation method based on a dual-base synthetic aperture radar. Background Art

[0002] In the field of modern radar detection technology, bistatic synthetic aperture radar (BiSAR) has shown many unique advantages over traditional monostatic SAR. From the perspective of system configuration, the separation of its transmitter and receiver gives BiSAR excellent forward-looking imaging potential, which can break through the visual angle limitation of monostatic SAR, greatly expand the observation field, and provide more dimensional information for target detection in complex scenes. In actual application scenarios, especially in battlefield reconnaissance and surveillance and precision-guided strike, accurate imaging and precise repositioning of moving targets are particularly important in bistatic synthetic aperture radar systems. Only by accurately grasping the key parameters such as the position and speed of moving targets can we provide solid data support for subsequent tactical decision-making and weapon guidance, and thus achieve efficient combat effectiveness. However, the current bistatic synthetic aperture radar faces a series of severe challenges in imaging and positioning moving targets. The core difficulty focuses on the high uncertainty of moving targets. The complex motion situation of non-cooperative targets triggers unknown range migration and additional azimuth phase modulation phenomena. This directly leads to image defocus problems during the imaging process of moving targets, and the focus position deviates significantly from the actual position, which greatly reduces the probability of target detection and the positioning accuracy is insufficient, thus weakening the actual combat effectiveness of reconnaissance and guidance.

[0003] At present, the existing technology has proposed a series of solutions for the parameter estimation of moving targets in dual-base synthetic aperture radar, but all of them have limitations to varying degrees. For example, the parameter search method based on image minimum entropy requires repeated azimuth focusing imaging of the moving target and complex and tedious image entropy calculations, resulting in a high overall time complexity of the algorithm and a complex calculation process, which is difficult to meet the application scenarios with strict real-time requirements. For another example, the method of using the keystone transform in the distance dimension combined with the azimuth dimension fractional Fourier transform (FrFT) can compensate for the distance migration to a certain extent and estimate the Doppler centroid and Doppler modulation rate of the moving target, but the connection and adaptation between the various links and the adaptability to complex motion scenes still need to be optimized, and estimation errors are prone to occur under variable actual working conditions. In addition, some solutions that directly rely on optimization algorithms to transform the estimation of moving target imaging parameters into parameter search problems have a large search space and high computational complexity, which not only puts extremely high requirements on hardware computing power, but also performs poorly in terms of real-time and stability, making it difficult to achieve large-scale engineering applications.

[0004] In summary, the core of existing algorithms for imaging and repositioning of dual-base moving targets is all centered around parameter estimation, and focusing or direct motion parameters are obtained through a variety of estimation algorithms to achieve target positioning and eliminate motion errors. However, the existing technologies generally have technical problems such as complex calculations and poor real-time performance. The present invention proposes a fast parameter estimation algorithm that unifies imaging and repositioning, which can directly complete the repositioning of moving targets during the imaging process, while achieving imaging focusing of moving targets. The estimation process does not require repeated imaging processing of echo data, which improves the real-time tracking of moving targets and the computational efficiency. Therefore, it is suitable for scenarios where guidance applications are performed on moving targets. Summary of the invention

[0005] In order to achieve parameter estimation and relocation of moving targets simultaneously and improve computational efficiency, the present invention aims to provide a moving target imaging and relocation method based on a bistatic synthetic aperture radar. The technical scheme adopted is as follows:

[0006] The technical solution of the present invention provides a moving target imaging and relocation method based on a bistatic synthetic aperture radar, the method comprising:

[0007] The bistatic synthetic aperture radar obtains the original echo signal of the moving target and corrects the original echo signal based on the second-order ladder transformation;

[0008] Extract the first-order Doppler parameter estimation value of the echo signal after the second-order trapezoidal transformation and the moving target distance information under different azimuth blocks;

[0009] Construct parameter estimation and relocation model, solve the second-order Doppler parameter estimation and relocation information according to the first-order Doppler parameter estimation and moving target distance information in different azimuth blocks;

[0010] According to the second-order Doppler parameter estimation and relocation information, a matching function is constructed to perform focused imaging on the moving target.

[0011] Furthermore, the bistatic synthetic aperture radar obtains the original echo signal of the moving target, and corrects the original echo signal based on the second-order ladder transformation, including:

[0012] Obtain the position and speed information of the receiving station, transmitting station and moving target, and extract the dual-base slant range history of the moving target at the target moment;

[0013] Calculate the Doppler center frequency and Doppler modulation rate of the moving target according to the dual-base slant range history of the moving target at the target moment;

[0014] Perform pulse compression on the original echo signal to obtain a range frequency domain echo signal;

[0015] The echo signal in the range frequency domain is corrected by using the second-order ladder shape transformation to obtain the echo signal after the second-order ladder shape transformation.

[0016] Furthermore, extracting the first-order Doppler parameter estimation value of the echo signal after the second-order trapezoidal transformation and the moving target distance estimation value under different azimuth blocks includes:

[0017] The echo signal after the second-order ladder transformation is converted into a two-dimensional time domain based on Fourier transformation;

[0018] Estimate the slope of the moving target migration curve using Radon transform;

[0019] The first-order Doppler parameter estimation value is calculated based on the slope of the moving target migration curve combined with the pulse repetition frequency and the signal baseband signal sampling rate.

[0020] Furthermore, extracting the first-order Doppler parameter estimation value of the echo signal after the second-order trapezoidal transformation and the moving target distance estimation value under different azimuth blocks also includes:

[0021] Performing azimuth block processing on the echo signal after the second-order ladder transformation;

[0022] Doppler pre-filtering is performed on the echo signal after azimuth block using a pre-filtering function;

[0023] Performing a first-step ladder transformation on the echo signal after Doppler pre-filtering;

[0024] Based on the echo signal after the first-step ladder transformation, the constant false alarm rate detection method is used to detect the moving targets in each block and extract the distance information of the moving targets.

[0025] Furthermore, a parameter estimation and relocation model is constructed, and the second-order Doppler parameter estimation and relocation information are solved according to the first-order Doppler parameter estimation and the moving target distance information under different azimuth blocks, including:

[0026] According to the position and speed information of the moving target, the transmitting station and the receiving station, a nonlinear equation group is constructed based on the distance information of the moving target in each block;

[0027] Estimating the initial Doppler modulation rate according to the acceleration effect of the moving target under the preset initial conditions;

[0028] Iteratively solves the nonlinear equations and outputs second-order motion parameters and relocation information.

[0029] Furthermore, the expression of the nonlinear equations is:

[0030]

[0031] Where X represents the position information of the moving target at the initial moment; Xs express The position information of the moving target at any moment, T s represents the synthetic aperture time; X e express The position information of the moving target at any moment; X t represents the location information of the transmitting station at the initial moment, X t =(x t ,y t ,z t ) T ;X ts express The location information of the transmitting station at the moment, X ts =(x ts ,y ts ,z ts ) T ;X te express The location information of the transmitting station at the moment, X te =(x te ,y te ,z te ) T ;X r represents the location information of the receiving station at the initial moment, X r =(x r ,y r ,z r ) T ;X rs express The location information of the receiving station at any time, X rs =(x rs ,y rs ,z rs ) T ;X re express The location information of the receiving station at any time, X re =(x re ,y re ,z rr ) T ; R b represents the bistatic slant distance at the initial moment; f dc Doppler center frequency; R bs express The bistatic slant distance at the moment; R be express The bistatic slant distance at time f dr represents the Doppler modulation frequency; λ represents the wavelength; V t ′ represents the velocity vector of the transmitting station; V r ′ represents the velocity vector of the receiving station; Rt0 Indicates the reference position of the transmitting station; R r0 Indicates the reference position of the receiving station.

[0032] Furthermore, constructing a parameter estimation and relocation model, solving the second-order Doppler parameter estimation value and relocation information according to the first-order Doppler parameter estimation value and the moving target distance information under different azimuth blocks also includes:

[0033] Construct a Jacobian matrix and convert it into an inverse matrix, use the Jacobian inverse matrix to correct the current target parameter estimate, and obtain the corrected target parameter estimate;

[0034] According to the corrected target parameter estimation value, the first-order Doppler parameter estimation value and the second-order Doppler parameter estimation value are updated;

[0035] According to the preset iteration termination condition, the second-order Doppler parameter estimation value and relocation information are output.

[0036] Furthermore, according to the second-order Doppler parameter estimation value and the relocation information, a matching function is constructed to focus the moving target for imaging, including:

[0037] The global Doppler pre-filtering function is constructed based on the first-order Doppler parameter estimation value, and its expression is:

[0038]

[0039] In the formula, H1(f τ ,η) represents the global Doppler pre-filtering function; j represents the imaginary unit; f τ represents the range frequency variable; f0 represents the center frequency of the radar; represents the first-order Doppler parameter estimate; η represents the azimuth slow time variable; c represents the speed of light.

[0040] Furthermore, constructing a matching function to focus imaging of a moving target according to the second-order Doppler parameter estimation value and the relocation information also includes:

[0041] According to the second-order Doppler parameter estimation, the range bending correction function is constructed, and its expression is:

[0042]

[0043] In the formula, H2(f τ ,η t ) represents the range bending correction function; represents the second-order Doppler parameter estimate; η t Indicates the azimuth slow time after a step-by-step transformation.

[0044] Furthermore, constructing a matching function to focus imaging of a moving target according to the second-order Doppler parameter estimation value and the relocation information also includes:

[0045] According to the second-order Doppler parameter estimation, the azimuth compression function is constructed, and its expression is:

[0046]

[0047] In the formula, H3(τ,η t ) represents the azimuth compression function; τ represents the slow time.

[0048] The present invention has the following beneficial effects:

[0049] The invention provides a moving target imaging and relocation method based on a dual-base synthetic aperture radar. The method corrects the original echo signal through a second-order ladder transformation to provide high-quality original data, thereby reducing error propagation caused by signal distortion. The method constructs a parameter estimation and relocation model, solves the second-order Doppler parameter estimation value and relocation information according to the first-order Doppler parameter estimation value and the moving target distance information under different azimuth blocks, thereby avoiding the inefficient calculation process of repeated imaging iterations in the traditional method, converts the optimization problem into a problem of solving a nonlinear equation group, and replaces the original parameter estimation process of repeated imaging iterations with the solution of the nonlinear equation group. In addition, the moving target can be relocated synchronously in the process of estimating the imaging parameters, thereby greatly saving calculation resources and time costs and improving calculation efficiency. Through expansion, the moving positioning of multiple targets can be realized, which is convenient for tracking and guidance applications in complex environments, so that the moving targets can be quickly and accurately detected and positioned in complex environments, thereby improving the response speed of the dual-base SAR system to time-sensitive targets and enhancing its strike accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. 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 paying creative work.

[0051] Figure 1 A method flow chart of a moving target imaging and relocation method based on a bistatic synthetic aperture radar provided by an embodiment of the present invention;

[0052] Figure 2 A schematic flow chart of a moving target imaging and relocation method based on a bistatic synthetic aperture radar provided by an embodiment of the present invention;

[0053] Figure 3A schematic diagram of moving target detection by a bistatic synthetic aperture radar provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following is a detailed description of the specific implementation method, structure, features and effects of a moving target imaging and relocation method based on a bistatic synthetic aperture radar proposed by the present invention in combination with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0055] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0056] A specific scheme of a moving target imaging and relocation method based on a bistatic synthetic aperture radar provided by the present invention is described in detail below in conjunction with the accompanying drawings.

[0057] See also Figure 1 and Figure 2 As shown, an embodiment of the present invention provides a moving target imaging and relocation method based on a bistatic synthetic aperture radar, the method comprising:

[0058] Step S100: The bistatic synthetic aperture radar obtains the original echo signal of the moving target, and corrects the original echo signal based on a second-order ladder transformation;

[0059] Step S100 specifically includes:

[0060] Step S110: Obtain the position and speed information of the receiving station, the transmitting station, and the moving target, and extract the dual-base slant range history of the moving target at the target time; for details, see Figure 3 As shown, Figure 3 Medium V r Represents the receiving station speed, V r =[V rx V ry V rz ] T ; V t Indicates the transmitting station speed, V t =[V tx V ty V tz ] T ; P represents an arbitrary moving target within the beam illumination area of ​​the bistatic synthetic aperture radar. The speed of the moving target is expressed as v = [v x v y vz ] T , v x Represents the velocity component parameter of the moving target along the flight track; v z represents the velocity component parameter along the trajectory; v y Indicates the pitch speed of the moving target, generally v y =0;

[0061] Define the beam center moment, the location coordinate of the transmitting station is X t =(x t ,y t ,z t ) T , the receiving station's location coordinate is X r =(x r ,y r ,z r ) T , the position coordinates of the moving target are (x, y, z) T , the double base slant range history of the moving target at the target time can be expressed as:

[0062] R b (η) = R t (η)+R r (η)

[0063]

[0064] In the formula, R b (η) represents the dual-base slant range history of the moving target, that is, the sum of the distances from the transmitting station to the moving target and then to the receiving station; R t (η) represents the slant range from the transmitting station to the moving target; R r (η) represents the slant range from the receiving station to the moving target; η represents the azimuth slow time variable, η∈[-T s / 2,T s / 2], T s represents the synthetic aperture time; V t ′ V represents the relative motion vector between the transmitting station and the moving target; r ′ Represents the relative motion vector between the receiving station and the moving target; where:

[0065]

[0066] According to the dual-base slant range history of the moving target at the target time, the original echo signal received by the receiving station can be expressed as:

[0067]

[0068] Where s(τ,v) represents the original echo signal, τ represents the slow time in the range direction, η represents the slow time in the azimuth direction; σ(x,y,z) represents the scattering coefficient of the moving target; represents the rectangular function, T p represents the pulse width, and the rectangular function is used to limit the time range of the echo signal in the range direction; ω(η) represents the antenna pattern function in the azimuth direction; j represents the imaginary unit; k r represents the frequency modulation in the range direction; c represents the speed of light; f0 represents the center frequency of the radar;

[0069] The double base slant range history is expanded twice at η = 0, which can be expressed as:

[0070]

[0071] In the formula, R b0 Represents the dual-base slant range history of the moving target at the initial moment; R t0 Represents the slant range from the transmitting station to the moving target at the initial moment; R r0 Indicates the slant range from the receiving station to the moving target at the initial moment; where:

[0072] R b0 =R t0 +R r0

[0073]

[0074] The first-order Doppler parameters for constructing the dual-base slant range history can be expressed as:

[0075]

[0076] In the formula, R b1 Represents the first-order Doppler parameter, reflecting the rate of change of distance due to the speed of the moving target

[0077] The second-order Doppler parameters of the dual-base slant range history can be expressed as:

[0078]

[0079] In the formula, R b2 represents the second-order Doppler parameter, reflecting the nonlinear range walk, i.e., the range bending caused by target acceleration or relative motion;

[0080] Then the double base slant range history of the moving target can be expressed as:

[0081]

[0082] In this embodiment, since R b1 and R b2The velocity and position information of the moving target is contained in the data, so it is unknown; by accurately acquiring key information from all parties and constructing the dual-base slant range history and its related parameters, the foundation is laid for the entire moving target imaging and repositioning process. On the one hand, the detailed position and velocity information collection enables the radar system to fully grasp the detection scene situation and avoid result deviations caused by initial data errors. On the other hand, the dual-base slant range history and its derived first-order and second-order Doppler parameters concisely and accurately describe the target motion characteristics, quantify the performance of complex target motion in the distance dimension, and these parameters are directly integrated into the subsequent echo signal expression, model construction, and parameter solution links, which greatly improves the processing efficiency from raw data to target imaging and positioning, reduces unnecessary repeated trials and error correction processes, and improves the detection accuracy and response speed of the entire dual-base SAR system to moving targets.

[0083] Step S120: Calculate the Doppler center frequency and Doppler modulation rate of the moving target according to the dual-base slant range history of the moving target at the target time; specifically, calculate the Doppler center frequency and Doppler modulation rate of the moving target according to the dual-base slant range history R of the moving target at the target time. b (η), calculate the Doppler phase function of the moving target, which is expressed as:

[0084]

[0085] Where φ(η) represents the Doppler phase function of the moving target; f0 represents the center frequency of the radar; c represents the speed of light;

[0086] Then the Doppler phase function of the moving target is differentiated and η=0 is set to obtain the Doppler center frequency of the moving target, which can be expressed as:

[0087]

[0088] In the formula, f dc represents the Doppler center frequency of the moving target; λ represents the wavelength; d represents the differential operator; the Doppler center frequency of the moving target reflects the center frequency deviation of the moving target echo signal in the azimuth direction, and is an intuitive reflection of the target's moving speed in the echo frequency characteristics;

[0089] Then, the second-order derivative of the Doppler phase is calculated to obtain the Doppler modulation rate of the moving target:

[0090]

[0091] In the formula, f dr Indicates the Doppler modulation rate of a moving target; the Doppler modulation rate of a moving target describes the rate of change of the Doppler frequency with azimuth time, which is related to the second-order Doppler parameter R in the dual-base slant range process. b2It is associated with the wavelength λ and can reflect the echo frequency changes caused by more complex motion characteristics such as acceleration during target motion.

[0092] This embodiment performs a derivative operation on the Doppler phase function to extract the two key parameters of the moving target, the Doppler center frequency and the Doppler modulation frequency, from the phase perspective, providing a basis for subsequent imaging and relocation work. The Doppler center frequency can help distinguish targets of different speeds, and plays a key role in target detection and preliminary positioning, allowing the radar system to more accurately lock the frequency range of the target from complex echoes. The Doppler modulation frequency further describes the complexity of the target's motion, and can accurately correct the echo signal distortion caused by the target's motion, achieve precise focus imaging, and precise relocation. These two parameters together improve the accuracy and reliability of the entire dual-base synthetic aperture radar for imaging and relocation of moving targets, and improve the link from the echo signal to the acquisition of precise target information.

[0093] Step S130: Pulse compression is performed on the original echo signal to obtain a range frequency domain echo signal, which can be expressed as:

[0094]

[0095] In the formula, s1(f τ ,η) represents the distance frequency echo signal after pulse compression; From this formula, it can be seen that the distance frequency f τ It changes with the azimuth time η, which means that the distance of the target changes with time, that is, there is distance migration; b1 It is related to the speed of the moving target, but the speed of the moving target is unknown. Therefore, to remove the Doppler ambiguity of the moving target echo of the dual-base SAR, it is necessary to first estimate R b1 value; This step converts the original echo signal into a range frequency domain echo signal through pulse compression operation, realizes effective signal processing in the range dimension, improves the resolution of the radar system in the range dimension, and enables the subsequent more clear distinction of targets at different distances.

[0096] Step S140: Correct the echo signal in the range frequency domain by using a second-order trapezoidal transformation to obtain an echo signal after the second-order trapezoidal transformation; specifically, the expression of the second-order trapezoidal transformation is as follows:

[0097]

[0098] Where η t represents the azimuth slow time after the second-order ladder shape transformation; the azimuth slow time η in the range frequency domain echo signal is replaced by the azimuth slow time η after the second-order ladder shape transformation tThe purpose of substituting the expression of is to change the time representation of the signal in the azimuth direction, so as to realize the subsequent correction of problems such as range bending; after substituting the range frequency domain echo signal, the echo signal after the second-order ladder transformation is obtained, and its expression is:

[0099]

[0100] In the formula, s1(f τ ,η t ) represents the echo signal after the second-order transformation; f τ represents the distance frequency variable; η t represents the azimuth slow time after the second-order ladder transformation; j represents the imaginary unit; f0 represents the center frequency of the radar; R b0 Represents the dual-base slant range history of the moving target at the initial moment; R b1 represents the first-order Doppler parameter; R b2 represents the second-order Doppler parameter; c represents the speed of light; it can be understood that after the second-order trapezoidal transformation, the secondary coupling between the range frequency and the azimuth time domain has been removed, that is, the range curvature has been corrected, and only the linear range migration remains, and the migration curve of the moving target becomes a straight line in the range compression domain; the second-order trapezoidal transformation effectively corrects the nonlinear range movement, so that the migration curve of the target becomes a straight line in the range compression domain, thereby improving the imaging quality and target positioning accuracy.

[0101] Step S200: extracting the first-order Doppler parameter estimation value of the echo signal after the second-order trapezoidal transformation and the moving target distance information under different azimuth blocks;

[0102] Step S200 specifically includes:

[0103] Step S210: Based on Fourier transform, the echo signal after the second-order trapezoidal transform is converted to the two-dimensional time domain; specifically, the echo signal after the second-order trapezoidal transform is converted from the frequency domain to the time domain using the fast Fourier transform, and the fast Fourier transform operation is performed on the corresponding dimensions for the two-dimensional frequency domain signal (range frequency domain and azimuth slow time domain). In the range frequency domain dimension, FFT is performed along the range frequency direction to convert the range frequency information into the corresponding range time domain information, thereby realizing the mapping from the frequency domain to the time domain; at the same time, in the azimuth slow time domain dimension, the FFT operation is also performed to convert the frequency domain information of the azimuth slow time domain into the time domain information. In this process, according to the mathematical principles and algorithm flow of the fast Fourier transform, it is ensured that after the two-dimensional transformation, the moving target echo signal, which originally presents a complex migration curve in the frequency domain, can be transformed into a straight line in the two-dimensional time domain. This is because the fast Fourier transform can accurately convert the frequency domain characteristics of the signal into time domain characteristics, and based on a series of preprocessing of the echo signal in the previous steps, such as the second-order ladder transform, combined with the characteristics of the fast Fourier transform itself, the target range migration in the time domain presents a straight line form that is more conducive to subsequent analysis and processing; it simplifies the signal presentation, which is more conducive to the subsequent extraction of the first-order Doppler parameter estimation value of the moving target and the position information under different azimuth blocks.

[0104] Step S220: Estimate the slope of the migration curve of the moving target using Radon transform; specifically, obtain the echo signal in the two-dimensional time domain after processing in step S210 and whose migration curve becomes a straight line. This signal carries the information related to the target movement, and it is necessary to further explore the key feature of the slope of its migration curve to assist in the subsequent parameter estimation. The Radon transform can be expressed as:

[0105] Ra=∫f(x(u,v),y(u,v))dv

[0106] In the formula, Ra represents Radon transformation; this formula rotates the original rectangular coordinate system xoy along the origin by (180°-α) to obtain the new rectangular coordinate system uov, and then integrates parallel to the v axis with different u values ​​to obtain the result after Radon transformation. The conversion relationship between the coordinate systems is:

[0107]

[0108] In the formula, u represents the translation of the intercept v, that is, along; v represents the axis of the new rectangular coordinate system; α represents the rotation angle;

[0109] Then the Radon transform can be reformulated as:

[0110] Ra=∫f(-u cosα-v sinα,u sinα-v cosα)dv

[0111] Then, search and integrate along different intercepts u and rotation angles α, that is, within a certain range of values, traverse different combinations of u and α, perform integration operations on each combination according to the formula re-expressed by the above Radon transform, and obtain the corresponding Ra value; from which the rotation angle that makes Ra reach the maximum value is extracted as α max , at this time, the slope of the moving target migration curve can be expressed as:

[0112]

[0113] Wherein, k represents the slope of the moving target migration curve; this embodiment uses Radon transform to estimate the slope of the moving target migration curve, and the slope information reflects the key characteristics of the target motion under a specific geometric relationship, providing a basis for the subsequent accurate estimation of the first-order Doppler parameters.

[0114] Step S230: Calculate the first-order Doppler parameter estimation value according to the slope of the moving target migration curve, combined with the pulse repetition frequency and the signal baseband signal sampling rate; specifically, the first-order Doppler parameter estimation value can be expressed as:

[0115]

[0116] In the formula, represents the first-order Doppler parameter estimate; F s It represents the sampling rate of the baseband signal, and PRF represents the pulse repetition frequency of the system.

[0117] Step S240: performing azimuth block processing on the echo signal after the second-order trapezoidal transformation; specifically, in addition to the traditional target distance estimation, this embodiment also needs to estimate two distances of the moving target. Therefore, this embodiment divides the echo signal after the second-order trapezoidal transformation into three blocks in the azimuth slow time, and focuses the moving target at the time zero point of each block. The echo signal after the second-order trapezoidal transformation is in a space composed of a specific distance frequency domain and an azimuth slow time domain, and carries various complex information related to the target motion. According to the given synthetic aperture time and pulse repetition time (PRT) two known parameters related to the radar system, the slow time setting of each block is as follows:

[0118]

[0119] Among them, t s Indicates the slow time of the position after block division; T srepresents synthetic aperture time; PRT represents pulse repetition time; in the division process, the echo signal after the second-order ladder transformation is divided in the time dimension, so that each block corresponds to a specific azimuth slow time interval, which is equivalent to focusing the moving target on the time zero point of each block, so as to achieve more refined processing for each block and further estimate the distance of the moving target at different times; by performing block processing on the azimuth slow time, the time structure of the echo signal in the azimuth direction is changed, so that the characteristics of the moving target in different time periods can be analyzed more carefully in the subsequent process, which is convenient for additional estimation of the distance information corresponding to the moving target at different times, and improves the accuracy of the final imaging and positioning of the moving target.

[0120] Step S250: perform Doppler pre-filtering on the echo signal after the azimuth block using a pre-filtering function; specifically, the pre-filtering function can be expressed as:

[0121]

[0122] In the formula, H1(d τ ,t s ) represents the Doppler pre-filter function; f τ represents the distance frequency variable; t s Indicates the slow time of the position after block division; Represents the first-order Doppler parameter estimation value; the echo signal of each block is complex multiplied with the corresponding pre-filtering function value, that is, the phase and amplitude of the echo signal are adjusted according to the rule specified by the pre-filtering function, so as to realize the Doppler pre-filtering of the echo signal after each azimuth block, suppress unnecessary interference factors such as Doppler frequency shift components, and make the echo signal more conducive to subsequent further processing and target parameter extraction.

[0123] Step S260: Perform a first-step ladder transformation on the echo signal after Doppler pre-filtering; specifically, firstly, perform a first-step ladder transformation on the azimuth slow time t s Transform, the expression is:

[0124]

[0125] Where η t It represents the azimuth slow time after a step-by-step transformation;

[0126] Then, the echo form after a ladder transformation and sorting can be expressed as:

[0127]

[0128] In the formula, s4(f τ ,η t) represents the echo signal after a step-shaped transformation; it can be understood from this formula that the linear migration of the moving target has been corrected, and there is still a certain distance bending term. Therefore, the echo signal after a step-shaped transformation can be directly non-coherently accumulated to achieve coarse focusing of the moving target, which facilitates further fine focusing, precise imaging, and repositioning.

[0129] Step S270: Based on the echo signal after the first-step ladder shape transformation, the moving target of each block is detected by using the constant false alarm rate detection method to extract the moving target distance information; specifically, the echo signal after the first-step ladder shape transformation has been greatly optimized. The present embodiment uses the constant false alarm rate (CFAR) detection, and its purpose is to accurately identify the moving target signal from each azimuth block in a complex radar echo environment. Through the CFAR detection, the signal threshold can be adaptively determined according to a certain false alarm probability setting, and the real target echo can be distinguished from the noise and other interference signals, thereby realizing the accurate positioning and detection of the moving target in each block;

[0130] For the moving targets in each block, according to the known synthetic aperture time T s and positional slow time variables The azimuth slow time corresponding to each distance can be expressed as:

[0131]

[0132] In the formula, R b (i) represents the dual-base slant range history of the i-th moving target; R t (η i ) represents the azimuth slow time variable η i The slant range from the transmitting station to the moving target at 1:00:00; R r (η i ) represents the azimuth slow time variable η i The slant range from the receiving station to the moving target at time T s represents the synthetic aperture time;

[0133] exist At three specific moments, the position information of the moving target can be expressed as:

[0134]

[0135] Among them, X s express The moving target distance information; X represents η t = 0 moving target distance information; X e express The moving target distance information; ΔT represents the time interval, This embodiment uses a constant false alarm rate detection method to adaptively screen out real target echoes in a complex radar echo environment based on a reasonably set false alarm probability, and then accurately extracts the position information of each moving target block by accurately calculating the dual-base slant range history and using the position information expression at a specific moment, providing key target position data for the subsequent construction of parameter estimation and repositioning models, ensuring that the final imaging and positioning results can accurately reflect the actual state of the target.

[0136] Step S300: constructing a parameter estimation and relocation model, solving the second-order Doppler parameter estimation value and relocation information according to the first-order Doppler parameter estimation value and the moving target distance information under different azimuth blocks;

[0137] Step S310: According to the position and speed information of the moving target, the transmitting station and the receiving station, a nonlinear equation group is constructed based on the distance information of the moving target of each block; specifically, the expression of the nonlinear equation group is:

[0138]

[0139] Where X represents the position information of the moving target at the initial moment; X s express The position information of the moving target at any moment, T s represents the synthetic aperture time; X e express The position information of the moving target at any moment; X t represents the location information of the transmitting station at the initial moment, X t =(x t ,y t ,z t ) T ;X ts express The location information of the transmitting station at the moment, X ts =(x ts ,y ts ,z ts ) T ;X te express The location information of the transmitting station at the moment, X te =(x te ,y te ,z te ) T ;X r represents the location information of the receiving station at the initial moment, X r =(x r ,y r ,z r ) T ;X rs express The location information of the receiving station at any time, X rs =(x rs ,y rs ,z rs ) T ;X re express The location information of the receiving station at any time, X re =(x re ,y re ,z re ) T ; R b represents the bistatic slant distance at the initial moment; f dc Doppler center frequency; R bs express The bistatic slant distance at the moment; R be express The bistatic slant distance at time f dr represents the Doppler modulation frequency; λ represents the wavelength; V t ′ represents the velocity vector of the transmitting station; V r ′ represents the velocity vector of the receiving station; R t0 Indicates the reference position of the transmitting station; R r0 represents the reference position of the receiving station; where:

[0140]

[0141] This formula is constructed based on the geometric relationship between the target and the transmitting station and the receiving station in the bistatic radar. It reflects that the sum of the distances from the target to the transmitting station and the receiving station at the initial moment is equal to the bistatic slant distance at the initial moment, reflecting the spatial position relationship between the three from the distance dimension.

[0142]

[0143] This formula combines the relative speed relationship between the target and the transmitting station and the receiving station and the principle of the Doppler effect, and links the Doppler center frequency generated by the target movement with the relative position and speed of the target and each station. Through this equation, the corresponding relationship between the target movement characteristics and the echo frequency characteristics is constrained.

[0144]

[0145] This formula is for At that moment, it describes the dual-base slant distance between the target and the transmitting station and the receiving station at that moment, reflects the spatial position constraint relationship at that specific time point, and provides the distance conditions at different time points for the subsequent comprehensive description of the target's motion trajectory;

[0146]

[0147] This formula is for The dual-base slant range equation between the target and the transmitting and receiving stations constructed at all times further enriches the position and distance information constraints of the target at different times;

[0148]

[0149] This formula takes into account the deep relationship between the Doppler modulation frequency and the target motion. Based on operations such as the square of the target's velocity and the cube of the distance, the Doppler modulation frequency is associated with the target's position, velocity and the reference position of each station at different times. It is used to accurately describe the impact of the nonlinear characteristics of the target motion on the frequency modulation of the echo signal.

[0150] This embodiment makes full use of the various information obtained in the previous steps, carefully constructs a nonlinear equation group based on the physical principles and geometric relationships in radar detection, and builds a mathematical model foundation for the subsequent accurate solution of the second-order Doppler parameter estimation value and relocation information. The key elements such as the position, speed and frequency of the radar echo at different times of the target are associated and constrained in the form of equations, so that the entire imaging and relocation process of the moving target based on the dual-base synthetic aperture radar can deeply explore the target motion characteristics based on nonlinear mathematical relationships, thereby improving the accuracy and reliability of imaging and positioning. An extended range Doppler positioning equation group is constructed, and the motion parameter estimation problem is converted into an extended target position and velocity nonlinear equation group solution problem. For the unknown problem of frequency modulation, a search loop iteration method is adopted to solve it. Finally, according to the estimated parameters, the imaging and relocation of the moving target are completed. The whole process realizes parameter estimation and relocation synchronously, and there is no need to repeatedly iterate the imaging of the echo data, which improves the calculation efficiency.

[0151] Step S320: Estimate the initial Doppler modulation rate according to the acceleration effect of the moving target under the preset initial conditions; Specifically, to solve the nonlinear equation group of step S310, it is first necessary to clearly solve the five key parameters on the right side of the nonlinear equation group, namely, the three distance information R bs , R be , R b , Doppler center frequency f dc 、Doppler modulation frequency f dr , which can be expressed as:

[0152]

[0153] Among them, the initial Doppler modulation frequency information f dr0 The expression is:

[0154]

[0155] In the formula, f dr (0) Initial Doppler modulation rate information; R b2 (0) represents the acceleration effect of the moving target, that is, given the initial stationary state of the target (v x ,v z )=0、(x,y,z)=X ref Under the condition of , the initial conditions for starting the solution of the nonlinear equations obtained by velocity vector and distance calculation;

[0156] Step S330: Iteratively solve the nonlinear equations and output second-order motion parameters and relocation information;

[0157] Step S330 specifically includes:

[0158] Step S331: construct a Jacobian matrix and convert it into an inverse matrix, and use the Jacobian inverse matrix to correct the current target parameter estimate to obtain a corrected target parameter estimate; specifically, this embodiment uses the Newton iterative equations to solve:

[0159]

[0160] In the formula, is the inverse matrix of the Jacobian matrix of the nonlinear equation system; F(X k ) represents the function value vector obtained by substituting the current estimate into the nonlinear equation system; X k represents the target parameters of the kth iteration, including position and velocity components; X k+1 represents the target parameter of the k+1th iteration. The iteration process continuously corrects X k Approach the true solution and gradually optimize the solution using the current estimate and the characteristics of the nonlinear equations; the Jacobian matrix is ​​defined as:

[0161]

[0162] In the formula, Represents the Jacobian matrix; it is a 5×5 matrix whose elements Represents the partial derivative of the i-th equation in the nonlinear equation system with respect to the j-th target parameter, i = 1, 2, 3, 4, 5, j = x, y, z, v x ,v z , which is used to measure the sensitivity of each equation to the change of the target parameter. In the Newton iteration method, its inverse matrix It plays a key guiding role, guiding the iteration direction according to the deviation of the current estimated value, so that the estimated value of the next iteration is closer to the true solution;

[0163] Step S332: updating the first-order Doppler parameter estimation value and the second-order Doppler parameter estimation value according to the corrected target parameter estimation value;

[0164] Step S333: outputting the second-order Doppler parameter estimation value and the relocation information according to the preset iteration termination condition; specifically, in order to ensure the convergence and solution accuracy in the iteration process, the present embodiment sets the iteration termination condition and the convergence condition respectively, wherein the expression of the iteration termination condition is:

[0165] ‖F(X k+1 )-F(X k )‖2≤ε

[0166] Where ε is a given error limit, preferably ε = 10e-6, which is used to measure the difference in function value vectors obtained after two consecutive iteration results are substituted into the nonlinear equation system. k+1 )-F(X k )‖2≤ε, the iteration is close to convergence from the perspective of the stability of the solution of the overall system of equations;

[0167] The expression of the convergence condition is:

[0168] |R b2 (k+1)-R b2 (k)|≤ε1

[0169] Where ε1 is the given convergence threshold;

[0170] Based on R b2 (0), we can solve a set of moving target parameters, which can be expressed as:

[0171] P X (0)=(x(0),y(0),z(0),v x (0),v z (0)) T ;

[0172] The iterative update formula can be expressed as:

[0173]

[0174] In each iteration, we first calculate the estimated value of the current target parameter (P X (k-1)), calculate R b1 (k), R b1 (k), the estimated value of the target parameter is continuously updated through these two parameters, and this cycle is repeated until the set convergence threshold is finally met, achieving R b2The high-precision estimation and acquisition of key parameters of the moving target are realized, so as to realize the relocation of the moving target and the accurate estimation of the parameters, and provide data for subsequent target imaging, tracking and monitoring, etc. It should be noted that as long as one of the convergence condition and the iteration termination condition is not met, the steps S331 and S332 are repeated for the next round of iteration; when both conditions are met, the iteration is considered to have converged, and the second-order Doppler parameter estimation value R is output at this time. b2 As well as repositioning information (key parameter information such as the final target position and speed), these output results can provide an accurate data basis for subsequent applications such as moving target imaging, tracking and monitoring.

[0175] This embodiment uses the Newton iteration method to construct the Jacobian matrix and perform iterative solution, uses the inverse of the Jacobian matrix to correct the target parameter estimation value, and continuously updates and judges the iteration result according to the set iteration termination condition and convergence condition, thereby achieving high-precision solution of the second-order Doppler parameter estimation value and relocation information. This provides accurate and reliable key parameters for the entire imaging and relocation process of moving targets based on dual-base synthetic aperture radar, so that subsequent imaging can clearly focus on the target, and relocation can accurately determine the target position, greatly improving the accuracy and effectiveness of the entire radar system for detecting, positioning and imaging moving targets.

[0176] Step S400: constructing a matching function to focus and image the moving target according to the second-order Doppler parameter estimation value and the relocation information;

[0177] Step S400 specifically includes:

[0178] Step S410: construct a global Doppler pre-filtering function according to the first-order Doppler parameter estimation value, and its expression is:

[0179]

[0180] In the formula, H1(f τ ,η) represents the global Doppler pre-filtering function; j represents the imaginary unit; f τ represents the range frequency variable; f0 represents the center frequency of the radar; Represents the first-order Doppler parameter estimation value; η represents the azimuth slow time variable; c represents the speed of light; Specifically, the global Doppler pre-filtering function is used to perform Doppler pre-filtering on the echo signal. It uses an exponential function to combine the first-order Doppler parameter estimation value, the azimuth slow time variable, the radar center frequency, the speed of light and other parameters to construct a phase modulation function related to the original echo signal frequency and azimuth time; The global Doppler pre-filtering function is based on the Doppler pre-filtering function H1(f τ ,η) as the starting point, within the given range of azimuth time η, for different distance frequencies f τThe corresponding phase value is calculated by taking the value; the original echo signal is exponentially multiplied with the phase value to realize the phase rotation of the original echo signal, thereby preliminarily offsetting the influence of Doppler frequency shift caused by the speed of the moving target. In this way, the moving target signal can be preliminarily screened out from the complex original echo signal, which can reduce noise and other interference signal components;

[0181] Step S420: construct a range curvature correction function according to the second-order Doppler parameter estimation value, and its expression is:

[0182]

[0183] In the formula, H2(f τ ,η t ) represents the range bending correction function; represents the second-order Doppler parameter estimate; η t Represents the azimuth slow time after a first-order trapezoidal transformation; Specifically, the range curvature correction function is used to correct the range curvature phenomenon caused by factors such as target motion, radar system geometry, and electromagnetic wave propagation characteristics; The exponential function is based on the second-order Doppler parameter estimate Key position time η t And the distance frequency f τ , speed of light c and other parameters, and calculate the phase value used to correct the distance curvature. The echo signal after Doppler pre-filtering in step S410 is exponentially multiplied with the corrected phase value again at the corresponding key azimuth moment to compensate for the signal phase distortion caused by the distance curvature. In this process, based on the phase correction, the curved trajectory of the echo signal of the moving target in the distance direction caused by various factors is gradually corrected, and the real distance information of the moving target is restored, thereby improving the ability to distinguish the target in the distance dimension during subsequent imaging, so that the imaging result can more accurately reflect the actual position and shape of the target in the distance direction.

[0184] Step S430: construct an azimuth compression function according to the second-order Doppler parameter estimation value, and its expression is:

[0185]

[0186] In the formula, H3(τ,η t ) represents the azimuth compression function; τ represents the slow time; Specifically, the azimuth compression function is used to compress and focus the target echo in the azimuth direction, and at the key azimuth moment η t , combined with f0 and light speed c and other parameters are used to calculate the phase value required for azimuth compression for the azimuth echo data corresponding to the slow time τ; the echo signal after the distance bending correction in step S420 is exponentially multiplied with the phase value in the azimuth direction to achieve energy focusing of the target echo in the azimuth direction. By adjusting the phase to change the energy distribution of the echo signal in the azimuth direction, the energy originally dispersed in a certain azimuth range will gradually converge according to the phase adjustment to achieve energy focusing of the target echo in the azimuth direction, so that the signal strength of the target in the azimuth direction is enhanced, and finally the precise focusing imaging and repositioning processing of the moving target is achieved, so that the imaging result can clearly show the key information such as the position and shape of the target in the azimuth direction, and provide high-quality image data and accurate target position information for subsequent advanced applications such as target recognition, tracking and monitoring.

[0187] In summary, the imaging and relocation method of moving targets based on bistatic synthetic aperture radar firstly accurately obtains and corrects the original echo signal, effectively removes many interference factors in the signal and distortion caused by complex target motion, such as range bending and Doppler frequency shift, thereby improving the quality of the echo signal. Then, by accurately extracting the first-order and second-order Doppler parameter estimates of the moving target and the position information under different azimuth blocks, the constructed parameter estimation and relocation model is used to obtain high-precision second-order Doppler parameter estimates and relocation information through iterative solution, thus achieving deep insight into the target motion state, and transforming the motion parameter estimation problem into the problem of solving the extended target position and velocity nonlinear equations. For the unknown problem of modulation frequency, the search loop iteration method is used to solve it. Finally, the imaging and relocation of the moving target are completed according to the estimated parameters. The entire process achieves parameter estimation and repositioning simultaneously, and there is no need for repeated iterative imaging of the echo data, which improves the computing efficiency while ensuring the accuracy of positioning. It provides high-quality image data and precise target position information for subsequent advanced applications such as target recognition, tracking and monitoring, and greatly expands the ability of dual-base synthetic aperture radar to detect, image and locate moving targets in complex environments.

[0188] It should be noted that the sequence of the above embodiments of the present invention is only for description and does not represent the advantages and disadvantages of the embodiments. The processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0189] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

Claims

1. A moving target imaging and relocation method based on a bistatic synthetic aperture radar, characterized in that: The method comprises: The bistatic synthetic aperture radar obtains the original echo signal of the moving target and corrects the original echo signal based on the second-order ladder transformation; Extract the first-order Doppler parameter estimation value of the echo signal after the second-order trapezoidal transformation and the moving target distance information under different azimuth blocks; Construct parameter estimation and relocation model, solve the second-order Doppler parameter estimation and relocation information according to the first-order Doppler parameter estimation and moving target distance information in different azimuth blocks; According to the second-order Doppler parameter estimation and relocation information, a matching function is constructed to perform focused imaging on the moving target.

2. The moving target imaging and relocation method based on bistatic synthetic aperture radar as claimed in claim 1, characterized in that: The bistatic synthetic aperture radar obtains the original echo signal of the moving target, and the correction of the original echo signal based on the second-order ladder transformation includes: Obtain the position and speed information of the receiving station, transmitting station and moving target, and extract the dual-base slant range history of the moving target at the target moment; Calculate the Doppler center frequency and Doppler modulation frequency of the moving target according to the dual-base slant range history of the moving target at the target moment; Perform pulse compression on the original echo signal to obtain a range frequency domain echo signal; The echo signal in the range frequency domain is corrected by using the second-order ladder shape transformation to obtain the echo signal after the second-order ladder shape transformation.

3. The moving target imaging and relocation method based on bistatic synthetic aperture radar as claimed in claim 1, characterized in that: Extracting the first-order Doppler parameter estimation value of the echo signal after the second-order trapezoidal transformation and the moving target distance estimation value under different azimuth blocks includes: The echo signal after the second-order ladder transformation is converted into a two-dimensional time domain based on Fourier transformation; Estimate the slope of the moving target migration curve using Radon transform; The first-order Doppler parameter estimation value is calculated based on the slope of the moving target migration curve combined with the pulse repetition frequency and the signal baseband signal sampling rate.

4. The moving target imaging and relocation method based on bistatic synthetic aperture radar as claimed in claim 1, characterized in that: Extracting the first-order Doppler parameter estimation value of the echo signal after the second-order trapezoidal transformation and the moving target distance estimation value under different azimuth blocks also includes: Performing azimuth block processing on the echo signal after the second-order ladder transformation; Doppler pre-filtering is performed on the echo signal after azimuth block using a pre-filtering function; Performing a first-step ladder transformation on the echo signal after Doppler pre-filtering; Based on the echo signal after the first-step ladder transformation, the constant false alarm rate detection method is used to detect the moving targets in each block and extract the distance information of the moving targets.

5. The moving target imaging and relocation method based on bistatic synthetic aperture radar as claimed in claim 1, characterized in that: Constructing a parameter estimation and relocation model, solving the second-order Doppler parameter estimation and relocation information based on the first-order Doppler parameter estimation and the moving target distance information under different azimuth blocks includes: According to the position and speed information of the moving target, the transmitting station and the receiving station, a nonlinear equation group is constructed based on the distance information of the moving target in each block; Estimating the initial Doppler modulation rate according to the acceleration effect of the moving target under the preset initial conditions; Iteratively solves the nonlinear equations and outputs second-order motion parameters and relocation information.

6. The moving target imaging and relocation method based on bistatic synthetic aperture radar according to any one of claims 1 to 5, characterized in that: The expression of the nonlinear equation system is: Where X represents the position information of the moving target at the initial moment; X s express The position information of the moving target at any moment, T s represents the synthetic aperture time; X e express The position information of the moving target at any moment; X t represents the location information of the transmitting station at the initial moment, X t =(x t ,y t ,z t ) T ;X ts express The location information of the transmitting station at the moment, X ts =(x ts ,y ts ,z ts ) T ;X te express The location information of the transmitting station at the moment, X te =(x te ,y te ,z te ) T ;X r represents the location information of the receiving station at the initial moment, X r =(x r ,y r ,z r ) T ;X rs express The location information of the receiving station at any time, X rs =(x rs ,y rs ,z rs ) T ;X re express The location information of the receiving station at any time, X re =(x re ,y re ,z re ) T ; R b represents the bistatic slant distance at the initial moment; f dc Doppler center frequency; R bs express The bistatic slant distance at the moment; R be express The bistatic slant distance at time f dr represents the Doppler modulation frequency; λ represents the wavelength; V t ′ represents the velocity vector of the transmitting station; V r ′ represents the velocity vector of the receiving station; R t0 Indicates the reference position of the transmitting station; R r0 Indicates the reference position of the receiving station.

7. The moving target imaging and relocation method based on bistatic synthetic aperture radar as claimed in claim 6, characterized in that: Constructing a parameter estimation and relocation model, solving the second-order Doppler parameter estimation and relocation information based on the first-order Doppler parameter estimation and the moving target distance information under different azimuth blocks also includes: Construct a Jacobian matrix and convert it into an inverse matrix, use the Jacobian inverse matrix to correct the current target parameter estimate, and obtain the corrected target parameter estimate; According to the corrected target parameter estimation value, the first-order Doppler parameter estimation value and the second-order Doppler parameter estimation value are updated; According to the preset iteration termination condition, the second-order Doppler parameter estimation value and relocation information are output.

8. The moving target and relocation method based on bistatic synthetic aperture radar as claimed in claim 6, characterized in that: According to the second-order Doppler parameter estimation value and relocation information, a matching function is constructed to focus the moving target for imaging, including: The global Doppler pre-filtering function is constructed based on the first-order Doppler parameter estimation value, and its expression is: In the formula, H1(f τ ,η) represents the global Doppler pre-filtering function; j represents the imaginary unit; f τ represents the range frequency variable; f0 represents the center frequency of the radar; represents the first-order Doppler parameter estimate; η represents the azimuth slow time variable; c represents the speed of light.

9. The moving target and relocation method based on bistatic synthetic aperture radar as claimed in claim 8, characterized in that: According to the second-order Doppler parameter estimation value and relocation information, constructing a matching function to focus imaging of a moving target also includes: According to the second-order Doppler parameter estimation, the range bending correction function is constructed, and its expression is: In the formula, H2(f τ ,η t ) represents the range bending correction function; represents the second-order Doppler parameter estimate; η t Indicates the azimuth slow time after a step-by-step transformation.

10. The moving target and relocation method based on bistatic synthetic aperture radar as claimed in claim 9, characterized in that: According to the second-order Doppler parameter estimation value and relocation information, constructing a matching function to focus imaging of a moving target also includes: According to the second-order Doppler parameter estimation, the azimuth compression function is constructed, and its expression is: In the formula, H3(τ,η t ) represents the azimuth compression function; τ represents the slow time.

Images