A multi-objective particle swarm optimization based multi-baseline SAR space configuration design method

Abstract

The application discloses a multi-target particle swarm optimization-based multi-base SAR space configuration design method, which comprises the following steps: firstly, setting multi-base SAR space configuration design parameters, modeling a multi-base SAR echo model, and then performing multi-base SAR imaging wave number spectrum analysis; secondly, modeling a space configuration optimization design problem, inputting space configuration optimization design problem system parameters and configuration parameters, initializing MOPSO, then updating the speed and position of the particle swarm, and finally outputting the optimized configuration through iterative updating. The method of the application converts the space configuration design problem into a constrained multi-target optimization problem, introduces a multi-target particle swarm optimization algorithm for solving, realizes high-resolution imaging through the optimized space configuration, breaks through the strict limitation of the multi-base SAR space configuration, and can complete the optimization design of the relative positions and flight speed directions of multiple radar platforms under certain time and system resource conditions, so that higher-resolution images can be obtained within a certain observation time.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to a multi-base SAR spatial configuration design method based on multi-target particle swarm optimization. Background Technology

[0002] The imaging quality of airborne SAR can be improved within a shorter observation time by increasing the number of radar platforms and coherently fusing multiple measurement results—this is known as coherent multi-base airborne SAR. It plays a crucial role in reconnaissance, collaborative search and rescue, and topographic surveying. In multi-base SAR systems, in addition to time and spatial synchronization of multiple radar platforms, high-resolution imaging can also be achieved through appropriate spatial configurations.

[0003] Existing spatial configuration design methods for multi-base SAR systems are mainly divided into analytical methods and optimization methods. Regarding analytical methods, the literature "J. Zhu, D. Mao, Y. Zhang, Y. Zhang, Y. Huang, and H. Yang, 'A topology design method based on wavenumber spectrum generation for multistatic synthetic aperture radar,'" in 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, 2021, pp. 5453–5456, generates spatial configurations based on wavenumber spectra to improve imaging resolution. However, this method typically cannot quantitatively evaluate the advantages and disadvantages of spatial configurations.

[0004] In addition, some optimization-based methods have been proposed to improve resolution. The paper “H. An, J. Wu, Z. Sun, J. Yang, Y. Huang, and H. Yang, “Topology design for geosynchronous spaceborne–airborne multistatic SAR,” IEEE Geoscience and Remote Sensing Letters, vol. 15, no. 11, pp. 1715–1719, 2018” proposes a spatial configuration design method to achieve optimal spatial resolution by appropriately adjusting the imaging spatial configuration. The paper “D. Mao, Y. Zhang, J. Pei, W. Huo, Y. Zhang, Y. Huang, and J. Yang, “Forward-looking geometric configuration optimization design for spaceborne-airborne multistatic synthetic aperture radar,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing Letters, vol. 15, no. 11, pp. 1715–1719, 2018” proposes a spatial configuration design method to achieve optimal spatial resolution by appropriately adjusting the imaging spatial configuration. The paper "Sensing, vol.14, pp.8033–8047, 2021" transforms the geometric configuration design problem into a multi-objective optimization problem and uses optimization algorithms to obtain a feasible configuration design solution set. This method can obtain high-quality front view images in a shorter observation time. However, when the spatial configuration is constrained, the above method is difficult to plan spatial configurations that are conducive to high-quality imaging results. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a multi-base SAR spatial configuration design method based on multi-target particle swarm optimization. Under certain time and system resource conditions, this method optimizes the design of the multi-base SAR spatial configuration, enabling the acquisition of higher resolution images in the shortest possible time.

[0006] The technical solution adopted in this invention is: a multi-base SAR space configuration design method based on multi-target particle swarm optimization, the specific steps of which are as follows:

[0007] Step 1: Set the design parameters for the multi-base SAR space configuration;

[0008] Step 2: Multi-base SAR echo modeling;

[0009] Step 3: Perform multi-base SAR imaging wavenumber spectrum analysis based on the echo model from Step 2;

[0010] Step 4: Modeling the spatial configuration optimization design problem;

[0011] Step 5: Input system parameters and configuration parameters for the spatial configuration optimization design problem;

[0012] Step 6: Initialize MOPSO;

[0013] Step 7: Update the velocity and position of the particle swarm;

[0014] Step 8: After iterative updates based on Step 7, output the optimized configuration.

[0015] Furthermore, step one is specifically as follows:

[0016] All parameters that need to be designed in the spatial configuration design problem are represented by the vector l = (Δx) n ,Δy n ,Δz n ,θ TR1 ,θ vn )express.

[0017] Where, Δx n ,Δy n ,Δz n θ represents the distance between the nth (n = 2, 3, ..., N) receiver and the main receiver along the X, Y, Z axes. TR1 θ represents the angle between the transmitter and the main receiver. vn The velocity deviation angle represents the angle between the velocity direction of the nth receiver and the negative direction of the Y-axis.

[0018] Furthermore, step two is detailed as follows:

[0019] According to the geometric model of a multi-base SAR system, the transmitter transmits a linear frequency modulated signal. For the nth (n = 1, 2, ..., N) receiver, the echo s from the target point P is... n (t,τ) is represented as:

[0020]

[0021] Where t represents the range time variable (faster), τ represents the azimuth time variable (slower), A represents the amplitude of the echo signal, and T... a c represents the synthetic aperture time and electromagnetic wave velocity, respectively, and T represents the time to synthesize the aperture and the electromagnetic wave velocity. r K represents the pulse width. r f represents the frequency modulation slope. c R represents the carrier frequency of the transmitted signal. nP (τ) represents the distance history of the target point P.

[0022] By coherently projecting the echoes from all receivers in a multi-base SAR system onto the wavenumber domain, the fused wavenumber spectrum is represented as:

[0023]

[0024] Wherein, s(k x ,k y ) represents the wavenumber spectrum, k x ,k y A' represents the projection coordinate axis of the echo onto the beam domain. n k represents the normalized amplitude of the wavenumber spectrum. xn (f t ,τ) and k yn (f t ,τ) are determined by the frequency of the transmitted signal and the spatial position of the radar platform, and represent the echo signal received by the nth receiver after being projected into the wavenumber domain, k and k respectively. x and k y Spatial frequency variable of direction, f t Ω represents the frequency variable. n This represents the coverage area of ​​the wavenumber spectrum formed by the transmitter and the nth receiver, which is approximately a parallelogram-shaped region in the wavenumber domain.

[0025] According to the matrix Fourier transform, the point spread function is expressed as:

[0026]

[0027] Where σ(x,y) represents the scattering coefficient of the target point, x,y represent the coordinates of the target point, and Ω represents the coverage of all wavenumber spectra in the multi-base SAR system.

[0028] Furthermore, step three is detailed as follows:

[0029] The wavenumber spectrum distributions of the main receiver and the nth (n = 1, 2, ..., N) receiver are selected for analysis;

[0030] Where, k vn ,k un Let Q1ABC and Q be vectors corresponding to two adjacent sides of the parallelogram of wavenumber spectrum formed by the nth receiver. n DEF represent the vertices of the parallelogram of wavenumber spectra formed by the main receiver and the nth receiver, respectively. Let k represent vectors respectively. v1 ,k u1 Sum vector k vn ,k un The included angle between them; several intermediate variables of the master receiver and slave receiver are defined as follows:

[0031]

[0032]

[0033] Where, α T ,α R1 θ represents the elevation angle of the transmitter and the main receiver, respectively. T ,θ R1 R1 and R2 represent the azimuth angles of the transmitter and main receiver, respectively. n ,R T These represent the distances from the main receiver, the nth receiver, and the transmitter to the center of the observation scene, respectively; v T v1, v n V represents the speeds of the transmitter, the main receiver, and the nth receiver, respectively; Tx ,v Ty These represent the velocity components of the transmitter along the X and Y axes, respectively; v 1x ,v 1y x1 and y1 represent the velocity components of the main receiver along the X and Y axes, respectively; x1 and y1 represent the coordinates of the main receiver.

[0034] Wavenumber spectrum parallelogram Q n The starting vertex of (n = 1, 2, ..., N) is represented as:

[0035]

[0036] Where B represents the bandwidth of the transmitted signal.

[0037] Q n The distribution of the wavenumber spectrum parallelogram in the wavenumber domain is determined by (n = 2, ..., N). Taking it as a vertex, the vectors corresponding to two adjacent sides of the wavenumber spectrum parallelogram formed by the transmitter and a certain receiver are expressed as follows:

[0038]

[0039] Vector k un and k vn The included angle between them corresponds to the included angle between two adjacent sides of the wavenumber spectrum parallelogram, and is expressed as:

[0040]

[0041] The vectors corresponding to two adjacent sides of the parallelogram of the wavenumber spectrum formed by the echo from the main receiver are k. v1 and k u1 Choose vector k v1 The direction is used as the new projected coordinate system k u Okay v Chinese K u The positive directions of the coordinate axes; the new projected coordinate system ku Okay v It can be seen as k x Okay y The result of rotating γ, specifically γ is:

[0042]

[0043] Where β represents vector k v1 With k x The angle between the coordinate axes.

[0044] For the nth receiver, the wavenumber spectrum is in ψ i The projected slice in the direction is represented as:

[0045]

[0046] Among them, (k r ,ψ) represents the polar coordinates of the projected wavenumber spectrum, k r s represents the polar radius at a point on the projected wavenumber spectrum; n (k xn ,k yn ) represents the wavenumber spectrum of the echo generated by the nth receiver; k xn and k yn This indicates that the echo signal received by the nth receiver, after being projected into the wavenumber domain, appears in the wavenumber domain k. x and k y The spatial frequency variable of the direction; δ(·) represents the Dirac delta function.

[0047] The nth receiver is at ψ i The coherent imaging profile in the direction is represented as:

[0048]

[0049] Where, σ profile (r,ψ) represents the point spread function, where r represents the relative distance between the point and the selected reference point O; K represents the variable k. r The range of values ​​for is specifically as follows: k cn B represents the center of the distribution range of the wavenumber spectrum variable formed by the nth receiver. kn This indicates that the wavenumber spectrum formed by the nth receiver is in the direction ψ. i The projection bandwidth, when ψ i =γ indicates that at k u The projection bandwidth along the positive direction of the coordinate axis.

[0050] When the wavenumber spectrum formed by the master and slave receivers is in k u When the projections along the positive axes overlap, the point spread function corresponding to the wavenumber spectrum will not exhibit main lobe splitting.n Let Δk represent the wavenumber spectrum centers formed by the main receiver and the nth receiver, respectively. c(1,n) =||O1′O n ′|| indicates that the centers of the two wavenumber spectra are at k in the projected coordinate system. u The projected lengths along the positive axes, O1′, O n ′ represent O1 and O respectively. n In k u Projection along the positive direction of the coordinate axes, B k1 B kn These represent the wavenumber spectra formed by the main receiver and the nth receiver at k, respectively. u The projection bandwidth along the positive direction of the coordinate axes; when the wavenumber spectrum formed by the master and slave receivers is in k u When the projections along the positive axes of the coordinate system are separated, HIJK represents the vertex of the possible location of the parallelogram wavenumber spectrum of the nth receiver. gap Indicates the width of the missing data. Let Δk represent the maximum width of the missing data. c(1,n) The calculation formula is:

[0051] Δk c(1,n) =l gap +(B k1 +B kn ) / 2 (12)

[0052] l gap The following relationship must be satisfied:

[0053]

[0054] in, This represents the minimum value of the wavenumber spectrum projection bandwidth.

[0055] Projected bandwidth of wavenumber spectrum and l gap The effect of the width on image quality can be shown by the peak sidelobe ratio (PSLR) of the point spread function, expressed as:

[0056]

[0057] in, Indicates by and l gap The kernel function is determined by the relative width of the kernel.

[0058] Furthermore, step four is detailed as follows:

[0059] The spatial configuration optimization design problem can be established as follows:

[0060]

[0061] Where θ(l) reflects the orthogonality of the two resolution directions of the point spread function. The angle between two adjacent sides of the wavenumber spectrum parallelogram is represented; D(l) reflects the consistency of the wavenumber spectrum data along the distance direction, and d1(l) and d n (l) represents the projected bandwidth of the wavenumber spectrum of the main receiver and the nth receiver in the distance direction, respectively; η(l) reflects the length difference between the projected bandwidths of the wavenumber spectrum in the two directions, ∑B u (l) and ∑B v (l) represents the projections of all wavenumber spectra onto the azimuth and range directions, respectively. |v n | represents the speed amplitude of the nth receiver. This indicates the maximum speed limit for the drone. Δk c(1,2) (l) indicates that the wavenumber spectral center corresponding to the main receiver and the wavenumber spectral center corresponding to the second receiver are at k u Projected length in the direction, Δk c(N-1,N) (l) represents the wavenumber spectral center corresponding to the (N-1)th receiver and the wavenumber spectral center corresponding to the Nth receiver at k. u Projected length in the direction, This represents the maximum gap width that ensures the main lobe of the point spread function does not split. This represents the gap width between the center of the wavenumber spectrum of the main receiver and the nth (n = 2, 3, ..., N) receiver when the sidelobe of the point spread function is -3 dB. Ψ represents the search space for all parameters that need to be designed.

[0062] Furthermore, in step five, the parameters that need to be input in the optimization problem include: system parameters and configuration design parameters of the optimization problem.

[0063] Furthermore, step six is ​​detailed as follows:

[0064] First, initialize the population P = [p1, p2, ..., p L ], L represents the number of particles; secondly, the initial velocity u of each particle is set. l =0 and initial position p l =random(lb,ub), where lb and ub represent the lower and upper bounds of the particle position distribution range; then, each particle in the population P is evaluated by calculating the objective function and the repository REP is updated. At the same time, the historical best value reached by each particle is initialized and recorded. And store it in REP; finally, set the maximum number of iterations i. max .

[0065] Furthermore, step seven is detailed as follows:

[0066] In each iteration, the velocity u of each particle is updated according to the following expression. l :

[0067]

[0068] in, Let w represent the velocity in the current iteration and the velocity in the previous iteration, respectively. w∈[0,1] represents the inertia weight, c1,c2∈[0,1] are acceleration coefficients, and r1,r2 are random numbers between [0,1]. This represents the globally optimal particle selected from REP up to the current iteration number. l This represents the current position of the l-th particle.

[0069] Update the position p of each particle according to the following expression. l The particle position is updated by adding the particle velocity generated in the previous step to the previous position:

[0070]

[0071] in, These represent the current and previous positions during the iteration process, respectively, based on the current particle position p. l With the best historical particle Obtain the new historical best particle. Re-evaluate every particle in the population P and update REP until the maximum number of iterations i is reached. max When the iteration process stops, the iteration process is stopped.

[0072] Furthermore, step eight is detailed as follows:

[0073] After completing step seven, the iterative update step, outputs the final non-dominated solution set in REP.

[0074] A comprehensive performance evaluation of each objective function is performed by defining an evaluation function f(l).

[0075]

[0076] The beneficial effects of this invention are as follows: First, the method of this invention sets the spatial configuration design parameters for multi-base SAR, performs multi-base SAR echo modeling, and then performs multi-base SAR imaging wavenumber spectrum analysis. Next, it models the spatial configuration optimization design problem, inputting the system parameters and configuration parameters of the spatial configuration optimization design problem, initializing MOPSO, updating the velocity and position of the particle swarm, and finally outputting the optimized configuration after iterative updates. This invention transforms the spatial configuration design problem into a constrained multi-objective optimization problem and introduces a multi-objective particle swarm optimization algorithm for solving it. Through the optimized spatial configuration, high-resolution imaging is achieved, breaking through the strict limitations of multi-base SAR spatial configuration. Under certain time and system resource conditions, it can complete the optimization design of the relative spatial positions and flight velocity directions of multiple radar platforms, achieving higher resolution images within a certain observation time. Attached Figure Description

[0077] Figure 1 This is a flowchart of a multi-base SAR spatial configuration design method based on multi-target particle swarm optimization according to the present invention.

[0078] Figure 2 This is a flowchart of the multi-objective particle swarm optimization algorithm in an embodiment of the present invention.

[0079] Figure 3 This is a geometric observation model diagram of the multi-base SAR system in an embodiment of the present invention.

[0080] Figure 4 This is a wavenumber spectrum distribution diagram of the main receiver and the nth receiver in an embodiment of the present invention.

[0081] Figure 5 This is a distribution diagram of the wavenumber spectra of the main receiver and the nth receiver when they overlap in an embodiment of the present invention.

[0082] Figure 6 This is a distribution diagram of the wavenumber spectrum separation of the main receiver and the nth receiver in an embodiment of the present invention.

[0083] Figure 7 This is a non-dominated solution set diagram for spatial configuration optimization in an embodiment of the present invention.

[0084] Figure 8 This is an optimized spatial configuration and flight path diagram of the radar platform under the "one launch, two receive" scenario in this embodiment of the invention.

[0085] Figure 9 The images show the wavenumber spectra and point target imaging effects of three spatial configurations in this embodiment of the invention.

[0086] Figure 10 These are imaging results for three spatial configurations in embodiments of the present invention.

[0087] Figure 11 The images show the imaging performance of three spatial configurations in the embodiments of the present invention. Detailed Implementation

[0088] This invention uses simulation experiments to demonstrate the effectiveness of the proposed method. All steps and conclusions of this invention are verified on the Matlab2021 simulation platform. In order for those skilled in the art to understand the invention, the invention will be further described below with reference to the accompanying drawings and embodiments.

[0089] like Figure 1 The flowchart of a multi-base SAR space configuration design method based on multi-target particle swarm optimization according to the present invention is shown below. The specific steps are as follows:

[0090] Step 1: Set the design parameters for the multi-base SAR space configuration;

[0091] Step 2: Multi-base SAR echo modeling;

[0092] Step 3: Perform multi-base SAR imaging wavenumber spectrum analysis based on the echo model from Step 2;

[0093] Step 4: Modeling the spatial configuration optimization design problem;

[0094] Step 5: Input system parameters and configuration parameters for the spatial configuration optimization design problem;

[0095] Step 6: Initialize MOPSO (Multi-Objective Particle Swarm Optimization);

[0096] Step 7: Update the velocity and position of the particle swarm;

[0097] Step 8: After iterative updates based on Step 7, output the optimized configuration.

[0098] In this embodiment, the method of the present invention is based on a multi-objective particle swarm optimization algorithm, and the flowchart is as follows. Figure 2 As shown.

[0099] In this embodiment, steps one, two, and three involve obtaining the multi-base SAR spatial configuration design parameters, as detailed below:

[0100] This embodiment employs a multi-base airborne SAR system comprising one transmitter and two receivers. The geometric observation model of the multi-base SAR system is as follows: Figure 3 As shown, where v T v1, v n Δx represents the speeds of the transmitter, the main receiver, and the nth receiver, respectively. n ,Δy n ,Δzn θ represents the distance between the nth receiver and the main receiver along the coordinate axes X, Y, and Z, respectively; TR1 θ is the angle between the transmitter and the main receiver. R1 ,θ T α represents the azimuth angle of the main receiver and the transmitter, respectively. R1 ,α T R represents the elevation angle of the main receiver and the transmitter, respectively; TP (τ),R TO (τ) represents the distance from the transmitter to the target point P and the reference point O, respectively, R RnP (τ),R RnO (τ) represents the distance from the nth receiver to the target point P and the reference point O, respectively, and R1(τ) represents the distance from the main receiver to the reference point O; P(x P ,y P ,0) represents the position of the target point P; θ v2 This indicates the velocity deviation angle from the receiver.

[0101] The system parameters and spatial configuration parameters of the multi-base airborne SAR are shown in Table 1.

[0102] Table 1

[0103]

[0104] The wavenumber spectrum distributions of the main receiver and the nth (n = 1, 2, ..., N) receiver are as follows: Figure 4 As shown, where k vn ,k un Let Q1 be the vector corresponding to two adjacent sides of the parallelogram of wavenumber spectrum formed by the nth receiver, and Q1 be the vector corresponding to the two adjacent sides of the parallelogram. n DEF represent the vertices of the parallelogram of wavenumber spectra formed by the main receiver and the nth receiver, respectively. Let k represent vectors respectively. v1 ,k u1 Sum vector k vn ,k un The angle between them. To achieve higher azimuth resolution in a shorter synthetic aperture time, the direction ψ that yields the maximum azimuth synthetic projection bandwidth is selected. i =γ is analyzed in detail; for different spatial configurations of multi-base SAR systems, the projection of the wavenumber spectrum formed by the master and slave receivers in a certain direction will show two situations: overlap and separation, which will affect the shape of the main lobe of the point spread function.

[0105] When the wavenumber spectrum formed by the master and slave receivers is in k u When projections along the positive axes overlap, such as Figure 5As shown, the point spread function corresponding to the wavenumber spectrum does not exhibit main lobe splitting. Figure 5 O1,O n Let Δk represent the wavenumber spectrum centers formed by the main receiver and the nth receiver, respectively. c(1,n) =||O1′O n ′|| indicates that the centers of the two wavenumber spectra are at k in the projected coordinate system. u The projected lengths along the positive axes, O1′, O n ′ represent O1 and O respectively. n In k u Projection along the positive direction of the coordinate axes, B k1 B kn These represent the wavenumber spectra formed by the main receiver and the nth receiver at k, respectively. u The projection bandwidth along the positive direction of the coordinate axes; when the wavenumber spectrum formed by the master and slave receivers is in k u When the projections along the positive axes of the coordinate system are separated, such as Figure 6 As shown, Figure 6 In the middle HIJK, the vertex of the parallelogram wavenumber spectrum of the nth receiver is represented. gap Indicates the width of the missing data. Indicates the maximum width of missing data.

[0106] From equation (13), it can be seen that when When the point spread function main lobe does not split, this interval is divided into the narrow gap case. The peak sidelobe ratio varies with l in the azimuth direction. gap Simulations of the changes show that when At this point, the main lobe of the point spread function will split, resulting in unacceptable imaging performance. This interval is therefore classified as the wide-slot case. (Select...) As an optimized search interval, a spatial configuration is designed within the optimized search interval.

[0107] The range of values ​​for spatial configuration parameters in the optimization design problem is shown in Table 2.

[0108] Table 2

[0109] Spatial configuration parameters Parameter value range Positional spacing between master and slave receivers <![CDATA[Δx2∈[Δx min ,300m]]]> Positional spacing between master and slave receivers <![CDATA[Δy2∈[Δy min ,300m]]]> Positional spacing between master and slave receivers <![CDATA[Δz2∈[Δz min ,300m]]]> Angle between the transmitter and the main receiver <![CDATA[θ TR1 ∈[10°,70°]]]> From the receiver's velocity deviation angle <![CDATA[θ v2 ∈[-4°,4°]]]>

[0110] Where, Δx min ,Δy min ,Δz min These represent the safe distance and l, respectively. gap The minimum width determines the distance between the master receiver and slave receiver along the coordinate axes X, Y, Z, and the angle θ between the transmitter and the master receiver. TR1 The range is 10° to 70°, from the receiver's velocity deviation angle θ v2 The range is -4° to 4°.

[0111] In this embodiment, step four is specifically as follows:

[0112] The spatial configuration optimization design problem is transformed into a constrained multi-objective optimization problem:

[0113]

[0114] Where θ(l) reflects the orthogonality of the two resolution directions of the point spread function. The angle between two adjacent sides of the wavenumber spectrum parallelogram is represented; D(l) reflects the consistency of the wavenumber spectrum data along the distance direction, and d1(l) and d n (l) represents the projected bandwidth of the wavenumber spectrum of the main receiver and the nth (n=1,2) receiver in the distance direction, respectively; η(l) reflects the length difference between the projected bandwidths of the wavenumber spectrum in the two directions, ∑B u (l) and ∑B v (l) represents the projections of all wavenumber spectra onto the azimuth and range directions, respectively. |v n | represents the speed amplitude of the nth receiver. This indicates the maximum speed limit for the drone. Δk c(1,2) (l) indicates that the wavenumber spectral center corresponding to the main receiver and the wavenumber spectral center corresponding to the second receiver are at k u Projected length in the direction, This represents the maximum gap width that ensures the main lobe of the point spread function does not split. This represents the gap width between the wavenumber spectrum centers of the master and slave receivers when the point spread function sidelobe is -3dB. Ψ represents the search space for all parameters that need to be designed, as shown in Table 2.

[0115] In this embodiment, the parameters that need to be input in step five of the optimization problem are shown in Table 1, including system parameters and configuration design parameters of the optimization problem.

[0116] In this embodiment, step six is ​​specifically as follows:

[0117] First, set the number of particles L = 120 and initialize the population P = [p1, p2, ..., p 120 Secondly, set the initial velocity u of each particle. l =0 and initial position p l =random(lb,ub), where lb and ub represent the lower and upper bounds of the particle position distribution range; then, each particle in the population P is evaluated by calculating the objective function and the repository REP is updated. At the same time, the historical best value reached by each particle is initialized and recorded. And store it in REP, where the space of the repository REP is 60; finally, set the maximum number of iterations i. max =90.

[0118] In this embodiment, step seven is specifically as follows:

[0119] In each iteration, the velocity of each particle is updated according to the following expression:

[0120]

[0121] in, Let w represent the velocity in the current iteration and the velocity in the previous iteration, respectively. w∈[0,1] represents the inertia weight, c1,c2∈[0,1] are acceleration coefficients, and r1,r2 are random numbers between [0,1]. This represents the globally optimal particle selected from REP up to the current iteration number. l This represents the current position of the l-th particle.

[0122] Update the position of each particle according to the following expression, adding the particle velocity generated in the previous step to the previous position:

[0123]

[0124] in, These represent the current and previous positions during the iteration process, respectively, based on the current particle position p. l With the best historical particle Obtain the new historical best particle. Re-evaluate every particle in the population P and update REP until the maximum number of iterations i is reached. max When the value reaches 90, the iteration process stops.

[0125] In this embodiment, step eight is specifically as follows:

[0126] After completing step seven (iterative update), output the final non-dominated solution set in REP, such as... Figure 7 As shown, each dot represents a non-dominated solution, and each solution in the solution set is an optimized spatial configuration.

[0127] A comprehensive performance evaluation of each objective function is performed by defining an evaluation function f(l).

[0128]

[0129] Based on the ranking results of f(l), the solution corresponding to minf(l) is selected as the optimal configuration, as shown in SC3 in Table 3. Figure 7For points with a triangular shape, the optimized spatial configuration and the flight track of the radar platform are plotted using their corresponding non-dominated solution sets, as shown below. Figure 8 As shown, T represents the transmitter, and R1 and R2 represent the master receiver and slave receiver, respectively.

[0130] Table 3

[0131] Spatial configuration <![CDATA[(Δx2,Δy2,Δz2)(m)]]> <![CDATA[θ TR1 (°)]]> <![CDATA[θ v2 (°)]]> θ(l) D(l) η(l) SC1 (Narrow Gap) (145.03，-134.80，243.33) 22.29 3.98 0.03 0.12 0.65 SC2 (Wide Clearance) (-191.88，-110.08，271.74) 20.13 3.26 0.09 0.08 0.66 SC3 (Optimization Result) (285.77，-148.35，294.00) 11.49 3.59 0.18 0.02 0.70

[0132] The final simulation results are as follows Figure 9 As shown in Tables 10 and 11, the parameters and objective function values ​​corresponding to the three spatial configurations in the simulation are shown in Table 3, and the hardware and software platform environment for this simulation is shown in Table 4.

[0133] Table 4

[0134] Hardware or software parameter CPU Intel® Core™ i5-10600KF RAM 32GB Simulation platform Matlab 2021

[0135] Figure 9 (a), (b), and (c) represent the wavenumber spectra corresponding to three different spatial configurations (SC1, SC2, and SC3), respectively. Figure 9 (d), (e), and (f) respectively represent the corresponding Figure 9 Image results of 25 point targets in wavenumber spectra from (a), (b), and (c), selected Figure 9 The three points P1, P2, and P3 marked in (d), (e), and (f) are used to calculate some imaging performance parameters. Figure 9 In (d), (e), and (f), the scene center point P2 is the reference point. Figure 10 (a)-(c), (d)-(f) and (g)-(i) represent the imaging results from the master receiver, slave receiver and master-slave receiver fusion reference point under three different spatial configurations (SC1, SC2 and SC3), respectively. Figure 11 (a)(d)(g) represent the lateral profiles of the point spread function at the reference point under three different spatial configurations (SC1, SC2, SC3), where ρ rg , ρ az θ represents the -3dB main lobe width of the point spread function along the range and azimuth directions, respectively. r-a S represents the angle between these two resolution expansion directions. cell This represents the area of ​​a -3dB resolution cell; Figure 11 (b)(e)(h) indicates the corresponding Figure 11 (a)(d)(g) are distance profiles of reference points, where PSLR and ISLR represent peak sidelobe ratio and integral sidelobe ratio, respectively; Figure 11 (c)(f)(i) represents the corresponding Figure 11(a)(d)(g) are azimuth profiles of the reference points, where PSLR and ISLR represent the peak sidelobe ratio and integral sidelobe ratio, respectively. It can be seen that the method of the present invention... gap When the gap is wider than the gap is narrower, high-resolution imaging results can be obtained through spatial configuration optimization.

[0136] In summary, the method of this invention constructs a mapping system between the spatial configuration parameters, wavenumber spectrum distribution characteristics, and imaging performance of a multi-base radar platform; then quantitatively derives the relationship between the wavenumber spectrum gap width and image quality, and divides the search interval of the spatial configuration solution space according to the peak-to-sidelobe ratio; finally, the configuration design problem is transformed into a constrained multi-objective optimization problem, and solved using a multi-objective particle swarm optimization method, achieving high-resolution imaging through optimized spatial configuration. Compared with current spatial configuration design methods, the method of this invention breaks through the strict limitations of the spatial configuration of multi-base SAR systems, and the related methods are still within the protection scope of this invention.

[0137] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A multi-target particle swarm optimization-based multi-baseline SAR space configuration design method, the specific steps being as follows: Step one, setting multi-baseline SAR space configuration design parameters; Step two, multi-baseline SAR echo model modeling; Step three, multi-baseline SAR imaging wave number spectrum analysis based on the echo model of step two; The step three is specifically as follows: The wave number spectrum distribution of the main receiver and the first receiver is analyzed. The wave number spectrum distribution of the main receiver and the first receiver is analyzed. wherein Indicates the first The vectors corresponding to two adjacent sides of the wavenumber spectrum parallelogram formed by the receivers , They represent the main receiver and the second receiver, respectively. The vertices of the parallelogram of wavenumber spectra formed by the receivers. Representing vectors respectively sum vector The included angle between them; several intermediate variables of the master receiver and slave receiver are defined as follows: （1）； （2）； wherein respectively denote the elevation angles of the transmitter and the main receiver; respectively denote the azimuth angles of the transmitter and the main receiver; respectively denote the distances of the main receiver, the first receiver and the transmitter to the center of the observed scene; respectively denote the velocities of the transmitter, the main receiver and the first receiver; respectively denote the velocity components of the transmitter along the x-axis; respectively denote the velocity components of the main receiver along the x-axis; denotes the coordinates of the main receiver; is the velocity deviation angle, which denotes the angle between the velocity direction of the first receiver and the negative direction of the x-axis; axis. Wave number spectrum parallelogram The starting vertex of the parallelogram is denoted as: （3）； wherein denotes the bandwidth of the transmitted signal; The distribution position of the wave number spectrum parallelogram in the wave number domain is determined, and two adjacent edges of the wave number spectrum parallelogram formed by the transmitter and a certain receiver correspond to vectors represented as: （4）； Vector and The angle between the two adjacent sides of the wave number spectrum parallelogram corresponds to the angle between the two adjacent sides of the wave number spectrum parallelogram, which is expressed as: （5）； The vectors corresponding to two adjacent sides of the parallelogram of the wavenumber spectrum formed by the echo from the main receiver are: and Choose vector The direction is used as the new projected coordinate system middle Positive directions of the coordinate axes; new projected coordinate system It can be seen as Rotation As a result, Specifically, it is expressed as follows: （6）； wherein denotes a vector and the angle between the coordinate axes; For the first receiver, the projection slice of the wave number spectrum in the direction is represented as: （7）； wherein, denotes polar coordinates of the projected wave number spectrum, denotes the polar radius of a point on the projected wave number spectrum; denotes the wave number spectrum formed by the echoes of the first receiver; and denotes the wave number spectrum formed by the echoes of the second receiver; and denotes the spatial frequency variable in the direction of the denotes the Dirac function; The first receiver in direction is represented by a coherent imaging profile: （8）； wherein, represents a point spread function, represents the relative distance between the point and a selected reference point target ; represents the range of values of a variable , in particular , represents the center of the range of the wave number spectrum variable distribution formed by the th receiver, represents the projection bandwidth of the wave number spectrum formed by the th receiver in the direction , and represents the projection bandwidth in the positive direction of the coordinate axis when ; when the projections of the wave number spectra formed by the master and slave receivers in the positive direction of the coordinate axis overlap each other, the wave number spectrum corresponding to the point spread function does not have a main lobe splitting phenomenon, respectively represent the centers of the wave number spectra formed by the master receiver and the first respectively represent the centers of the wave number spectra formed by the master receiver and the first respectively represent the lengths of the projections of the centers of the two wave number spectra in the positive direction of the coordinate axis in the projection coordinate system, respectively represent the lengths of the projections of the centers of the two wave number spectra in the positive direction of the coordinate axis in the projection coordinate system, respectively represent the lengths of the projections of the centers of the two wave number spectra in the positive direction of the coordinate axis in the projection coordinate system, respectively represent the lengths of the projections of the centers of the two wave number spectra in the positive direction of the coordinate axis in the projection coordinate system, respectively represent the lengths of the projections of the centers of the two wave number spectra in the positive direction of the coordinate axis in the projection coordinate system, respectively represent the bandwidths of the projections of the wave number spectra formed by the master receiver and the first respectively represent the bandwidths of the projections of the wave number spectra formed by the master receiver and the first respectively represent the bandwidths of the projections of the wave number spectra formed by the master receiver and the first when the projections of the wave number spectra formed by the master and slave receivers in the positive direction of the coordinate axis separate from each other, respectively represent the vertices of the positions where the parallelogram wave number spectrum of the first respectively represent the vertices of the positions where the parallelogram wave number spectrum of the first respectively represent the widths of the missing data, respectively represent the maximum widths of the missing data, then the calculation formula is: （9）； The following relation needs to be satisfied: (10)； wherein denotes the minimum value of the wave number spectrum projection bandwidth; Projection bandwidth of wave number spectrum and The impact of the width of the projection bandwidth on the imaging quality can be shown by the peak side lobe ratio of the point spread function and is expressed as: (11)； wherein represents a kernel function determined jointly by and the relative widths of the Step four, space configuration optimization design problem modeling; Step five, space configuration optimization design problem system parameters and configuration parameters input; Step six, MOPSO initialization; Step seven, updating the speed and position of the particle swarm; Step eight, outputting the optimized configuration based on the iterative update of step seven.

2. The multi-objective particle swarm optimization based multi-baseline SAR space configuration design method according to claim 1, characterized in that, The step one is specifically as follows: All the parameters to be designed in the spatial configuration design problem are represented by a vector X = (x1, x2, x3,..., xn) wherein represents the distance between the th receiver and the main receiver along the coordinate axis in the direction, represents the included angle between the transmitter and the main receiver, is the velocity deviation angle, representing the included angle between the velocity direction of the th receiver and the negative direction of the coordinate axis axis.

3. The multi-objective particle swarm optimization based multi-baseline SAR space configuration design method according to claim 1, characterized in that, The step two is specifically as follows: According to the geometric model of the multi-base SAR system, the transmitter transmits a linear frequency modulation signal, and for the first receiver, the echo of the target point is expressed as: ​​ （12）； wherein, represents a range slow time variable, represents an azimuth fast time variable, represents an amplitude of an echo signal, , respectively represent a synthetic aperture time and an electromagnetic wave velocity, represents a pulse width, represents a frequency modulation slope, represents a carrier frequency of a transmitted signal, represents a range history of a target point . The echo coherent projections of all receivers in the multi-baseline SAR system are projected into the wave number domain, and the fused wave number spectrum is expressed as: （13）； wherein, represents a wave number spectrum, represents a projection coordinate axis of echo projection to the beam domain; represents a normalized amplitude of the wave number spectrum, and respectively represent the spatial frequency variables of the echo signals received by the first and the second receiver in the direction of the first and directions, represents a frequency variable, represents the coverage range of the wave number spectrum formed by the transmitter and the first and the second receiver in the wave number domain, which is approximately a parallelogram region. According to the matrix Fourier transform, the point spread function is expressed as: （14）； wherein, denotes the scattering coefficient of the target point, denotes the coordinates of the target point, denotes the coverage of all wave number spectra in a multi-basis SAR system.

4. The multi-objective particle swarm optimization based multi-baseline SAR space configuration design method according to claim 1, characterized in that, The step four is specifically as follows: The space configuration optimization design problem can be established as: (15)； wherein, reflects the orthogonality of the two resolution directions of the point spread function, denotes the angle between two adjacent sides of the wave number spectrum parallelogram; reflects the consistency of the wave number spectrum data along the range direction, and denote the projection bandwidths of the wave number spectrum of the main receiver and the th receiver in the range direction, respectively; reflects the length difference between the projection bandwidths of the wave number spectrum in the two directions, and denote the projections of all wave number spectrums in the azimuth direction and the range direction, respectively; denotes the velocity amplitude of the th receiver, denotes the upper limit of the velocity of the UAV; denotes the projection length of the wave number spectrum center corresponding to the main receiver and the wave number spectrum center corresponding to the th receiver in the direction, denotes the projection length of the wave number spectrum center corresponding to the th receiver and the wave number spectrum center corresponding to the th receiver in the direction, denotes the maximum gap width that ensures that the main lobe of the point spread function is not split, , denotes the gap width between the wave number spectrum centers corresponding to the main receiver and the th receiver when the side lobe of the point spread function is ; denotes the search space of all parameters that need to be designed.

5. The multi-objective particle swarm optimization based multi-baseline SAR space configuration design method according to claim 1, characterized in that, In the step five, the parameters that need to be input in the optimization problem include: system parameters and configuration design parameters of the optimization problem.

6. The multi-objective particle swarm optimization based multi-baseline SAR space configuration design method according to claim 1, characterized in that, The step six is specifically as follows: First, initialize the population , N represents the number of particles; second, set the initial velocity and initial position , of each particle; then, evaluate each particle in the population by calculating the objective function and update the repository , at the same time, initialize and record the historical optimal value reached by each particle and store it in ; finally, set the maximum number of iterations .

7. The multi-objective particle swarm optimization based multi-baseline SAR space configuration design method according to claim 1, characterized in that, The step seven is specifically as follows: At each iteration, the velocity of each particle is updated according to the following expression : (16)； wherein, denote the velocity at the current and previous iteration, respectively, denotes the inertia weight, is the acceleration coefficient, is the random number between 0 and 1 ; denotes the global best particle selected from the population up to the current iteration number; denotes the current position of the th particle; The position of each particle is updated according to the following expression The update of the particle position is achieved by adding the previous position to the particle velocity generated in the previous step: (17)； wherein, respectively represent the current and previous positions of the iteration, according to the position of the current particle and the historical best particle , a new historical best particle is obtained; each particle in the population is evaluated again and is updated until the maximum number of iterations is reached, the iteration process is stopped.

8. The multi-objective particle swarm optimization based multi-baseline SAR space configuration design method according to claim 1, characterized in that, The step eight is specifically as follows: After completing the iteration update step of step seven, output the final non-dominated solution set in the middle Formulating evaluation functions Overall performance evaluation of each objective function: (18)。

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