A Method for Joint Performance Optimization and Resource Management and Control of a Microwave Imaging System

Abstract

The present invention discloses a method for jointly optimizing the performance and managing resources of a microwave imaging system. First, according to the geometric configuration of the generalized beam steering bistatic SAR and the antenna rotation coefficient, analytical expressions for the imaging swath, resolution, NESZ, and oversampling rate are derived. Then, the relationship between the imaging performance, geometric configuration, and antenna rotation coefficient is analyzed, and a constrained single-objective optimization model is established. Finally, the resource management of the generalized beam steering bistatic SAR is guided according to the optimization model to achieve joint performance optimization. The method of the present invention solves the problem that it is difficult to obtain better imaging quality results with existing optimization methods, and solves the problem that the low degree of freedom of the bistatic SAR system in the prior art leads to the inability to achieve good platform beam footprint coordination. The method can be used to achieve joint performance optimization and resource management of the beam steering bistatic SAR.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a method for jointly optimizing the performance and controlling resources of a microwave imaging system. Background Art

[0002] Synthetic Aperture Radar (SAR) can continuously observe an area of interest and is not affected by weather and lighting conditions, thus being widely used in civilian fields. From single-base SAR to the gradually developed diverse application modes such as bi-static, multi-static, and moving target observation, SAR technology has become increasingly mature and rich. However, how to obtain high-resolution and wide-swath SAR images has always been the main goal of SAR imaging. High resolution can obtain more detailed information within the observation area, improving the image quality and application scope of SAR. Wide swath can obtain scene information over a larger range in one observation, thereby shortening the revisit period and expanding the observation range. However, existing single-channel SAR has a minimum antenna area limitation. To obtain higher azimuth resolution means reducing the azimuth dimension of the antenna, resulting in a higher Doppler bandwidth, but a larger PRF is required to ensure no azimuth ambiguity; a larger swath means a larger acquisition window is needed to record echo data, that is, a smaller Pulse Repetition Frequency (PRF) is required to ensure no range ambiguity. Therefore, for a specific SAR system, given the requirements of resolution and swath, a reasonable design of PRF is needed to ensure no range ambiguity and azimuth ambiguity.

[0003] Different imaging modes can be used to achieve the reconciliation of resolution and mapping bandwidth. The spotlight mode increases the synthetic aperture time of the targets in the observation scene by adjusting the main lobe beam of the antenna to increase the azimuth Doppler bandwidth and improve the azimuth resolution. However, spotlight SAR still requires a relatively high PRF to meet the Nyquist sampling rate. The TOPS mode divides the entire azimuth aperture into different sub-apertures, and each sub-aperture scans a sub-mapping strip, thereby achieving an increase in the range-direction mapping strip width. And usually, the ground beam scanning speed is greater than the platform movement speed, resulting in a reduction in the synthetic aperture time and a decrease in resolution. In addition, domestic and foreign scholars have also proposed other working modes, such as the scan mode, the sliding spotlight mode, and the mosaic mode, etc. But none of them can achieve wide mapping and high resolution simultaneously.

[0004] Compared with monostatic SAR, bistatic SAR has two independent transmit-receive platforms, and both the transmit and receive beams can be rotated azimuthally, thus achieving more geometric diversity. Compared with current SAR systems, beam-rotating bistatic SAR has higher degrees of freedom, including the bistatic SAR system configuration, beam rotation mode, and pulse repetition frequency. These system resources are closely related to imaging performance metrics, especially imaging area, spatial resolution, NESZ, etc. Therefore, in order to achieve comprehensive optimization of imaging performance, it is very necessary to manage the system resources of bistatic SAR.

[0005] The literature "Mission planning for energy-efficient passive UAV radar imaging system based on substage division collaborative search" proposed a configuration design method to obtain the required spatial resolution. By modeling the configuration design problem as a multi-objective optimization problem and obtaining the optimal solution through a non-dominated evolutionary algorithm. However, this method only considered the spatial configuration of bistatic SAR and did not fully utilize all the system resources of bistatic SAR.

[0006] The literature "Optimal configuration of spaceborne bistatic SAR with GEO transmitter and LEO receiver" established an index evaluation system for GEO-LEO bistatic SAR systems, modeled it as a multi-objective optimization problem, and obtained the optimal solution using the simulated annealing algorithm.

[0007] The literature "SAR Cross-Ambiguities in SAOCOM-CS Large Baseline Bistatic Configuration" focused on studying the ambiguity signal ratio (ASR) performance of the SAOCOM-CS system in a large baseline bistatic (LBB) configuration. By studying the influence of cross-ambiguity, it extended the previous performance analysis. However, the spatial variations of the resolution and NESZ of beam-steering bistatic SAR (BS-BiSAR) are also affected by complex imaging geometries, and this influence becomes more serious as the imaging area increases, resulting in limited imaging capabilities.

[0008] Due to the geometric diversity of bistatic SAR, more angular observations of targets can be obtained. Its SAR images are used for search and rescue, UAV navigation, aircraft assisted landing under weak line-of-sight conditions, and stealth target detection. Research on bistatic SAR includes configuration design, synchronization method, performance analysis, imaging and GMTI algorithms, and experiments. Among them, the research on configuration design methods provides important theoretical support for the resource management problem of bistatic SAR. Based on the bistatic resolution theory, some scholars modeled the configuration design problem of GEO satellite-aircraft bistatic SAR as a multi-objective optimization problem and solved this problem using the non-dominated sorting genetic algorithm (NSGA-II). Some scholars extended the configuration design problem to the path planning problem of GEO-UAV bistatic SAR, so as to ensure receiving effective echoes, meeting the resolution requirements, and ensuring the flight safety of UAVs. Some scholars studied the configuration optimization problems of monostatic and bistatic SARs to achieve the noise equivalent sigma zero (NESZ), range ambiguity to signal ratio (RASR), and azimuth ambiguity to signal ratio (AASR). However, the above methods consider a relatively low degree of freedom of the bistatic SAR system and are difficult to be applied to the case where both the transmitting and receiving stations have beam control capabilities. Inspired by the optimal design of beam steering monostatic SAR and the design method of beam steering bistatic SAR (BS-BiSAR) system, the existing technology models the bistatic beam control problem as a resource management problem, and expects to achieve the joint optimization of swath width, resolution, NESZ, and oversampling factor through beam control, PRF design, and the design of bistatic configuration parameters. Summary of the Invention

[0009] To solve the above technical problems, the present invention provides a method for joint performance optimization and resource management of a microwave imaging system, which realizes non-ambiguous imaging and has an imaging swath width (imaging area meeting the resolution requirements) as large as possible, an oversampling rate and NESZ as small as possible, and obtains the solution to the joint performance optimization and resource management problem.

[0010] The technical solution adopted by the present invention is as follows: A method for joint performance optimization and resource management of a microwave imaging system, and the specific steps are as follows:

[0011] S1. Establish a geometric configuration model of a generalized beam steering bistatic SAR;

[0012] According to the beam rotation mode of the receiving station, the speed of the beam footprint of the receiving station along the y-axis is set to v bR , v bR The expression is as follows:

[0013] v bR =A rot,R v R (1)

[0014] Among them, v R Indicates the speed of the receiving station; A rot,R Represents the beam turning factor of the receiving station, indicating different beam turning modes.

[0015] Similarly, the beam footprint speed of the transmitting station is affected by the transmitting station beam rotation factor A rot,T The control of different beam modes of the platform uses the beam factor A rot It is expressed as follows:

[0016]

[0017] Assume that for any target P tar (x,y), the beam center passes through time t c The calculation expressions for the start irradiation t1 and end irradiation time t2 of the overlapping beam are as follows:

[0018]

[0019] Among them, L R Represents the length of the receiving station footprint along the y-axis, M R Represents the length of the receiving station footprint along the x-axis.

[0020] S2. Establishing a mathematical model of imaging width;

[0021] For BS-BiSAR, the movement speed of the beam footprint is related to the beam steering mode, so the imaging area S o The expression is as follows:

[0022] S o =(x max -x min )×(y max -y min ) (4)

[0023] Among them, x max 、x min 、y max and y min Indicates the extent of the overlapping area.

[0024] Assume that the footprint function of the transmitting station and the receiving station is expressed as f T (x,y,t)=0 and fR (x, y, t) = 0, where t represents the azimuth slow time. Then when the equation (5) is satisfied, the target P tar (x, y) is simultaneously illuminated by both the transmitting and receiving stations, and the expression is as follows:

[0025]

[0026] Set the start illumination time and end illumination time of the receiving station to be represented as t1(x, y) and t2(x, y) respectively. Then the imaging swath of this BS - BiSAR is represented by an inequality group, and the expression is as follows:

[0027]

[0028] By solving the inequality group of equation (6), the boundary of the overlapping area is obtained, and the expression is as follows:

[0029]

[0030] Among them, M R represents the coverage length of the receiving station beam on the x - axis; Δθ T and Δθ R respectively represent the maximum beam rotation angle limits of the transmitting station and the receiving station; T op represents the illumination duration of the transmitting station; ω Trot and ω Rrot respectively represent the beam rotation angular velocities of the transmitting station and the receiving station; d x and d y represent the side lengths of the overlapping area. The imaging area represented by equation (7) is the area with full - aperture resolution.

[0031] S3. Establish a mathematical model of resolution and NESZ;

[0032] The calculation expression of NESZ is as follows:

[0033]

[0034] Among them, ||P T || and ||P R || respectively represent the slant ranges from the transmitting station and the receiving station to the target point; k represents the Boltzmann constant; T0 represents the equivalent noise temperature; F n represents the noise figure of the receiving station; L p represents the propagation loss; ξ ra represents the angular resolution; P t represents the peak transmit power; G T and G R respectively represent the antenna gains of the transmitting station and the receiving station; ρ r and ρ a respectively represent the range resolution and azimuth resolution; Dc represents the pulse duty cycle; T a represents the aperture time; λ represents the signal wavelength.

[0035] S4. Establish a ambiguity model;

[0036] The upper and lower limits of the incident angles of the transmitting station and the receiving station are respectively represented as and Then the corresponding bistatic echo delay window is obtained by calculation and is represented as [T min , T max , and then the constraint condition C1(p) of the PRF and the bistatic incident angle is obtained. The expression is as follows:

[0037]

[0038] where, f PRF represents the pulse repetition frequency, T ref , T dir respectively represent the delays of the specularly reflected wave and the direct wave, represents the pulse

[0039] sum of the width τ and the pulse protection width τ g of, represents the maximum integer value of finding a certain number, p represents the vector composed of the configuration of the bistatic SAR, the bistatic beam rotation factor and the PRF. The expression is as follows:

[0040]

[0041] where, α bi represents the bistatic velocity angle, γ bi represents the bistatic angle, θ R represents the squint angle of the receiving platform, represents the incident angle of the transmitting platform, represents the incident angle of the receiving platform, [·] T represents the transpose of the matrix;

[0042] For azimuth ambiguity, the sampling oversampling factor σ os is used to estimate the performance of azimuth ambiguity. The expression is as follows:

[0043]

[0044] where, B scene represents the Doppler width of the entire imaging area, which is mainly determined by the spatial variation of the Doppler centroid and the azimuth resolution. The calculation expression is as follows:

[0045]

[0046] where, c represents the speed of light, B rDenotes the bandwidth, and respectively denote the imaging swath widths along the x-axis and y-axis that meet the resolution index requirements, f dc denotes the Doppler centroid, and respectively denote the linear change rates of the Doppler centroid with respect to the coordinate axes x and y; f dr denotes the Doppler modulation frequency; k T1 and k R1 denote the linear terms of the bistatic distance; B dop denotes the Doppler bandwidth of the reference point, B sv denotes the spectral broadening caused by the spatial variation of the Doppler centroid, which is related to the beam rotation mode and the shifting bistatic configuration, B inc denotes the spectral broadening caused by spectral tilt.

[0047] And the PRF needs to satisfy the constraint condition C2(p), and the expression is as follows:

[0048]

[0049] where, B ins denotes the instantaneous Doppler bandwidth.

[0050] S5. Establish a joint performance optimization and resource management and control problem model;

[0051] The mathematical expression corresponding to the joint performance optimization and resource management and control (JPO-RM) problem is as follows:

[0052]

[0053] where, denotes the imaging performance requirements for a specific SAR application scenario, and L denotes the corresponding requirements of the index.

[0054] Transform the inequality solution problem of Equation (14) into an optimization problem solution, and the expression of the optimization problem is as follows:

[0055]

[0056] where, f(p) denotes a single-objective optimization problem, and μ k (k = 1, 2, 3) denotes the weighting coefficient, and h k (p) denotes the magnitude by which the imaging performance exceeds the requirements, and the expression is as follows:

[0057]

[0058] The single-objective optimization problem f(p) in Equation (15) is a constrained optimization problem, and it is transformed into an unconstrained form by the adaptive penalty function method, and the expression is as follows:

[0059]

[0060] Among them, P j (p) represents the violation amount of the PRF to the range ambiguity and azimuth ambiguity constraints, successively including three constraints in C1(p) ≤ 0 and one constraint in C2(p) ≤ 0, P j (p) is expressed as follows:

[0061] P j (p) = max(0, c j,low (p) - c j (p), c j (p) - c j,upp (p)) (18)

[0062] Among them, c j (p) represents the j-th constraint, c j,low (p) and c j,upp (p) represent the upper and lower bounds of the j-th constraint. The solution that satisfies {p | P j (p) = 0, j = 1, 2, 3, 4} is called a feasible solution; represents the adaptive fuzzy penalty function factor, and the expression is as follows:

[0063]

[0064] Among them, represents scaling different constraint violation amounts to the same scale and updating it in each iteration. χ m represents the proportion of the feasible solution in the m-th iteration.

[0065] S6. According to the actual requirements, input the required indicators of the imaging performance;

[0066] S7. Initialize the system parameters, the number of particles, and the number of iterations;

[0067] Perform system initialization, randomly generate N1 particles, and set the maximum number of iterations G1, and initialize the velocity of each particle.

[0068] S8. Solve the optimization problem by the particle swarm optimization method based on separated learning and supervised learning.

[0069] Furthermore, the specific steps of step S8 are as follows:

[0070] S81. Calculate the objective function values of all particles in the current generation;

[0071] Calculate the respective performance indicators of the i-th particle in the m-th generation and calculate the respective constraint violation amounts ​Determine whether the current particle is a feasible solution. Denote the set of all infeasible solutions as Ψ0 and the set of all feasible solutions as Ψ1, and calculate the proportion χ of feasible solutions in the m-th iteration. m Calculate the objective function value.

[0072] S82. Calculate the local optimal and the individual historical optimal.

[0073] Compare the local optimal and the individual historical optimal of all particles in the m-th generation. If the i-th particle in the m-th generation is better than , then is replaced by , otherwise remains unchanged.

[0074] Among them, represents the individual historical optimal of the i-th particle in the m-th generation.

[0075] Then update the local optimal. represents the optimal solution in the p i neighboring area, and the expression is as follows:

[0076]

[0077] Among them, represents taking out the smallest k numbers in a certain vector; D i represents the row vector of the i-th row or the column vector of the i-th column of the normalized distance matrix D. D is a symmetric matrix, indicating the normalized distance between any two elements and , then the element d ij m of the matrix has the following expression:

[0078]

[0079] S83. Update the relevant parameters and the velocity and position of the particles.

[0080] Currently, through the separated learning strategy, the particle set is divided into a feasible solution set and an infeasible solution set, and different learning methods are adopted for the two solution sets.

[0081] If the feasible solution learns the position information from the global optimal and is transformed into an infeasible solution. If learns from the local optimal and searches the local space to avoid being transformed into an infeasible solution. The velocity of the infeasible solution is not affected by other particles, then randomly searches the entire solution space to search for the global optimal solution. The expression of the velocity update method is as follows:

[0082]

[0083] Among them, w represents the inertia coefficient, r1 and r2 represent random numbers uniformly distributed from 0 to 1, and c1 and c2 represent adaptive triangular acceleration factors, which are non-negative and guide the search process of the current particle; represents the velocity of the i-th particle in the m-th generation. In the particle swarm optimization method based on separation learning and supervised learning, trigonometric functions are used as the variation mode of the search factor to adjust the step size of iteration, and the expression is as follows:

[0084]

[0085] Among them, c max and c min respectively represent the upper and lower limits of the acceleration factor. The adaptive triangular acceleration factors c1 and c2 make the particle swarm focus on the optimal solution in the current feasible solution interval at the beginning of the search, and focus on the individual optimal solution in the later stage of iteration.

[0086] S84. Update the global optimal solution Denote the optimal solution among all solutions in the m-th generation as

[0087] S85. Calculate the supervised learning function and update the inactive solutions;

[0088] A supervised learning strategy is proposed. By adopting a new activity evaluation method, the inactive solutions are screened and regenerated. Then the expression of the supervised learning strategy is as follows:

[0089]

[0090] Among them, represents the activity, and ||D i || represents the crowding degree; the particles with low activity and high crowding degree are updated again.

[0091] If it satisfies Delete s, represents the preset screening threshold.

[0092] S86. Judge whether the imaging performance requirements are met. If not, re-iterate steps S81 - S85 until the iteration is completed. If the imaging performance requirements are met, stop the iteration and output the optimal solution, that is, the optimization result.

[0093] Advantages of the present invention: The method of the present invention first derives the analytical expressions of imaging swath, resolution, NESZ, and oversampling rate according to the geometric configuration of the generalized beam-steering bistatic SAR and the antenna rotation coefficient, then analyzes the relationship between imaging performance and geometric configuration and antenna rotation coefficient, establishes a constrained single-objective optimization model, and finally guides the resource management and control of the generalized beam-steering bistatic SAR according to the optimization model to achieve joint performance optimization. The method of the present invention solves the problem that it is difficult to obtain better imaging quality results with existing optimization methods, and solves the problem that the bistatic SAR system in the prior art has a low degree of freedom, resulting in poor platform beam footprint coordination. The method can be used to achieve joint performance optimization and resource management and control of beam-steering bistatic SAR. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 FIG. is a flowchart of a method for joint performance optimization and resource management and control of a microwave imaging system according to the present invention.

[0095] Figure 2 FIG. is a schematic diagram of the iterative process of the objective function of an airborne bistatic SAR in an embodiment of the present invention.

[0096] Figure 3 FIG. is a schematic diagram of the simulation result of a surface target of an airborne bistatic SAR in an embodiment of the present invention.

[0097] Figure 4 FIG. is a point target distribution diagram in an embodiment of the present invention.

[0098] Figure 5 FIG. is a schematic diagram of the imaging results of points T1, T5, and T9 in an airborne bistatic SAR in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0099] The present invention is mainly verified by simulation experiments, and all steps and conclusions are verified correctly on Matlab2012. The method of the present invention will be further described below with reference to the drawings and embodiments.

[0100] To facilitate the description of the content of the method of the present invention, the following terms are first explained:

[0101] Term 1: Bistatic SAR;

[0102] A bistatic SAR refers to a SAR system in which the transmitter and receiver are located on different platforms, and at least one of the platforms is a moving platform, which conceptually belongs to a bistatic radar.

[0103] Term 2: Beam-steering bistatic SAR (BS-BiSAR);

[0104] The beam-steering bistatic SAR refers to a bistatic SAR in which both the transmitting station and the receiving station platforms have beam-steering capabilities.

[0105] Term 3: NESZ;

[0106] NESZ refers to the equivalent noise backscattering coefficient.

[0107] Term 4: JPO-RM problem;

[0108] Joint performance optimization and resource management problem.

[0109] As Figure 1 shown, the flowchart of the method for joint performance optimization and resource management of a microwave imaging system according to the present invention is as follows:

[0110] S1. Establish a geometric configuration model of a generalized beam-steering bistatic SAR;

[0111] According to the beam rotation mode of the receiving station, set the moving speed of the beam footprint of the receiving station along the y-axis as v bR , v bR The expression is as follows:

[0112] v bR = A rot,R v R (1)

[0113] Among them, v R represents the speed of the receiving station; A rot,R represents the beam rotation factor of the receiving station, indicating different beam rotation modes.

[0114] Similarly, the beam footprint speed of the transmitting station is controlled by the beam rotation factor A rot,T of the transmitting station, and different beam modes of the platform are represented by the beam factor A rot as follows:

[0115]

[0116] For any target P tar (x, y), the beam center crossing time is t c , and the calculation expressions for the start illumination t1 and the end illumination time t2 of the overlapping beam are as follows:

[0117]

[0118] Among them, L R represents the length of the receiving station footprint along the y-axis, and M R represents the length of the receiving station footprint along the x-axis.

[0119] In this embodiment, the oblique angle of the receiving station is set to 30°, and the speeds of the transmitting station and the receiving station are v T = 200 m / s and v R = 50 m / s, the ranges of γ bi and α bi are both [0, 360), the incident angle of the platform is [20, 60], the range of PRF is [100, 2000], and the range of the beam rotation factor is [0, 30]. The simulation parameters for the performance analysis of the bistatic airborne SAR are shown in Table 1.

[0120] Table 1

[0121]

[0122] S2. Establish the mathematical model of the imaging swath;

[0123] For BS-BiSAR, the moving speed of the beam footprint is related to the beam control mode, so the imaging area S o The expression is as follows:

[0124] S o = (x max - x min ) × (y max - y min ) (4)

[0125] where, x max , x min , y max and y min represent the range of the overlapping area.

[0126] Set the footprint functions of the transmitting station and the receiving station as f T (x, y, t) = 0 and f R (x, y, t) = 0, where t represents the azimuth slow time. Then when the condition of Equation (5) is satisfied, the target P tar (x, y) is simultaneously illuminated by both the transmitting and receiving stations, and the expression is as follows:

[0127]

[0128] Set the start illumination time and the end illumination time of the receiving station as t1(x, y) and t2(x, y) respectively, then the imaging swath of this BS-BiSAR is represented by an inequality group, and the expression is as follows:

[0129]

[0130] By solving the inequality group of Equation (6), the boundary of the overlapping area is obtained, and the expression is as follows:

[0131]

[0132] Among them, M R represents the coverage length of the receiving station beam on the x-axis; Δθ T and Δθ R respectively represent the maximum beam turning angle limits of the transmitting station and the receiving station; T op represents the irradiation duration of the transmitting station; ω Trot and ω Rrot respectively represent the beam rotation angular velocities of the transmitting station and the receiving station; d x and d y represent the side length of the overlapping area. The imaging area represented by Equation (7) is the area with full aperture resolution.

[0133] S3. Establish a mathematical model of resolution and NESZ;

[0134] The calculation expression of NESZ is as follows:

[0135]

[0136] Among them, ||P T || and ||P R || respectively represent the slant ranges from the transmitting station and the receiving station to the target point; k represents the Boltzmann constant; T0 represents the equivalent noise temperature; F n represents the noise figure of the receiving station; L p represents the propagation loss; ξ ra represents the angular resolution; P t represents the peak transmit power; G T and G R respectively represent the antenna gains of the transmitting station and the receiving station; ρ r and ρ a respectively represent the range resolution and the azimuth resolution; D c represents the pulse duty cycle; T a represents the aperture time; λ represents the signal wavelength.

[0137] S4. Establish an ambiguity model;

[0138] For BS-BiSAR, usually higher resolution and larger imaging swath can be obtained. Then, for the cases of various combinations of beam rotation modes of the transceiver bistatic stations, a sufficiently large PRF is required to meet the non-ambiguity requirement. Since the range ambiguity and azimuth ambiguity are closely related to the PRF, they need to be analyzed.

[0139] To avoid amplifier oversaturation, the echo sampling window cannot overlap with the specular reflection wave and the direct wave. The upper and lower limits of the incident angles of the transmitting station and the receiving station are respectively represented as and Then the corresponding bistatic echo delay window is obtained through calculation and expressed as [T min , T max . Then the constraint condition C1(p) of PRF and the bistatic incident angle is obtained, and the expression is as follows:

[0140]

[0141] Among them, f PRF represents the pulse repetition frequency, T ref , T dir respectively represent the delays of the specularly emitted wave and the direct wave, represents the sum of the pulse width τ and the pulse protection width τ g , represents the maximum integer value of finding a certain number, and p represents the vector composed of the configuration of the bistatic SAR, the bistatic beam rotation factor, and the PRF. The expression is as follows:

[0142]

[0143] Among them, α bi represents the bistatic velocity angle, γ bi represents the bistatic angle, θ R represents the squint angle of the receiving platform, represents the incident angle of the transmitting platform, represents the incident angle of the receiving platform, [·] T represents the transpose of the matrix.

[0144] To avoid range ambiguity, it is necessary to avoid the overlap of the echo, the direct wave, and the specularly emitted wave generated by a single pulse, as well as the overlap between pulses. However, the smaller the PRF, the more likely it is to cause azimuth ambiguity. For azimuth ambiguity, the oversampling coefficient σ os is used to estimate the performance of azimuth ambiguity. The expression is as follows:

[0145]

[0146] Among them, B scene represents the Doppler width of the entire imaging area, which is mainly determined by the spatial variation of the Doppler centroid and the azimuth resolution. The calculation expression is as follows:

[0147]

[0148] Among them, c represents the speed of light, B r represents the bandwidth, and respectively represent the imaging swath widths along the x-axis and y-axis that meet the resolution index requirements, f dc represents the Doppler centroid, and respectively represent the linear change rates of the Doppler centroid with respect to the x and y coordinate axes; f dr represents the Doppler modulation frequency; k T1 and k R1 represent the linear terms of the bistatic distance; B dop represents the Doppler bandwidth of the reference point, B sv represents the spectral broadening caused by the spatial variation of the Doppler centroid, which is related to the beam rotation mode and the varying bistatic configuration, B inc represents the spectral broadening caused by spectral tilt.

[0149] And the PRF needs to satisfy the constraint condition C2(p), and the expression is as follows:

[0150]

[0151] where, B ins represents the instantaneous Doppler bandwidth.

[0152] S5. Establish a joint performance optimization and resource control problem model;

[0153] Under the conditions of a given bistatic platform type, motion ability, and signal carrier frequency bandwidth, the solution of the JPO-RM (Joint Performance Optimization and Resource Management) problem can output the bistatic SAR configuration, beam rotation mode, and PRF, satisfying all imaging performance requirements and having no ambiguity. The mathematical expression corresponding to the joint performance optimization and resource control (JPO-RM) problem is as follows:

[0154]

[0155] where, represents the imaging performance requirements for a specific SAR application scenario, and L represents the requirements corresponding to the indicators.

[0156] In order to obtain the solution that satisfies the above inequality equations, the inequality solution problem in Equation (14) is transformed into an optimization problem solution, and the expression of the optimization problem is as follows:

[0157]

[0158] where, f(p) represents a single-objective optimization problem, μ k (k = 1, 2, 3) represents the weighting coefficient, h k (p) represents the magnitude by which the imaging performance exceeds the requirements, and the expression is as follows:

[0159]

[0160] In the single-objective optimization problem \(f(p)\) in Equation (15), it is an optimization problem with constraints. By using the adaptive penalty function method, it is transformed into an unconstrained form, and the expression is as follows:

[0161]

[0162] Among them, \(P\) j (p) represents the violation amount of the PRF to the range ambiguity and azimuth ambiguity constraints, successively including the three constraints in \(C1(p)\leq0\) and one constraint in \(C2(p)\leq0\). The expression of \(P\) j (p) is as follows:

[0163] \(P\) j (p)=\(\max(0,c\) j,low (p)-c\) j (p),c\) j (p)-c\) j,upp (p)) (18)

[0164] Among them, \(c\) j (p) represents the \(j\)-th constraint, and \(c\) j,low (p) and \(c\) j,upp (p) represent the upper and lower bounds of the \(j\)-th constraint. The solution that satisfies \(\{pP\) j (p)=0,j = 1,2,3,4\}\) is called a feasible solution; represents the adaptive fuzzy penalty function factor, and the expression is as follows:

[0165]

[0166] Among them, represents scaling different constraint violation amounts to the same scale and updating it in each iteration. \(\chi\) m represents the proportion of the feasible solution in the \(m\)-th iteration.

[0167] S6. According to the actual requirements, input the required indicators of the imaging performance;

[0168] The imaging performance requirements are as follows:

[0169]

[0170] S7. Initialize the system parameters, the number of particles, and the number of iterations;

[0171] In this embodiment, system initialization is performed, and \(N1 = 200\) particles are randomly generated. The number of particles is input by the user. The larger the number of particles, the more beneficial it is for the iterative solution of the particle swarm algorithm, but it will reduce the calculation efficiency. And set the maximum number of iterations \(G1 = 100\) and initialize the velocity of each particle.

[0172] S8. Solve the optimization problem by a particle swarm optimization method based on separated learning and supervised learning;

[0173] S81. Calculate the objective function values of all particles in the current generation;

[0174] Calculate the corresponding various performance metrics of the i-th particle in the m-th generation and calculate each constraint violation amount, determine whether the current particle is a feasible solution, denote the set of all infeasible solutions as Ψ0, the set of all feasible solutions as Ψ1, and calculate the feasible solution ratio χ in the m-th iteration m , and calculate the objective function value

[0175] S82. Calculate the neighborhood best and individual historical best;

[0176] Compare the neighborhood best and individual historical best of all particles in the m-th generation. If the i-th particle in the m-th generation is better than then is replaced by , otherwise

[0177] remains unchanged. where represents the individual historical best of the

[0178] i-th particle in the m-th generation. Then update the neighborhood best, i denoted as p

[0179]

[0180] where represents taking out the smallest k numbers in a certain vector; D i represents the row vector of the i-th row or the column vector of the i-th column of the normalized distance matrix D. D is a symmetric matrix, representing the normalized distance between any two elements and , then the element d ij m of the matrix is expressed as follows:

[0181]

[0182] S83. Update the relevant parameters and the velocity and position of the particles;

[0183] Currently, through the separated learning strategy, the particle set is divided into a feasible solution set and an infeasible solution set, and different learning methods are adopted for the two solution sets.

[0184] If the feasible solution learns the position information from the global optimal solution and is transformed into an infeasible solution. If learns from the local optimal solution, searches the local space, and avoids being transformed into an infeasible solution. If the velocity of the infeasible solution is not affected by other particles, then it will randomly search the entire solution space to search for the global optimal solution. The expression for the velocity update method of this improved method is as follows:

[0185]

[0186] where w = 0.8 represents the inertia coefficient, r1 and r2 represent random numbers uniformly distributed between 0 and 1, c1 and c2 represent the adaptive triangular acceleration factors, which are non-negative and guide the search process of the current particle; represents the velocity of the i-th particle in the m-th generation. In the particle swarm optimization method based on separated learning and supervised learning, trigonometric functions are used as the variation method of the search factor to adjust the iteration step size. The expression is as follows:

[0187]

[0188] where c max = 0.9 and c min = 0.1 represent the upper and lower limits of the acceleration factor respectively. The adaptive triangular acceleration factors c1 and c2 make the particle swarm focus on the optimal solution in the current feasible solution interval at the beginning of the search, and focus on the individual optimal solution in the later stage of the iteration.

[0189] S84. Update the global optimal solution Record the optimal solution among all solutions in the m-th generation as

[0190] S85. Calculate the supervised learning function and update the inactive solutions;

[0191] A supervised learning strategy is proposed. A new activity evaluation method is adopted to screen the inactive solutions and regenerate them. Then the expression of the supervised learning strategy is as follows:

[0192]

[0193] where represents the activity, and ||D i || represents the crowding degree; the particles with low activity and high crowding degree are updated again, so as to avoid some local optimal solutions from being changed.

[0194] If it satisfies delete s, represents the preset screening threshold.

[0195] S86. Determine whether the imaging performance requirements are met. If not, re-iterate steps S81 - S85 until the iteration is completed. If the imaging performance requirements are met, stop the iteration and output the optimal solution, i.e., the optimization result.

[0196] After the iteration of this embodiment is completed, the optimal solution of the single-objective optimization problem f(p) in Equation (15) is p = [258.0, 3.5, 2.4, 13.4, 1923.2, 60.0, 60.0] T , and the corresponding imaging performance is:

[0197]

[0198] Then the positions of the transmitting station and the receiving station are P T = [-4, 14, 8] km and P R = [-8, -5, 5] km, and the velocities are V T = [-12, -200, 0] m / s and V R = [0, 50, 0] m / s. The iterative process of the objective function is as Figure 2 shown, where the global optimum of each generation is selected and normalized. It can be seen that after the 22nd generation, the objective function value has dropped to a relatively low level. The point target simulation and the area target simulation verify the accuracy of the imaging performance calculation and the satisfaction of the performance requirements.

[0199] As Figure 3 shown, the schematic diagram of the area target simulation result of the airborne bistatic SAR. The imaging result of the area target verifies the ambiguity of the optimal solution and the imaging size. The area target is distributed in the area, and is processed by the BP method. Figure 3 The yellow dashed box in Figure 3 (a) represents the area of the imaging region that meets the resolution requirements. Two un-designed solutions are used for comparison with the optimal solution. In Figure 3 (b), the flight trajectories of the platforms are parallel at this time, the squint angle of the receiving station is 30°, and the beam rotation factors of the transmitting station and the receiving station are 5 and 10. In this case, the imaging swath is 1.4 km × 2.1 km, which is much smaller than the imaging swath of the optimal solution, and the resolution does not meet the performance requirements. The imaging result of the un-designed solution 2 is as Figure 3(c), the transmitting station operates in the sliding spotlight mode, while the receiving station operates in the TOPS mode, and the bistatic angle γ bi = 50°, and the bistatic velocity angle α bi = 20°. Although the resolution of the un-designed solution 2 is much higher than the optimal solution, the imaging quality is affected by azimuth ambiguity. At this time, σ os = 1.3. For the optimal solution, the azimuth bandwidth B scene is 1733 Hz, and the oversampling rate is 0.91, verifying the accuracy of the oversampling rate calculation.

[0200] The distribution of point targets is as Figure 4 shown. For the point target simulation, the target points are evenly distributed throughout the scene, and the scene size is determined by and . The imaging results of points T1, T5, and T9 are shown in Figure 5 . Figure 5 (a)-(c) of Figure 5 correspond to the point target imaging results of the optimal solution. The theoretical resolutions are listed in parentheses, verifying the accuracy of the resolution calculation, and proving that the optimal solution output by the method of the present invention can meet the resolution index requirements. In Figure 5 (d)-(f), the range resolution of the un-designed solution 1 is 5 m, far exceeding the resolution requirement. In Figure 5 (g)-(i), the resolution of the un-designed solution 2 exceeds the optimal solution, but at the cost of sacrificing the imaging swath width and having azimuth ambiguity.

[0201] In summary, the method of the present invention solves the problem that it is difficult to obtain better imaging quality results by existing optimization methods, and solves the problem that the low degree of freedom of the bistatic SAR system in the prior art leads to the inability to achieve good platform beam footprint coordination. The method can be used to realize the joint performance optimization and resource management and control of the beam-controlled bistatic SAR.

[0202] Those of ordinary skill in the art will realize that the above embodiments are for helping the reader understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, various changes and modifications can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A method for joint performance optimization and resource management of a microwave imaging system, comprising the following steps: S1. Establish the geometric configuration model of generalized beam-steering bistatic SAR; According to the beam rotation mode of the receiving station, the speed of the beam footprint of the receiving station along the y-axis is set to v bR , v bR The expression is as follows: in bR =A rot,R in R (1) in, v R Indicates the speed of the receiving station; A rot,R Indicates the beam rotation factor of the receiving station, corresponding to different beam rotation modes; Similarly, the beam footprint speed of the transmitting station is affected by the transmitting station beam rotation factor A rot,T The control of different beam modes of the platform uses the beam factor A rot It is expressed as follows: Assume that for any target P tar (x,y), the beam center passes through time t c The calculation expressions for the start irradiation t1 and end irradiation time t2 of the overlapping beam are as follows: Among them, L R represents the length of the receiving station footprint along the y-axis; S2. Establishing a mathematical model of imaging width; For BS-BiSAR, the movement speed of the beam footprint is related to the beam steering mode, so the imaging area S o The expression is as follows: S o =(x max -x min )×(and max -and min ) (4) Among them, x max 、x min 、y max and y min Indicates the extent of the overlapping area; Assume that the footprint function of the transmitting station and the receiving station is expressed as f T (x,y,t)=0 and f R (x, y, t) = 0, t represents the azimuth slow time; when equation (5) is satisfied, the target P tar (x,y) is illuminated by both the transmitting and receiving stations at the same time, and the expression is as follows: Assuming that the start and end times of the irradiation at the receiving station are denoted as t1(x, y) and t2(x, y), respectively, the imaging width of the BS-BiSAR is expressed by a set of inequalities as follows: By solving the inequality group of formula (6), the boundary of the overlapping area is obtained, which is expressed as follows: Among them, M R represents the coverage length of the receiving station beam on the x-axis; Δθ T and Δθ R Respectively represent the maximum beam angle limits of the transmitting station and the receiving station; T op Indicates the irradiation time of the transmitting station; ω Trot and ω Rrot Represents the beam rotation angular velocity of the transmitting station and the receiving station respectively; d x and d y represents the side length of the overlapping area, and the imaging area represented by formula (7) is the area of full aperture resolution; S3, establish resolution and NESZ mathematical model; The NESZ calculation expression is as follows: Among them, ||P T || and ||P R || represents the slant distances from the transmitting station and the receiving station to the target point respectively; k represents the Boltzmann constant; T0 represents the equivalent noise temperature; F n Represents the noise coefficient of the receiving station; L p represents the propagation loss; ξ ra Indicates angular resolution; P t Indicates peak transmit power; G T and G R Represent the antenna gains of the transmitting station and the receiving station respectively; ρ r and ρ a Represents the range resolution and azimuth resolution respectively; D c Indicates the pulse duty cycle; T a represents aperture time; λ represents signal wavelength; S4. Establish fuzzy model; The upper and lower limits of the incident angles of the transmitting station and the receiving station are expressed as and The corresponding bistatic echo delay window is obtained by calculation and is expressed as [T min ,T max ], and then the constraint condition C1(p) between PRF and bistatic incident angle is obtained, which is expressed as follows: Among them, f PRF represents the pulse repetition frequency, T ref ,T dir represent the delays of the mirror-emitted wave and the direct wave, Indicates pulse width τ and pulse protection width τ g of and, Indicates finding the maximum integer value of a number, p represents the configuration of the bistatic SAR, the bistatic beam rotation factor, and the vector consisting of the PRF. The expression is as follows: Among them, α bi represents the angle between the two base velocities, γ bi Denotes the double base angle, θ R Indicates the oblique viewing angle of the receiving platform, represents the incident angle of the launch platform, represents the incident angle of the receiving platform, [·] T Represents the transpose of a matrix; For orientation ambiguity, the oversampling factor σ os To estimate the performance of azimuth ambiguity, the expression is as follows: Among them, B scene It represents the Doppler width of the entire imaging area, which is mainly determined by the spatial variation of the Doppler centroid and the azimuthal resolution. The calculation expression is as follows: Where c represents the speed of light, B r Indicates bandwidth, and They represent the imaging width along the x-axis and y-axis that meet the resolution index requirements, respectively, dc represents the Doppler centroid, and Respectively represent the linear change rate of the Doppler centroid about the coordinate axis x and y; f dr represents the Doppler modulation frequency; k T1 and k R1 represents the linear term of the double base distance; B dop Denotes the Doppler bandwidth of the reference point, B sv It represents the spectrum broadening caused by the Doppler center of mass variation, which is related to the beam rotation mode and the shifted dual-base configuration. inc Indicates spectrum broadening caused by spectrum tilt; And PRF needs to satisfy the constraint C2(p), which is expressed as follows: Among them, B ins represents the instantaneous Doppler bandwidth; S5. Establish a joint performance optimization and resource management problem model; The mathematical expression corresponding to the joint performance optimization and resource management (JPO-RM) problem is as follows: in, It represents the imaging performance requirements for specific SAR application scenarios, and L represents the requirements corresponding to the indicators; The inequality problem of formula (14) is transformed into an optimization problem, and the optimization problem expression is as follows: Where f(p) represents a single-objective optimization problem, μ k represents the weighting coefficient, h k (p) indicates that the imaging performance exceeds the required size, and the expression is as follows: The single-objective optimization problem f(p) in formula (15) is a constrained optimization problem. It is transformed into an unconstrained form through the adaptive penalty function method, and the expression is as follows: Among them, P j (p) represents the violation of PRF on the range ambiguity and azimuth ambiguity constraints, which includes three constraints in C1(p)≤0 and one constraint in C2(p)≤0. j (p) is expressed as follows: P j (p)=max(0,c j,low (p)-c j (p),c j (p)-c j,upp (p)) (18) Among them, c j (p) represents the jth constraint, c j,low (p) and c j,upp (p) represents the upper and lower bounds of the jth constraint; satisfying {p|P j The solution with (p) = 0, j = 1, 2, 3, 4} is called a feasible solution; Represents the adaptive fuzzy penalty function factor, which is expressed as follows: in, Indicates that different constraint violations are scaled to the same scale and updated in each iteration; m represents the proportion of feasible solutions in the mth iteration; S6. Input the required imaging performance indicators according to actual needs; S7, initialize system parameters, number of particles and number of iterations; Initialize the system, randomly generate N1 particles, set the maximum number of iterations G1, and initialize the speed of each particle; S8. Solve the optimization problem through particle swarm optimization method based on compartmentalized learning and supervised learning.

2. The method for combined performance optimization and resource management of a microwave imaging system according to claim 1, characterized in that: The step S8 is specifically as follows: S81, calculating the objective function values of all particles in the current generation; Calculate the i-th particle of the m-th generation Corresponding performance indicators And calculate the amount of each constraint violation Determine whether the current particle is a feasible solution, record the set of all infeasible solutions as Ψ0, the set of all feasible solutions as Ψ1, and calculate the proportion of feasible solutions χ at the mth iteration m , calculate the objective function value S82, calculation of domain optimality and individual historical optimality; Compare the domain optimality and individual historical optimality of all particles in the mth generation. If the i-th particle in the mth generation Compare Good, then quilt Instead, otherwise remain unchanged; in, represents the i-th particle of the m-th generation The individual history of the best; Then update the neighborhood optimal, Indicates p i The optimal solution in the adjacent area is expressed as follows: in, Indicates taking out the smallest k numbers in a vector; D i Represents the row vector of the i-th row or the column vector of the i-th column of the normalized distance matrix D; D is a symmetric matrix, representing any two elements and The normalized distance between the two, then the element d of the matrix ij m The expression is as follows: S83, updating relevant parameters and the speed and position of particles; Currently, the particle set is divided into feasible solution set and infeasible solution set through the separation learning strategy, and different learning methods are adopted for the two parts of the solution set; If feasible solution Learning position information from the global optimum is transformed into an infeasible solution; if Learn from the domain optimality, search the domain space, and avoid transformation into infeasible solutions; infeasible solutions The speed of is not affected by other particles, then Randomly search the entire solution space to find the global optimal solution; the speed update method is expressed as follows: Where w represents the inertia coefficient, r1 and r2 represent random numbers uniformly distributed from 0 to 1, c1 and c2 represent adaptive triangular acceleration factors, which are non-negative and guide the search process of the current particle; Represents the speed of the i-th particle in the m-th generation. In the particle swarm optimization method based on compartmentalized learning and supervised learning, trigonometric functions are used as the variation of the search factor to adjust the iterative step size. The expression is as follows: Among them, c max and c min Respectively represent the upper and lower limits of the acceleration factor. The adaptive triangular acceleration factors c1 and c2 make the particle swarm focus on the optimal solution interval at the beginning of the search, and focus on the individual optimal solution in the later stage of the iteration. S84. Update the global optimal solution The optimal solution among all solutions of the mth generation is recorded as S85, calculating the supervised learning function and updating the inactive solution; A supervised learning strategy is proposed, which uses a new activity evaluation method to screen inactive solutions and regenerate them. The supervised learning strategy is expressed as follows: in, Indicates activity, ||D i || indicates the degree of congestion; particles with low activity and high congestion are updated again; If satisfied Delete s, Indicates the pre-set screening threshold; S86: Determine whether the imaging performance requirements are met. If not, reiterate steps S81-S85 until the iteration is complete. If the imaging performance requirements are met, stop the iteration and output the optimal solution, i.e., the optimization result.

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