GEO target translation compensation method based on GRFT and GAPSO

Abstract

The present invention relates to a method for compensating for GEO target translation based on GRFT and GAPSO. The method comprises: acquiring a GEO target echo signal at an optimal imaging aperture; constructing a target translation polynomial based on the target translation trajectory in the preprocessed signal; initializing a parameter search space; performing long-term coherent integration under various parameters in the parameter search space; obtaining an initial solution based on the long-term coherent integration results; updating the historical optimal values ​​of the swarm and each particle based on the initial solution; performing crossover and mutation operations on the particles; iteratively updating the historical optimal values ​​of the swarm and each particle based on the long-term coherent integration results of the current particle; and, when an iteration stop condition is met, outputting the historical optimal value of the current swarm as the optimal polynomial coefficient vector; and performing translation compensation on the GEO target echo signal based on the optimal polynomial coefficient vector. This method can effectively compensate for GEO target translation and form a well-focused image.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular to a GEO target translation compensation method based on GRFT and GAPSO. Background Art

[0002] For ISAR imaging, rotation is crucial for azimuth resolution, while translation can cause range migration and phase errors, resulting in defocus and distortion in the resulting ISAR image. When target motion is complex, RID imaging algorithms based on time-frequency analysis can mitigate Doppler defocus in ISAR images to some extent, but they still suffer from issues such as low azimuth resolution and severe cross-interference. Therefore, refined and robust translational compensation for space targets over long coherence times remains essential.

[0003] Existing translational compensation methods can be categorized into two types: non-parametric and parametric. Traditional non-parametric methods typically do not rely on specific models or parameter estimation and primarily involve a two-step translational compensation approach: envelope alignment and phase correction. Envelope alignment aims to align echo envelopes without prior information. However, existing methods are sensitive to echo signal-to-noise, particularly in low signal-to-noise ratio (SNR) environments, where they often struggle to accurately extract echo envelope information. Key phase correction methods include the prominent point method and image minimum entropy-based phase correction. The prominent point method fails when the primary scattering point is overwhelmed by strong noise. While image minimum entropy-based methods are more robust than the prominent point method at low SNRs, they are still prone to local optima and failure at extremely low SNRs. Furthermore, good envelope alignment is a prerequisite for phase correction. When the target echo envelope is contaminated by strong noise, envelope alignment performance degrades dramatically, hindering subsequent phase correction accuracy.

[0004] In recent years, GEO targets have become a research hotspot. Compared to space targets, GEO targets offer advantages such as wide surface coverage, short revisit periods, and strong survivability, leading to their widespread application in fields such as topographic mapping and information communications. Currently, research on imaging GEO targets primarily focuses on Inverse Synthetic Aperture Lidar (ISAL), while relatively little research has been conducted using ground-based ISAR imaging. Therefore, ISAR imaging of GEO targets remains a promising area.

[0005] Current research on ISAR imaging of GEO targets assumes that the target's translational motion is fully compensated. This primarily addresses the cross-range unit motion correction caused by rotation, without considering the GEO target's translational motion. However, due to factors such as high orbital altitude, GEO target echo signals typically exhibit extremely low signal-to-noise ratios. Furthermore, the target's motion is complex within the long coherent processing time required for detection and imaging. This makes it difficult to effectively compensate for the translational motion of GEO targets during ISAR imaging, resulting in low imaging success rates and insufficient focusing accuracy. Summary of the Invention

[0006] Based on this, it is necessary to provide a GEO target translation compensation method based on GRFT (Generalized RadonFourier Transform) and GAPSO to address the above technical problems.

[0007] A GEO target translation compensation method based on GRFT and GAPSO, the method comprising:

[0008] Acquiring a GEO target echo signal at a preset optimal imaging aperture, preprocessing the GEO target echo signal, and constructing a target translation polynomial based on the translation trajectory of the target in the preprocessed signal; the target translation polynomial includes a polynomial coefficient vector;

[0009] Initializing the parameter search space, the number of particles, and the position and velocity of each particle, performing long-term coherent accumulation under each parameter in the parameter search space, obtaining a rough estimate of the polynomial coefficient vector based on the long-term coherent accumulation result, using the rough estimate as the initial solution, updating the historical optimal value of the swarm and each particle based on the initial solution, performing crossover and mutation operations on the particles, iteratively updating the historical optimal value of the swarm and each particle based on the long-term coherent accumulation result of the current particle, stopping the iteration until a condition for stopping the iteration is met, and outputting the historical optimal value of the current swarm as the optimal polynomial coefficient vector;

[0010] The GEO target echo signal is subjected to translation compensation according to the optimal polynomial coefficient vector, and ISAR imaging is achieved according to the translation compensation result.

[0011] In one embodiment, the method further includes: traversing each vector in the parameter search space, calculating the translation trajectory corresponding to the current vector, performing long-term coherent accumulation of the signal along the translation trajectory, and obtaining a corresponding long-term coherent accumulation result; selecting a vector corresponding to the optimal value from the long-term coherent accumulation results corresponding to each vector, and obtaining a rough estimate of the polynomial coefficient vector.

[0012] In one embodiment, the method further includes: in each iteration, calculating the fitness of the particle based on the long-term coherent accumulation result of the current particle, and updating the historical optimal value of the group and each particle based on the fitness of each particle; updating the particle position based on the position and velocity of the current particle, and updating the particle velocity based on the position of the current particle, the historical optimal value, and the historical optimal value of the group; performing crossover and mutation operations on particles whose fitness is lower than a threshold, updating the group based on the crossover result and the mutation result, and updating the historical optimal value of the group and each particle; iteratively updating the historical optimal value of the group and each particle based on the long-term coherent accumulation result of the current particle until the condition for stopping the iteration is met, stopping the iteration, and outputting the historical optimal value of the current group as the optimal polynomial coefficient vector.

[0013] In one embodiment, the method further includes: calculating the fitness of the particle according to the long-term coherent accumulation result of the current particle as follows:

[0014]

[0015] Among them, f fit (·) represents the fitness function of the particle, s GRFT (·) represents the peak energy after long-term coherent accumulation, represents the i-th particle at the J-th iteration, J = 0, 1, 2, ..., J max represents the number of iterations, f r represents the range frequency domain, τ represents the fast time, s represents the target echo signal, f c is the carrier frequency of the transmitted signal, and K represents the signal frequency modulation slope.

[0016] In one embodiment, the method further includes: a change in the group historical optimal value is less than a threshold; and the change in the group historical optimal value is a difference between the group historical optimal value of the current iteration and the group historical optimal value of the previous iteration.

[0017] In one of the embodiments, the method further includes: a condition for stopping the iteration includes reaching a maximum number of iterations.

[0018] In one embodiment, the method further includes: predicting the ERV amplitude of the GEO target based on prior information of the space target orbit, selecting the optimal imaging aperture of the GEO target within the time interval when the ERV amplitude of the GEO target is maximum and the ERV direction is relatively stable, observing the GEO target based on the optimal imaging aperture, and obtaining the GEO target echo signal.

[0019] In one embodiment, the method further includes: selecting discrete sample points from the parameter search space, performing interpolation according to a preset interpolation method and the discrete sample points, covering the parameter search space, and initializing the parameter search space.

[0020] A GEO target translation compensation device based on GRFT and GAPSO, the device comprising:

[0021] a polynomial construction module, configured to obtain a GEO target echo signal at a preset optimal imaging aperture, preprocess the GEO target echo signal, and construct a target translation polynomial based on the target translation trajectory in the preprocessed signal; the target translation polynomial includes a polynomial coefficient vector;

[0022] A coefficient solving module is used to initialize the parameter search space, the number of particles, and the position and velocity of each particle, perform long-term coherent accumulation under each parameter in the parameter search space, obtain a rough estimate of the polynomial coefficient vector based on the long-term coherent accumulation result, use the rough estimate as the initial solution, update the historical optimal value of the group and each particle based on the initial solution, perform crossover and mutation operations on the particles, iteratively update the historical optimal value of the group and each particle based on the long-term coherent accumulation result of the current particle, and stop iteration when the iteration stopping condition is met, and output the historical optimal value of the current group as the optimal polynomial coefficient vector;

[0023] The result output module is used to perform translation compensation on the GEO target echo signal according to the optimal polynomial coefficient vector, and realize ISAR imaging according to the translation compensation result.

[0024] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0025] Acquiring a GEO target echo signal at a preset optimal imaging aperture, preprocessing the GEO target echo signal, and constructing a target translation polynomial based on the translation trajectory of the target in the preprocessed signal; the target translation polynomial includes a polynomial coefficient vector;

[0026] Initializing the parameter search space, the number of particles, and the position and velocity of each particle, performing long-term coherent accumulation under each parameter in the parameter search space, obtaining a rough estimate of the polynomial coefficient vector based on the long-term coherent accumulation result, using the rough estimate as the initial solution, updating the historical optimal value of the swarm and each particle based on the initial solution, performing crossover and mutation operations on the particles, iteratively updating the historical optimal value of the swarm and each particle based on the long-term coherent accumulation result of the current particle, stopping the iteration until a condition for stopping the iteration is met, and outputting the historical optimal value of the current swarm as the optimal polynomial coefficient vector;

[0027] The GEO target echo signal is subjected to translation compensation according to the optimal polynomial coefficient vector, and ISAR imaging is achieved according to the translation compensation result.

[0028] The GEO target translation compensation method based on GRFT and GAPSO obtains GEO target echo signals under a preset optimal imaging aperture, preprocesses the GEO target echo signals, and constructs a target translation polynomial based on the translation trajectory of the target in the preprocessed signals. The parameter search space, the number of particles, and the position and velocity of each particle are initialized. Long-term coherent integration is performed under various parameters in the parameter search space. A rough estimate of the polynomial coefficient vector is obtained based on the long-term coherent integration result. The rough estimate is used as the initial solution. The historical optimal value of the group and each particle is updated based on the initial solution. Crossover and mutation operations are performed on the particles. The historical optimal value of the group and each particle is iteratively updated based on the long-term coherent integration result of the current particle until the iteration stop condition is met. The iteration is stopped and the historical optimal value of the current group is output as the optimal polynomial coefficient vector. The GEO target echo signals are translated according to the optimal polynomial coefficient vector, and ISAR imaging is achieved based on the translation compensation result. The embodiment of the present invention can effectively compensate for GEO target translation and form a well-focused image, while maintaining imaging quality. The computational complexity is greatly reduced, thereby improving the efficiency of ISAR imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 1 is a flow chart of a GEO target translation compensation method based on GRFT and GAPSO in one embodiment;

[0030] Figure 2 Schematic diagram of the change of ERV amplitude and direction of a GEO target over time in one embodiment, where (a) is a GEO target in a circular orbit, and (b) is a GEO target in an elliptical orbit with an eccentricity of 0.2;

[0031] Figure 3 Schematic diagram of an ISAR imaging turntable model in one embodiment;

[0032] Figure 4 1 is a flow chart of a GEO target translation compensation method based on GRFT and GAPSO in one embodiment;

[0033] Figure 5 A schematic diagram showing a comparison of mean square errors among the method of the present invention, GRFT, and IQEM-BFGS in one embodiment;

[0034] Figure 6 FIG1 is a structural block diagram of a GEO target translation compensation device based on GRFT and GAPSO in one embodiment;

[0035] Figure 7 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0037] In one embodiment, Figure 1 As shown in FIG, a GEO target translation compensation method based on GRFT and GAPSO is provided, which includes the following steps:

[0038] Step 102 : Acquire a GEO target echo signal under a preset optimal imaging aperture, preprocess the GEO target echo signal, and construct a target translation polynomial based on the translation trajectory of the target in the preprocessed signal.

[0039] Due to the movement of GEO targets and the geometric observation relationship between the radar and the GEO targets, not every time interval is suitable for GEO target detection and ISAR imaging: within a certain time interval, the radar cannot observe the GEO target; the GEO target moves in a complex manner within the observation interval, making it difficult to focus and achieve coherent accumulation and ISAR imaging; too short an observation time leads to insufficient signal-to-noise ratio and imaging resolution, while too long an observation time leads to a sharp increase in computational complexity. The movement of space targets is relatively stable and can be predicted to a certain extent, and the attitude of space targets is generally strictly controlled, and the angular change of the target relative to the radar line of sight can be accurately calculated based on the orbital information. Therefore, the present invention selects the optimal imaging aperture based on the prior information of the space target to achieve the detection and imaging of the GEO target.

[0040] The target translation polynomial includes the polynomial coefficient vector. When using GRFT for long-term coherent integration, the target echo signal will experience range migration after range compression due to the influence of target translation. Coherent integration of the signal along different path trajectories can produce different accumulation results. When the signal follows the correct translation trajectory, When performing coherent accumulation, A peak is formed at this point. is the optimal polynomial coefficient vector.

[0041] Step 104: Initialize the parameter search space, the number of particles, and the position and velocity of each particle. Perform long-term coherent accumulation under each parameter in the parameter search space. Obtain a rough estimate of the polynomial coefficient vector based on the long-term coherent accumulation result. Use the rough estimate as the initial solution. Update the historical optimal values ​​of the swarm and each particle based on the initial solution. Perform crossover and mutation operations on the particles. Iteratively update the historical optimal values ​​of the swarm and each particle based on the long-term coherent accumulation result of the current particle. Stop the iteration when the condition for stopping the iteration is met, and output the historical optimal value of the current swarm as the optimal polynomial coefficient vector.

[0042] Since GRFT obtains the translation polynomial coefficients by traversing all parameters in the parameter search space Γ and performing coherent accumulation over the full aperture, the amount of calculation is extremely large, and as the parameter search dimension K increases, the computational complexity increases exponentially. The present invention uses a particle swarm optimization algorithm (GAPSO) based on an improved genetic algorithm to solve the translation polynomial coefficients, which can reduce the computational complexity while maintaining imaging quality. In addition, the heuristic optimization algorithm is used to optimize the parameter search process, eliminating the need to exhaustively enumerate all possible solutions in the parameter space. By simulating the social behavior of animals and utilizing the collective wisdom of a group with an information sharing mechanism, it can more efficiently find the global optimal solution in the parameter space, avoiding blind searches in the parameter space, thereby effectively reducing the algorithm complexity and improving the efficiency of target translation compensation.

[0043] Step 106 : performing translation compensation on the GEO target echo signal according to the optimal polynomial coefficient vector, and implementing ISAR imaging according to the translation compensation result.

[0044] The method of the present invention not only performs long-term coherent accumulation of target echoes, ensuring that a well-focused ISAR image can be formed under ultra-low signal-to-noise ratio, but also uses GAPSO for parameter search optimization. While ensuring algorithm robustness and imaging quality, it greatly reduces the computational complexity, can effectively compensate for target translation and form a well-focused image.

[0045] In the GEO target translation compensation method based on GRFT and GAPSO, a GEO target echo signal is obtained under a preset optimal imaging aperture, the GEO target echo signal is preprocessed, and a target translation polynomial is constructed based on the translation trajectory of the target in the preprocessed signal; a parameter search space, the number of particles, and the position and velocity of each particle are initialized; a long-term coherent integration is performed under various parameters in the parameter search space; a rough estimate of the polynomial coefficient vector is obtained based on the long-term coherent integration result; the rough estimate is used as the initial solution; the historical optimal value of the group and each particle is updated based on the initial solution; crossover and mutation operations are performed on the particles; the historical optimal value of the group and each particle is iteratively updated based on the long-term coherent integration result of the current particle until the iteration stop condition is met, the iteration is stopped, and the historical optimal value of the current group is output as the optimal polynomial coefficient vector; translation compensation of the GEO target echo signal is performed based on the optimal polynomial coefficient vector, and ISAR imaging is achieved based on the translation compensation result. The embodiment of the present invention can effectively compensate for GEO target translation and form a well-focused image, while maintaining imaging quality and greatly reducing computational complexity, thereby improving ISAR imaging efficiency.

[0046] In one embodiment, obtaining a GEO target echo signal at a preset optimal imaging aperture includes: predicting the ERV amplitude of the GEO target based on prior information about the space target's orbit, selecting the optimal imaging aperture of the GEO target within a time interval when the ERV amplitude of the GEO target is maximum and the ERV direction is relatively stable, observing the GEO target based on the optimal imaging aperture, and obtaining the GEO target echo signal.

[0047] In this embodiment, orbital dynamics shows that the six elements of a GEO target's orbit can be used to derive the target's trajectory in different coordinate systems. Assuming the satellite coordinate system's origin is at the center of the Earth, the X-axis points to the orbit's perigee, the Z-axis points to the normal to the orbital plane, and the Y-axis direction is determined by the right-hand rule. Kepler's laws and the two-body motion equation show that the GEO target's position vector and velocity in the satellite coordinate system can be expressed as:

[0048]

[0049] Where k = a(1-e 2 ) is the semi-diameter, r is the distance between the GEO target and the center of the earth, e is the eccentricity, a is the semi-major axis, f is the true anomaly, μ = 398600.44 km 3 / s 2 is the gravitational constant.

[0050] Through coordinate system transformation, the effective rotation angular velocity of the three-axis steady-state GEO target can be analytically expressed as

[0051]

[0052] Among them, ω e is the effective rotation angular velocity (ERV) of the target, v Radar，e is the speed of the target perpendicular to the radar line of sight in the radar coordinate system, × represents the cross product, I represents the unit vector in the radar line of sight, and R0 represents the distance between the radar and the target.

[0053] The direction of ERV is defined as the angle between it and the initial moment at any moment. The schematic diagram of the change of ERV amplitude and direction of GEO target over time is as follows: Figure 2 As shown in the figure, (a) shows a GEO target on a circular orbit, and (b) shows a GEO target on an elliptical orbit with an eccentricity of 0.2. As can be seen from the figure, the target exhibits complex motion relative to the radar during long coherence times, and the target's ERV exhibits a dual time-varying characteristic, meaning both the ERV amplitude and direction change over time. This poses a significant challenge to traditional ISAR imaging. Therefore, considering the dual time-varying nature of the ERV when selecting the optimal imaging aperture is crucial for achieving refined translational compensation and successful detection and imaging of GEO targets.

[0054] Since the amplitude and direction of the GEO target ERV are time-varying, the selection of the optimal imaging aperture should be considered from both the amplitude and direction aspects. On the one hand, due to the azimuth resolution ρ a satisfy:

[0055]

[0056] Where λ is the signal wavelength, T p Therefore, the larger the ERV amplitude, the higher the azimuth resolution, and the imaging aperture should be selected where the amplitude is maximum.

[0057] On the other hand, the change of ERV direction will make the imaging projection plane change in the coherent integration time, and any change of the imaging projection plane in the coherent integration time will seriously affect the imaging quality. Therefore, the imaging aperture should be selected within the time interval when the ERV direction is relatively stable. In summary, the imaging aperture of the geosynchronous orbit target should be selected within ω e The time interval with large amplitude and relatively stable direction. The relatively stable time interval refers to the time interval when the time derivative of the angle between the ERV direction and the initial moment is close to 0.

[0058] In one embodiment, after obtaining the GEO target echo signal under the preset optimal imaging aperture, the GEO target echo signal is pre-processed. The schematic diagram of the ISAR imaging turntable model is as follows: Figure 3As shown. The instantaneous distance between the scattering point (x, y) on the target and the radar is:

[0059] r(t)=R(t)+x sinθ(t)-g cosθ(t) (4)

[0060] Where t represents the slow time, R(t) represents the instantaneous distance between the radar and the target's rotation center, which usually represents the translational component of the target, and θ(t) represents the instantaneous rotation angle of the target.

[0061] Assume that the radar transmits a linear frequency modulated pulse signal

[0062]

[0063] Where τ represents fast time, T p represents the pulse duration, f c is the carrier frequency of the transmitted signal, and K represents the signal frequency modulation slope. Therefore, the baseband signal of the target echo after down-conversion can be expressed as

[0064]

[0065] Where σ(x, y) represents the scattering coefficient of the target scattering point with coordinates (x, g), and c is the speed of light. After matching the echo signal, perform FFT in the fast time dimension, ignoring the constant term introduced, and the signal can be expressed as

[0066]

[0067] Substituting formula (4) into formula (7), we can get

[0068]

[0069] Assume that the amplitude of the effective rotation angular velocity during the coherent integration time is ω eff , we can get the rotation angle during this period of time as θ(t) = ω eff For ISAR imaging, the rotation angle during the coherent integration time is usually small, typically 3-4°. Therefore, there is an approximate expression:

[0070]

[0071] Based on this approximation, we can get

[0072]

[0073] In motion compensation, in addition to compensating for the translational component, it is also necessary to compensate for the migration across range units, that is, rotation compensation. Generally, when the target rotation angle is small, the range unit migration can be limited to one range unit. Therefore, this chapter assumes that the target rotation is small and can be approximated as a uniform rotation, that is, θ(t) = ω eff t, the cross-range unit migration caused by rotation has been well corrected when performing translation compensation.

[0074] In formula (10), the phase term Represents the envelope shift caused by translation, the phase term is the phase error caused by translation. These two terms correspond exactly to the two steps in traditional translation compensation, namely envelope alignment and phase correction. Generally, the accuracy of envelope alignment is very small, about one range unit. However, the phase error caused by translation is related to the radar wavelength and is much smaller than one range unit. Due to the limitation of range resolution, the estimation of the translation component during envelope alignment usually cannot meet the requirements of accurate phase correction. Therefore, envelope alignment can be regarded as a rough estimate of the target translation, while phase correction is a precise estimate of the translation component. In fact, it can be found from Equation (10) that when performing translation compensation, as long as the target's translation history R(t) can be accurately estimated, accurate phase correction can be achieved simultaneously during envelope alignment.

[0075] Based on the signal model, this paper also models the target's translational history as a polynomial when performing translational compensation, employing a parameterized translational compensation method. The signal model indicates that different scattering points on the target have the same translational history, R(t). Therefore, this paper uses the strongest scattering point on the target as the reference point, ignoring the influence of the rotational component at that point and focusing on the translational component at that point. We perform a coherent accumulation of all echoes from that point. Once the translational polynomial coefficients for that point are found during the GRFT traversal search, a peak is formed in the parameter search space. The parameters corresponding to this peak can be considered as the coefficients of the translational polynomial.

[0076] In one embodiment, long-term coherent accumulation is performed under each parameter in the parameter search space, and a rough estimate of the polynomial coefficient vector is obtained based on the long-term coherent accumulation result, including: traversing each vector in the parameter search space, calculating the translation trajectory corresponding to the current vector, performing long-term coherent accumulation of the signal along the translation trajectory, and obtaining the corresponding long-term coherent accumulation result; and selecting the vector corresponding to the optimal value from the long-term coherent accumulation result corresponding to each vector to obtain a rough estimate of the polynomial coefficient vector.

[0077] In this embodiment, first, in order to more accurately estimate the coefficient α of the target translation polynomial, it is necessary to establish a K-dimensional parameter search space Γ containing real parameters.

[0078] Γ=[α 1，L , α 1，R ]×[α 2，L , α 2，R ]×…×[α K，L , α K，R ] (11)

[0079] Among them, α n，L and α n，R Represent the upper and lower bounds of the nth dimension of the parameter search space Γ respectively. For any vector in Γ The corresponding time-varying translational component is

[0080]

[0081] Next, GRFT is used to perform translation compensation and convert the echo signal after pulse compression into a multi-dimensional parameter domain, that is, the translation compensation results are coherently accumulated along the slow time dimension.

[0082]

[0083] The vector corresponding to the optimal value is selected from the long-term coherent accumulation results corresponding to each vector to obtain a rough estimate of the polynomial coefficient vector.

[0084] In one embodiment, initializing the parameter search space includes: selecting discrete sample points from the parameter search space, performing interpolation according to a preset interpolation method and the discrete sample points, covering the parameter search space, and initializing the parameter search space.

[0085] In one embodiment, iteratively updating the historical optimal values ​​of the group and each particle based on the long-term coherent accumulation result of the current particle until the condition for stopping the iteration is met, stopping the iteration, and outputting the historical optimal value of the current group as the optimal polynomial coefficient vector includes: in each iteration, calculating the fitness of the particle based on the long-term coherent accumulation result of the current particle, and updating the historical optimal value of the group and each particle based on the fitness of each particle; updating the particle position based on the position and velocity of the current particle, and updating the particle velocity based on the position of the current particle, the historical optimal value, and the historical optimal value of the group; performing crossover and mutation operations on particles whose fitness is lower than a threshold, updating the group based on the crossover and mutation results, and updating the historical optimal value of the group and each particle; iteratively updating the historical optimal value of the group and each particle based on the long-term coherent accumulation result of the current particle until the condition for stopping the iteration is met, stopping the iteration, and outputting the historical optimal value of the current group as the optimal polynomial coefficient vector.

[0086] Specifically, if Figure 4As shown in the figure, a flow chart for an algorithm for estimating polynomial coefficient vectors based on GRFT and GAPSO is provided. The concept of the particle swarm algorithm originates from the study of bird foraging behavior. Birds share information within the group to find the optimal destination. This algorithm converges quickly but is prone to getting stuck in local optima. To address this problem, the present invention evaluates the fitness of each particle and applies the crossover and mutation operations of the genetic algorithm to particles with low fitness, thereby enhancing the algorithm's global search capability and avoiding getting stuck in local optima. The specific steps of the algorithm are as follows:

[0087] Step 1: Initialization. Initialize the parameters of the GAPSO algorithm, including the parameter search space Γ, the number of particles I, and the maximum number of iterations J. max etc., initialize the position and velocity of each particle

[0088]

[0089] Among them, i=1, 2,...,I.

[0090] Step 2: Rough estimation based on GRFT. As with other optimization algorithms, providing an initial solution close to the true value can accelerate convergence. Therefore, before running the GAPSO algorithm, a rough estimate of α can be obtained at a low computational cost. This rough estimate is achieved by performing a line search within the parameter search space Γ. To improve computational efficiency, this paper only uses a small number of discrete sample points and interpolates to cover the entire parameter search space. The rough estimate of α is determined by finding the maximum point on the interpolated function.

[0091] Step 3: Calculate the fitness function. In the Jth iteration, calculate the fitness function of the i-th particle

[0092]

[0093] Where J = 0, 1, 2, ..., J max Represents the number of iterations.

[0094] Step 4: Update the historical optimal value and position of the group and each particle in is the optimal position of the i-th particle, is the optimal position of the group.

[0095] Step 5: Update the position and velocity vectors.

[0096]

[0097] Among them, ω J is the inertia weight in the Jth iteration, and the inertia weight ω is usually adjusted dynamically during the iteration process. JIn order to balance the globality and convergence speed of convergence, r1 and r2 are two independent random variables uniformly distributed between (0, 1], c1 and c2 are individual and group learning factors, respectively, representing the weights of the individual and group optimal positions.

[0098] Step 6: Perform crossover and mutation operations on particles.

[0099] Step 7: Determine whether the termination condition is reached (the change in the historical optimal value of the group Less than the preset value or reaching the maximum number of iterations J max ). If the termination condition is met, then output Otherwise, return to Step 3.

[0100] In one embodiment, calculating the fitness of the particle according to the long-term coherent accumulation result of the current particle includes: calculating the fitness of the particle according to the long-term coherent accumulation result of the current particle as:

[0101]

[0102] Among them, f fit (·) represents the fitness function of the particle, s GRFT (·) represents the peak energy after long-term coherent accumulation, represents the i-th particle at the J-th iteration, J = 0, 1, 2, ..., J max represents the number of iterations, f r represents the range frequency domain, τ represents the fast time, s represents the target echo signal, f c is the carrier frequency of the transmitted signal, and K represents the signal frequency modulation slope.

[0103] In one embodiment, the conditions for stopping iteration include: the change in the group's historical optimal value is less than a threshold; the change in the group's historical optimal value is the difference between the group's historical optimal value in the current iteration and the group's historical optimal value in the previous iteration.

[0104] In one embodiment, the condition for stopping the iteration includes reaching a maximum number of iterations.

[0105] In a specific example, the effectiveness of the proposed algorithm was verified using a simulated point target consisting of 70 scattering points, 47.5 meters long and 32 meters wide. To compare the performance of different methods at different signal-to-noise ratios, independent white Gaussian noise with different signal-to-noise ratios was added to the echo data. Tables 1, 2, and 3 respectively show the image entropy, peak value, and contrast of the images generated by the different algorithms at different signal-to-noise ratios.

[0106] Table 1 Comparison of image entropy under different signal-to-noise ratios

[0107]

[0108] Table 2 Comparison of image peak values ​​at different signal-to-noise ratios

[0109]

[0110] Table 3 Image contrast comparison under different signal-to-noise ratios

[0111]

[0112] As can be seen from the table, the imaging results of the proposed method achieve superior image quality compared to the IQEM (Image Quality Evaluation Metric)-BFGS (Quasi-Newton Method) and MCRA (Maximum Correlation Range Alignment)-SDS (Single Dominant Scatter Method). Although the proposed method exhibits slightly higher image entropy and lower image contrast than GRFT, its computational complexity is significantly lower than that of GRFT. This is primarily due to GRFT's traversal search approach to search for appropriate parameters in parameter space. This means that as long as the traversal search interval is sufficiently small, GRFT can almost always find the optimal coefficients at the expense of computational complexity. This is what gives GRFT a slight advantage in image entropy and image contrast entropy. In summary, the proposed method not only offers improved stability at ultra-low signal-to-noise ratios, but also significantly reduces computational complexity while producing target images of higher quality.

[0113] In addition, the mean square error between the estimated parameters and the true parameters can be used to measure the accuracy of parameter estimation. The mean square error comparison diagram of the method of the present invention, GRFT and IQEM-BFGS is shown in the figure below. Figure 5 As shown in the figure, it can be seen that the translation polynomial coefficients estimated by the proposed method are almost close to the true parameters, while the mean square error of IQEM-BFGS increases sharply under ultra-low signal-to-noise ratio.

[0114] Table 4 shows the runtime of the proposed algorithm and GRFT at different signal-to-noise ratios. As can be seen from the table, the proposed algorithm takes almost half the time of GRFT. This is because GRFT uses an ergodic parameter search, while the proposed algorithm utilizes a heuristic optimization algorithm, eliminating the need to exhaustively search for all possible solutions in the parameter space. By simulating the social behavior of animals and leveraging the collective intelligence of animals with information sharing mechanisms, the proposed algorithm can more efficiently find the global optimal solution in the parameter space.

[0115] Table 4 Running time of the proposed algorithm and GRFT under different signal-to-noise ratios

[0116]

[0117] In summary, the proposed method is significantly superior to IQEM-BFGS and MCRA-SDS, especially in ultra-low signal-to-noise ratio environments. Its performance is very similar to GRFT, but with significantly reduced algorithmic complexity, resulting in a significantly shorter time to generate well-focused ISAR images.

[0118] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0119] In one embodiment, Figure 6 As shown in FIG, a GEO target translation compensation device based on GRFT and GAPSO is provided, comprising:

[0120] A polynomial construction module 602 is configured to obtain a GEO target echo signal at a preset optimal imaging aperture, preprocess the GEO target echo signal, and construct a target translation polynomial based on the target translation trajectory in the preprocessed signal; the target translation polynomial includes a polynomial coefficient vector;

[0121] The coefficient solving module 604 is used to initialize the parameter search space, the number of particles, and the position and velocity of each particle, perform long-term coherent accumulation under each parameter in the parameter search space, obtain a rough estimate of the polynomial coefficient vector based on the long-term coherent accumulation results, use the rough estimate as the initial solution, update the historical optimal value of the swarm and each particle based on the initial solution, perform crossover and mutation operations on the particles, iteratively update the historical optimal value of the swarm and each particle based on the long-term coherent accumulation results of the current particle, and stop the iteration when the iteration stop condition is met, outputting the historical optimal value of the current swarm as the optimal polynomial coefficient vector;

[0122] The result output module 606 is used to perform translation compensation on the GEO target echo signal according to the optimal polynomial coefficient vector, and realize ISAR imaging according to the translation compensation result.

[0123] In one embodiment, the method further includes: traversing each vector in the parameter search space, calculating the translation trajectory corresponding to the current vector, performing long-term coherent accumulation of the signal along the translation trajectory, and obtaining a corresponding long-term coherent accumulation result; selecting a vector corresponding to the optimal value from the long-term coherent accumulation results corresponding to each vector, and obtaining a rough estimate of the polynomial coefficient vector.

[0124] In one embodiment, the method further includes: in each iteration, calculating the fitness of the particle based on the long-term coherent accumulation result of the current particle, and updating the historical optimal value of the group and each particle based on the fitness of each particle; updating the particle position based on the position and velocity of the current particle, and updating the particle velocity based on the position of the current particle, the historical optimal value, and the historical optimal value of the group; performing crossover and mutation operations on particles whose fitness is lower than a threshold, updating the group based on the crossover result and the mutation result, and updating the historical optimal value of the group and each particle; iteratively updating the historical optimal value of the group and each particle based on the long-term coherent accumulation result of the current particle until the condition for stopping the iteration is met, stopping the iteration, and outputting the historical optimal value of the current group as the optimal polynomial coefficient vector.

[0125] In one embodiment, the method further includes: calculating the fitness of the particle according to the long-term coherent accumulation result of the current particle as follows:

[0126]

[0127] Among them, f fit (·) represents the fitness function of the particle, s GRFT (·) represents the peak energy after long-term coherent accumulation, represents the i-th particle at the J-th iteration, J = 0, 1, 2, ..., J max represents the number of iterations, f r represents the range frequency domain, τ represents the fast time, s represents the target echo signal, f c is the carrier frequency of the transmitted signal, and K represents the signal frequency modulation slope.

[0128] In one embodiment, the method further includes: a change in the group's historical optimal value is less than a threshold; and the change in the group's historical optimal value is a difference between the group's historical optimal value in the current iteration and the group's historical optimal value in the previous iteration.

[0129] In one of the embodiments, the method further includes: a condition for stopping iteration includes reaching a maximum number of iterations.

[0130] In one embodiment, the method further includes: predicting the ERV amplitude of the GEO target based on prior information of the space target orbit, selecting the optimal imaging aperture of the GEO target within the time interval when the ERV amplitude of the GEO target is maximum and the ERV direction is relatively stable, observing the GEO target based on the optimal imaging aperture, and obtaining the GEO target echo signal.

[0131] In one embodiment, the method further includes: selecting discrete sample points from the parameter search space, performing interpolation according to a preset interpolation method and the discrete sample points, covering the parameter search space, and initializing the parameter search space.

[0132] The specific definitions of the GRFT- and GAPSO-based GEO target translation compensation device can be found in the definitions of the GRFT- and GAPSO-based GEO target translation compensation method described above and will not be repeated here. Each module in the GRFT- and GAPSO-based GEO target translation compensation device described above can be implemented in whole or in part via software, hardware, or a combination thereof. Each of these modules can be embedded in or independent of a processor in a computer device in hardware form, or can be stored in a computer device memory in software form, allowing the processor to call and execute the corresponding operations of each of these modules.

[0133] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 7 As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a GEO target translation compensation method based on GRFT and GAPSO is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad provided on the computer device housing, or an external keyboard, touchpad or mouse.

[0134] Those skilled in the art will understand that Figure 7 The structure shown in the figure is merely a block diagram of a portion of the structure related to the solution of the present invention and does not constitute a limitation on the computer device to which the solution of the present invention is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0135] In one embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps of the method in the above embodiment when executing the computer program.

[0136] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0137] The above-described embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that a person skilled in the art would be able to make numerous modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A GEO target translation compensation method based on GRFT and GAPSO, characterized by: The method comprises: Acquiring a GEO target echo signal at a preset optimal imaging aperture, preprocessing the GEO target echo signal, and constructing a target translation polynomial based on the translation trajectory of the target in the preprocessed signal; the target translation polynomial includes a polynomial coefficient vector; Initializing the parameter search space, the number of particles, and the position and velocity of each particle, performing long-term coherent accumulation under each parameter in the parameter search space, obtaining a rough estimate of the polynomial coefficient vector based on the long-term coherent accumulation result, using the rough estimate as the initial solution, updating the historical optimal value of the swarm and each particle based on the initial solution, performing crossover and mutation operations on the particles, iteratively updating the historical optimal value of the swarm and each particle based on the long-term coherent accumulation result of the current particle, stopping the iteration until a condition for stopping the iteration is met, and outputting the historical optimal value of the current swarm as the optimal polynomial coefficient vector; performing translation compensation on the GEO target echo signal according to the optimal polynomial coefficient vector, and implementing ISAR imaging according to the translation compensation result; The historical optimal values ​​of the group and each particle are iteratively updated according to the long-term coherent accumulation results of the current particle until the conditions for stopping the iteration are met. The iteration stops and the historical optimal value of the current group is output as the optimal polynomial coefficient vector, including: In each iteration, the fitness of the particle is calculated based on the long-term coherent accumulation results of the current particle, and the historical optimal values ​​of the group and each particle are updated according to the fitness of each particle; Update the particle position according to the current particle position and velocity, and update the particle velocity according to the current particle position, historical optimal value and historical optimal value of the group; Perform crossover and mutation operations on particles whose fitness is lower than the threshold, update the population based on the crossover and mutation results, and update the historical optimal values ​​of the population and each particle; The historical optimal values ​​of the group and each particle are iteratively updated according to the long-term coherent accumulation results of the current particle until the conditions for stopping the iteration are met. The iteration stops and the historical optimal value of the current group is output as the optimal polynomial coefficient vector.

2. The method according to claim 1, characterized in that Performing long-term coherent accumulation under each parameter in the parameter search space and obtaining a rough estimate of the polynomial coefficient vector according to the long-term coherent accumulation result includes: Traversing each vector in the parameter search space, calculating the translation trajectory corresponding to the current vector, and performing long-term coherent accumulation of the signal along the translation trajectory to obtain a corresponding long-term coherent accumulation result; The vector corresponding to the optimal value is selected from the long-term coherent accumulation results corresponding to each vector to obtain a rough estimate of the polynomial coefficient vector.

3. The method according to claim 1, characterized in that The fitness of the particle calculated based on the long-term coherent accumulation result of the current particle includes: The fitness of the particle is calculated based on the long-term coherent accumulation result of the current particle: in, represents the fitness function of the particle, It represents the peak energy after long-term coherent accumulation. Indicates the The first iteration particles, represents the number of iterations, represents the distance frequency domain, Indicates fast time, Indicates the target echo signal, is the carrier frequency of the transmitted signal, represents the signal frequency modulation slope, Indicates slow time.

4. The method according to claim 1, wherein The conditions for stopping the iteration include: The change in the historical optimal value of the group is less than a threshold; the change in the historical optimal value of the group is the difference between the historical optimal value of the group in the current iteration and the previous iteration.

5. The method according to claim 1, wherein The condition for stopping the iteration includes reaching the maximum number of iterations.

6. The method according to claim 1, characterized in that Acquiring a GEO target echo signal at a preset optimal imaging aperture includes: Based on the prior information of the space target's orbit, the ERV amplitude of the GEO target is predicted. The optimal imaging aperture of the GEO target is selected within the time interval when the ERV amplitude of the GEO target is maximum and the ERV direction is relatively stable. The GEO target is observed based on the optimal imaging aperture to obtain the GEO target echo signal.

7. The method according to claim 1, characterized in that The initialization parameter search space includes: Discrete sample points are selected from the parameter search space, and interpolation is performed according to a preset interpolation method and the discrete sample points to cover the parameter search space, thereby initializing the parameter search space.

8. A GEO target translation compensation device based on GRFT and GAPSO applied to the method according to any one of claims 1 to 7, characterized in that: The device comprises: a polynomial construction module, configured to obtain a GEO target echo signal at a preset optimal imaging aperture, preprocess the GEO target echo signal, and construct a target translation polynomial based on the target translation trajectory in the preprocessed signal; the target translation polynomial includes a polynomial coefficient vector; A coefficient solving module is used to initialize the parameter search space, the number of particles, and the position and velocity of each particle, perform long-term coherent accumulation under each parameter in the parameter search space, obtain a rough estimate of the polynomial coefficient vector based on the long-term coherent accumulation result, use the rough estimate as the initial solution, update the historical optimal value of the group and each particle based on the initial solution, perform crossover and mutation operations on the particles, iteratively update the historical optimal value of the group and each particle based on the long-term coherent accumulation result of the current particle, and stop iteration when the iteration stopping condition is met, and output the historical optimal value of the current group as the optimal polynomial coefficient vector; The result output module is used to perform translation compensation on the GEO target echo signal according to the optimal polynomial coefficient vector, and realize ISAR imaging according to the translation compensation result.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

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