A frequency-agile waveform HRRP integrated imaging method with multidimensional non-ideal factor errors

Abstract

This invention provides a frequency-agile waveform HRRP integrated imaging method for multi-dimensional non-ideal factor errors. It involves determining the estimated parameters of the HRRP image; in the current search loop, inputting the estimated parameters corresponding to the previous cost function into the cost function of the current search loop in an optimization algorithm combining the sparrow search algorithm and the simulated annealing algorithm; repeating the process of determining the cost function and estimated parameters until the loop termination condition is met to obtain the optimal estimated parameters; and using the optimal value of the estimated parameters to determine the optimal HRRP image. This invention transforms the error correction problem into a target parameter estimation problem, designs a more accurate and robust cost function for searching the optimal parameters, and proposes a joint optimization algorithm of simulated annealing and sparrow search algorithms to reduce the possibility of the search algorithm getting trapped in local optima, thereby expanding the overall search range and achieving high-precision HRRP and ISAR synthesis under unstable radar system conditions.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to a frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors. Background Technology

[0002] As a radio device with all-weather, all-day, and long-range detection capabilities, radar detects targets and determines their spatial location by emitting electromagnetic waves and utilizing the backscattered echoes. It is a crucial target detection tool in the military field. A high-resolution range profile (HRRP) is the vector sum of all scattered echoes from the electromagnetic wave signal emitted by a high-resolution broadband radar within each resolution range cell of the target. It contains relatively detailed information such as the target's shape, structure, size, and the distribution of scattering centers. Compared to two-dimensional synthetic aperture radar (SAR) images / inverse synthetic aperture radar (ISAR) images, HRRP has advantages such as convenient acquisition, small data volume, and fast processing speed. Target recognition technology based on HRRP is also a research hotspot in the field of radar automatic target recognition (RATR). Traditional HRRP synthesis algorithms are based on the assumption that the received signal has a constant amplitude and a stable carrier frequency. This assumption is valid when the radar system is stable. However, when the radar system is unstable, errors in system parameters can occur, leading to time-varying amplitude and carrier frequency shifts in the echo. These factors result in low accuracy for traditional parameter estimation algorithms based on constant amplitude signals and constant carrier models, especially when the target is moving at high speed. Therefore, it is necessary to develop a new imaging algorithm to achieve high-speed target HRRP imaging under non-ideal conditions.

[0003] Existing methods for synthesizing broadband signals from narrowband signals to obtain HRRP (High Range Resolved Potential) mainly fall into two categories: time-domain bandwidth synthesis and frequency-domain bandwidth synthesis. The basic idea of ​​time-domain bandwidth synthesis is to combine the echo signals of multiple narrowband linear frequency modulated (LFM) sub-pulses from a single LFM agile signal pulse group into a large-bandwidth LFM signal through time shifting, frequency shifting, and phase compensation. Matched filtering then yields a high-resolution range signal. The basic idea of ​​frequency-domain bandwidth synthesis is to concatenate the spectra of multiple sub-pulses after phase compensation to obtain frequency domain data with a support domain expanded several times. Performing an inverse Fourier transform yields an HRRP with a range resolution several times higher. Compared to time-domain bandwidth synthesis, frequency-domain bandwidth synthesis has lower computational complexity and a simpler processing flow. However, regardless of the algorithm used, motion compensation is a prerequisite for successful bandwidth synthesis. Therefore, a reasonable mathematical model needs to be established, and parameters such as target motion need to be estimated.

[0004] Existing methods are based on the premise that the radar system is stable, the amplitude of the radar echo is constant, and the carrier frequency does not shift. However, when the radar system is unstable, errors in system parameters will occur, resulting in time-varying amplitude and carrier frequency shifts in the echo. These factors will lead to low accuracy of traditional parameter estimation algorithms based on constant amplitude signals and constant carrier models, especially when the target is moving at high speed, this effect is more pronounced. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention provides a frequency-agile waveform HRRP integrated imaging method for multi-dimensional non-ideal factor errors. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors, comprising:

[0007] S100, determine the estimated parameters of the HRRP image; the estimated parameters include the time-varying amplitude, velocity and carrier frequency offset of the target;

[0008] S200, in the current search loop, the estimated parameters corresponding to the cost function of the previous time are input into the optimization algorithm that combines the sparrow optimization algorithm and the simulated annealing algorithm to obtain the undetermined estimated parameters. Based on the undetermined estimated parameters, the echo signal imaging process is performed to obtain a one-dimensional HRRP image, and the cost function of the current search loop is evaluated.

[0009] S300: Take each search loop number as the current search loop number, and repeat the process of S200 until the loop termination condition is met, and obtain the optimal estimated parameters;

[0010] S400, determine the optimal HRRP image using the optimal estimation parameters.

[0011] Beneficial effects:

[0012] 1. The frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors proposed in this invention can be adapted to more complex scenarios. For cases with carrier frequency offset and amplitude time-varying multidimensional non-ideal factor errors, the target echo is established as a refined multidimensional joint correction error signal model in this invention, which transforms the error correction problem into a target parameter estimation problem, and realizes high-precision HRRP and ISAR synthesis under unstable radar system conditions.

[0013] 2. Based on the proposed multi-dimensional non-ideal factor error-based frequency-agile waveform HRRP comprehensive imaging method, this invention designs a novel multi-criteria fusion cost function based on image entropy, peak signal-to-noise ratio, and signal energy. By rationally combining multiple image evaluation indicators, compared with single-criteria methods based on image quality measures such as entropy, contrast, or sharpness, the cost function used by this invention to search for optimal parameters is more accurate and robust.

[0014] 3. This invention addresses the problem of estimating parameters by probabilistically combining simulated annealing and sparrow search algorithms. By utilizing the characteristic of simulated annealing to receive poor solutions, the optimal fitness update mechanism in the sparrow search algorithm is modified, reducing the possibility of the search algorithm getting trapped in local optima. This expands the overall search range and achieves accurate estimation of radar parameters.

[0015] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors provided by the present invention.

[0017] Figure 2 This is a flowchart of echo imaging using an optimized algorithm provided by the present invention;

[0018] Figure 3 This is a schematic diagram of the target HRRP synthesis when non-ideal factors exist;

[0019] Figure 4 This is a schematic diagram of an HRRP image obtained after processing echoes affected by non-ideal factors using the method proposed in this invention.

[0020] Figure 5 A schematic diagram of a 3D point cloud model of an aircraft target;

[0021] Figure 6A composite HRRP image of an aircraft target under low-speed conditions with non-ideal factors;

[0022] Figure 7 This is a schematic diagram of the HRRP synthesis results for an aircraft target under non-ideal conditions.

[0023] Figure 8 HRRP composite images of aircraft targets in different scenarios. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0025] Before introducing the present invention, the concept of the present invention will be briefly described first.

[0026] To address the problem of synthesizing high-resolution one-dimensional range profiles using frequency agility to counteract waveform in the presence of non-ideal factors such as unstable carrier frequency and amplitude, this invention establishes a corresponding mathematical model and proposes a corresponding HRRP synthesis strategy: First, a refined mathematical model of the radar echo with multi-dimensional non-ideal factors such as unstable carrier frequency and amplitude is established, transforming the error correction problem into a parameter estimation problem; then, the echo is mixed, and the resulting signal is multiplied by the derived corresponding coefficients to remove the influence of time-varying amplitude and carrier frequency offset on the signal; subsequently, pulse compression is performed, and the influence of target motion and sub-pulse jumps on the signal phase is eliminated in the frequency domain; the signal is then frequency-shifted, stitched together, and IFFT is used to obtain a one-dimensional range profile; finally, a multi-criteria fusion cost function is designed, and a parameter search algorithm combining simulated annealing and sparrow search is used to search for the parameters used in the above process to synthesize the one-dimensional range profile, selecting appropriate parameter search results to achieve HRRP synthesis under non-ideal conditions.

[0027] This invention focuses on the problem of synthesizing high-resolution one-dimensional range images of high-speed targets in space under non-ideal conditions such as unstable carrier frequency and amplitude. Based on a mathematical model of the non-ideal scenario, the invention gradually eliminates the influence of unstable echo carrier frequency and inconsistent echo amplitude on the target echo through derivation, and eliminates the phase shift in the echo caused by the high-speed movement of the target in the frequency domain. Using a composite optimization algorithm, a suitable cost function is selected, and the optimal parameters are searched using a parameterization method, thereby achieving bandwidth synthesis in the frequency domain and realizing the synthesis of high-resolution one-dimensional range images of linear frequency modulated step signals.

[0028] The details of the present invention are described below.

[0029] Combination Figure 1 and Figure 3 This invention provides a frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors, including:

[0030] S100, determine the estimated parameters of the HRRP image; the estimated parameters include the time-varying amplitude, velocity and carrier frequency offset of the target;

[0031] S200, in the current search loop, the estimated parameters corresponding to the cost function of the previous time are input into the optimization algorithm that combines the sparrow optimization algorithm and the simulated annealing algorithm to obtain the undetermined estimated parameters. Based on the undetermined estimated parameters, the echo signal imaging process is performed to obtain a one-dimensional HRRP image, and the cost function of the current search loop is evaluated.

[0032] Suppose a linear frequency modulated signal consists of M chirp sub-pulses, and the m-th sub-pulse is:

[0033]

[0034] Where A is the amplitude of the sub-pulse, which is a constant under stable radar system conditions. m It is the carrier frequency, f m =f0+xΔf is the carrier frequency of the m-th sub-pulse signal, Δf is the carrier frequency step, and x is a random permutation of {0,1,2,3,…,M-1}, which allows the transmitted signal carrier frequency to change rapidly. μ=B / T p It is the frequency modulation slope, B is the bandwidth, and T is the frequency modulation slope. p This represents the pulse width. To save time, t m =mT r Let T be the transmission time of the m-th sub-pulse. r This is the pulse repetition period.

[0035] Assuming the target consists of n scattering points, the distance between the nth scattering point and the radar when the mth sub-pulse signal is emitted is:

[0036] R nm =R n -V T ·mT r

[0037] Where R n V represents the initial position of the nth scattering point. T Let represent the radial velocity of the target, and 'a' be the acceleration. The m-th subpulse echo signal received by the radar is:

[0038]

[0039] Most existing signal models for synthesizing HRRP maps using radar signals are based on ideal conditions. However, in practical applications, factors such as radar system instability can affect the received echo, degrading the image synthesis quality to some extent. Therefore, it is necessary to consider these factors. When considering amplitude time-varying and carrier frequency shift, the echo signal can be expressed as:

[0040]

[0041] Where amplitude A(t) represents the amplitude as a function of time, and Δf' represents the carrier frequency offset.

[0042] refer to Figure 3 The echo signal imaging process of the present invention includes:

[0043] Step 1: Obtain the echo signal of the m-th sub-pulse;

[0044] Step 2: Mix the echo signal of the m-th sub-pulse to obtain the baseband signal after mixing the m-th sub-pulse, denoted as...

[0045]

[0046] Among them, theoretically It is a theoretical estimate of the carrier frequency offset.

[0047] Step 3: Remove the influence of time-varying amplitude on the baseband signal after mixing the m-th sub-pulse to obtain the time-varying amplitude processed signal, represented as:

[0048]

[0049] Step 4: Remove the influence of carrier frequency offset from the time-varying amplitude processed signal to obtain the processed signal, represented as:

[0050]

[0051] Step 5: Perform pulse compression on the processed signal to obtain the result of the pulse compression in the frequency domain, as follows:

[0052]

[0053] First, use the envelope alignment algorithm to Φ m (f) After compensation, the parameterization method is used to compensate Φ. 0m The corresponding phase yields the following signal:

[0054]

[0055] Step 6: After compressing the signal pulses in the frequency domain, perform frequency spectrum shifting and splicing in the corresponding order to obtain the spliced ​​signal, represented as:

[0056]

[0057] Step 7: Perform IFFT transform on the spliced ​​signal to obtain the HRRP image, represented as:

[0058] s 8c (t) = IFFT[S 7r (f)];

[0059] in, f is the carrier frequency, and Δf is the carrier frequency offset.

[0060] The process of finding the optimal HRRP image, or the process of finding the optimal estimated parameters, is a cost function optimization problem. The cost function proposed in this invention is...

[0061] K = S + ω1B + ω2C

[0062] Where S is the image entropy of the HRRP image, B is the energy change of the sub-pulse before and after removing the time-varying amplitude, C is the reciprocal of the peak signal-to-noise ratio (PSNR) of the HRRP image, and ω1 and ω2 are control parameters that control the influence of parameters B and C on the result within a certain proportion. Image entropy is used to characterize the image sharpness; the smaller the entropy, the sharper the image. The smaller B is, the more consistent the energy before and after removing the time-varying amplitude, and the smaller the impact on the echo. The smaller C is, the higher the PSNR of the obtained HRRP image, and the clearer the pattern. Therefore, the smaller the cost function K, the better the image quality.

[0063] The method proposed in this invention for correcting time-varying amplitude and carrier frequency offset and synthesizing HRRP maps of high-speed targets based on the minimum cost function criterion aims to find the method that minimizes the cost function K. Then use This involves correcting signals containing irrational factors. This problem can be viewed as a cost function optimization problem, where the optimization function can be expressed as:

[0064]

[0065] This invention searches for parameters by setting a reasonable search step size and search range, and by using an optimization algorithm that combines the proposed cost function with the sparrow optimization algorithm and the simulated annealing algorithm.

[0066] In an optional embodiment of the present invention, S200 includes:

[0067] S210, In the current search loop, the estimated parameters corresponding to the cost function of the previous time are input into the optimization algorithm that combines the sparrow optimization algorithm and the simulated annealing algorithm. The position and fitness of the sparrow are updated using the fitness and position update formula of the optimization algorithm to obtain the position and fitness of the current search loop.

[0068] The fitness is obtained by performing an echo signal imaging process using the updated position to obtain a one-dimensional HRRP image and evaluating the one-dimensional HRRP image.

[0069] 1. Sparrow Optimization Algorithm

[0070] The Sparrow Search Algorithm (SSA) is a swarm intelligence optimization algorithm based on the behavior of sparrows foraging for food and escaping predators. This algorithm exhibits strong search capabilities and parallelism when solving global optimization problems in practical applications. The SSA has two main characteristics: attributes and behaviors. Attributes refer to the sparrows' location, while behaviors are primarily threefold: individuals who find better food act as discoverers, other individuals act as followers, and discoverers are responsible for searching for food to provide location and direction. Followers obtain food by following discoverers. The roles of producers and predators change dynamically, but their proportion in the overall population remains constant. Simultaneously, a certain proportion of individuals in the population are selected for scouting and early warning; if danger is detected, they abandon food, prioritizing safety.

[0071] Simulated annealing is derived from the principle of solid-state annealing. Solid-state annealing gradually reduces the objective function f (internal energy) until it reaches the global minimum by decreasing the control parameter T. The characteristic of simulated annealing is that it starts from a relatively high temperature and accepts inferior solutions with a certain probability P, thus escaping local optima. That is, during the decrease of T, random perturbations generate new solutions. If the new solution is better than the current solution, it is accepted; otherwise, the Metropolis criterion is used to determine whether to accept the new solution.

[0072] Because the Sparrow Search Algorithm (SSA) updates its algorithm greedily by replacing the optimal position and fitness, it is prone to getting trapped in local optima in the later stages. Simulated Annealing (SSA), on the other hand, has a certain probability of accepting "poor" performing solutions, meaning it can probabilistically escape local optima, thus helping to expand the overall search range of the sparrow population. Therefore, this invention introduces the Metropolis criterion from simulated annealing into the Sparrow Search Algorithm to address the SSA's tendency to get trapped in local optima.

[0073] Combination Figure 1 and Figure 3 In an optional embodiment of the present invention, S210 includes:

[0074] S211, set the current search loop count as t;

[0075] S212, input the estimated parameters corresponding to the cost function of the (t - 1)-th time into the optimization algorithm combining the sparrow optimization algorithm and the simulated annealing algorithm, and use the sparrow position update formula of the sparrow optimization algorithm to update the positions of the discoverers, followers, and scouts in the sparrow group to obtain the positions of the discoverers, followers, and scouts of the t-th time;

[0076] In S212, the position of the n-th sparrow in the sparrow group is expressed as:

[0077]

[0078] where, x n,d represents the position of the n-th sparrow in the d-th dimension;

[0079] The fitness value of the n-th sparrow in the D-dimensional solution space is expressed as:

[0080]

[0081] where, k is the fitness value, and the subscript d represents the dimension in the D-dimensional solution space.

[0082] The sparrow update formula in S212 includes the discoverer, follower, and scout update formulas;

[0083] The discoverer position update formula is expressed as:

[0084]

[0085] where, i = 1, 2, 3,..., n is the sparrow serial number; t is the search loop count; iter max is the maximum iteration count; α is rand(0, 1); the variable Q follows a Gaussian distribution; L is a 1·d matrix with all elements being 1; R2 (R2 ∈ [0, 1)) and ST (ST ∈ [0.5, 1)) are the warning value and the safety value respectively. R2 < ST indicates that there is no danger in the surrounding external environment at this time, and the discoverer can fully execute the search strategy; R2 ≥ ST indicates that the follower is discovered by an individual in the sparrow population and needs to immediately send a warning message to the other sparrow individuals in the population so that the sparrow population can quickly escape to a safe area;

[0086] The position update formula of the follower is:

[0087]

[0088] where, X best and X worstThese represent the optimal and worst positions of the producer, respectively; A is a matrix of size 1·D, where each dimension is randomly selected from {-1,1}, and A+ = AT(AAT)-1; N is the size of the sparrow population; i>N / 2 indicates that follower i has not received food and is in a state of hunger, needing to obtain more energy to replenish itself;

[0089] While sparrows forage, some are on guard. When danger approaches, they abandon their current food and move to a new location. The formula for updating the position of the scouts is:

[0090]

[0091] in, The current global best position is represented by J; the range of J is rand(-1,1); β is the step size control parameter; ki is the optimal fitness value of the sparrow; kg is the global optimal fitness value; kω is the worst fitness value; ε is the minimum constant to avoid division by zero error; when ki>kg, the sparrow will move to the vicinity of the optimal position, and when ki=kg, the sparrow will move to the vicinity of itself.

[0092] S213, using the positions of the discoverer, follower, and scout in the t-th iteration, calculate the fitness of each sparrow in the t-th iteration;

[0093] S214. Using the Metropolis criterion of the simulated annealing algorithm, determine whether to select the fitness of the target sparrow i-1 times with a certain probability P as the fitness of the target sparrow in the tth time to obtain the judgment result.

[0094] The probability P in S214 is expressed as:

[0095]

[0096] Where kt represents the fitness of the current search cycle t, kt+1 represents the fitness of the search cycle t+1; μ represents the Boltzmann constant, and T represents the control parameter.

[0097] S215, if the judgment result indicates that the fitness of the target sparrow in the (t-1)th iteration is selected as the fitness of the target sparrow in the i-th iteration, then the fitness of the target sparrow in the (t-1)th iteration is accepted as the fitness of the target sparrow in the i-th iteration; otherwise, the fitness of the target sparrow in the t-th iteration in S213 is determined.

[0098] S216, retain the fitness and position of each sparrow in the t-th iteration.

[0099] The improved algorithm updates the fitness and position of each sparrow in the t-th iteration, denoted as:

[0100]

[0101] S220, the fitness of the current search iteration is used as the cost function of the current search iteration, and the position of the current search iteration is used as the estimated parameter of the current search iteration.

[0102] S300: Take each search loop number as the current search loop number, and repeat the process of S200 until the loop termination condition is met, and obtain the optimal estimated parameters;

[0103] This step includes: S310, repeating the process of S200 to update the sparrow's fitness and position until the maximum number of cycles is satisfied; S320, determining the estimated parameters when the maximum number of cycles is satisfied as the optimal estimated parameters.

[0104] S400, determine the optimal HRRP image using the optimal estimation parameters.

[0105] The actual effects of the present invention will be verified below.

[0106] 1. Simulation experiment based on a single point target

[0107] This invention focuses on addressing the impact of multidimensional non-ideal factors, such as time-varying amplitude and carrier frequency shift, on the quality of synthesized images when radar systems are unstable. First, a simulation experiment is conducted using a single scattering point to visually observe the influence of non-ideal factors on HRRP synthesis. The main simulation parameters are shown in Table 1. The radar transmission signal uses a frequency-agile signal.

[0108] Table 1. Main parameters of the target and radar

[0109]

[0110]

[0111] Figure 3 The effects of non-ideal factors on the synthesis of the target HRRP are demonstrated. Figure 3 Figure (a) shows a comparison between the amplitude variation of a single sub-pulse with time-varying amplitude and an ideal constant amplitude. Figure 3 Figure (b) shows a comparison between the synthesized HRRP under non-ideal conditions of amplitude variation over time and the synthesized HRRP under constant amplitude. It can be seen that, compared with ideal conditions, the time-varying subpulse amplitude affects the main-to-side lobe ratio of the synthesized HRRP image, resulting in a decrease in the main-to-side lobe ratio of the synthesized image. Figure 3 Figure (c) shows a comparison of the results with and without carrier frequency offset in the radar echo. The image results demonstrate that carrier frequency offset causes range deviation, leading to inaccurate ranging results. It also reduces the main-to-sidelobe ratio of the synthesized image, resulting in degraded image quality. Figure 3As can be seen in Figure (d), when there are multidimensional non-ideal factors, the image quality is reduced compared with the ideal HRRP result.

[0112] By processing radar echoes using the method proposed in this invention, the influence of non-ideal factors can be effectively eliminated. For example... Figure 4 As shown. Figure 4 This invention describes the processing of HRRP images obtained after the echoes are affected by non-ideal factors. The processed images are compared with a reference image under ideal conditions and an HRRP image with errors. It can be observed that after parameter compensation using the algorithm of this invention, the synthesized HRRP image is very close to the reference image. This confirms the effectiveness of the proposed method.

[0113] 2. Simulation experiment based on multi-point targets

[0114] This invention verifies the effectiveness of the proposed method by utilizing multiple experimental scenarios of multi-objective HRRP synthesis.

[0115] Figure 5 A 3D point cloud model of the aircraft target was depicted, along with corresponding XY, XZ, and YZ axis images. Table 2 shows the key simulation parameters used in the experiment. Figure 6 This is a composite HRRP image of an aircraft target under low-speed conditions with non-ideal factors. Figure 6 (a) shows the reference signal, and (b) shows the image synthesis result with non-ideal factors when the target velocity is 100 m / s. The image entropy (IE) of the synthesized HRRP with non-ideal factors and its correlation coefficient (CC) with the reference image were calculated. It can be seen that when the velocity is low, the impact of non-ideal factors on the synthesis result is relatively small. In practical applications, aircraft targets are usually low-speed. However, for specific radar systems, such as satellite radar and missile-borne radar, the relative velocity between the radar platform and the aircraft target can be significantly increased. Subsequent experiments were conducted based on this.

[0116] Table 2 Key Simulation Parameters

[0117] parameter numerical values Synthetic bandwidth 400MHz carrier frequency 10GHz Sub-pulse number 15 Sub-pulse width 50MHz Sub-pulse step frequency 25MHz Carrier frequency offset 10kHz Time-varying amplitude <![CDATA[0.66·sin(7×10 5 ·t+3)+0.8]]>

[0118] Figure 7 The purpose is to verify the effects of amplitude time variation and carrier frequency offset on the synthesized HRRP of aircraft targets. Figure 7 Figure (a) is an ideal reference figure when the target is stationary and without error. Figure 7 Figure (b) is a composite HRRP map of the target with time-varying amplitude. Figure 7 Figure (c) is the synthesized HRRP map when the target has a carrier frequency shift. Figure 7Figure (d) shows the synthesized HRRP image when the target has multidimensional non-ideal errors. The comparison shows that when the signal amplitude varies over time, the target's main-to-side lobe ratio decreases, and the similarity to the reference signal decreases slightly. When the signal has carrier frequency shift, the similarity between the target and the reference signal decreases significantly. When joint errors exist, the image quality of the synthesized HRRP is worse than that synthesized with a single error. Therefore, it is necessary to study error compensation techniques to restore image quality.

[0119] Figure 8 HRRP composite images of aircraft targets in different scenarios. Figure 8 The middle (a) image is a reference image, which represents an ideal scenario where the target is stationary and without error. Figure 8 Figure (b) shows the HRRP synthesis results when multidimensional non-ideal errors exist. Figure 8 Figure (c) shows the HRRP synthesis results obtained using theoretical parameter compensation. Figure 8 Figure (d) shows the synthesized HRRP result obtained after parameter compensation using the algorithm proposed in this invention. It can be observed that for targets with non-ideal factors such as carrier frequency offset and time-varying amplitude, the synthesized HRRP result differs significantly from the reference image. Quantitatively, when non-ideal factors are introduced, the image entropy and cost function of the synthesized image increase, indicating a decrease in image quality. Furthermore, the correlation coefficient between the synthesized HRRP image and the reference image decreases, indicating reduced image correlation. The theoretical compensation result is to directly compensate the echo using the true parameters and obtain the target amplitude parameters by polynomial fitting of the time-varying amplitude using the least squares method; the synthesized result is very close to the reference image. Using the parameter estimation and compensation method proposed in this invention, the correlation coefficient between the synthesized HRRP image and the reference image reaches over 0.94. These results demonstrate the effectiveness of the proposed method in mitigating the influence of non-ideal factors.

[0120] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0121] Although this application has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0122] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors, characterized in that, include: S100, determine the estimated parameters of the HRRP image; the estimated parameters include the time-varying amplitude, velocity and carrier frequency offset of the target; S200, in the current search loop, the estimated parameters corresponding to the cost function of the previous time are input into the optimization algorithm that combines the sparrow optimization algorithm and the simulated annealing algorithm to obtain the undetermined estimated parameters. Based on the undetermined estimated parameters, the echo signal imaging process is performed to obtain a one-dimensional HRRP image, and the cost function of the current search loop is evaluated. S300: Take each search loop number as the current search loop number, and repeat the process of S200 until the loop termination condition is met, and obtain the optimal estimated parameters. S400, determine the optimal HRRP image using the optimal estimation parameters; S200 includes: S210, In the current search loop, the estimated parameters corresponding to the cost function of the previous time are input into the optimization algorithm that combines the sparrow optimization algorithm and the simulated annealing algorithm. The position and fitness of the sparrow are updated using the fitness and position update formula of the optimization algorithm to obtain the position and fitness of the current search loop. The fitness is obtained by performing an echo signal imaging process using the updated position to obtain a one-dimensional HRRP image and evaluating the one-dimensional HRRP image. S220, use the fitness of the current search iteration as the cost function of the current search iteration, and use the position of the current search iteration as the estimated parameter of the current search iteration; The cost function is expressed as: in, It is the image entropy of the HRRP image. It refers to the energy change of the sub-pulse before and after removing the time-varying amplitude. It is the reciprocal of the peak signal-to-noise ratio of the HRRP image. and These are control parameters; their function is to control the parameters. and The impact on the results should be controlled within a certain proportion.

2. The frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors according to claim 1, characterized in that, S210 includes: S211, Set the current search loop number to... ; S212, the first The estimated parameters corresponding to the cost function of the first step are input into an optimization algorithm that combines the sparrow optimization algorithm and the simulated annealing algorithm. The sparrow position update formula of the sparrow optimization algorithm is used to update the positions of the finder, follower, and scout in the sparrow flock to obtain the first step. The positions of the discoverers, followers, and scouts; S213, utilizing the first The positions of the discoverer, follower, and scout are calculated to determine the first... The adaptability of each sparrow in each round; S214, using the Metropolis criterion of the simulated annealing algorithm, determines whether to proceed with a certain probability. The fitness of the target sparrow is selected i-1 times as the first fitness value. The fitness of the target sparrow was then assessed. S215, if the judgment result indicates selection The fitness of the secondary target sparrow is used as the first The fitness of the target sparrow is then accepted. The fitness of the secondary target sparrow is used as the first The fitness of the target sparrow is then determined; otherwise, the fitness of the first sparrow in S213 is determined. The fitness of the secondary target sparrow; S216, retaining the first Next, we will assess the adaptability and location of each sparrow.

3. The frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors according to claim 1, characterized in that, The S300 includes: S310, repeat the process of S200 to update the sparrow's fitness and position until the maximum number of loops is satisfied; S320 determines the estimated parameters that satisfy the maximum number of iterations as the optimal estimated parameters.

4. The frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors according to claim 3, characterized in that, S212, the first in the sparrow flock The position of a sparrow is represented as: ； in, Indicates the first Only sparrows The position of the dimension; In the D-dimensional solution space, the first The fitness value of a sparrow is represented as: ； in, k For fitness values, subscript This represents the dimension in the D-dimensional solution space.

5. The frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors according to claim 4, characterized in that, The sparrow update formula in S212 includes update formulas for discoverers, followers, and scouts; The formula for updating the discoverer's location is expressed as: ； in, =1, 2, 3, ... The number is the number of the sparrow; For the number of search loops; This represents the maximum number of iterations. The variable is rand(0, 1). Q It follows a Gaussian distribution; L It is a 1•d matrix with all elements of size 1; and These are the warning value and the safety value, respectively. This indicates that there is no danger in the surrounding environment, and the discoverer can fully implement the search strategy. This indicates that the follower has been spotted by an individual in the sparrow population and must immediately send a warning message to the remaining sparrows in the population so that the sparrow population can quickly hide in a safe area. The formula for updating the position of followers is: ； in, and These represent the producer's optimal and worst positions, respectively. It is a matrix of size 1•D, where each dimension is randomly selected from {-1,1}. ; The size of the sparrow population; Indicates followers Having received no food and being in a state of hunger, they need to acquire more energy to replenish themselves; The scout's location update formula is: ； in, Indicates the current global best position; J The range is rand(-1,1); These are the step size control parameters; This represents the optimal fitness value for the sparrow. This is the globally optimal fitness value; This is the value with the worst fitness. It is the smallest constant, which avoids division by zero error; The sparrow will then move to a position near the optimal location. At that moment, the sparrow moved to its vicinity.

6. The frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors according to claim 5, characterized in that, The probability in S214 Represented as: ； in, Indicates the current search loop number. fitness Indicates the number of search loops. The fitness of; Represents the Boltzmann constant; This indicates the control parameters.

7. The frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors according to claim 1, characterized in that, The echo signal imaging process includes: Step 1, obtain the first m Individual pulse echo signals; Step 2, for the first m The sub-pulse echo signals are mixed to obtain the first... m The baseband signal after mixing of individual pulses; Step 3, remove the first m The baseband signal after sub-pulse mixing is processed into a time-varying amplitude signal due to the effect of time-varying amplitude. Step 4: Remove the influence caused by carrier frequency offset from the time-varying amplitude processed signal to obtain the processed signal; Step 5: Perform pulse compression on the processed signal to obtain the result of the pulse-compressed signal in the frequency domain; Step 6: After compressing the signal pulses, perform frequency spectrum shifting in the frequency domain and splice them together in the corresponding order to obtain the spliced ​​signal; Step 7: Perform IFFT transformation on the spliced ​​signal to obtain the HRRP image.

8. The frequency-agile waveform HRRP integrated imaging method for multidimensional non-ideal factor errors according to claim 7, characterized in that, The HRRP image is represented as follows: ； in, , It is the carrier frequency. It is the carrier frequency offset.

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