High-order maneuvering target Doppler compensation method and device based on starfish optimization

Abstract

The invention discloses a high-order maneuvering target Doppler compensation method and device based on starfish optimization, and the method comprises the steps: carrying out the down-conversion and pulse compression processing of a radar echo signal, the echo signal containing a D-order motion parameter of a target, and D being a positive integer greater than or equal to 3; based on a starfish optimization algorithm, iterative optimization is carried out on motion parameters of a target, the position of each starfish in the algorithm is a group of estimation values of D motion parameters, and a group of optimal estimation parameters are found through a judgment standard of fitness; and the group of optimal estimation parameters are substituted into a phase compensation function and multiplied by a signal after pulse compression, and finally, FFT operation is carried out, so that accumulation of target energy in a Doppler domain is realized. The method is high in detection probability and tracking precision and good in real-time performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and particularly relates to a high-order maneuvering target Doppler compensation method and device based on starfish optimization. Background Technique

[0002] In modern radar detection technology, detecting high-maneuvering targets such as aerial drones faces many challenges. Such targets have significant high-order maneuvering characteristics during flight, and their motion trajectories not only include acceleration but may also involve higher-order dynamic changes such as jerk. This complex motion state makes the phase of the radar echo exhibit obvious non-linear time-varying characteristics, bringing great difficulties to target detection. Traditional Moving Target Detection (MTD) technology has obvious limitations when dealing with such high-maneuvering targets. Due to the motion characteristics of high-maneuvering targets, the echo energy will spread among multiple Doppler channels, resulting in the dispersion of the target signal energy. This energy dispersion phenomenon significantly attenuates the signal-to-noise ratio of the target signal, thereby seriously affecting the radar's target detection performance. Therefore, it is of great significance to find new radar signal processing technologies to effectively address the detection challenges of high-maneuvering targets.

[0003] Traditional Doppler compensation methods are mainly based on the linear or low-order nonlinear assumptions of the target motion model, and achieve energy accumulation through phase correction. However, they face significant limitations in high-order maneuvering scenarios: (1) Phase compensation methods based on the uniform / constant acceleration model: MTD relies on the Fourier transform to accumulate the target Doppler frequency shift, assuming that the target maintains uniform or constant acceleration motion within the Coherent Processing Interval (CPI). For example, the Keystone transform corrects the range migration of a constant acceleration target through resampling, but it can only compensate for second-order phase terms. However, the high-order maneuverability of targets such as drones (e.g., acceleration, variable acceleration) will introduce third-order and higher-order phase errors, resulting in residual phase modulation in the compensated signal and further spreading of the Doppler spectrum energy, making it difficult to adapt to complex motion patterns with dynamic changes in practice; (2) Optimization algorithms based on parameter search: For the nonlinear phase compensation problem, Particle Swarm Optimization (PSO), genetic algorithms, etc. are used for motion parameter estimation. For example, by constructing an objective function to optimize parameters such as acceleration and jerk, phase compensation is achieved. However, these algorithms are prone to falling into local optima in high-dimensional parameter spaces (such as joint search of multi-order parameters), and have a slow convergence speed, making it difficult to meet the real-time processing requirements; (3) Methods based on the polynomial phase signal model: The echo of a high-order moving target can be modeled as a polynomial phase signal, and parametric methods (such as the high-order ambiguity function, fractional Fourier transform) are used to estimate the polynomial coefficients and compensate for the phase. For example, the fractional Fourier transform achieves energy focusing by rotating the time-frequency plane, but it needs to traverse multiple fractional orders, with extremely high computational complexity, making it difficult to meet the real-time requirements of drone swarm detection.

[0004] Therefore, the core problems of traditional methods lie in the insufficient model adaptability and computational efficiency, which are respectively reflected in: the low-order motion assumption cannot match the high-order maneuvering characteristics, resulting in compensation residuals; high-dimensional parameter search or fractional transformation is difficult to meet the real-time processing requirements. These problems lead to limited energy accumulation effect of traditional methods in detecting high-maneuver targets such as drones, restricting the radar detection probability and tracking accuracy. Summary of the Invention

[0005] The embodiments of the present invention provide a method and device for Doppler compensation of high-order maneuvering targets based on starfish optimization, which can solve the problems of low detection probability, low tracking accuracy, and poor real-time performance of traditional methods when facing targets in high-order maneuvering scenarios.

[0006] In a first aspect, a method for Doppler compensation of high-order maneuvering targets based on starfish optimization provided by the embodiments of the present invention includes:

[0007] Perform down-conversion and pulse compression processing on the echo signal to obtain the pulse-compressed echo signal, where the echo signal is represented by the D-order motion parameters of the target, and D is a positive integer greater than or equal to 3;

[0008] Based on the starfish optimization algorithm, jointly perform iterative optimization on the D-order motion parameters of the target, and take the position of the last optimal starfish as the optimal estimated value of the D-order motion parameters. Among them, in the starfish optimization algorithm, the position of each starfish is a set of estimated values of the D-order motion parameters, and the fitness of the last optimal starfish is the best;

[0009] Perform Doppler compensation operation on the pulse-compressed echo signal based on the optimal estimated value to obtain the optimal signal after Doppler compensation.

[0010] In a second aspect, an embodiment of the present invention provides a Doppler compensation device for high-order maneuvering targets based on starfish optimization, including:

[0011] A pulse compression unit, which is used to perform down-conversion and pulse compression processing on the echo signal to obtain a pulse-compressed echo signal, where the echo signal is represented by the D-order motion parameters of the target, and D is a positive integer greater than or equal to 3;

[0012] An estimation unit, which is used to jointly perform iterative optimization on the D-order motion parameters of the target based on the starfish optimization algorithm, and take the position of the last optimal starfish as the optimal estimated value of the D-order motion parameters. Among them, in the starfish optimization algorithm, the position of each starfish is a set of estimated values of the D-order motion parameters, and the fitness of the last optimal starfish is the best;

[0013] An output unit, which is used to perform Doppler compensation operation on the pulse-compressed echo signal based on the optimal estimated value to obtain the optimal signal after Doppler compensation.

[0014] The beneficial effects of the embodiments of the present invention compared with the prior art are as follows: Since the present invention uses multiple high-order motion parameters of the target to represent the echo signal and performs phase compensation on the echo signal based on the high-order motion parameters, the residual compensation is smaller when detecting the target in a high-order maneuvering scenario, and the detection accuracy of the target is better; Since the present invention uses the starfish optimization algorithm to jointly optimize the high-order motion parameters, and the starfish optimization algorithm has less computational complexity and computational amount compared with traditional algorithms such as the particle swarm algorithm and the polynomial algorithm, the computational efficiency of the present invention is higher and the real-time performance is better; At the same time, the global optimal solutions of multiple high-order motion parameters can be obtained, further improving the detection probability and tracking accuracy. Description of the Drawings

[0015] Figure 1Flowchart of the implementation of a Doppler compensation method for high-order maneuvering targets based on starfish optimization provided by an embodiment of the present invention;

[0016] Figure 2 Flowchart of the implementation of a method for estimating motion parameters based on starfish optimization algorithm provided by an embodiment of the present invention;

[0017] Figure 3 Schematic structural diagram of a Doppler compensation device for high-order maneuvering targets based on starfish optimization provided by an embodiment of the present invention;

[0018] Figure 4 Doppler domain distribution diagram of the pulse compression echo signal before compensation provided by an embodiment of the present invention;

[0019] Figure 5 Schematic comparison diagram of convergence curves provided by an embodiment of the present invention;

[0020] Figure 6a Doppler domain distribution diagram after compensation based on the method provided by the present invention provided by an embodiment of the present invention;

[0021] Figure 6b Doppler domain distribution diagram after compensation based on particle swarm optimization algorithm provided by an embodiment of the present invention. Detailed implementation manners

[0022] In the following description, specific details such as specific system structures and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present invention. However, those skilled in the art should clearly understand that the present invention can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present invention.

[0023] It should be understood that when used in the specification and appended claims of the present invention, the term "comprising" indicates the presence of the described features, wholes, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or their combinations.

[0024] It should also be understood that the term " / and" as used in the specification and appended claims of the present invention refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0025] As used in the specification of the present invention and the appended claims, the term "if" may be construed, depending on the context, as "when", "once", "in response to determining", or "in response to detecting". Similarly, the phrase "if it is determined" or "if [the described condition or event] is detected" may be construed, depending on the context, to mean "once it is determined", "in response to determining", "once [the described condition or event] is detected", or "in response to detecting [the described condition or event]".

[0026] In addition, in the description of the specification of the present invention and the appended claims, the terms "first", "second", "third", etc. are only used for distinguishing descriptions and cannot be construed as indicating or implying relative importance.

[0027] Referring to "one embodiment" or "some embodiments" described in the specification of the present invention means that a specific feature, structure, or characteristic described in connection with the embodiment is included in one or more embodiments of the present invention. Thus, statements such as "in one embodiment", "in some embodiments", "in other some embodiments", "in still other embodiments", etc. that appear in different places in this specification do not necessarily all refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "comprising", "including", "having" and their variants all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0028] The present invention will be further described in detail below in conjunction with specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0029] The high-order maneuvering target Doppler compensation method based on starfish optimization provided by the embodiments of the present invention can be applied to electronic devices such as mobile terminals, personal laptop computers, supercomputers, etc. The embodiments of the present invention do not impose any restrictions on the specific types of electronic devices.

[0030] Figure 1 Shown is a flowchart of the implementation of a high-order maneuvering target Doppler compensation method based on starfish optimization provided by the embodiments of the present invention. By way of example and not limitation, this method can be applied to the above-mentioned electronic devices. This method may include steps S101 - S103, which will be described below for each step.

[0031] S101, perform down-conversion and pulse compression processing on the echo signal to obtain a pulse-compressed echo signal.

[0032] In a possible implementation manner, the echo signal may be obtained by the target reflecting the transmitted signal of the radar. In order to better detect the target in a high-order maneuvering scenario, the echo signal may be represented by the D-order motion parameters of the target.

[0033] For example, D may be a positive integer greater than or equal to 3.

[0034] For example, the radar transmission signal may be a linear frequency modulation signal, which may satisfy the following formula:

[0035]

[0036] Among them, s t (t,t m ) is the transmitted signal, t, t m are fast time and slow time respectively, T p , f, K are the pulse width, carrier frequency and frequency modulation slope of the transmitted signal respectively, j is the imaginary unit, and the rectangular window function satisfies

[0037] For example, the baseband echo signal received by the radar may satisfy the following formula:

[0038]

[0039] Among them, s r (t,t m ) is the baseband echo signal, R(t m ) is the radial distance to the target, c is the light number, and λ is the wavelength.

[0040] Exemplarily, the pulse pressure echo signal may satisfy the following formula:

[0041]

[0042] Among them, s pc (t,t m ) is the pulse compression echo signal, A is the complex amplitude of the echo after the pulse compression. Here, considering the non-fluctuating situation, A is considered to be a constant; B = K·T p is the bandwidth of the transmitted linear FM signal.

[0043] In one example, the high-order motion parameters of the target may include the speed, angular velocity, etc. of the target.

[0044] For example, if the radial distance of the target in the echo signal is represented by the multi-order velocity of the target, for example, by the fourth-order motion parameters a1 to a4, then the pulse compression echo signal represented by the fourth-order motion parameters can satisfy the following formula:

[0045]

[0046] in:

[0047]

[0048] Optionally, although the moving target has strong maneuverability, in the case of narrowband signals, it can be assumed that the target does not have range walk, but only has Doppler walk or spread caused by high-order maneuver. Therefore, the pulse compression echo signal can approximately satisfy the following formula:

[0049]

[0050] S102. Estimate the D-order motion parameters of the target based on the starfish optimization algorithm to obtain the optimal estimated values of the D-order motion parameters.

[0051] In a possible implementation, a starfish population can be initially generated, which may include a preset number of starfish, and the position of each starfish is a set of estimated values of D-order motion parameters. Then calculate the fitness of each starfish in the initial population, and update the position of each starfish in the population according to the position of the starfish with the best fitness and / or the position of a random starfish to obtain the first starfish population; calculate the fitness of each starfish in the first starfish population, and update the position of each starfish according to the position of the starfish with the best fitness and / or the position of a random starfish to obtain the second starfish population;...; and so on, continue the above process, and iterate the preset number of iterations T max times, and use the position of the starfish with the best fitness in the T max th starfish population (i.e., the T max th optimal starfish) as the optimal estimated value of the D-order parameters.

[0052] Exemplarily, before generating the initial starfish population, the boundaries of each motion parameter can be set first, and then the starfish in the initial population can be randomly generated within the boundaries.

[0053] Specifically, the starfish population can be expressed as:

[0054]

[0055] where X represents a starfish population, and X ij represents the value of the j-th dimension of the position of the i-th starfish X i (i.e., the value of the j-th order motion parameter); i is a positive integer less than or equal to N, and N is the population size (i.e., the above preset number).

[0056] Specifically, in the initial starfish population, the position of each starfish can be calculated by the following formula:

[0057] X ij = l j + r′(u j - l j ), i = 1, 2,..., N, j = 1, 2,..., D (1.8)

[0058] where u j, l j They are the upper and lower limits of the j-th dimension position of the starfish respectively, and r′ is the second random number between [0, 1].

[0059] Optionally, all possible positions of the starfish and the fitness of the starfish at each position can be stored in advance. During optimization, the fitness value is called by indexing with the position of the starfish, simplifying the calculation process of each optimization.

[0060] In one example, the fitness of the starfish can be determined according to the entropy of the signal after Doppler compensation corresponding to the starfish.

[0061] Exemplarily, the estimated value of the motion parameter represented by the position of the starfish can be substituted into the phase compensation function, and the compensation function is multiplied by the pulse compression echo signal; then the multiplication result is subjected to Fourier transform to complete the Doppler compensation operation, obtaining the signal after Doppler compensation corresponding to the starfish; finally, the fitness of the starfish can be obtained according to the entropy of the signal after Doppler compensation corresponding to the starfish.

[0062] Specifically, the lower the entropy value, the better the fitness.

[0063] Exemplarily, if D = 4 and the high-order motion parameter of the target is the 4th-order velocity of the target, the phase compensation function can satisfy the following formula:

[0064]

[0065] Among them, H com represents the phase compensation function.

[0066] Exemplarily, the compensation function can be multiplied by the pulse compression echo signal through the following formula:

[0067] s com = s pc (t, t m )H com (1.10)

[0068] Among them, s com is the multiplication result, and s pc (t, t m ) is the pulse compression echo signal.

[0069] Exemplarily, the entropy of the signal after Doppler compensation can be calculated through the following formula:

[0070]

[0071] Among them, E is the entropy of S com , S com is the entropy of the signal after Doppler compensation corresponding to X i , S com = FFT(scom )

[0072] If the energy of the entropy of the signal after Doppler compensation, ∑|S com | 2 is a constant C, then the entropy of the signal after Doppler compensation can also be calculated by the following formula:

[0073]

[0074] In summary, the fitness of the starfish can satisfy the following formula (1.13) or (1.14):

[0075]

[0076] where F(X i ) is the fitness of the i-th starfish X i , E is the entropy of S com , S com is the entropy of the signal after Doppler compensation corresponding to X i ; C is a constant that satisfies ∑|S com | 2 = C.

[0077] S103. Perform a Doppler compensation operation on the pulse compression echo signal based on the optimal estimate value to obtain the optimal signal after Doppler compensation.

[0078] In one example, the optimal estimation parameter can be substituted into the phase compensation function and multiplied by the signal after pulse compression to obtain a multiplication result, and finally, a Fourier transform operation is performed on the multiplication result to complete the Doppler compensation operation and obtain the signal after Doppler compensation.

[0079] Exemplarily, if D = 4 and the high-order motion parameter of the target is the 4th-order velocity of the target, then the optimal estimate value can satisfy: where a″ j is the optimal estimate value of the j-th order velocity of the target, j is a positive integer less than or equal to D, indicates that the entropy of the optimal signal after Doppler compensation is the smallest.

[0080] Specifically, the optimal estimate value can be the position of the T max -th optimal starfish. Since the process of compensating the phase based on the motion parameter has been performed when calculating the fitness of each starfish in the T max -th starfish population, therefore, the signal after Doppler compensation corresponding to the T max -th optimal starfish can be directly used as the optimal signal after Doppler compensation.

[0081] Since the present invention represents the echo signal using multiple high-order motion parameters of the target and performs phase compensation on the echo signal based on the high-order motion parameters, the compensation residue is small when detecting the target in a high-order maneuvering scenario based on the present invention, and the detection accuracy of the target is better; since the present invention uses the starfish optimization algorithm to jointly optimize the high-order motion parameters, and the starfish optimization algorithm has less computational complexity and computational amount compared with traditional algorithms such as the particle swarm algorithm and the polynomial algorithm, the computational efficiency of the present invention is high and the real-time performance is good; at the same time, the global optimal solutions of multiple high-order motion parameters can also be obtained, further improving the detection probability and tracking accuracy.

[0082] Figure 2 The following shows a flowchart of an implementation of a method for estimating motion parameters based on the starfish optimization algorithm provided by an embodiment of the present invention. By way of example and not limitation, this method may be a possible specific implementation of step S102 in the above compensation method. This method may include the following steps S201-S209, and each step will be described below.

[0083] S201, randomly generate the (T + 1)-th first random number.

[0084] Exemplarily, the range of the first random number r may be between [0, 1]. T is the number of iterations and is a positive integer.

[0085] S202, determine whether the (T + 1)-th random number is greater than a preset stage threshold.

[0086] Generally, the preset stage threshold may be 0.5.

[0087] In one example, if the (T + 1)-th first random number is greater than the preset stage threshold, enter the exploration stage and step S203 can be performed.

[0088] In another example, if the (T + 1)-th first random number is not greater than the preset stage threshold, enter the exploitation stage and step S206 can be performed.

[0089] S203, determine whether D is greater than a preset dimension threshold.

[0090] Generally, the preset dimension threshold is the same as the maximum number of arms of the starfish and is equal to 5.

[0091] Exemplarily, in order to simulate the search ability of the 5 arms of the starfish in the exploration stage, the "eyes" of the starfish can be embedded at the end of the arms, perform 5-dimensional search when D > 5, and perform one-dimensional search when D ≤ 5.

[0092] In one example, if D is greater than a preset dimension threshold, it indicates that the search space for the problem is relatively wide, and the starfish needs to move all 5 arms to explore the surrounding environment. At this time, the arms of the starfish need to know the optimal positions between searches to guide their movements. Therefore, step S204 can be performed to update the model based on the first position, and update the positions of each starfish in the T-th starfish population and the (T + 1)-th starfish population according to the positions of the starfish in the T-th starfish population.

[0093] In another example, if D is not greater than 5, the exploration phase can update the position using one-dimensional search. In this case, only one arm of the starfish will use the positions of other starfish to search for food sources. Therefore, step S205 can be performed to update the model based on the second position, and update the positions of each starfish in the T-th starfish population according to the positions of the random starfish in the T-th starfish population to obtain the (T + 1)-th starfish population.

[0094] S204. Update the model based on the first position, and update the positions of each starfish in the T-th starfish population according to the position of the T-th optimal starfish to obtain the (T + 1)-th starfish population.

[0095] Exemplarily, the T-th optimal starfish is the starfish with the best fitness in the T-th starfish population. The 0-th starfish population can be the above-mentioned initial starfish population.

[0096] In a possible implementation, the model can be updated based on the first position first, and the candidate positions of each starfish in the T-th starfish population can be updated according to the position of the T-th optimal starfish; then it is determined whether there is a problem that the dimensions of the candidate positions of each starfish exceed the boundaries of the dimensions. If so, the starfish discards the candidate positions of that dimension and remains at the position before the update; if not, the candidate positions of that dimension are used as the updated positions of that dimension.

[0097] In one example, the first position update model can satisfy the following formula:

[0098]

[0099] where, is the p-dimensional candidate position of the i-th starfish in the (T + 1)-th starfish population, p is 5 dimensions randomly selected from D, is the p-dimensional position of the i-th starfish in the T-th starfish population, is the p-dimensional position of the T-th optimal starfish.

[0100] where:

[0101] b1 = (2r″ - 1)π(1.16)

[0102]

[0103] Among them, r″ is the third random number between (0, 1). During the exploration stage, b1 can be randomly generated, and can vary with the number of iterations. These two parameters can measure the influence of the distance between the best position and the current position in the selected update dimension.

[0104] Exemplarily, the p-dimensional position of the i-th starfish in the (T + 1)-th starfish population can be calculated by the following formula:

[0105]

[0106] where u b,p , l b,p are respectively the upper and lower limits of the p-dimensional position of the starfish, is the p-dimensional position of the i-th starfish in the (T + 1)-th starfish population.

[0107] S205, Based on the second update model, update the positions of each starfish in the T-th starfish population according to the positions of the random starfishes in the T-th starfish population to obtain the (T + 1)-th starfish population.

[0108] In a possible implementation manner, similarly, first, based on the second position update model, update the candidate positions of each starfish in the T-th starfish population according to the positions of the random starfishes (i.e., randomly selected starfishes) in the T-th starfish population; then determine whether there is a problem that each dimension of the candidate position of each starfish exceeds the boundary of that dimension. If so, the starfish discards the candidate position of that dimension and remains at the position before the update; if not, the candidate position of that dimension is used as the update position of that dimension.

[0109] In an example, the second position update model can satisfy the following formula:

[0110]

[0111] where A1, A2 are two fourth random numbers between [-1, 1], are the p-dimensional positions of two starfishes randomly selected from the T-th starfish population, and the energy of the starfish

[0112] Exemplarily, the sine term in formula (1.15) and the cosine term in the starfish energy respectively indicate that the arms of the starfish may twist to the left or right with the same probability to approach the food (i.e., the optimization target).

[0113] S206, Based on the third position update model / fourth position update model, update the positions of each starfish in the T-th starfish population according to the positions of the T optimal starfishes / the number of iterations to obtain the (T + 1)-th starfish population.

[0114] In some embodiments, predation and regeneration behaviors can be considered during the development stage to find the global solution of the motion parameters. Therefore, in order to simulate the predation behavior of starfish, a parallel bidirectional search strategy can be performed on the starfish with a previous order, and the positions of other starfish and the optimal starfish are used for updating.

[0115] Exemplarily, the index number i of the starfish with a previous order is not equal to N.

[0116] In a possible implementation manner, during the development stage, the model can be updated based on the third position first. According to the T-th optimal starfish, the candidate positions of the starfish with a previous order in the T-th starfish population are updated. Then, it is determined whether there is a problem that each dimension of the candidate position of each starfish exceeds the boundary of that dimension. If so, the starfish discards the candidate position of that dimension and stays at the boundary; if not, the candidate position of that dimension is used as the updated position of that dimension.

[0117] In an example, based on the parallel bidirectional search strategy, 5 other starfish can be randomly selected from the T-th starfish population Calculate the distances between the T-th optimal starfish and these 5 randomly selected starfish Randomly select two of them as benchmarks, and then update the candidate positions of the starfish with a previous order in the T-th starfish population according to the model updated based on the third position. During this process, the predation behavior of starfish is simulated based on the parallel bidirectional search strategy. The candidate positions of starfish can move towards a better guiding solution, while other starfish move backward in the same iteration. Therefore, these starfish with a previous order have the same ability to overcome the local optimal solution.

[0118] Exemplarily, the third position update model can satisfy the following formula:

[0119]

[0120] where r1 and r2 are two fourth random numbers in [0, 1], d m2 , d m1 are two distances randomly selected from d m .

[0121] Exemplarily, the position of the i-th starfish in the (T + 1)-th starfish population can satisfy:

[0122]

[0123] In some other embodiments, starfish are prone to being attacked by other predators during the predation process due to slow movement. If a predator catches a starfish, the starfish may cut and lose an arm to avoid being caught. To simulate the regeneration behavior of starfish, the positions of the starfish with a subsequent order can be updated based on the number of iterations.

[0124] Exemplarily, the index number i of the last starfish is equal to N.

[0125] In a possible implementation, similarly, the model can be updated based on the fourth position first, and the candidate positions of the starfish in the T-th starfish population that are in the front order can be updated according to the number of iterations. Then, it is determined whether there is a problem that the candidate position of each dimension of each starfish exceeds the boundary of that dimension. If so, the starfish discards the candidate position of that dimension and stays at the boundary; if not, the candidate position of that dimension is used as the updated position of that dimension.

[0126] In an example, since the regeneration stage requires several months of life and the movement speed of the starfish is very slow, the fourth update model can be expressed by the following formula:

[0127]

[0128] S207, determine whether T + 1 is less than the preset number of iterations.

[0129] Exemplarily, step S207 can be executed after steps S204 / S205 / S206 are executed.

[0130] In an example, if T + 1 is less than the preset number of iterations T max Then T can be set to T + 1, and the next round of iterative optimization can start from S201.

[0131] In another example, if T + 1 is not less than the preset number of iterations, the following step S208 can be executed to use the (T + 1)-th optimal starfish as the last optimal starfish.

[0132] S208, use the (T + 1)-th optimal starfish as the last optimal starfish.

[0133] Since the present invention represents the echo signal using multiple high-order motion parameters of the target and performs phase compensation on the echo signal based on the high-order motion parameters, the compensation residue is smaller when detecting the target in a high-order maneuvering scenario based on the present invention, and the detection accuracy of the target is better; since the present invention uses the starfish optimization algorithm to jointly optimize the high-order motion parameters, and the starfish optimization algorithm has less computational complexity and computational amount compared with traditional algorithms such as the particle swarm algorithm and the polynomial algorithm, the computational efficiency of the present invention is higher and the real-time performance is better; at the same time, the global optimal solutions of multiple high-order motion parameters can also be obtained, further improving the detection probability and tracking accuracy.

[0134] Figure 3The following is a schematic structural diagram of a high-order maneuvering target Doppler compensation device provided by an embodiment of the present invention. By way of example and not limitation, device 300 may include a pulse compression unit 310, an estimation unit 320, and an output unit 330.

[0135] Exemplarily, the pulse compression unit is configured to perform down-conversion and pulse compression processing on the echo signal to obtain a pulse-compressed echo signal, where the echo signal is represented by the D-order motion parameters of the target, and D is a positive integer greater than or equal to 3; the estimation unit is configured to jointly perform iterative optimization on the D-order motion parameters of the target based on the starfish optimization algorithm, and use the position of the last optimal starfish as the optimal estimated value of the D-order motion parameters, where in the starfish optimization algorithm, the position of each starfish is a set of estimated values of the D-order motion parameters, and the fitness of the last optimal starfish is the best; the output unit performs Doppler compensation operation on the pulse-compressed echo signal based on the optimal estimated value to obtain the optimal signal after Doppler compensation.

[0136] In order to better illustrate the beneficial effects of the present invention, the following simulation experiments were carried out:

[0137] Exemplarily, the parameters shown in Table 1 and Table 2 below can be used for the experiment, and all steps and conclusions of the experiment can be verified on Matlab2022a.

[0138] Table 1 Radar system simulation parameters

[0139] System parameters Value Carrier frequency 1.25 GHz Bandwidth 5 MHz Pulse repetition frequency 1000 Pulse width 20 μs Sampling rate 5 MHz Number of pulse accumulations 1000

[0140] Table 2 Target motion parameters

[0141] Motion parameters Value Initial distance 3000 Radial first-order velocity 30.21 Radial second-order velocity 15.56 Radial third-order velocity 5.34 Radial fourth-order velocity 4.25

[0142] Simulation experiment 1

[0143] Exemplarily, the simulation experiment can be carried out based on the parameters shown in Table 1 and Table 2 above. For the remaining simulation parameters, for example, the initial signal-to-noise ratio is set to -10 dB, the search parameter is 50, and the maximum number of iterations is 100; the search range of the radial first-order velocity a1 is [25, 35], the search range of the radial second-order velocity a2 is [10, 20], the search range of the radial third-order velocity a3 is [4, 8], and the search range of the radial fourth-order velocity a4 is [2, 5]. Under this condition, the Doppler domain energy diagrams obtained by the method based on the traditional particle swarm optimization method and the method provided by the present invention are compared. And, in order to ensure the reliability of the experimental results, 50 Monte Carlo experiments are respectively carried out on these two optimization methods and the estimation results are averaged.

[0144] See Figure 4The Doppler domain distribution map of the pre-compensation pulse pressure echo signal. It can be seen that the energy of the high-order maneuvering target is submerged in the noise, and the energy has serious diffusion in the frequency domain, with the maximum amplitude value being only 880.236. Therefore, the traditional MTD method is not applicable to target detection in high-order maneuvering scenarios.

[0145] At the same time, compare Figure 5 the convergence curves of the method provided by the present invention and the particle swarm optimization algorithm in Figure 6a the Doppler domain distribution map compensated by the method provided by the present invention in Figure 6b the Doppler domain distribution map compensated by the particle swarm optimization algorithm in

[0146] (1) The starfish optimization algorithm shows better global optimization ability in four-dimensional motion parameter estimation. The accuracies of the four dimensions are improved by 12.1%, 12.1%, 7.7%, and 27.8% respectively, and its comprehensive estimation error (total error 2.12) is reduced by 16.5% compared with the particle swarm algorithm (total error 2.54).

[0147] (2) The average iteration time of the starfish optimization algorithm is 16.73 seconds, which is shortened by 20.0% compared with the particle swarm algorithm (20.92 seconds), and the calculation efficiency is significantly improved.

[0148] (3) The energy concentration of the starfish optimization algorithm is increased by 12.3%, which is higher than that of the particle swarm optimization algorithm (11.8%). Although the absolute change magnitude of the entropy value is small, the estimation result is relatively accurate.

[0149] Table 3

[0150] Actual value Estimated value / error of the present invention Estimated value / error of PSO algorithm Initial distance 3000 - - Radial first-order velocity 30.21 29.63 / 0.58 29.55 / 0.66 Radial second-order velocity 15.56 15.27 / 0.29 15.23 / 0.33 Radial third-order velocity 5.34 5.94 / 0.6 5.99 / 0.65 Radial fourth-order velocity 4.25 3.60 / 0.65 3.35 / 0.9 Average entropy value 11.09 11.08471 / 0.00529 11.08475 Average time used for iteration (seconds) - 16.73 20.92

[0151] Therefore, it can be concluded that the method provided by the present invention has the following three advantages:

[0152] (1) Better initial search accuracy: The average initial entropy value (11.0854) of the method provided by the present invention is reduced by 0.0002 compared with the particle swarm algorithm (11.0856), indicating that the distribution of its initial population in the solution space is closer to the global optimal region.

[0153] (2) Faster convergence speed: The method provided by the present invention reaches the stable state when iterating to the 50th time, while the particle swarm algorithm needs to iterate 60 times, and the convergence speed is increased by about 10%.

[0154] (3) Higher optimization precision: After stabilization, the final average entropy value (11.08471) of the method provided by the present invention is further reduced compared with that of the particle swarm optimization algorithm (11.08475). Analyzed from the perspective of signal processing, the decrease in the entropy value directly reflects the improvement of the signal energy aggregation characteristics during the iteration process. A lower entropy value indicates that the signal energy is more concentrated in the frequency domain distribution.

[0155] Therefore, by using multiple high-order motion parameters of the target to represent the echo signal and performing phase compensation on the echo signal based on the high-order motion parameters, the present invention can have a smaller compensation residue and better detection accuracy for the target when detecting the target in a high-order maneuvering scenario; by using the starfish optimization algorithm to jointly optimize the high-order motion parameters, and the starfish optimization algorithm has less computational complexity and computational amount compared with traditional algorithms such as the particle swarm optimization algorithm and the polynomial algorithm, so the present invention has higher computational efficiency and better real-time performance; at the same time, it can also obtain the global optimal solution of multiple high-order motion parameters, further improving the detection probability and tracking accuracy.

[0156] In the above embodiments, the descriptions of the respective embodiments have their own emphases. For parts not detailed or recorded in a certain embodiment, reference may be made to the relevant descriptions of other embodiments.

Claims

1. A high-order maneuvering target Doppler compensation method based on starfish optimization, characterized in that, Including: Down-converting and pulse-compressing the echo signal to obtain a pulse-compressed echo signal, where the echo signal is represented by the D-order motion parameters of the target, and D is a positive integer greater than or equal to 3; Based on the starfish optimization algorithm, jointly iteratively optimizing the D-order motion parameters of the target, and taking the position of the last optimal starfish as the optimal estimated value of the D-order motion parameters. In the starfish optimization algorithm, the position of each starfish is a set of estimated values of the D-order motion parameters, and the fitness of the last optimal starfish is the best; Performing a Doppler compensation operation on the pulse-compressed echo signal based on the optimal estimated value to obtain an optimal signal after Doppler compensation.

2. The method according to claim 1, wherein The jointly iterative optimization of the D-order motion parameters of the target based on the starfish optimization algorithm includes: Determining whether the first random number in the (T + 1)-th iteration is greater than a preset stage threshold, where T is a positive integer, and the range of the first random number is between [0, 1]; If the first random number in the (T + 1)-th iteration is greater than the preset stage threshold, then enter the exploration stage. Based on the first position update model / second position update model, update the positions of each starfish in the T-th starfish population according to the position of the T-th optimal starfish / a random starfish in the T-th starfish population to obtain the (T + 1)-th starfish population; where each starfish population includes a preset number of starfish, and the T-th optimal starfish is the starfish with the best fitness in the T-th starfish population; If the first random number in the (T + 1)-th iteration is not greater than the preset stage threshold, then enter the exploitation stage. Based on the third position update model / fourth position update model, update the positions of each starfish in the T-th starfish population according to the position of the T-th optimal starfish / the number of iterations to obtain the (T + 1)-th starfish population; Determining whether T + 1 is less than a preset number of iterations. If T + 1 is not less than the preset number of iterations, then take the (T + 1)-th starfish as the optimal starfish.

3. The method according to claim 2, wherein The fitness of the starfish is obtained according to the entropy of the compensated Doppler signal corresponding to the starfish, and the compensated Doppler signal corresponding to the starfish is obtained by performing a Doppler compensation operation on the pulse-compressed echo signal based on the position of the starfish.

4. The method according to claim 3, wherein The fitness of the starfish satisfies the following formula: where F(X i ) is the fitness of the i-th starfish X i , E is the entropy of S com , and S com is the compensated Doppler signal corresponding to X i .

5. The method according to claim 3, wherein If the energy of the signal after Doppler compensation corresponding to the starfish is a constant, then the fitness of the starfish satisfies the following formula: Among them, F(X i ) is the fitness of the i-th starfish X i , E is the entropy of S com , S com is the compensated Doppler signal corresponding to X i , C is a constant, satisfying ∑|S com | 2 = C.

6. The method according to claim 2, characterized in that, The updating of the positions of each starfish in the T-th starfish population according to the position of the T-th optimal starfish / a random starfish in the T-th starfish population based on the first position update model / second position update model to obtain the (T + 1)-th starfish population includes: Determining whether D is greater than a preset dimension threshold; If D is less than or equal to the preset dimension threshold, then based on the first position update model, update the positions of each starfish in the T-th starfish population according to the position of the T-th optimal starfish to obtain the (T + 1)-th starfish population; If D is not less than the preset dimension threshold, then based on the second position update model, update the positions of each starfish in the T-th starfish population according to the position of a random starfish in the T-th starfish population to obtain the (T + 1)-th starfish population.

7. The method according to claim 2, characterized in that, The third-position update model / fourth-position update model updates the positions of each starfish in the T-th starfish population according to the positions / iteration times of the T optimal starfishes, and the (T + 1)-th starfish population obtained includes: Based on the third-position update model, the positions of the starfishes with earlier order in the T-th starfish population are updated according to the positions of the T optimal starfishes, where the index numbers of the starfishes with earlier order are less than N, and N is the preset number; Based on the fourth-position update model, the position of the last starfish in the T-th starfish population is updated according to the iteration times.

8. The method according to claim 1, wherein D = 4, and the D-order motion parameters include the first-order to fourth-order motion parameters of the target.

9. The method according to claim 8, wherein The optimal estimated value satisfies the following formula: where a” j is the optimal estimate of the j-th order velocity of the target, where j is a positive integer less than or equal to D, indicating that the entropy of the optimal signal after the Doppler compensation is minimized.

10. A high-order maneuvering target Doppler compensation device based on starfish optimization, characterized in that, including: A pulse compression unit, which is used to perform down-conversion and pulse compression processing on the echo signal to obtain a pulse-compressed echo signal, where the echo signal is represented by the D-order motion parameters of the target, and D is a positive integer greater than or equal to 3; An estimation unit, which is used to jointly perform iterative optimization on the D-order motion parameters of the target based on the starfish optimization algorithm, and use the position of the last optimal starfish as the optimal estimated value of the D-order motion parameters. In the starfish optimization algorithm, the position of each starfish is a set of estimated values of the D-order motion parameters, and the fitness of the last optimal starfish is the best; An output unit, which is used to perform Doppler compensation operation on the pulse-compressed echo signal based on the optimal estimated value to obtain an optimal signal after Doppler compensation.

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