Distribution Array Single Snapshot Direction Finding Method Based on Quantum Cheetah Optimization Mechanism of Watch Law

Abstract

The present invention discloses a distributed array single snapshot direction finding method based on a quantum cheetah optimization mechanism of the watch law, which relates to the technical field of array signal processing. The technical key points of the present invention include: constructing a Hankle matrix as a pseudo covariance matrix by using the single snapshot data received by the first sub-array for rough estimation to obtain an initial target range, and then constructing a Toeplitz matrix by using the single snapshot data received by the entire array in combination with the maximum likelihood estimation method. By combining the continuous quantum optimization theory with the cheetah optimization mechanism, the continuous quantum evolution mechanism is used to further accelerate the convergence speed of the cheetah optimization algorithm; finally, based on the watch law, the discrete quantum optimization theory and the cheetah optimization mechanism are combined. Under the condition that the target signal source is known, the most suitable distributed array structure for the algorithm is solved, realizing the single snapshot accurate direction finding of the distributed array, improving the convergence speed of the algorithm, reducing the computational complexity, and improving the direction finding accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and particularly relates to a direction finding method for a distributed array single snapshot based on a quantum cheetah optimization mechanism based on the watch law. Background Art

[0002] As an important branch in the field of antenna arrays, distributed arrays have a very wide range of applications in modern technologies. By integrating a large number of array antenna elements with relatively small apertures, a so-called distributed array system is formed. This design strategy can significantly improve the performance of the entire system while keeping the number of array elements unchanged. In addition, distributed arrays can better meet the requirements of specific application scenarios, showing extremely high adaptability and playing a key role in many fields.

[0003] In the research field of distributed array systems, the estimation of the direction of arrival (DOA) is a research hotspot that has received much attention. In a distributed array, when the sub-array spacing is greater than the signal half-wavelength, the spatial sampling theorem cannot be satisfied, resulting in an angle measurement ambiguity problem in the DOA estimation method of a conventional uniform array, and it cannot be directly applied to a distributed array. The algorithms for distributed arrays mainly include three categories. One is to construct virtual array elements through virtual interpolation to fill the gaps between sub-arrays, making the distributed array close to a uniform array. However, this method greatly increases the computational burden when the sub-array spacing is large. Another method is the auxiliary design method, which adds auxiliary array elements or improves the structure of the distributed array to eliminate the angle measurement ambiguity. However, this method will increase the hardware burden. It is also possible to achieve DOA estimation through a deblurring method. This method first obtains a DOA estimation result with ambiguity using a traditional DOA estimation method, and then uses the reference information obtained from the distributed array for deblurring. This method will have a large error in the case of low signal-to-noise ratio or large sub-array spacing.

[0004] According to the existing technical literature, Ma Yan, Chen Boxiao et al. published "DOA Estimation Method for Multi-Baseline Distributed Array Based on ESPRIT" in Systems Engineering and Electronics (2014, 36(08)). First, it obtains a DOA estimate within the subarray unit with low accuracy and no ambiguity through the subarray, then uses the rotational invariance between arrays to obtain a DOA estimate between subarray units with ambiguity but high accuracy, and finally obtains a DOA estimate with high accuracy and no ambiguity through ambiguity resolution. However, under low signal-to-noise ratio conditions, the estimation performance of this algorithm drops significantly. Yang Minglei, Zhang Yan et al. published "DOA Estimation for Distributed Array Based on Preprocessed MUSIC Algorithm" in Guidance & Fuze. First, it uses the rotational invariant subspace algorithm to obtain a rough estimate without ambiguity, which limits the search range of the MUSIC algorithm and solves the problem of angle measurement ambiguity for distributed arrays. However, this algorithm still requires eigenvalue decomposition. Weichuang Yu, Peiyu He et al. published "DOA Estimation Ambiguity Resolution Method for Near Field Distributed Array" at the 6th International Conference on Intelligent Computing and Signal Processing in 2021. Based on a double-V distributed array, it proposed an ambiguity resolution algorithm. It uses the MUSIC algorithm to obtain the spatial spectra of the two V-shaped subarrays respectively, and realizes ambiguity resolution by designing a threshold to retain the spectral peaks corresponding to the real targets. The above methods mainly target multi-snapshot data, while single-snapshot DOA estimation only processes the data of a single snapshot, greatly reducing the consumption of computing resources and improving the real-time response ability of the algorithm. This has important practical significance and application value for those application scenarios with high real-time requirements, such as mobile communication, real-time monitoring, and military reconnaissance. Summary of the Invention

[0005] Therefore, the present invention proposes a single-snapshot direction finding method for a distributed array based on the quantum cheetah optimization mechanism of the watch law to solve the problem of direction finding for a distributed array under single-snapshot conditions.

[0006] According to one aspect of the present invention, a single-snapshot direction finding method for a distributed array based on the quantum cheetah optimization mechanism of the watch law is proposed, and the method includes:

[0007] Step 1: Establish a single-snapshot sampling signal model for the distributed array;

[0008] Step 2: Use the single-snapshot data received by the distributed array to construct a pseudo-covariance matrix, and at the same time use the steering matrix of the distributed array to construct an orthogonal projection matrix to obtain a maximum likelihood estimation equation;

[0009] Step 3: Use the single snapshot data received by the first sub-array of the distributed array to construct a Hankel matrix as the pseudo-covariance matrix, and then use the reference information carried by the Hankel matrix to roughly estimate the direction of arrival of the incoming wave;

[0010] Step 4: Initialize the search cheetah population to generate the initial quantum positions; use the rough estimation value to obtain the initial hunting range, calculate the mapped positions of the search cheetahs and the corresponding fitness values, and obtain the local optimal quantum position and the global optimal quantum position;

[0011] Step 5: Update the quantum positions of each search cheetah according to the update strategy of the search cheetah population and calculate the mapped positions;

[0012] Step 6: Calculate the fitness values using the fitness function of the direction finding estimation, and update the local optimal quantum position and the global optimal quantum position;

[0013] Step 7: Determine whether the maximum number of iterations is reached. If so, output the mapped position of the global optimal quantum position to obtain the estimated direction of the incoming wave, and execute Step 8; if not, return to Step 5;

[0014] Step 8: Based on the law of the instrument, by setting the signal sources with known true directions of incoming waves, use the root mean square error between the obtained estimated direction of the incoming wave and the true direction of the incoming wave as the optimization objective to optimize the distributed array structure;

[0015] Step 9: Initialize the cheetah population, convert the cheetah positions into the distributed array structure, use the direction finding algorithm to obtain the estimated direction under the corresponding array structure, calculate the fitness values of each cheetah using the fitness function of the array optimization, and obtain the local optimal position and the global optimal position;

[0016] Step 10: Update the quantum velocities of each cheetah according to the update strategy of the cheetah population, and obtain the positions of the corresponding cheetahs through measurement;

[0017] Step 11: Convert the cheetah positions into the distributed array structure, use the direction finding algorithm to obtain the estimated direction under the corresponding array structure, calculate the fitness values of each cheetah using the fitness function of the array optimization, and update the local optimal position and the global optimal position;

[0018] Step 12: Determine whether the maximum number of iterations is reached. If so, output the global optimal position of the cheetah, convert it into the distributed array structure to obtain the corresponding optimal array structure, and obtain the final estimated direction of the incoming wave; if not, return to Step 10.

[0019] Furthermore, the single snapshot sampling signal model of the distributed array described in Step 1 is established as follows:

[0020] Assume a distributed array with a total number of array elements \(M\), and the number of array elements in each sub - array is \(M\). N , and the element spacing in the sub - array is where \(\lambda\) is the wavelength of the incident signal, the total number of sub - arrays is \(N\), the th sub - array and the th sub - array are spaced \(M = N\times M\) N , There are \(P\) far - field narrow - band signals incident on the distributed array from \(\theta\) p directions respectively, and the incident signals and the noise signals are uncorrelated, \(p = 1,2,\cdots,P\); Select the first element of the first sub - array as the reference element, then at time \(t\), the signal received by the \(k\)th element in the \(q\)th sub - array is:

[0021]

[0022] where is the incident signal, is the noise signal of the \(k\)th element in the \(q\)th sub - array, is the distance between the \(k\)th element in the \(q\)th sub - array and the reference element, \(q = 1,2,\cdots,N\), \(k = 1,2,\cdots,M\) N ;

[0023] The single - snapshot sampling signal model of the distributed array is expressed as:

[0024] \(y(1)=A(\theta)s(1)+n(1)\)

[0025] where \(y(1)=[y_1(1),y_2(1),\cdots,y N (1)] T , y q,k (1) represents the single - snapshot data received by the \(k\)th element in the \(q\)th sub - array, \(q = 1,2,\cdots,N\), \(k = 1,2,\cdots,M\) N ; \(A(\theta)=[A_1(\theta),A_2(\theta),\cdots,A N (\theta)] T is the array steering matrix, \(A q (\theta)=[a q (\theta_1),a q (\theta_2),\cdots,a q (\theta P )] T , is the distance between the \(k\)th element in the \(q\)th sub - array and the reference element, \(\theta=[\theta_1,\theta_2,\cdots,\theta Pis the azimuth vector of the incoming wave; s(1) = [s1(1), s2(1), …, s P (1)] T is the signal vector, n(1) = [n1(1), n2(1), …, n N (1)] T is the array noise vector, is the noise vector of the q-th subarray.

[0026] Furthermore, the pseudo-covariance matrix described in step 2 is as follows:

[0027]

[0028] Perform covariance processing on the constructed matrix R y (1), that is

[0029] The orthogonal projection matrix is: P A(θ) = A(θ)(A H (θ)A(θ)) -1 A H (θ); where H represents the conjugate transpose;

[0030] The maximum likelihood estimation equation is: where tr() is the matrix trace function.

[0031] Furthermore, the process of step 3 includes:

[0032] Divide the first subarray into two subarray units S1 and S2, where S1 consists of the first M N -1 array elements, and S2 consists of the last M N -1 array elements. Use the single-snapshot data received by S1 and S2 to construct two pseudo-covariance matrices H0(1) and H1(1), and the matrices H0(1) and H1(1) contain relevant single-snapshot information:

[0033]

[0034] Perform singular value decomposition on the pseudo-covariance matrix H0(1), where is the left singular vector, is the right singular component, and W are the singular values;

[0035] Calculate the matrix using the singular values and singular vectors of the obtained H0(1) matrix where are the first P larger singular values after performing singular value decomposition on the H0(1) matrix, that is, the singular values corresponding to the signal part, is the left singular vector of the singular value corresponding to the signal part, is the right singular vector of the singular value corresponding to the signal part. Using the matrix obtains a rough estimate of the search angle as where is the matrix 's eigenvalue,

[0036] Furthermore, the process of step four includes: assuming there are E search cheetahs in the hunting ground, each search cheetah has its own quantum position. Define the quantum position of the e-th search cheetah in the d-th generation during the iteration process as where e = 1, 2, …, E, p = 1, 2, …, P, and P is the maximum dimension of the solution space; obtain the mapped position of the e-th search cheetah in the d-th generation through mapping The mapping equation is which is within the range of the hunting ground, where L p is the lower limit of the p-th dimension of the hunting range, and U p is the upper limit of the p-th dimension of the hunting range. Determine the initial hunting range through the result of the rough estimate , is the range factor, e = 1, 2, …, E, p = 1, 2, …, P; substitute the position after mapping into the fitness function for fitness evaluation. The fitness equation is where Finally, record the optimal quantum position obtained after the optimized search of the e-th search cheetah until the d-th generation as the local optimal quantum position Record the quantum position with the optimal fitness value of the entire search cheetah population after the optimized search until the d-th generation as the global optimal quantum position

[0037] Furthermore, the process of step five includes: during the d-th iteration process, randomly shuffle the hunting order of E search cheetahs. Define the adjacent cheetah of the e-th search cheetah as the search cheetah that starts hunting after the e-th search cheetah finishes hunting. If the e-th search cheetah is the last one to start hunting, then define the search cheetah that hunted before the e-th search cheetah as the adjacent cheetah of the e-th search cheetah. The position of the adjacent cheetah is recorded as Use the simulated quantum rotation gate to update the p-th dimension quantum position of the e-th search cheetah in the d-th generation. The update equation is where is the p-th dimension of the quantum rotation angle of the e-th search cheetah in the (d + 1)-th generation; the update equation of the p-th dimension quantum rotation angle of the e-th search cheetah in the d-th generation is where D is the maximum number of iterations of the search cheetah population, is a random number uniformly distributed between [0, 1], is a random number uniformly distributed between [0, η1], where η1 is the search cheetah hunting factor, is a random number uniformly distributed between [0, 1], and w is the search factor; is a random number subject to the standard Gaussian distribution, is the p - dimension of the adjacent cheetah quantum position of the e - th search cheetah in the d - th generation; is the velocity factor, is a random number uniformly distributed between [-1, 1], is the p - dimension of the local optimal quantum position of the e - th search cheetah in the d - th generation; Finally, the quantum position of the e - th search cheetah in the (d + 1) - th generation is mapped to obtain the mapped position Mapping equation where L p is the lower limit value of the p - dimension of the hunting range, and U p is the upper limit value of the p - dimension of the hunting range,

[0038] Furthermore, the process of step six includes: substituting the mapped position of the search cheetah in the (d + 1) - th generation into the fitness function where calculate the fitness value of the updated search cheetah, and update the local optimal quantum position to and the global optimal quantum position to e = 1, 2, …, E; If the fitness value of the e - th hunting cheetah in the (d + 1) - th generation is greater than the fitness value of, then Otherwise e = 1, 2, …, E; If the fitness value of the local optimal position of the e - th hunting cheetah in the (d + 1) - th generation is greater than the fitness value of, then Otherwise

[0039] Furthermore, the process of step eight includes:

[0040] The watch law states that when a person has multiple watches with different time pointers at the same time, only the pointer of one watch gives the correct result; The root - mean - square error between the estimated direction of arrival and the known true direction of arrival in step seven is used as the fitness function for array structure optimization, where is the potential solution of the array structure, and θ p is the true direction of the p - th incoming wave, After performing the direction-finding algorithm under this array structure, the estimated direction of the p-th incoming wave is obtained, where p = 1, 2, ···, P.

[0041] Further, the process of step nine includes: assuming that there are I cheetahs in the hunting ground, and each cheetah has its own quantum velocity. Define the quantum velocity of the i-th cheetah in the t-th generation during the iteration as The position of the i-th cheetah in the t-th generation is obtained through measurement as The corresponding measurement equation is where is a random number uniformly distributed between [0, 1], i = 1, 2, …, I, j = 1, 2, …, J, and J is the maximum dimension of the solution space; the position obtained by measuring the quantum velocity of the i-th cheetah in the t-th generation is converted to the sub-array spacing of the distributed array, and then the direction-finding algorithm is executed, where is the array spacing between the -th sub-array and the -th sub-array in the t-th generation. The direction-finding result is brought into the fitness function to calculate the fitness value corresponding to each cheetah, where θ p is the true direction of the p-th incoming wave, is the array spacing corresponding to the i-th cheetah in the t-th generation and the estimated direction of the p-th incoming wave obtained after executing the direction-finding algorithm under The optimal position after optimization search of the i-th cheetah until the t-th generation is denoted as the local optimal position

[0042] Further, the process of step ten includes: in the t-th iteration process, randomly shuffle the hunting order of the I cheetahs. Define the adjacent cheetah as the cheetah that starts hunting after the i-th cheetah finishes hunting. If the i-th cheetah is the last one to hunt, then define the cheetah that hunted before the i-th cheetah as the adjacent cheetah of the i-th cheetah. The quantum velocity of the adjacent cheetah is denoted as Take the global optimal position in the t-th iteration as the hunting target position of the cheetah population, and the local optimal position of the i-th cheetah in the t-th iteration as the leader position of the i-th cheetah; in the t-th iteration process, when holds, the i-th cheetah selects the waiting strategy. At this time, the update equation of the j-th dimension quantum velocity of the i-th cheetah is where and They are all random numbers uniformly distributed between [0, 1], and K is a selection constant; otherwise, the i-th cheetah selects a predation strategy. At this time, the update equation for the j-th dimensional quantum velocity of the i-th cheetah is where μ t+1 is a random number uniformly distributed between [0, 1], is the j-th dimension of the quantum rotation angle of the i-th cheetah in the (t + 1)-th generation, represents When it is 0, the probability of performing an inversion operation on this qubit, and its value is a constant between [0, 1 / J]; the update equation for the j-th dimension of the quantum rotation angle of the i-th cheetah in the t-th generation is where, T is the maximum number of iterations of the cheetah population, is a random number uniformly distributed between [0, 1], is a random number uniformly distributed between [0, η2], and η2 is the cheetah hunting factor, is a random number subject to a Gaussian distribution; and are random numbers uniformly distributed between [0, 1], is the j-th dimension of the hunting target position in the t-th generation, is the j-th dimension of the leader position of the i-th cheetah in the t-th generation; is a random number subject to a Gaussian distribution; is the j-th dimension of the quantum velocity of the adjacent cheetah of the i-th cheetah in the t-th generation, i = 1, 2,..., I, j = 1, 2,..., J; finally, the updated quantum velocity of the i-th cheetah in the (t + 1)-th generation is measured, and the position of the i-th cheetah is updated to The corresponding measurement equation is where is a random number uniformly distributed between [0, 1];

[0043] The process of Step Eleven includes: converting the position corresponding to the cheetah in the (t + 1)-th generation into the subarray spacing of the distributed array where is the array spacing between the -th subarray and the -th subarray in the (t + 1)-th generation; assuming there are P far-field incoming wave signals, when the subarray spacing of the distributed array is , the direction finding algorithm is executed, and the direction finding result is substituted into the fitness function to calculate the fitness value corresponding to each cheetah, where θ p is the true direction angle of the p-th far-field incoming wave signal, is the p-th direction angle obtained after executing the direction finding algorithm under the array spacing corresponding to the i-th cheetah of the t+1th generation; the local optimal position of the cheetah is updated to and the global optimal position is If the fitness value of the i-th cheetah in the t+1th generation is Less than The fitness value of otherwise i=1,2,…,I;If the local optimal position of the i-th cheetah in the t+1th generation is The fitness value is less than The fitness value of otherwise

[0044] The beneficial technical effects of the present invention are:

[0045] 1) The current distributed array direction-finding algorithm mainly focuses on deambiguation and the use of special arrays. The phase ambiguity of the distributed array is avoided by pairing precise estimation with rough estimation. The accuracy of direction-finding depends to a certain extent on the accuracy of pairing, and a large number of snapshots are required to obtain information. The present invention combines quantum optimization theory with the cheetah population optimization mechanism, and uses the single snapshot data received by the first sub-array to make a rough estimate to obtain the initial search range, cleverly avoiding the phase ambiguity problem, and constructs a Toeplitz pseudo-covariance matrix at the same time. The maximum likelihood estimation method is used to achieve direction-finding, so that the algorithm can achieve direction-finding under single snapshot conditions. Among them, a new population update strategy is designed, and the direction-finding algorithm is designed using continuous quantum optimization theory combined with the cheetah optimization mechanism, which further reduces the complexity of the calculation and successfully achieves the direction-finding of the distributed array under single snapshot conditions.

[0046] 2) The layout structure of the distributed array has a certain influence on the direction finding result of the array. Many direction finding algorithms improve the accuracy of direction finding by using special array structures or setting auxiliary arrays. The present invention designs a distributed array layout structure optimization algorithm based on the watch law. By setting a known signal source and taking the root mean square error of the direction finding algorithm as the optimization target based on the result, the distributed array structure most suitable for the direction finding algorithm of the present invention is directly obtained, which further improves the direction finding accuracy.

[0047] 3) The present invention simultaneously adopts a discrete quantum optimization mechanism and a continuous quantum optimization mechanism in combination with a cheetah population optimization algorithm, updates the specific optimization steps, greatly reduces the number of iterations, reduces the computational amount to a certain extent, makes the search mechanism more concise, and obtains an algorithm that can achieve accurate direction finding for a distributed array under single snapshot conditions. At the same time, an optimized distributed array adapted to this algorithm is obtained, which greatly improves the direction finding accuracy. Through simulation comparison with a conventional uniform distributed array, the direction finding accuracy under single snapshot conditions is greatly improved, and the stability of the array is also greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings. The accompanying drawings, together with the following detailed description, are included in this specification and form a part of this specification, and are used to further illustrate the preferred embodiments of the present invention and explain the principles and advantages of the present invention.

[0049] Figure 1 is a flowchart of the single snapshot direction finding method for a distributed array based on the quantum cheetah optimization mechanism of the watch law according to an embodiment of the present invention.

[0050] Figure 2 is a schematic diagram of the sub-array layout of a distributed array in an embodiment of the present invention.

[0051] Figure 3 is a schematic diagram of the direction finding result in the case of two independent sources in an embodiment of the present invention.

[0052] Figure 4 is a schematic diagram of the direction finding result in the case of two coherent sources in an embodiment of the present invention.

[0053] Figure 5 is a schematic diagram of the direction finding result in the case of three mixed sources in an embodiment of the present invention.

[0054] Figure 6 is a schematic diagram of the direction finding result accuracy under different array structures in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0055] In order to enable those skilled in the art to better understand the solution of the present invention, the exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are only a part of the embodiments or examples of the present invention, rather than all of them. All other embodiments or examples obtained by those of ordinary skill in the art without creative efforts based on the embodiments or examples of the present invention shall fall within the scope of protection of the present invention.

[0056] Different from the existing methods for DOA estimation of distributed arrays, which mainly carry out DOA estimation by resolving ambiguity or constructing special distributed array structures, the present invention proposes a single snapshot direction finding method for distributed arrays based on the quantum cheetah mechanism of the watch law. By imitating the swarm intelligence behavior of cheetahs hunting and combining the continuous quantum optimization mechanism, the method realizes the accurate estimation of the signal source direction under the condition of a single snapshot, and optimizes the structure of the distributed array based on the watch law to further improve the accuracy of direction finding. The watch law means that when there are multiple watches with different time pointers at the same time, only the time of one watch is accurate, and the array structure of the distributed array has a great influence on the direction finding result. Therefore, the present invention combines the cheetah hunting mechanism with the discrete quantum optimization theory, and under the assumption that the target direction is known, solves the distributed array structure that is most suitable for the direction finding method proposed by the present invention. Through simulation experiments, it is verified that the single snapshot direction finding method for distributed arrays of the present invention can not only effectively realize the direction estimation under the condition of a single snapshot, but also show good direction finding accuracy when dealing with independent sources and coherent sources, and can still realize direction finding under low signal-to-noise ratio conditions, ensuring that reliable DOA estimation results can still be obtained in complex electromagnetic environments.

[0057] The present invention uses the single snapshot data received by the first sub-array to construct a Hankel matrix as the pseudo covariance matrix for rough estimation to obtain the initial target range. Then, it uses the single snapshot data received by the entire array to construct a Toeplitz matrix and combines it with the maximum likelihood estimation method. By combining the continuous quantum optimization theory with the cheetah optimization mechanism, the continuous quantum evolution mechanism is used to further accelerate the convergence speed of the cheetah optimization algorithm. Finally, based on the watch law, the discrete quantum optimization theory and the cheetah optimization mechanism are combined. Under the condition that the target signal source is known, the distributed array structure most suitable for this algorithm is solved. It not only realizes the single snapshot accurate direction finding of the distributed array, improves the convergence speed of the algorithm, reduces the computational complexity, but also further obtains a special distributed array structure and improves the direction finding accuracy.

[0058] The solutions and steps adopted by the present invention to solve the problem are as follows:

[0059] Step 1: Establish a single snapshot sampling signal model for the distributed array, where the distribution of each sub-array in space is one-dimensional arrangement.

[0060] According to the embodiment of the present invention, assume a distributed array with a total number of array elements M, and the number of array elements of each sub-array is M N , the element spacing in the sub-array is λ is the wavelength of the incident signal, the total number of sub-arrays is N, and the th sub-array and the th sub-array The spacing between them is M = N × M N,

[0061] There are P far - field narrow - band signals incident on the distributed array from θ p directions respectively, and the incident signals and the noise signals are uncorrelated, where p = 1, 2, …, P. Select the first element of the first sub - array as the reference element. Then, at time, the signal received by the k - th element in the q - th sub - array is:

[0062]

[0063] where, is the incident signal, is the noise signal of the k - th element in the q - th sub - array, is the distance between the k - th element in the q - th sub - array and the reference element, q = 1, 2, ···, N, k = 1, 2, ··· M N .

[0064] The single - snapshot signal model received by the distributed array can be expressed as:

[0065] y(1)=A(θ)s(1)+n(1)

[0066] In the formula, y(1)=[y1(1), y2(1), …, y N (1)] T , y q,k (1) represents the single - snapshot data received by the k - th element in the q - th sub - array, q = 1, 2, ···, N, k = 1, 2, ··· M N ; A(θ)=[A1(θ), A2(θ), …, A N (θ)] T is the array steering matrix, A q (θ)=[a q (θ1), a q (θ2), …, a q (θ P )] T , is the distance between the k - th element in the q - th sub - array and the reference element, θ=[θ1, θ2, …, θ P is the incoming wave azimuth vector, q = 1, 2, ···, N, k = 1, 2, ··· M N , p = 1, 2, ···, P; s(1)=[s1(1), s2(1), …, s P (1)] T is the signal vector, n(1)=[n1(1), n2(1), …, n N(1) T is the array noise vector, and is the noise vector of the q-th subarray.

[0067] Step 2: Given the subarray spacing of the distributed array, construct a pseudo-covariance matrix using the single-snapshot data received by the distributed array, and at the same time construct an orthogonal projection matrix using the steering matrix of the distributed array to obtain the maximum likelihood estimation equation.

[0068] According to an embodiment of the present invention, given the subarray spacing of the distributed array the single-snapshot sampling data of the entire distributed array can be obtained. Use the single-snapshot data received by the entire distributed array to construct a Toeplitz matrix as the pseudo-covariance matrix as follows:

[0069]

[0070] Perform covariance processing on the constructed matrix R y (1), that is, R(1) = R y (1)R y H (1). The orthogonal projection matrix is P A(θ) = A(θ)(A H (θ)A(θ)) -1 A H (θ), and the angle estimation value of the maximum likelihood equation is where H represents the conjugate transpose and tr() is the matrix trace function.

[0071] Step 3: Use the single-snapshot data received by the first subarray of the distributed array to construct a Hankel matrix as the pseudo-covariance matrix, and then use the reference information carried by the Hankel matrix to roughly estimate the direction of arrival of the incoming wave.

[0072] According to an embodiment of the present invention, to avoid the problem of phase ambiguity existing in the distributed array, the present invention divides the first subarray into two subarray units S1 and S2, where S1 is composed of the first M N -1 array elements, and S2 is composed of the last M N -1 array elements of the first subarray. Use the single-snapshot data received by S1 and S2 to construct two pseudo-covariance matrices H0(1) and H1(1), and the matrices H0(1) and H1(1) contain relevant single-snapshot information:

[0073]

[0074] After that, perform singular value decomposition on the pseudo-covariance matrix H0(1), where is the left singular vector, is the right singular component, and W are the singular values. Calculate the matrix using the singular values and singular vectors of the obtained H0(1) matrix where are the first P larger singular values after the singular value decomposition of the H0(1) matrix, that is, the singular values corresponding to the signal part is the left singular vector of the singular value corresponding to the signal part is the right singular vector of the singular value corresponding to the signal part. Use the matrix to obtain the rough estimated value of the search angle as where is the matrix eigenvalue of

[0075] Step 4: Initialize the search cheetah population, generate the initial quantum positions, and at the same time obtain the initial hunting range using the rough estimated value, calculate the mapped positions of the search cheetahs and the corresponding fitness values, and obtain the local optimal quantum position and the global optimal quantum position

[0076] According to the embodiment of the present invention, first assume that there are E search cheetahs in the hunting ground, and each search cheetah has its own quantum position. Define the quantum position of the e-th search cheetah in the d-th generation during the iteration process as where e = 1, 2,..., E, p = 1, 2,..., P, and P is the maximum dimension of the solution space. Obtain the mapped position of the e-th search cheetah in the d-th generation through mapping The mapping equation is is within the range of the hunting ground, where L p is the lower limit of the p-th dimension of the hunting range, and U p is the upper limit of the p-th dimension of the hunting range. Determine the initial hunting range through the result of the rough estimation , is the range factor, e = 1, 2,..., E, p = 1, 2,..., P. Substitute the mapped position into the fitness function for fitness evaluation. The fitness equation is where Finally, record the optimal quantum position obtained after the optimization search of the e-th search cheetah until the d-th generation as the local optimal quantum position Record the quantum position with the best fitness value of the entire search cheetah population until the d-th generation of optimization search as the global optimal quantum position e = 1, 2,..., E

[0077] Step 5: Update the quantum positions of each search cheetah according to the update strategy of the search cheetah population and calculate the mapped positions

[0078] According to an embodiment of the present invention, during the d-th iteration, the hunting order of E search cheetahs is randomly shuffled. Define the adjacent cheetah of the e-th search cheetah as the search cheetah that starts hunting after the e-th search cheetah finishes hunting. If the e-th search cheetah is the last one to start hunting, then define the search cheetah that hunted before the e-th search cheetah as the adjacent cheetah of the e-th search cheetah. The position of the adjacent cheetah is denoted as Use the simulated quantum rotation gate to update the p-th dimensional quantum position of the e-th search cheetah in the d-th generation. The update equation is where is the p-th dimension of the quantum rotation angle of the e-th search cheetah in the (d + 1)-th generation. The update equation for the p-th dimensional quantum rotation angle of the e-th search cheetah in the d-th generation is where D is the maximum number of iterations of the search cheetah population, is a random number uniformly distributed between [0, 1], is a random number uniformly distributed between [0, η1]. η1 is the hunting factor of the search cheetah, is a random number uniformly distributed between [0, 1], and w is the search factor; is a random number obeying the standard Gaussian distribution, is the p-th dimension of the quantum position of the adjacent cheetah of the e-th search cheetah in the d-th generation; is the velocity factor, is a random number uniformly distributed between [-1, 1], is the p-th dimension of the local optimal quantum position of the e-th search cheetah in the d-th generation, e = 1, 2, …, E, p = 1, 2, …, P. Finally, through the quantum position of the e-th search cheetah in the (d + 1)-th generation perform mapping to obtain the mapped position The mapping equation where L p is the lower limit value of the p-th dimension of the hunting range, U p is the upper limit value of the p-th dimension of the hunting range, e = 1, 2, …, E, p = 1, 2, …, P.

[0079] Step Six: Calculate the fitness value using the fitness function of direction finding estimation, and update the local optimal quantum position and the global optimal quantum position.

[0080] According to an embodiment of the present invention, substitute the mapped position of the search cheetah in the (d + 1)-th generation into the fitness function where Calculate the fitness value of the updated search cheetah, and update the local optimal quantum position to and the global optimal quantum position to e = 1, 2, …, E. If the fitness value of the e-th hunting cheetah in the (d + 1)-th generation is greater than the fitness value of otherwise e = 1, 2, …, E. If the fitness value of the local optimal position of the e-th hunting cheetah in the (d + 1)-th generation is greater than the fitness value of otherwise

[0081] Step Seven: Determine whether the maximum number of iterations D is reached. If the maximum number of iterations D is not reached, let d = d + 1, return to Step Five, and continue the iteration; otherwise, output the mapping position of i.e., the estimated direction of the incoming wave signal.

[0082] Step Eight: Based on the law of the instrument, by setting the signal sources with known true incoming wave directions, use the root mean square error between the estimated incoming wave direction and the true incoming wave direction as the optimization objective to optimize the distributed array structure.

[0083] According to the embodiments of the present invention, the law of the instrument means that when a person has multiple watches with different time indications at the same time, only the indication result of one watch is correct, and the structure of the array in the direction finding of the distributed array has a certain influence on the direction finding result. Applying the law of the instrument to the direction finding of the distributed array, it can be known that under the condition of a known direction finding algorithm, only one distributed array structure has the best direction finding result. The present invention, under the condition of setting the known incident signal sources and the known above-mentioned direction finding algorithm, uses the root mean square error between the incoming wave direction estimated by the algorithm and the known true incoming wave direction as the fitness function for array structure optimization, where is the potential solution of the array structure, θ p is the true direction of the p-th incoming wave, is the estimated direction of the p-th incoming wave obtained after performing the direction finding algorithm under this array structure, p = 1, 2, ···, P.

[0084] Step Nine: Initialize the cheetah population, convert the cheetah positions into distributed array structures, use the direction finding algorithm to obtain the estimated directions under the corresponding array structures, and calculate the fitness values of each cheetah using the fitness function for array optimization to obtain the local optimal position and the global optimal position.

[0085] According to the embodiments of the present invention, assume that there are I cheetahs in the hunting ground, and each cheetah has its own quantum speed. Define the quantum speed of the i-th cheetah in the t-th generation during the algorithm iteration process as After measurement, the position of the i-th cheetah in the t-th generation is The corresponding measurement equation is where is a random number uniformly distributed between [0, 1], i = 1, 2, …, I, j = 1, 2, …, J, and J is the maximum dimension of the solution space. The position obtained by measuring the quantum velocity of the i-th cheetah in the t-th generation is converted into the subarray spacing of the distributed array and then the direction finding algorithm is executed, where is the array spacing between the -th subarray and the -th subarray in the t-th generation. The direction finding result is brought into the fitness function to calculate the fitness value corresponding to each cheetah. Among them, θ p is the true direction of the p-th incoming wave, is the array spacing corresponding to the i-th cheetah in the t-th generation and the estimated direction of the p-th incoming wave obtained after executing the direction finding algorithm, i = 1, 2, …, I, p = 1, 2, ···, P. The optimal position of the i-th cheetah after the optimization search until the t-th generation is denoted as the local optimal position The position with the optimal fitness value of the entire cheetah population after the optimization search until the t-th generation is denoted as the global optimal position i = 1, 2, …, I.

[0086] Step ten: Update the quantum velocity of each cheetah according to the update strategy of the cheetah population, and obtain the corresponding position of the cheetah through measurement.

[0087] According to the embodiment of the present invention, during the t-th iteration process, randomly shuffle the hunting order of I cheetahs. Define the adjacent cheetah as the cheetah that hunts after the i-th cheetah finishes hunting. If the i-th cheetah is the last one to hunt, then define the cheetah that hunted before the i-th cheetah as the adjacent cheetah of the i-th cheetah. The quantum velocity of the adjacent cheetah is denoted as Take the global optimal position at the t-th iteration as the hunting target position of the cheetah population, and the local optimal position of the i-th cheetah at the t-th iteration as the leader position of the i-th cheetah. During the t-th iteration process, when , the i-th cheetah selects the waiting strategy. At this time, the update equation of the j-th dimensional quantum velocity of the i-th cheetah is where and are both random numbers uniformly distributed between [0, 1], and K is the selection constant; otherwise, the i-th cheetah selects the predation strategy. At this time, the update equation of the j-th dimensional quantum velocity of the i-th cheetah is where μ t+1is a random number uniformly distributed between [0, 1], is the j-th dimension of the quantum rotation angle of the i-th cheetah in the (t + 1)-th generation, represents When it is 0, the probability of performing an inversion operation on this qubit, and its value is a constant between [0, 1 / J], i = 1, 2, …, I, j = 1, 2, …, J. The update equation for the j-th dimension of the quantum rotation angle of the i-th cheetah in the t-th generation is where, T is the maximum number of iterations of the cheetah population, is a random number uniformly distributed between [0, 1], is a random number uniformly distributed between [0, η2], and η2 is the cheetah hunting factor, is a random number subject to a Gaussian distribution; and are random numbers uniformly distributed between [0, 1], is the j-th dimension of the hunting target position in the t-th generation, is the j-th dimension of the leader position of the i-th cheetah in the t-th generation; is a random number subject to a Gaussian distribution; is the j-th dimension of the quantum velocity of the adjacent cheetah of the i-th cheetah in the t-th generation, i = 1, 2, …, I, j = 1, 2, …, J. Finally, the updated quantum velocity of the i-th cheetah in the (t + 1)-th generation is measured, and the position of the i-th cheetah is updated to The corresponding measurement equation is where is a random number uniformly distributed between [0, 1], i = 1, 2, …, I, j = 1, 2, …, J.

[0088] Step Eleven: Convert the cheetah positions into a distributed array structure, use the direction finding algorithm to obtain the estimated direction under the corresponding array structure, calculate the fitness value of each cheetah using the fitness function optimized by the array, and update the local optimal position and the global optimal position;

[0089] According to the embodiment of the present invention, the positions corresponding to the cheetahs in the (t + 1)-th generation are converted into the sub-array spacing of the distributed array where is the array spacing between the n-th sub-array and the -th sub-array in the (t + 1)-th generation, i = 1, 2, …, I, Assuming there are P far-field incoming wave signals, when the sub-array spacing of the distributed array is perform steps two to seven of the direction finding algorithm, and substitute the direction finding result into the fitness function to calculate the fitness value corresponding to each cheetah, where θp is the true direction angle of the p-th far-field incoming wave signal, is the p-th direction angle obtained after performing the direction finding algorithm under the array pitch corresponding to the i-th cheetah in the (t + 1)-th generation, where i = 1, 2, …, I and p = 1, 2, ···, P. Update the local optimal position of the cheetah to and the global optimal position to If the fitness value of the i-th cheetah in the (t + 1)-th generation is less than the fitness value of, then Otherwise i = 1, 2, …, I. If the fitness value of the local optimal position of the i-th cheetah in the (t + 1)-th generation is less than the fitness value of, then Otherwise

[0090] Step Twelve: Determine whether the maximum number of iterations is reached. If so, output the global optimal position of the cheetah, convert it to a distributed array structure, obtain the corresponding optimal array structure, and obtain the final estimated direction of the incoming wave; if not, return to Step Ten.

[0091] Step Twelve: Determine whether the maximum number of iterations T of the cheetah is reached. If the maximum number of iterations T is not reached, let t = t + 1 and return to Step Ten to continue the iteration; otherwise, output the global optimal position Convert the global optimal position of the cheetah into a distributed array structure to obtain the corresponding optimal array structure; when there is a far-field source incoming wave, under this distributed array structure, perform Steps Two to Seven to obtain the estimated direction of the incoming wave signal.

[0092] Further verify the technical effect of the present invention through experiments.

[0093] For the quantum cheetah optimization mechanism, it is hereinafter briefly denoted as QCO. Simulate the distributed array single snapshot direction finding method based on the quantum cheetah optimization mechanism of the watch law. First, set the parameters of the distributed array system, where the total number of array elements M of the distributed system is 50, the number of array elements M N of each sub-array is 10, the array element pitch in the sub-array, the total number of sub-arrays N is 5, and the overall arrangement of each sub-array is as Figure 2 . When the number of signal sources P = 2, the incoming wave directions are θ = [50°, -10°]; when the number of signal sources P = 3, the incoming wave directions are θ = [50°, 10°, -30°]. Then, the parameters of QCO are set as follows: the number of searching cheetahs E = 50, the number of cheetahs I = 50, the maximum number of iterations D of the searching cheetahs is 100, the maximum number of iterations T of the cheetahs is 30, and the range factor The search factor w = 0.1, and the velocity factor The selection constant K = 0.2, the cheetah hunting factor η1 = 3, and the cheetah hunting factor η2 = 3.

[0094] Under the above parameter settings, through the method of taking the optimal value of the results of the direction-finding algorithm after multiple tests, the final layout structure of the distributed array system is obtained, and the distance between adjacent sub-arrays is: Wherein,

[0095] In order to further verify the superiority of the direction-finding algorithm and the array structure, the MUSIC algorithm is compared with the algorithm of the present invention. The direction-finding effects of the direction-finding algorithm of the present invention under the conditions of independent sources and coherent sources are respectively tested, and the direction-finding accuracies in the case of distributed arrays including two uniform arrangement structures with sub-array spacings of 10d and 20d are compared. Subsequently, they are abbreviated as 10-fold spacing and 20-fold spacing.

[0096] Figure 3 It represents the direction-finding result diagram under the incidence of two independent signal sources. The generalized signal-to-noise ratio is 15 dB, and a total of 30 Monte Carlo experiments are carried out. From the simulation Figure 3 It can be seen that due to the existence of false peaks in the distributed array pattern, the MUSIC algorithm almost fails, and the direction-finding results are concentrated on one signal source direction, while the algorithm proposed in this paper can better realize the DOA estimation of two independent sources.

[0097] Figure 4 It represents the direction-finding result diagram under the incidence of two coherent signal sources. The generalized signal-to-noise ratio is 15 dB, and a total of 30 Monte Carlo experiments are carried out. From the simulation Figure 4 It can be seen that due to the existence of false peaks in the distributed array pattern, the MUSIC algorithm basically fails, and the direction-finding results are largely concentrated on one signal source direction, while the algorithm proposed in this paper can better realize the DOA estimation of two coherent sources.

[0098] Figure 5 It represents the direction-finding result diagram under the incidence of three mixed signal sources. Among them, the signal source incident from 50° is independent, and the other two incident signal sources are coherent. The generalized signal-to-noise ratio is 15 dB. From the simulation Figure 5 It can be seen that when mixed signal sources are incident, the direction-finding results of the MUSIC algorithm are largely concentrated on the direction of the independent signal source incident due to the influence of false peaks, while the algorithm proposed in the present invention can better realize the DOA estimation of mixed signal sources.

[0099] Figure 6It represents the probability of successful direction finding for different array structures under different generalized signal-to-noise ratio conditions. It is defined that the direction finding is successful when the error between the direction finding estimation result and the accurate signal source direction is less than. 50 Monte Carlo experiments are carried out under each generalized signal-to-noise ratio. From Figure 6 It can be seen that in the case of low signal-to-noise ratio, the special array of the direction finding algorithm has a certain improvement in the accuracy of direction finding compared with the array structures with 10-fold spacing and 20-fold spacing. Moreover, the method of using the first sub-array for rough estimation in the direction finding algorithm proposed in the present invention has a certain applicability, and the gap in accuracy among the three array structures is small.

[0100] Although the present invention has been described based on a limited number of embodiments, those skilled in the art in this technical field understand that other embodiments can be envisioned within the scope of the present invention thus described. For the scope of the present invention, the disclosure made for the present invention is illustrative rather than restrictive, and the scope of the present invention is defined by the appended claims.

Claims

1. A distribution array single snapshot direction finding method based on the quantum cheetah optimization mechanism of the watch law, characterized in that Including: Step 1: Establish a single snapshot sampling signal model for a distributed array; Step 2: Use the single snapshot data received by the distributed array to construct a pseudo covariance matrix, and at the same time use the steering matrix of the distributed array to construct an orthogonal projection matrix to obtain the maximum likelihood estimation equation; Step 3: Use the single snapshot data received by the first sub-array of the distributed array to construct a Hankel matrix as the pseudo covariance matrix, and then use the reference information carried by the Hankel matrix to roughly estimate the direction of arrival of the incoming wave; Step 4: Initialize the search cheetah population to generate the initial quantum positions; Use the rough estimation value to obtain the initial hunting range, calculate the mapped positions of the search cheetahs and the corresponding fitness values, and obtain the local optimal quantum position and the global optimal quantum position; Step 5: Update the quantum positions of each search cheetah according to the update strategy of the search cheetah population and calculate the mapped positions; Step 6: Use the fitness function of direction finding estimation to calculate the fitness values, and update the local optimal quantum position and the global optimal quantum position; Step 7: Determine whether the maximum number of iterations is reached. If it is reached, output the mapped position of the global optimal quantum position, obtain the estimated direction of the incoming wave, and execute Step 8; if not, return to Step 5; Step 8: Based on the law of watches, by setting a signal source with a known true direction of arrival of the incoming wave, use the root mean square error between the obtained estimated direction of the incoming wave and the true direction of arrival of the incoming wave as the optimization goal to optimize the distributed array structure; Step 9: Initialize the cheetah population, convert the cheetah positions into the distributed array structure, use the direction finding algorithm to obtain the estimated direction under the corresponding array structure, use the fitness function of array optimization to calculate the fitness values of each cheetah, and obtain the local optimal position and the global optimal position; Step 10: Update the quantum velocities of each cheetah according to the update strategy of the cheetah population, and obtain the positions of the corresponding cheetahs through measurement; Step 11: Convert the cheetah positions into the distributed array structure, use the direction finding algorithm to obtain the estimated direction under the corresponding array structure, use the fitness function of array optimization to calculate the fitness values of each cheetah, and update the local optimal position and the global optimal position; Step 12: Determine whether the maximum number of iterations is reached. If it is reached, output the global optimal position of the cheetah, convert it into the distributed array structure, obtain the corresponding optimal array structure, and obtain the final estimated direction of the incoming wave; if not, return to Step 10.

2. A single-snapshot direction finding method for a distribution array based on the quantum cheetah optimization mechanism of the watch law according to claim 1, characterized in that The establishment of the single snapshot sampling signal model for the distributed array in Step 1 is as follows: Assume a distributed array with a total number of array elements \(M\), and the number of array elements in each sub - array is \(M\). N , the element spacing in the sub - array is \(\lambda\) is the wavelength of the incident signal, the total number of sub - arrays is \(N\), the \(i\) - th sub - array and the \(j\) - th sub - array, the spacing between them is \(M = N\times M\) N , There are \(P\) far - field narrow - band signals incident on the distributed array from \(\theta\) p directions respectively, and the incident signals and the noise signals are uncorrelated, \(p = 1,2,\cdots,P\). Select the first element of the first sub-array as the reference element. Then, at the signal received by the k-th element of the q-th sub-array at time is: Among them, is the incident signal, is the noise signal of the k-th element in the q-th subarray, is the distance between the k-th element and the reference element in the q-th subarray, The single snapshot sampling signal model for the distributed array is expressed as: y(1) = A(θ)s(1) + n(1) where \(y(1)=[y_1(1),y_2(1),\cdots,y N (1)] T , y q,k (1) represents the single snapshot data received by the \(k\)-th element in the \(q\)-th sub-array, \(q = 1,2,\cdots,N\), \(k = 1,2,\cdots,M N ; \(A(\theta)=[A_1(\theta),A_2(\theta),\cdots,A N (\theta)] T is the array steering matrix, \(A q (\theta)=[a q (\theta_1),a q (\theta_2),\cdots,a q (\theta P )] T , is the distance between the \(k\)-th element and the reference element in the \(q\)-th sub-array, \(\theta=[\theta_1,\theta_2,\cdots,\theta P is the incident wave azimuth vector; \(s(1)=[s_1(1),s_2(1),\cdots,s P (1)] T is the signal vector, \(n(1)=[n_1(1),n_2(1),\cdots,n N (1)] T is the array noise vector, is the noise vector of the \(q\)-th sub-array.

3. The distributed array single snapshot direction finding method of a quantum cheetah optimization mechanism based on the watch law according to claim 2, characterized in that, The pseudo covariance matrix in Step 2 is as follows: For the constructed matrix R y (1) perform covariance processing, i.e., The orthogonal projection matrix is: P A(θ) = A(θ)(A H (θ)A(θ)) -1 A H (θ); where H represents the conjugate transpose; The maximum likelihood estimation equation is as follows: where tr() is the matrix trace function.

4. A single snapshot direction finding method for a distribution array of a quantum cheetah optimization mechanism based on the watch law according to claim 3, characterized in that, The process of Step 3 includes: Divide the first sub-array into two sub-array units S1 and S2, where S1 is composed of the first M N -1 array elements of the first sub-array, and S2 is composed of the last M N -1 array elements of the first sub-array. Use the single snapshot data received by S1 and S2 to construct two pseudo covariance matrices H0(1) and H1(1). The matrices H0(1) and H1(1) contain relevant single snapshot information: Perform singular value decomposition on the pseudo-covariance matrix H0(1). where is the left singular vector, is the right singular component, and W is the singular value; Calculate the matrix using the singular values and singular vectors of the obtained H0(1) matrix where are the first P larger singular values after the singular value decomposition of the H0(1) matrix, i.e., the singular values corresponding to the signal part is the left singular vector of the singular values corresponding to the signal part is the right singular vector of the singular values corresponding to the signal part. Using the matrix the rough estimated value of the search angle is obtained as where is the matrix 's eigenvalue 5. A single-snapshot direction finding method for a distribution array based on the quantum cheetah optimization mechanism of the watch law according to claim 4, characterized in that, The process of Step 4 includes: assuming there are E search cheetahs in the hunting ground, and each search cheetah has its respective quantum position. Define the quantum position of the e-th search cheetah in the d-th generation during the iteration process as where P is the maximum dimension of the solution space; obtain the mapped position of the e-th search cheetah in the d-th generation through mapping The mapping equation is within the range of the hunting ground, where L p is the lower limit of the p-th dimension of the hunting range, and U p is the upper limit of the p-th dimension of the hunting range. Determine the initial hunting range through the result of rough estimation , is the range factor, e = 1, 2, …, E, p = 1, 2, …, P; substitute the position after mapping into the fitness function for fitness evaluation. The fitness equation is where Finally, denote the optimal quantum position obtained after the optimized search of the e-th search cheetah until the d-th generation as the local optimal quantum position Denote the quantum position with the optimal fitness value of the entire search cheetah population after the optimized search until the d-th generation as the global optimal quantum position 6. A distributed array single snapshot direction finding method for a quantum cheetah optimization mechanism based on the watch law according to claim 5, characterized in that, The process of Step 5 includes: In the d-th iteration process, randomly shuffle the hunting order of E search cheetahs. Define the adjacent cheetah of the e-th search cheetah as the search cheetah that starts hunting after the e-th search cheetah finishes hunting. If the e-th search cheetah is the last one to hunt, then define the search cheetah that hunted before the e-th search cheetah as the adjacent cheetah of the e-th search cheetah. Denote the position of the adjacent cheetah as Update the p-th dimensional quantum position of the e-th search cheetah in the d-th generation using the simulated quantum rotation gate. The update equation is where is the p-th dimension of the quantum rotation angle of the e-th search cheetah in the (d + 1)-th generation; the update equation for the p-th dimensional quantum rotation angle of the e-th search cheetah in the d-th generation is where D is the maximum number of iterations of the search cheetah population, is a random number uniformly distributed between [0, 1], is a random number uniformly distributed between [0, η1], where η1 is the hunting factor of the search cheetah, is a random number uniformly distributed between [0, 1], and w is the search factor; is a random number following the standard Gaussian distribution, is the p-th dimension of the quantum position of the adjacent cheetah of the e-th search cheetah in the d-th generation; is the velocity factor, is a random number uniformly distributed between [-1, 1], is the p-th dimension of the local optimal quantum position of the e-th search cheetah in the d-th generation; Finally, through the quantum position of the e-th search cheetah in the (d + 1)-th generation obtain the mapped position The mapping equation where L p is the lower limit value of the p-th dimension of the hunting range, and U p is the upper limit value of the p-th dimension of the hunting range, 7. A distribution array single snapshot direction finding method of a quantum cheetah optimization mechanism based on the watch law according to claim 6, characterized in that The process of Step 6 includes: substituting the mapped position of the (d + 1)-th generation of search cheetahs into the fitness function where calculate the fitness value of the updated search cheetahs, update the local optimal quantum position to and the global optimal quantum position to If the fitness value of the e-th hunting cheetah in the (d + 1)-th generation is greater than the fitness value of, then Otherwise If the fitness value of the local optimal position of the e-th hunting cheetah in the (d + 1)-th generation is greater than the fitness value of, then Otherwise 8. A single-snapshot direction finding method for a distribution array based on the quantum cheetah optimization mechanism of the watch law according to claim 7, characterized in that The process of Step 8 includes: The watch law states that when a person has multiple watches with different time indications at the same time, only the indication of one watch is correct; the root mean square error between the estimated direction of arrival obtained in step seven and the known true direction of arrival is used as the fitness function for array structure optimization. where is the potential solution of the array structure, and θ p is the true direction of the p-th wave arrival, is the estimated direction of the p-th wave arrival obtained after performing the direction finding algorithm under this array structure, and p = 1, 2, ···, P.

9. A single-snapshot direction finding method for a distribution array based on the quantum cheetah optimization mechanism of the watch law according to claim 8, characterized in that, The process of Step Nine includes: assuming there are I cheetahs in the hunting ground, and each cheetah has its own quantum speed. Define the quantum speed of the i-th cheetah in the t-th generation during the iterative process as After measurement, the position of the i-th cheetah in the t-th generation is The corresponding measurement equation is where is a random number uniformly distributed between [0, 1], J is the maximum dimension of the solution space; Convert the position measured from the quantum speed of the i-th cheetah in the t-th generation to the sub-array spacing of the distributed array and then execute Steps Two to Seven, where is the array spacing between the -th sub-array and the -th sub-array in the t-th generation. Substitute the direction finding result into the fitness function to calculate the fitness value corresponding to each cheetah. Where θ p is the true direction of the p-th incoming wave, is the array spacing corresponding to the i-th cheetah in the t-th generation and the estimated direction of the p-th incoming wave obtained after executing Steps Two to Seven; Denote the optimal position after optimizing the search of the i-th cheetah until the t-th generation as the local optimal position Denote the position with the optimal fitness value of the entire cheetah population after optimizing the search until the t-th generation as the global optimal position 10. A single-snapshot direction finding method for a distribution array based on the quantum cheetah optimization mechanism of the watch law according to claim 9, characterized in that, The process of Step 10 includes: In the t-th iteration process, randomly shuffle the hunting order of I cheetahs. Define the adjacent cheetah as the cheetah that starts hunting after the i-th cheetah finishes hunting. If the i-th cheetah is the last one to start hunting, then define the cheetah that hunted before the i-th cheetah as the adjacent cheetah of the i-th cheetah. The quantum speed of the adjacent cheetah is denoted as Take the global optimal position at the t-th iteration as the hunting target position of the cheetah population, and the local optimal position of the i-th cheetah at the t-th iteration as the leader position of the i-th cheetah; In the t-th iteration process, when holds, the i-th cheetah selects the waiting strategy. At this time, the update equation of the j-th dimensional quantum speed of the i-th cheetah is where and are both random numbers uniformly distributed between [0, 1], and K is the selection constant; Otherwise, the i-th cheetah selects the predation strategy. At this time, the update equation of the j-th dimensional quantum speed of the i-th cheetah is where μ t+1 is a random number uniformly distributed between [0, 1], is the j-th dimension of the quantum rotation angle of the i-th cheetah in the (t + 1)-th generation, represents When it is 0, the probability of performing an inversion operation on this qubit, and its value is a constant between [0, 1 / J]; The update equation of the j-th dimension of the quantum rotation angle of the i-th cheetah in the t-th generation is where, T is the maximum number of iterations of the cheetah population, is a random number uniformly distributed between [0, 1], is a random number uniformly distributed between [0, η2], and η2 is the cheetah hunting factor, is a random number subject to a Gaussian distribution; and are random numbers uniformly distributed between [0, 1], is the j-th dimension of the hunting target position in the t-th generation, is the j-th dimension of the leader position of the i-th cheetah in the t-th generation; is a random number subject to a Gaussian distribution; is the j-th dimension of the quantum speed of the adjacent cheetah of the i-th cheetah in the t-th generation, i = 1, 2,..., I, j = 1, 2,..., J; Finally, measure the updated quantum speed of the i-th cheetah in the (t + 1)-th generation, and update the position of the i-th cheetah to The corresponding measurement equation is where is a random number uniformly distributed between [0, 1]; The process of Step Eleven includes: converting the position corresponding to the (t + 1)-th generation of cheetahs into the subarray spacing of the distributed array where is the array spacing between the -th subarray and the -th subarray of the (t + 1)-th generation; assuming there are P far-field incoming wave signals, when the subarray spacing of the distributed array is , perform Steps Two to Seven, substitute the direction finding result into the fitness function to calculate the fitness value corresponding to each cheetah, where θ p is the true direction angle of the p-th far-field incoming wave signal, is the p-th direction angle obtained after performing the direction finding algorithm under the array spacing corresponding to the i-th cheetah of the (t + 1)-th generation; update the local optimal position of the cheetah to and the global optimal position to If the fitness value of the i-th cheetah of the (t + 1)-th generation is less than 's fitness value, then Otherwise If the fitness value of the local optimal position of the i-th cheetah of the (t + 1)-th generation is less than 's fitness value, then Otherwise

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