Distribution array single snapshot direction finding method of quantum hunting optimization mechanism based on watch law

Abstract

The invention discloses a distribution array single snapshot direction finding method of a quantum hunting optimization mechanism based on a watch law, and relates to the technical field of array signal processing. According to the technical key points, the method comprises the following steps: constructing a Hankle matrix as a pseudo covariance matrix by using single snapshot data received by a first sub-array, carrying out coarse estimation to obtain an initial target range, constructing a Toeplitz matrix by using the single snapshot data received by the whole array, and combining the Toeplitz matrix with a maximum likelihood estimation method, a continuous quantum optimization theory and a hunting optimization mechanism are combined, and a continuous quantum evolution mechanism is utilized to further accelerate the convergence speed of a hunting optimization algorithm; and finally, on the basis of the watch law, in combination with a discrete quantum optimization theory and a hunting optimization mechanism, a distributed array structure which is most adaptive to the algorithm is solved under the condition that a target information source is assumed to be known, so that single-snapshot accurate direction finding of the distributed array is realized, the convergence speed of the algorithm is improved, the calculation complexity is reduced, and the direction finding accuracy is improved.

Description

Technical Field

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

[0002] As an important branch of the antenna array field, distributed arrays have a wide range of applications in modern technology. By integrating many array antenna units with smaller calibers, 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 system elements unchanged. In addition, distributed arrays can better meet the needs of specific application scenarios, showing extremely high adaptability and playing a key role in many fields.

[0003] In the field of distributed array system research, the estimation of direction of arrival (DOA) is a hot topic of research that has attracted much attention. In a distributed array, when the subarray spacing is greater than the half wavelength of the signal, the spatial sampling theorem cannot be satisfied, resulting in the DOA estimation method of a conventional uniform array having an angle measurement ambiguity problem and cannot be directly applied to a distributed array. There are three main types of algorithms for distributed arrays. One is to construct virtual array elements through virtual interpolation to fill the gaps between subarrays, so that the distributed array is close to a uniform array. However, this method greatly increases the computational burden when the subarray spacing is large. Another method is an auxiliary design method, which adds auxiliary array elements or improves the structure of the distributed array to eliminate angle measurement ambiguity. However, this method will increase the burden on the hardware. DOA estimation can also be achieved through a deambiguation method. This method first uses the traditional DOA estimation method to obtain a DOA estimation result with ambiguity, and then uses the reference information obtained from the distributed array for deambiguation. This method will result in large errors in the case of low signal-to-noise ratio or large subarray spacing.

[0004] According to the existing technical literature, the "Multi-baseline distributed array DOA estimation method based on ESPRIT" published by Ma Yan, Chen Boxiao et al. in "System Engineering and Electronic Technology" (2014, 36 (08)) first obtains the unambiguous sub-array unit DOA estimation with low accuracy through the sub-array, and then uses the rotational invariance between arrays to obtain the ambiguity but high-precision sub-array unit DOA estimation, and finally obtains the unambiguous and high-precision DOA estimation through deambiguation. However, under low signal-to-noise ratio conditions, the estimation performance of this algorithm decreases significantly. The "Distributed array DOA estimation based on preprocessing MUSIC algorithm" published by Yang Minglei, Zhang Yan et al. in "Guidance and Fuze" first uses the rotational invariant subspace algorithm to obtain an unambiguous rough estimate, which limits the search range of the MUSIC algorithm and solves the angle measurement ambiguity problem of the distributed array. However, this algorithm still needs to perform eigendecomposition. WeichuangYu, Peiyu He and others 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 the dual V-shaped distributed array, a deambiguation algorithm was proposed. The spatial spectrum of the two V-shaped sub-arrays was obtained by the MUSIC algorithm, and the spectral peak corresponding to the real target was retained by designing the threshold to achieve deambiguation. The above method is mainly aimed at multi-snapshot data, while the single-snapshot DOA estimation only processes the data of a single snapshot, which greatly reduces the consumption of computing resources and improves the real-time response capability of the algorithm. This has important practical significance and application value for application scenarios with high real-time requirements, such as mobile communications, real-time monitoring, and military reconnaissance. Summary of the invention

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

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

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

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

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

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

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

[0012] Step 6: Calculate the fitness value using the fitness function estimated by direction finding, and update the local optimal quantum position and the global optimal quantum position;

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

[0014] Step 8: Based on the watch law, a source with a known real wave direction is set, and the root mean square error between the estimated wave direction and the real wave direction is used as the optimization target to optimize the distributed array structure;

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

[0016] Step 10: Update the quantum speed of each cheetah according to the update strategy of the cheetah population, and obtain the position of the corresponding cheetah by measurement;

[0017] Step 11: convert the cheetah position into a distributed array structure, use a direction finding algorithm under the corresponding array structure to obtain an estimated direction, use the array optimized fitness function to calculate the fitness value of each cheetah, and update the local optimal position and the global optimal position;

[0018] Step 12: determine whether the maximum number of iterations has been reached. If so, output the cheetah's global optimal position, convert it into 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 10.

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

[0020] Assume a distributed array with a total number of M array elements and M array elements in each subarray. N , the spacing between the array elements in the subarray is λ is the wavelength of the incident signal, the total number of subarrays is N, and the The subarray and The spacing between the subarrays is M=N×M N , There are P far-field narrowband signals from θ p The incident signal is incident on the distributed array from different directions, and the incident signal and the noise signal are uncorrelated, p = 1, 2, ..., P; the first array element of the first subarray is selected as the reference array element, then The signal received by the kth element in the qth subarray at the moment is:

[0021]

[0022] in, is the incident signal, is the noise signal of the kth element in the qth subarray, is the distance between the kth array element in the qth subarray and the reference array element, q=1,2,···,N, k=1,2,···M N ;

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

[0024] y(1)=A(θ)s(1)+n(1)

[0025] 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 array element in the q-th subarray, 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 kth array element in the qth subarray and the reference array element, θ=[θ1,θ2,…,θ P] is the wave direction vector; 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 qth subarray.

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

[0027]

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

[0029] The orthogonal projection matrix is: 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 three includes:

[0032] The first subarray is divided into two subarray units S1 and S2, where S1 consists of the first M subarrays. N -1 array element, S2 consists of the last M of the first subarray N -1 array element, and two pseudo covariance matrices H0(1) and H1(1) are constructed using the single snapshot data received by S1 and S2. The matrices H0(1) and H1(1) contain the relevant single snapshot information:

[0033]

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

[0035] Using the obtained singular values ​​and singular vectors of the H0(1) matrix, we can calculate the matrix in are the first P larger singular values ​​after 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 values ​​corresponding to the signal part, is the right singular vector of the singular value corresponding to the signal part, using the matrix The rough estimate of the search angle is in is a matrix The characteristic value of

[0036] Furthermore, the process of step 4 includes: assuming that there are E search cheetahs in the hunting ground, each search cheetah has its own quantum position, and the quantum position of the e-th search cheetah in the d-th generation in the iterative process is defined as in e=1,2,…,E,p=1,2,…,P,P is the maximum dimension of the solution space; the mapping position of the e-th searching cheetah of the d-th generation is obtained by mapping The mapping equation is Within the hunting grounds, L p is the lower limit of the p-th dimension of the hunting range, U p is the upper limit of the p-th dimension of the hunting range, and the result of rough estimation is To determine the initial hunting range, is the range factor, e=1,2,…,E, p=1,2,…,P; the position after mapping Substitute the fitness function for fitness evaluation, and the fitness equation is: in Finally, the optimal quantum position obtained after the e-th search of the cheetah until the d-th generation optimization search is recorded as the local optimal quantum position The quantum position with the best fitness value of the entire search cheetah population after the d-th generation optimization search is recorded as the global optimal quantum position

[0037] Furthermore, the process of step five includes: in the dth iteration process, randomly disrupting the hunting order of the E-th search cheetahs, defining the adjacent cheetahs of the e-th search cheetah as the search cheetahs that hunt after the e-th search cheetah finishes hunting, and if the e-th search cheetah is the last cheetah to hunt, then the search cheetahs that hunted before the e-th search cheetah are defined as the adjacent cheetahs of the e-th search cheetah, and the positions of the adjacent cheetahs are recorded as Use the simulated quantum revolving gate to update the p-dimensional quantum position of the e-th searching cheetah of the d-th generation. The update equation is: in The update equation for the quantum rotation angle of the cheetah in the e-th search of the cheetah in the p-th dimension in the d+1 generation is: in D is the maximum number of iterations for searching the cheetah population. is a random number that follows a uniform distribution between [0,1]. is a random number that follows a uniform distribution between [0,η1], η1 is the cheetah hunting factor, is a random number uniformly distributed between [0,1], and w is the search factor; is a random number that follows a standard Gaussian distribution, The p-th dimension of the adjacent cheetah quantum position of the e-th generation searching cheetah; is the speed factor, is a random number that follows a uniform distribution between [-1,1]. The pth dimension of the local optimal quantum position of the cheetah is searched for the eth cheetah in the dth generation; finally, the quantum position of the cheetah is searched for the eth cheetah in the d+1th generation. Mapping to get the mapping position Mapping equation Where L p is the lower limit of the p-th dimension of the hunting range, U p is the upper limit of the p-th dimension of the hunting range,

[0038] Further, the process of step six includes: mapping the position of the d+1 generation search cheetah Substitute into the fitness function in Calculate the fitness value of the updated search cheetah and update the local optimal quantum position to And the global optimal quantum position is e=1,2,…,E; if the eth cheetah in the d+1th generation hunts The fitness value is greater than The fitness value of otherwise e=1,2,…,E;If the e-th hunting cheetah in the d+1th generation has the local optimal position The fitness value is greater than The fitness value of otherwise

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

[0040] The watch law states that when a person has multiple watches pointing to different times at the same time, only one watch has the correct direction. The root mean square error between the estimated direction of the incoming wave obtained in step 7 and the known true direction of the incoming wave is used as the fitness function for array structure optimization. in is the potential solution of the array structure, θ p is the true direction of the pth incoming wave, To obtain the estimated direction of the pth incoming wave after executing the direction finding algorithm under the array structure, p = 1, 2, ···, P.

[0041] Furthermore, the process of step nine includes: assuming that there are I cheetahs in the hunting ground, each cheetah has its own quantum speed, and defining the quantum speed of the i-th cheetah of the t-th generation in the iterative process as After measurement, the position of the i-th cheetah of the t-th generation is The corresponding measurement equation is in is a random number that follows a uniform distribution between [0,1]. i=1,2,…,I,j=1,2,…,J,J is the maximum dimension of the solution space; the position obtained by measuring the quantum speed of the i-th cheetah of the t-th generation Convert to distributed array subarray spacing Then execute the direction finding algorithm, where For the tth generation The subarray and The array spacing of the sub-arrays is used to bring the direction finding results into the fitness function Calculate the fitness value corresponding to each cheetah, where θ p is the true direction of the pth incoming wave, is the array spacing corresponding to the i-th cheetah of the t-th generation The estimated direction of the pth incoming wave is obtained after executing the direction finding algorithm; the optimal position of the i-th cheetah until the t-th generation optimization search is recorded as the local optimal position The position with the best fitness value of the entire cheetah population after the t-th generation optimization search is recorded as the global optimal position

[0042] Furthermore, the process of step ten includes: in the t-th iteration process, randomly disrupting the hunting order of the cheetahs, defining the adjacent cheetahs as the cheetahs that hunt after the ith cheetah finishes hunting, and if the ith cheetah is the last cheetah to hunt, then the cheetahs hunted before the ith cheetah are defined as the adjacent cheetahs of the ith cheetah, and the quantum speed of the adjacent cheetahs is recorded as The global optimal position at the tth iteration is 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 of the ith cheetah; in the tth iteration, when When , the i-th cheetah chooses the waiting strategy. At this time, the j-dimensional quantum speed update equation of the i-th cheetah is in and are all random numbers with uniform distribution between [0,1], and K is a selection constant; otherwise, the i-th cheetah chooses a predation strategy, and the update equation of the j-dimensional quantum velocity of the i-th cheetah is where μ t+1 is a random number that follows a uniform distribution between [0,1]. is the jth dimension of the quantum rotation angle of the ith cheetah of the t+1th generation, represent The probability of reversing the qubit when it is 0 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 in, T is the maximum number of iterations of the cheetah population, is a random number that follows a uniform distribution between [0,1]. is a random number uniformly distributed between [0,η2], η2 is the cheetah hunting factor, is a random number that follows a Gaussian distribution; and is a random number that follows a uniform distribution between [0,1]. is the jth dimension of the hunting target position of the tth generation, is the jth dimension of the leader position of the i-th cheetah of the t-th generation; is a random number that follows a Gaussian distribution; is the jth dimension of the quantum speed of the neighboring cheetahs of the i-th cheetah of the t-th generation, i = 1, 2, ..., I, j = 1, 2, ..., J; finally, the updated quantum speed of the i-th cheetah of the t+1-th generation is Measure and update the position of the i-th cheetah to The corresponding measurement equation is in is a random number between [0,1] that follows a uniform distribution;

[0043] The process of step 11 includes: moving the position corresponding to the cheetah of the t+1 generation Convert to distributed array subarray spacing in is the t+1th generation The subarray and The array spacing of the sub-arrays is ; Assuming there are P far-field incoming wave signals, the sub-array spacing of the distributed array is Execute the direction finding algorithm under the condition of , and substitute the direction finding result into the fitness function Calculate the fitness value corresponding to each cheetah, where θ p is the true direction angle of the pth 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 combines discrete quantum optimization mechanism and continuous quantum optimization mechanism with the cheetah population optimization algorithm, updates the specific optimization steps, greatly reduces the number of iterations, reduces the amount of calculation to a certain extent, makes the search mechanism more concise, and obtains an algorithm that can achieve accurate direction finding of distributed arrays under single snapshot conditions. At the same time, an optimized distributed array adapted to the algorithm is obtained, which greatly improves the direction finding accuracy. The simulation and comparison of conventional uniformly distributed arrays show that the direction finding accuracy under single snapshot conditions has been greatly improved, and the stability of the array has also been 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, which 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 It is a flow chart of a single-snap direction finding method of a quantum cheetah optimization mechanism distributed array based on the watch law described in an embodiment of the present invention.

[0050] Figure 2 Schematic diagram of the layout of distributed array sub-arrays in an embodiment of the present invention.

[0051] Figure 3 2 is a schematic diagram of direction finding results in the case of two independent sources in an embodiment of the present invention.

[0052] Figure 4 2 is a schematic diagram of direction finding results in the case of two coherent sources in an embodiment of the present invention.

[0053] Figure 5 1 is a schematic diagram of direction finding results in the case of three mixed sources in an embodiment of the present invention.

[0054] Figure 6 Schematic diagram of the accuracy of direction finding results under different array structures in an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0056] Different from the existing methods, which estimate the DOA of distributed arrays mainly by defuzzification or constructing a special distributed array structure, the present invention proposes a distributed array single-snapshot direction finding method based on the quantum cheetah mechanism of the watch law. By imitating the group intelligent behavior of cheetahs hunting and combining the continuous quantum optimization mechanism, the accurate estimation of the source direction under the single-snapshot condition is realized, and the structure of the distributed array is optimized 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 points 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 result of direction finding. Therefore, the present invention uses the cheetah hunting mechanism combined with discrete quantum optimization theory, and solves the distributed array structure that is most suitable for the direction finding method proposed by the present invention under the assumption that the target direction is known. It is verified by simulation experiments that the distributed array single-snapshot direction finding method 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 processing independent sources and coherent sources. It 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 Hankle matrix as a pseudo-covariance matrix for rough estimation to obtain the initial target range, and then uses the single snapshot data received by the entire array to construct a Toeplitz matrix combined 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, and the distributed array structure most suitable for the algorithm is solved under the assumption that the target source is known. Not only does it realize the single snapshot precise direction finding of the distributed array, improve the convergence speed of the algorithm, and reduce the computational complexity, but it also further obtains a special distributed array structure and improves the direction finding accuracy.

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

[0059] Step 1: Establish a distributed array single snapshot sampling signal model, in which each sub-array is distributed in one dimension in space.

[0060] According to an embodiment of the present invention, assuming that a distributed array has a total number of M array elements and each subarray has M array elements. N , the spacing between the array elements in the subarray is λ is the wavelength of the incident signal, the total number of subarrays is N, and the The subarray and The spacing between the subarrays is M=N×M N,

[0061] There are P far-field narrowband signals from θ p The incident signal is incident on the distributed array from multiple directions, and the incident signal and the noise signal are uncorrelated, p = 1, 2, ..., P. Select the first array element of the first subarray as the reference array element, then The signal received by the kth element in the qth subarray at the moment is:

[0062]

[0063] in, is the incident signal, is the noise signal of the kth element in the qth subarray, is the distance between the kth array element in the qth subarray and the reference array 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 array element in the q-th subarray, 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 kth array element in the qth subarray and the reference array element, θ=[θ1,θ2,…,θ P ] is the wave direction 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, is the noise vector of the qth subarray.

[0067] Step 2: When the sub-array spacing of the distributed array is known, the pseudo-covariance matrix is ​​constructed using the single snapshot data received by the distributed array, and the orthogonal projection matrix is ​​constructed using the steering matrix of the distributed array to obtain the maximum likelihood estimation equation.

[0068] According to an embodiment of the present invention, the sub-array spacing of the known distributed array The single snapshot sampling data of the entire distributed array can be obtained. The Toeplitz matrix is ​​constructed as the pseudo covariance matrix using the single snapshot data received by the entire distributed array as follows:

[0069]

[0070] For the constructed matrix R y (1) Perform covariance processing, 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), the angle estimate 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 sub-array of the distributed array to construct a Hankle matrix as a pseudo-covariance matrix, and then use the reference information carried by the Hankle matrix to roughly estimate the incoming wave direction.

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

[0073]

[0074] Then the pseudo-covariance matrix H0(1) is subjected to singular value decomposition. in is the left singular vector, is the right singular component, and W is the singular value. The matrix is ​​calculated using the singular values ​​and singular vectors of the obtained H0(1) matrix in are the first P larger singular values ​​after 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 values ​​corresponding to the signal part, is the right singular vector of the singular value corresponding to the signal part, using the matrix The rough estimate of the search angle is in is a matrix The characteristic value of

[0075] Step 4: Initialize the search cheetah population, generate an initial quantum position, and use a rough estimate to obtain the initial hunting range, calculate the mapping position of the search cheetah and the corresponding fitness value, and obtain the local optimal quantum position and the global optimal quantum position.

[0076] According to an embodiment of the present invention, first assume that there are E search cheetahs in the hunting ground, each of which has its own quantum position, and define the quantum position of the e-th search cheetah in the d-th generation in the iterative process as in e=1,2,…,E,p=1,2,…,P,P is the maximum dimension of the solution space. The mapping position of the e-th searching cheetah in the d-th generation is obtained by mapping The mapping equation is Within the hunting grounds, L p is the lower limit of the p-th dimension of the hunting range, U p is the upper limit of the p-th dimension of the hunting range, and the result of rough estimation is To determine the initial hunting range, is the range factor, e=1,2,…,E, p=1,2,…,P. The position after mapping Substitute the fitness function for fitness evaluation, and the fitness equation is: in Finally, the optimal quantum position obtained after the e-th search of the cheetah until the d-th generation optimization search is recorded as the local optimal quantum position The quantum position with the best fitness value of the entire search cheetah population after the d-th generation optimization search is recorded as the global optimal quantum position e=1,2,…,E.

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

[0078] According to an embodiment of the present invention, during the dth iteration, the hunting order of the E-th searching cheetahs is randomly disrupted, and the adjacent cheetahs of the e-th searching cheetah are defined as the searching cheetahs that hunt after the e-th searching cheetah finishes hunting. If the e-th searching cheetah is the last cheetah to hunt, the searching cheetahs that hunted before the e-th searching cheetah are defined as the adjacent cheetahs of the e-th searching cheetah, and the positions of the adjacent cheetahs are recorded as Use the simulated quantum revolving gate to update the p-dimensional quantum position of the e-th searching cheetah of the d-th generation. The update equation is: in The update equation for the quantum rotation angle of the cheetah in the e-th search of the cheetah in the p-th dimension in the d+1 generation is in, D is the maximum number of iterations for searching the cheetah population. is a random number that follows a uniform distribution between [0,1]. is a random number that follows a uniform distribution between [0,η1], η1 is the cheetah hunting factor, is a random number uniformly distributed between [0,1], and w is the search factor; is a random number that follows a standard Gaussian distribution, The p-th dimension of the adjacent cheetah quantum position of the e-th generation searching cheetah; is the speed factor, is a random number that follows a uniform distribution between [-1,1]. The pth dimension of the local optimal quantum position of the cheetah is searched for the eth cheetah in the dth generation, e = 1, 2, ..., E, p = 1, 2, ..., P. Finally, the quantum position of the cheetah is searched for the eth cheetah in the d+1th generation. Mapping to get the mapping position Mapping equation Where L p is the lower limit of the p-th dimension of the hunting range, U p is the upper limit of the p-th dimension of the hunting range, e=1,2,…,E, p=1,2,…,P.

[0079] Step 6: Use the fitness function of direction finding estimation to calculate the fitness value and update the local optimal quantum position and the global optimal quantum position.

[0080] According to an embodiment of the present invention, the mapping position of the d+1 generation search cheetah is Substitute the fitness function in Calculate the fitness value of the updated search cheetah and update the local optimal quantum position to And the global optimal quantum position is e=1,2,…,E. If the eth cheetah in the d+1th generation hunts The fitness value is greater than The fitness value of otherwise e=1,2,…,E. If the e-th hunting cheetah in the d+1th generation has the local optimal position The fitness value is greater than The fitness value of otherwise

[0081] Step 7: Determine whether the maximum number of iterations D has been reached. If it has not been reached, set d = d + 1, return to step 5, and continue iterating; otherwise, output the global optimal position. The mapping position of , that is, the estimated direction of the incoming signal.

[0082] Step 8: Based on the watch law, a signal source with a known true wave direction is set, and the root mean square error between the estimated wave direction and the true wave direction is used as the optimization target to optimize the distributed array structure.

[0083] According to an embodiment of the present invention, the watch law refers to when a person has multiple watches pointing to different times at the same time, only the pointing result of one watch is correct. The structure of the array in the distributed array direction finding has a certain influence on the direction finding result. By applying the watch law 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 sets a known incident signal source and the above-mentioned direction finding algorithm, and 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. in is the potential solution of the array structure, θ p is the true direction of the pth incoming wave, To obtain the estimated direction of the pth incoming wave after executing the direction finding algorithm under this array structure, p = 1, 2, ···, P.

[0084] Step 9: Initialize the cheetah population, convert the cheetah position into a distributed array structure, use the direction finding algorithm under the corresponding array structure to get the estimated direction, use the array optimized fitness function to calculate the fitness value of each cheetah, and obtain the local optimal position and the global optimal position.

[0085] According to an embodiment of the present invention, assuming that there are I cheetahs in the hunting ground, each cheetah has its own quantum speed, and the quantum speed of the i-th cheetah in the t-th generation during the algorithm iteration is defined as After measurement, the position of the i-th cheetah of the t-th generation is The corresponding measurement equation is in is a random number that follows a uniform distribution between [0,1]. i=1,2,…,I,j=1,2,…,J,J is the maximum dimension of the solution space. The position obtained by measuring the quantum speed of the ith cheetah of the tth generation Convert to distributed array subarray spacing Then execute the direction finding algorithm, where For the tth generation The subarray and The array spacing of the sub-arrays is used to bring the direction finding results into the fitness function Calculate the fitness value corresponding to each cheetah, where θ p is the true direction of the pth incoming wave, is the array spacing corresponding to the i-th cheetah of the t-th generation The estimated direction of the pth incoming wave obtained after executing the direction finding algorithm is: i=1,2,…,I,p=1,2,···,P。 The optimal position of the i-th cheetah after the t-th generation optimization search is recorded as the local optimal position The position with the best fitness value of the entire cheetah population after the t-th generation optimization search is recorded as the global optimal position i=1,2,…,I.

[0086] Step 10: Update the quantum speed of each cheetah according to the update strategy of the cheetah population, and obtain the position of the corresponding cheetah through measurement.

[0087] According to the embodiment of the present invention, during the t-th iteration, the hunting order of I cheetahs is randomly disrupted, and the adjacent cheetah is defined as the cheetah that hunts after the ith cheetah finishes hunting. If the ith cheetah is the last cheetah to hunt, the cheetah hunted before the ith cheetah is defined as the adjacent cheetah of the ith cheetah, and the quantum speed of the adjacent cheetah is recorded as The global optimal position at the tth iteration is 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 of the ith cheetah. In the tth iteration, when When , the i-th cheetah chooses the waiting strategy. At this time, the j-dimensional quantum speed update equation of the i-th cheetah is in and are all random numbers with uniform distribution between [0,1], and K is a selection constant; otherwise, the i-th cheetah chooses a predation strategy, and the update equation of the j-dimensional quantum velocity of the i-th cheetah is where μ t+1is a random number that follows a uniform distribution between [0,1]. is the jth dimension of the quantum rotation angle of the ith cheetah of the t+1th generation, represent The probability of reversing the qubit when it is 0 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 of the t-th generation is in, T is the maximum number of iterations of the cheetah population, is a random number that follows a uniform distribution between [0,1]. is a random number uniformly distributed between [0,η2], η2 is the cheetah hunting factor, is a random number that follows a Gaussian distribution; and is a random number that follows a uniform distribution between [0,1]. is the jth dimension of the hunting target position of the tth generation, is the jth dimension of the leader position of the i-th cheetah of the t-th generation; is a random number that follows a Gaussian distribution; is the jth dimension of the quantum speed of the neighboring cheetahs of the i-th cheetah of the t-th generation, i = 1, 2, ..., I, j = 1, 2, ..., J. Finally, the updated quantum speed of the i-th cheetah of the t+1-th generation is Measure and update the position of the i-th cheetah to The corresponding measurement equation is in is a random number that follows a uniform distribution between [0,1], i=1,2,…,I, j=1,2,…,J.

[0088] Step 11: convert the cheetah position into a distributed array structure, use a direction finding algorithm under the corresponding array structure to obtain an estimated direction, use the array optimized fitness function to calculate the fitness value of each cheetah, and update the local optimal position and the global optimal position;

[0089] According to an embodiment of the present invention, the position corresponding to the t+1th generation cheetah Convert to distributed array subarray spacing in is the nth subarray of the t+1th generation and the The array spacing of the sub-arrays, i = 1, 2, ..., I, Assuming there are P far-field incoming wave signals, the sub-array spacing of the distributed array is Execute the direction finding algorithm steps 2 to 7 under the condition of , and bring the direction finding result into the fitness function Calculate the fitness value corresponding to each cheetah, where θp is the true direction angle of the pth 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, i=1,2,…,I, p=1,2,···,P. 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

[0090] Step 12: determine whether the maximum number of iterations has been reached. If so, output the cheetah's global optimal position, convert it into 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 10.

[0091] Step 12: Determine whether the maximum number of iterations T of the cheetah has been reached. If not, set t=t+1 and return to step 10 to continue iterating; otherwise, output the global optimal position. The cheetah's global optimal position Convert to distributed array structure The corresponding optimal array structure is obtained; when there is an incoming wave from a far-field source, under the distributed array structure, steps 2 to 7 are executed to obtain the estimated direction of the incoming wave signal.

[0092] The technical effect of the present invention is further verified through experiments.

[0093] For the quantum cheetah optimization mechanism, it is abbreviated as QCO below. To simulate the distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law, the distributed array system parameters are first set, where the total number of array elements in the distributed system is M = 50, and the number of array elements in each subarray is M. N =10, the spacing between array elements in the subarray The total number of sub-arrays N = 5, and the overall arrangement of each sub-array is as follows Figure 2 When the number of signal sources P = 2, the direction of the incoming wave is θ = [50°, -10°]; when the number of signal sources P = 3, the direction of the incoming wave is θ = [50°, 10°, -30°]. Then the parameters of QCO are set as follows: the number of search cheetahs E = 50, the number of cheetahs I = 50, the maximum number of iterations of the search cheetah D = 100, the maximum number of iterations of the cheetah T = 30, and the range factor Search factor w = 0.1, speed factor Select constant K=0.2, search for cheetah hunting factor η1=3, cheetah hunting factor η2=3.

[0094] Under the above parameter settings, the final distributed array system layout structure is obtained by taking the optimal value of the direction finding algorithm after multiple tests. The spacing between adjacent sub-arrays is: in,

[0095] In order to further verify the superiority of the direction finding algorithm and the array structure, the MUSIC algorithm is used to compare with the algorithm of the present invention, and the direction finding effects of the direction finding algorithm of the present invention under independent source and coherent source conditions are tested respectively, and the accuracy of direction finding under two uniformly arranged structures including 10d and 20d of the sub-array spacing is compared, which are hereinafter referred to as 10 times the spacing and 20 times the spacing.

[0096] Figure 3 The figure shows the direction finding results when two independent signal sources are incident. The generalized signal-to-noise ratio is 15dB, and a total of 30 Monte Carlo experiments were performed. Figure 3 It can be seen that due to the existence of pseudo peaks in the distributed array pattern, the MUSIC algorithm is almost ineffective, and the direction finding results are concentrated in the direction of one source. The algorithm proposed in this paper can better realize the DOA estimation of two independent sources.

[0097] Figure 4 The figure shows the direction finding result when two coherent signal sources are incident. The generalized signal-to-noise ratio is 15dB, and a total of 30 Monte Carlo experiments were performed. Figure 4 It can be seen from the figure that due to the existence of pseudo peaks in the distributed array pattern, the MUSIC algorithm is basically ineffective, and the direction finding results are largely concentrated in the direction of one source. The algorithm proposed in this paper can better realize the DOA estimation of two coherent sources.

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

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

[0100] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments are contemplated within the scope of the invention thus described. The disclosure of the present invention is intended to be illustrative rather than restrictive of the scope of the invention, which is defined by the appended claims.

Claims

1. A distributed array single-snap direction finding method based on the quantum cheetah optimization mechanism of the watch law, characterized in that: include: Step 1: Establish a distributed array single snapshot sampling signal model; Step 2: construct a pseudo covariance matrix using the single snapshot data received by the distributed array, and construct an orthogonal projection matrix using the steering matrix of the distributed array to obtain a maximum likelihood estimation equation; Step 3: Use the single snapshot data received by the first subarray of the distributed array to construct a Hankle matrix as a pseudo covariance matrix, and then use the reference information carried by the Hankle matrix to roughly estimate the incoming wave direction; Step 4: Initialize the search cheetah population and generate the initial quantum position; The initial hunting range is obtained using the rough estimate, the mapping position of the searching cheetah and the corresponding fitness value are calculated, and the local optimal quantum position and the global optimal quantum position are obtained; Step 5: Update the quantum position of each search cheetah according to the update strategy of the search cheetah population and calculate the mapping position; Step 6: Calculate the fitness value using the fitness function estimated by direction finding, and update the local optimal quantum position and the global optimal quantum position; Step 7: Determine whether the maximum number of iterations has been reached. If so, output the global optimal quantum position mapping position, obtain the estimated direction of the incoming wave, and execute step 8; if not, return to step 5; Step 8: Based on the watch law, a source with a known real wave direction is set, and the root mean square error between the estimated wave direction and the real wave direction is used as the optimization target to optimize the distributed array structure; Step 9: Initialize the cheetah population, convert the cheetah positions into a distributed array structure, use a direction finding algorithm under the corresponding array structure to obtain an estimated direction, use the array optimized fitness function to calculate the fitness value of each cheetah, and obtain the local optimal position and the global optimal position; Step 10: Update the quantum speed of each cheetah according to the update strategy of the cheetah population, and obtain the position of the corresponding cheetah by measurement; Step 11: convert the cheetah position into a distributed array structure, use a direction finding algorithm under the corresponding array structure to obtain an estimated direction, use the array optimized fitness function to calculate the fitness value of each cheetah, and update the local optimal position and the global optimal position; Step 12: determine whether the maximum number of iterations has been reached. If so, output the cheetah's global optimal position, convert it into 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 10.

2. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 1 is characterized in that: The distributed array single snapshot sampling signal model described in step 1 is established as follows: Assume a distributed array with a total number of M array elements and M array elements in each subarray. N , the spacing between the array elements in the subarray is λ is the wavelength of the incident signal, the total number of subarrays is N, The subarray and The spacing between the subarrays is M=N×M N , There are P far-field narrowband signals from θ p The incident signal is incident on the distributed array from different directions, and the incident signal and the noise signal are uncorrelated, p = 1, 2, ..., P; Select the first element of the first subarray as the reference element, then The signal received by the kth element in the qth subarray at the moment is: in, is the incident signal, is the noise signal of the kth element in the qth subarray, is the distance between the kth array element in the qth subarray and the reference array element, The distributed array single snapshot sampling signal model is expressed as: y(1)=A(θ)s(1)+n(1) 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 array element in the q-th subarray, 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 kth array element in the qth subarray and the reference array element, θ=[θ1,θ2,…,θ P ] is the wave direction vector; 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 qth subarray.

3. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 2 is characterized in that: The pseudo covariance matrix in step 2 is as follows: For the constructed matrix R y (1) Perform covariance processing, that is, The orthogonal projection matrix is: 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: Where tr() is the matrix trace function.

4. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 3 is characterized in that: The process of step three includes: The first subarray is divided into two subarray units S1 and S2, where S1 consists of the first M subarrays. N -1 array element, S2 is composed of the last M of the first subarray N -1 array element, and two pseudo covariance matrices H0(1) and H1(1) are constructed using the single snapshot data received by S1 and S2. The matrices H0(1) and H1(1) contain the relevant single snapshot information: Perform singular value decomposition on the pseudo covariance matrix H0(1), in is the left singular vector, is the right singular component, W is the singular value; Using the obtained singular values ​​and singular vectors of the H0(1) matrix, we can calculate the matrix in are the first P larger singular values ​​after 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 values ​​corresponding to the signal part, is the right singular vector of the singular value corresponding to the signal part, using the matrix The rough estimate of the search angle is in is a matrix The characteristic value of 5. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 4 is characterized in that: The process of step 4 includes: Assuming that there are E search cheetahs in the hunting ground, each search cheetah has its own quantum position, and the quantum position of the e-th search cheetah in the d-th generation in the iterative process is defined as in P is the maximum dimension of the solution space; the mapping position of the e-th search cheetah in the d-th generation is obtained by mapping The mapping equation is Within the hunting grounds, L p is the lower limit of the p-th dimension of the hunting range, U p is the upper limit of the p-th dimension of the hunting range, and the result of rough estimation is To determine the initial hunting range, is the range factor, e=1,2,…,E, p=1,2,…,P; the position after mapping Substitute the fitness function for fitness evaluation, and the fitness equation is: in Finally, the optimal quantum position obtained after the e-th search of the cheetah until the d-th generation optimization search is recorded as the local optimal quantum position The quantum position with the best fitness value of the entire search cheetah population after the d-th generation optimization search is recorded as the global optimal quantum position 6. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 5 is characterized in that: The process of step five includes: in the dth iteration process, randomly disrupting the hunting order of the E-th search cheetahs, defining the adjacent cheetahs of the e-th search cheetah as the search cheetahs that hunt after the e-th search cheetah finishes hunting, if the e-th search cheetah is the last cheetah to hunt, then the search cheetahs that hunted before the e-th search cheetah are defined as the adjacent cheetahs of the e-th search cheetah, and the positions of the adjacent cheetahs are recorded as Use the simulated quantum revolving gate to update the p-dimensional quantum position of the e-th searching cheetah of the d-th generation. The update equation is: in The update equation for the quantum rotation angle of the cheetah in the e-th search of the cheetah in the p-th dimension in the d+1 generation is: in D is the maximum number of iterations for searching the cheetah population. is a random number that follows a uniform distribution between [0,1]. is a random number that follows a uniform distribution between [0,η1], η1 is the cheetah hunting factor, is a random number uniformly distributed between [0,1], and w is the search factor; is a random number that follows a standard Gaussian distribution, The p-th dimension of the adjacent cheetah quantum position of the e-th generation searching cheetah; is the speed factor, is a random number that follows a uniform distribution between [-1,1]. The pth dimension of the local optimal quantum position of the cheetah is searched for the eth cheetah in the dth generation; finally, the quantum position of the cheetah is searched for the eth cheetah in the d+1th generation. Mapping to get the mapping position Mapping equation Where L p is the lower limit of the p-th dimension of the hunting range, U p is the upper limit of the p-th dimension of the hunting range, 7. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 6 is characterized in that: The process of step six includes: mapping the position of the d+1 generation search cheetah Substitute into the fitness function in Calculate the fitness value of the updated search cheetah and update the local optimal quantum position to And the global optimal quantum position is If the eth person in the d+1th generation hunts cheetahs The fitness value is greater than The fitness value of otherwise If the e-th hunting cheetah in the d+1th generation has the local optimal position The fitness value is greater than The fitness value of otherwise 8. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 7 is characterized in that: The process of step eight includes: The watch law states that when a person has multiple watches pointing to different times at the same time, only one watch has the correct direction. The root mean square error between the estimated direction of the incoming wave obtained in step 7 and the known true direction of the incoming wave is used as the fitness function for array structure optimization. in is the potential solution of the array structure, θ p is the true direction of the pth incoming wave, To obtain the estimated direction of the pth incoming wave after executing the direction finding algorithm under this array structure, p = 1, 2, ···, P.

9. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 8 is characterized in that: The process of step nine includes: assuming that there are I cheetahs in the hunting ground, each cheetah has its own quantum speed, and defining the quantum speed of the i-th cheetah in the t-th generation during the iteration process as After measurement, the position of the i-th cheetah of the t-th generation is The corresponding measurement equation is in is a random number that follows a uniform distribution between [0,1]. J is the maximum dimension of the solution space; the position obtained by measuring the quantum speed of the ith cheetah of the tth generation Convert to distributed array subarray spacing Then execute steps 2 to 7, where For the tth generation The subarray and The array spacing of the sub-arrays is used to bring the direction finding results into the fitness function Calculate the fitness value corresponding to each cheetah, where θ p is the true direction of the pth incoming wave, is the array spacing corresponding to the i-th cheetah of the t-th generation The estimated direction of the pth incoming wave is obtained after executing steps 2 to 7; the optimal position of the i-th cheetah until the t-th generation optimization search is recorded as the local optimal position The position with the best fitness value of the entire cheetah population after the t-th generation optimization search is recorded as the global optimal position 10. The distributed array single snapshot direction finding method of the quantum cheetah optimization mechanism based on the watch law according to claim 9 is characterized in that: The process of step ten includes: in the t-th iteration process, randomly disrupting the hunting order of the cheetahs, defining the adjacent cheetahs as the cheetahs that hunt after the ith cheetah finishes hunting, if the ith cheetah is the last cheetah to hunt, then the cheetahs hunted before the ith cheetah are defined as the adjacent cheetahs of the ith cheetah, and the quantum speed of the adjacent cheetahs is recorded as The global optimal position at the tth iteration is 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 of the ith cheetah; in the tth iteration, when When , the i-th cheetah chooses the waiting strategy, and the j-dimensional quantum speed update equation of the i-th cheetah is in and are all random numbers with uniform distribution between [0,1], and K is a selection constant; otherwise, the i-th cheetah chooses a predation strategy, and the update equation of the j-dimensional quantum velocity of the i-th cheetah is where μ t+1 is a random number that follows a uniform distribution between [0,1]. is the jth dimension of the quantum rotation angle of the ith cheetah of the t+1th generation, represent The probability of reversing the qubit when it is 0 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 in, T is the maximum number of iterations of the cheetah population, is a random number that follows a uniform distribution between [0,1]. is a random number uniformly distributed between [0,η2], η2 is the cheetah hunting factor, is a random number that follows a Gaussian distribution; and is a random number that follows a uniform distribution between [0,1]. is the jth dimension of the hunting target position of the tth generation, is the jth dimension of the leader position of the i-th cheetah of the t-th generation; is a random number that follows a Gaussian distribution; is the jth dimension of the quantum speed of the neighboring cheetahs of the i-th cheetah of the t-th generation, i = 1, 2, ..., I, j = 1, 2, ..., J; finally, the updated quantum speed of the i-th cheetah of the t+1-th generation is Measure and update the position of the i-th cheetah to The corresponding measurement equation is in is a random number between [0,1] that follows a uniform distribution; The process of step 11 includes: moving the position corresponding to the cheetah of the t+1 generation Convert to distributed array subarray spacing in is the t+1th generation The subarray and The array spacing of the sub-arrays is ; Assuming there are P far-field incoming wave signals, the sub-array spacing of the distributed array is Execute steps 2 to 7 in the case of , and substitute the direction finding results into the fitness function Calculate the fitness value corresponding to each cheetah, where θ p is the true direction angle of the pth 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 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

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