An optimal arrangement method of non-uniform linear array for direction finding
By optimizing the non-uniform linear array arrangement using the quantum particle swarm optimization algorithm, the problem of direction finding accuracy under constrained conditions in array arrangement was solved, achieving high-precision direction finding and array aperture expansion, and reducing sidelobe interference.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN ENG UNIV
- Filing Date
- 2023-09-25
- Publication Date
- 2026-06-26
AI Technical Summary
Existing technologies make it difficult to design optimal special array arrangements under constraints such as certain no-fly array elements, which affects the direction finding accuracy and array aperture expansion.
A quantum particle swarm optimization algorithm based on the minimum spacing criterion and the minimum maximum relative sidelobe level is adopted to optimize the arrangement of non-uniform linear arrays. The optimal array arrangement is found under specific conditions through the quantum particle swarm search mechanism.
High-precision direction finding under specific constraints was achieved. The array aperture was expanded, which improved the direction finding accuracy and the convergence speed of the algorithm, and reduced sidelobe interference.
Smart Images
Figure CN117272809B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array signal processing technology, and particularly relates to an optimal arrangement method for a non-uniform linear array used for direction finding. Background Technology
[0002] An array antenna is not simply a matter of placing antennas in different positions; rather, it involves arranging and combining antennas according to specific rules to form an antenna system. The graph describing the amplitude characteristics and spatial scanning angle of an array antenna system is called its radiation pattern. In practical engineering applications, the radiation pattern of the array antenna is controlled by rationally arranging different parameters such as the placement of antenna elements, the distribution of the array antenna, and the excitation amplitude and phase of the elements. This is the basis for solving the problem of constructing array antenna positions in practical engineering.
[0003] According to the radiation pattern, when the scanning angle is the same as the angle of the incoming wave direction, the radiation pattern has a clear main lobe, but side lobes will also appear at other scanning angles. These side lobes will affect the accuracy of the incoming wave direction estimation. When the level of the side lobe is lower than that of the main lobe, the interference it causes to the direction finding accuracy will be smaller.
[0004] Furthermore, the element arrangement rules of the three existing special arrays—minimum redundancy array, maximum continuous delay array, and minimum gap array—can also provide inspiration for optimal array arrangement under specific constraints. A minimum redundancy array is one where the set of position differences between elements is fully expanded and is a continuous natural number, meaning there are no gaps in the set of position differences. A maximum continuous delay array is one where the position differences between all elements in the entire array satisfy the maximum continuous delay number N. max The maximum consecutive delay N of the array max Assume that there exists a condition such that the positional differences between the actual elements of the entire array can be expressed as a number from 0 to N. max consecutive integers, but for array element position differences greater than N. max The situation may no longer be continuous. A minimum-gap array refers to an array where the set of positional differences between elements is not necessarily continuous; it allows for the loss of some elements, but it must satisfy the condition that the number of lost elements is minimized and the positional differences within the two groups preceding and following the lost element remain continuous. Combining the element arrangement rules of the above three existing classic special arrays, we can derive that when the set of element positional differences τ... ij The smaller the number of missing positions, i.e. the smaller the interval, the better the direction finding capability of the array, and the greater the expansion of the array aperture. That is, the array composed of multiple small antennas is used to simulate a large antenna, thereby effectively increasing the size of the receiving antenna.
[0005] In existing technologies, Zhang Ming et al.'s "A Review of Sparse Optimization Techniques for Large-Scale Planar Arrays" published in *Space Electronics Technology* proposed a new method for reducing sidelobes, but it cannot solve the problem of selecting the optimal special array arrangement under constraints. Most existing methods do not address the design of array arrangements with constraints such as certain no-fly elements. To solve this problem, this invention designs an optimal special array arrangement method based on the minimum spacing criterion and the minimum maximum relative sidelobe level. It utilizes discrete quantum particle swarm optimization to find the optimal array arrangement, achieving high-precision direction finding for the optimal array arrangement under specific conditions and requirements. Summary of the Invention
[0006] To address the aforementioned technical problems, this invention proposes an optimal arrangement method for non-uniform linear arrays used for direction finding. The designed method can be used as a new method for high-precision direction finding of a target using a special non-uniform linear array arrangement under specific constraints such as the maximum correlation delay range, the number of existing real array elements, and the positions of the forbidden array elements. It meets the requirements of specific position constraints and can achieve high-precision direction finding with an extended array aperture.
[0007] To achieve the above objectives, the present invention provides an optimal arrangement method for a non-uniform linear array used for direction finding, comprising:
[0008] Based on the preset optimal array arrangement model, the initial position, velocity, and initial local optimal position of the quantum particle are generated;
[0009] Based on the preset optimal array arrangement model, a first fitness function is constructed based on the minimum interval criterion and the minimum maximum relative sidelobe level.
[0010] Based on the first fitness function, the initial global optimal position of the quantum particle is obtained;
[0011] Based on the initial local optimal position and the initial global optimal position, the velocity and position of the quantum particle are updated to obtain the global optimal position;
[0012] Based on the globally optimal position, the optimal array arrangement result is obtained.
[0013] Optionally, generating the initial position, velocity, and initial local optimum position of the quantum particle includes:
[0014] Construct an optimal array arrangement model based on the minimum gap criterion and the minimum maximum relative sidelobe level, determine the parameters of the quantum particle swarm search mechanism corresponding to the optimal array arrangement model, and generate the initial position, velocity, and local optimal position of the quantum particles.
[0015] Optionally, obtaining the initial globally optimal position of the quantum particle includes:
[0016] The position of the quantum particle is substituted into the first fitness function to obtain the fitness function of the quantum particle. The fitness function of the quantum particle is evaluated to obtain the initial global optimal position.
[0017] Optionally, updating the velocity and position of the quantum particle includes:
[0018] The velocity of the quantum particle is updated based on the initial local optimal position and the initial global optimal position;
[0019] The position is updated based on the updated velocity of the quantum particle.
[0020] Optionally, obtaining the globally optimal position includes:
[0021] The fitness value corresponding to the new position of the updated quantum particle is calculated, the local optimal position of the quantum particle is updated, and the updated global optimal position is obtained.
[0022] Determine whether the update of the quantum particle has reached the preset maximum number of iterations. If not, continue to update the velocity and position of the quantum particle. If it has reached the maximum number of iterations, terminate the loop and output the current global optimal position.
[0023] Optionally, obtaining the optimal array arrangement result includes:
[0024] The direction-finding accuracy of the array arrangement corresponding to the global optimal position is compared and evaluated with that of a uniform linear array with the same number of array elements. If the direction-finding accuracy of the corresponding array arrangement is lower than that of a uniform linear array with the same number of array elements, i.e., the root mean square error is large, it is determined to be a failure. At this time, the maximum delay number is randomly changed within a set range, and the first fitness function based on the minimum interval criterion and the minimum maximum relative sidelobe level is reconstructed. Otherwise, the corresponding array arrangement is regarded as the optimal array arrangement result.
[0025] Optionally, the first fitness function is:
[0026]
[0027] Where f0 is the matching constant, q is the number of intervals, and a is the weighting constant. This is the proportionality coefficient. For the tth generation The position of a quantum particle.
[0028] Optionally, obtaining the updated global optimal position includes:
[0029] The updated position of each quantum particle is mapped to a preset special array arrangement. The maximum relative sidelobe level corresponding to the preset special array arrangement is obtained. The fitness of each quantum particle's new position based on the minimum spacing criterion and the minimum maximum relative sidelobe level, as well as the fitness of the corresponding special array, are obtained. The nth quantum particle is updated using the optimal quantum particle experienced up to generation t+1. Local optimal position of a quantum particle Simultaneously, find the globally optimal position found by the entire quantum particle swarm up to generation t+1.
[0030] Compared with the prior art, the present invention has the following advantages and technical effects:
[0031] (1) This invention enables the estimation of direction of arrival for a large number of incoming waves using fewer real array elements, and can achieve high-precision direction of arrival estimation with extended array aperture.
[0032] (2) Compared with traditional special array construction methods, this invention can take advantage of quantum theory and discrete particle swarm search mechanism to obtain the optimal special array arrangement that meets the conditions under specific constraints, such as the known and fixed number of real array elements, maximum delay range and forbidden array element positions, thus proving the versatility of the method proposed in this invention.
[0033] (3) Simulation results show that the optimal special array arrangement based on the minimum spacing criterion and the minimum maximum relative sidelobe level designed in this invention has higher direction finding accuracy than other special array arrangements, and improves the convergence accuracy and convergence speed of the algorithm, demonstrating the effectiveness of the optimal special array construction method based on the proposed discrete quantum particle search mechanism. Attached Figure Description
[0034] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:
[0035] Figure 1 This is a schematic diagram of an optimal arrangement method for a non-uniform linear array used for direction finding, according to an embodiment of the present invention.
[0036] Figure 2 As provided in the embodiments of the present invention A schematic diagram showing the change in the success probability of direction finding estimation with the generalized signal-to-noise ratio for different array element arrangements of 5 sources when N=10 and b=[3,4,5,6,7].
[0037] Figure 3 As provided in the embodiments of the present invention A schematic diagram showing the change in the success probability of direction finding estimation with the generalized signal-to-noise ratio for different array element arrangements of 11 sources when N=10 and b=[3,4,5,6,7].
[0038] Figure 4 As provided in the embodiments of the present invention A schematic diagram showing the change in the success probability of direction finding estimation with the generalized signal-to-noise ratio for different array element arrangements of 5 sources when N=15 and b=[3,7,9,24,36,42].
[0039] Figure 5 As provided in the embodiments of the present invention A schematic diagram showing the change in the success probability of direction finding estimation with the generalized signal-to-noise ratio for different array element arrangements of 11 sources when N=15 and b=[3,7,9,24,36,42].
[0040] Figure 6 As provided in the embodiments of the present invention The optimal array arrangement pattern is obtained when N=10 and b=[3,4,5,6,7].
[0041] Figure 7 As provided in the embodiments of the present invention The optimal array arrangement pattern is obtained when N=15 and b=[3,7,9,24,36,42]. Detailed Implementation
[0042] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0043] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.
[0044] like Figure 1 As shown, this embodiment proposes an optimal arrangement method for a non-uniform linear array used for direction finding, including the following steps:
[0045] Step 1: Establish an optimal arrangement model for a special array based on the minimum gap criterion and the minimum maximum relative sidelobe level, determine some parameters of the quantum particle swarm search mechanism corresponding to the special array, and generate... The position of the initial quantum particle The speed of quantum particles and the local optimal position of quantum particles
[0046] Suppose the linear array to be optimized consists of N non-directional elements arranged in a simple configuration. Let θ be the angle between the incoming wave direction and the array normal. Then, the number of elements is determined to be N, and the excitation amplitude weight vector is defined as... The specific representation is as follows in The magnitude weights of the nth array element are represented by n = 1, 2, ..., N; the phase weight vector is defined as... The specific representation is as follows in The phase weight of the nth element, satisfying n = 1, 2, ..., N; the spacing between adjacent elements.
[0047] use To represent, specifically in the form of in This represents the spacing between the 1st and nth array elements, where n = 1, 2, ..., N. Their combined effect determines the pattern function of this linear array. Excitation The mathematical expression is Suppose that when a unit plane wave is incident on a linear array at an angle of incidence θ, the input steering vector a(θ) of this special linear array is formed by combining two parts: the first part, It is generated by the change in the relative positions between adjacent array elements, and its expression is derived from... Determined as in, Here, λ is the wave constant, and λ represents the wavelength; the second part... in, Therefore, the expression for the pattern function is: The expression for the relative pattern function is: U max =max|F(θ)|, satisfying n = 1, 2, ..., N.
[0048] Set the range of the known maximum delay as follows: The actual number of array elements N and the position vector of the forbidden array elements are already known. This is the lower bound of the maximum delay number. Let be the upper bound of the maximum delay number, where satisfying It is the minimum spacing between virtual array elements.
[0049] Based on the above constraints, the key parameters of the quantum particle search mechanism corresponding to the special optimal arrangement array based on the minimum spacing criterion are determined. Assume the number of variables to be solved, i.e., the spatial search dimension, is D, and the number of quantum particles in the quantum particle swarm is... Then the first in the population The quantum velocity of a quantum particle in the t-th generation can be defined as... In the formula, 1≤d≤D. When initializing the population, for the case where the number of actual array elements is fixed, the number of "1"s, d, at randomly selected quantum particle positions is determined. x Make restrictions to ensure that d is satisfied. x = N, where N is the actual number of array elements. For the case of forbidden array elements, the forbidden position vector is... When initializing the population, all The dimension of all the elements in the forbidden array corresponding to the positions of each quantum individual is set to "0", that is, let in, The local optimal position of the quantum particle is determined in the first iteration as follows:
[0050] Step 2: Based on the designed array arrangement rules, design a fitness function based on the minimum spacing criterion and the minimum maximum relative sidelobe level.
[0051] The core idea of the new array arrangement rule based on the minimum spacing criterion and the minimum maximum relative sidelobe level is to design an array arrangement rule that, under the conditions of determining the maximum delay range, the number of existing real array elements, and the positions of the forbidden array elements, minimizes the number of lost positions in the array element position difference set, i.e., the number of spacing q. The maximum relative sidelobe level of the constructed special array is The maximum relative sidelobe level is defined as the ratio of the radiation intensity in the direction of the maximum value of the main lobe to the radiation intensity in the direction of the maximum value of the sidelobe, thereby achieving the optimal array arrangement under specific requirements.
[0052] Therefore, the tth generation is the tth The position of a quantum particle The fitness function is Where f0 is the matching constant, q is the number of intervals, a is the weighting constant, and a is the proportional coefficient.
[0053] Step 3: Substitute the quantum particle's position into the fitness function, calculate the quantum particle's fitness function, evaluate it, and thus obtain the globally optimal position.
[0054] Then, the evolutionary process of quantum particles is represented by the update of quantum velocity. The position of the nth quantum particle in the tth generation is denoted as... The t-th generation quantum speed is denoted as The local optimum position up to the t-th generation is denoted as The global optimal position of the population up to generation t is
[0055] Step 4: Update the quantum velocity and position of the quantum particles using an update strategy for array arrangement under specific conditions.
[0056] The t+1th generation The formula for updating the quantum velocity of a quantum particle is: Where c1 and c2 are two selection constants used to determine the degree to which the quantum particle approaches the local optimal position and the global optimal position, i.e., the degree of influence it receives, satisfying the following conditions: 1≤d≤D, and Where η1 is the mutation factor. For the case where the number of actual array elements is fixed, when updating positions based on quantum particle velocities, to ensure that the number of "1"s in the quantum particle positions remains constant during the update process, the quantum velocities of each dimension of the same entity are sorted, and only the dimensions corresponding to the N largest quantum velocities are selected and updated to "1". For the case of forbidden array elements, the forbidden position vector is b = [b1, b2, ..., b...]. B When updating the position based on the quantum particle velocity, it is ensured that the dimension corresponding to the position of the forbidden array element in the quantum particle position always remains "0" during the update process.
[0057] Step 5: Calculate the fitness value corresponding to the new position of the updated quantum particle, update the nth local optimum position, and find the global optimum position.
[0058] The new position of each quantum particle is mapped to a special array arrangement. The corresponding maximum relative sidelobe level is calculated. The fitness of each quantum particle's new position based on the minimum spacing criterion and the minimum maximum relative sidelobe level, as well as the fitness of the corresponding special array, are calculated. The nth quantum particle is updated using the best quantum particle experienced up to generation t+1. Local optimal position of a quantum particle Simultaneously, find the globally optimal position found by the entire quantum particle swarm up to generation t+1.
[0059] Step Six: Determine if the algorithm has reached the predetermined maximum number of iterations. If not, let t = t + 1, then return to Step Four and continue the loop; otherwise, terminate the loop and output the current global optimal position. This current global optimal position corresponds to the optimal array arrangement to be solved, and the corresponding optimal special array arrangement vector is l = [l1, l2, ..., l N ].
[0060] Step 7: Compare and evaluate the direction-finding accuracy of the special array arrangement obtained from the above steps with that of a uniform linear array with the same number of elements. If the direction-finding accuracy of the special array is lower than that of the uniform linear array with the same number of elements (i.e., the root mean square error is large), it is determined to be a failure. In this case, the maximum delay number is randomly changed within the set range. Then return to step two; otherwise, output the optimal array arrangement result.
[0061] The optimal array arrangement is used as the element placement position during direction finding. The MUSIC algorithm is used to search for spectral peaks. The angle corresponding to the peak in the spatial spectral function is the direction of arrival of the signal source to be determined, and the direction finding result is output.
[0062] Assuming that there exists in the space A far-field narrowband signal source is incident on a receiving antenna array composed of a non-uniform special array arrangement. The N array elements form a non-uniform special array arrangement vector l = [l1, l2, ..., ln]. N Position vector but in This represents the minimum element spacing of a virtual uniform or approximately uniform linear array, forming a set. gather Excluding the element 0, there is a maximum delay number. There are n distinct elements. The received signal of the nth element at time t can be expressed as: In the formula, n = 1, 2, ..., N, For the i-th incident signal, ω0 is the center frequency of the incident signal, θ i Let τ be the azimuth angle of the incident signal for the i-th signal. n (θ i The time delay of the nth array element receiving the signal relative to the reference point is given by ( ). Let be the additive impulse noise of the nth array element. Then the received signal vector... The source signal vector in space is The noise vector received by the array is The noise is a complex impulse noise that is spatially and temporally independent and follows an SαS distribution. The array's steering matrix... for 1-th order matrix Wherein, the guide vector a(θ) corresponding to the i-th angle i The formula for calculating ) is Therefore, the signal model of the receiving array is If the actual number of snapshots received is K, then the model of the sampling signal of the kth snapshot from the receiving array is:
[0063] The signal processed by the infinite norm of the k-th snapshot of the received data is: Where max{·} is the maximum value function. Then the low-order covariance matrix of the infinite norm fractions of the K snapshot samples is: its first Line 1 Column elements are k = 1, 2, ..., K, where K is the maximum number of snapshots, γ is the fractional lower-order covariance parameter, and * denotes conjugate operation. Let Among them, satisfying 1≤ρ, Then the extended infinity norm low-order covariance matrix of the Kth snapshot is: in The expanded guidance matrix is The extended guide vector is For the lower-order covariance matrix of extended infinity norm fractions By performing eigenvalue decomposition, we can obtain in, It is the signal subspace, composed of eigenvectors corresponding to large eigenvalues. It is a noise subspace, composed of eigenvectors corresponding to small eigenvalues; It is a diagonal matrix composed of large eigenvalues. It is a diagonal matrix composed of small eigenvalues. Therefore, the spectral estimation formula for the non-uniform linear matrix MUSIC algorithm is: This is the azimuth variable. The angle corresponding to the spectral peak in the spatial spectral function is the estimate of the direction of arrival for a special non-uniform linear array.
[0064] A uniform linear array can be considered a special case of a non-uniform linear array, assuming that there exists in space... A far-field narrowband signal source is incident on a uniform linear array; only setting... The estimated value of the direction of arrival of a uniform linear array can then be obtained using special methods for solving non-uniform linear arrays.
[0065] If the direction finding results of the special array are obtained The root mean square error is greater than that of a uniform linear array with the same number of elements in the direction finding results. The root mean square error is then used to randomly change the maximum delay number within the set range. Then return to step two; otherwise, output the optimized special array, which is the result of the optimal array arrangement.
[0066] This embodiment achieves an optimal array arrangement based on the minimum gap criterion and the minimum maximum relative sidelobe level, even under the conditions of a determined maximum delay range, the number of existing real array elements, and the positions of the forbidden array elements. The steps include: establishing a special array optimal arrangement model based on the minimum gap criterion and the minimum maximum relative sidelobe level; determining some parameters of the quantum particle swarm search mechanism corresponding to the special array; and generating... The initial position, velocity, and local optimal position of the quantum particle are determined. Based on the designed array arrangement rules, a fitness function is designed based on the minimum spacing criterion and the minimum maximum relative sidelobe level. The quantum particle position is substituted into the fitness function to calculate and evaluate the fitness function, thereby obtaining the global optimal position. The quantum velocity and position of the quantum particle are updated using an update strategy for the array arrangement under specific conditions. The fitness value corresponding to the new position of the updated quantum particle is calculated, and the position of the quantum particle is updated. Find the local optimum and the global optimum; determine if the algorithm has reached the predetermined maximum number of iterations. If not, let t = t + 1, and return to step four to continue the loop; otherwise, terminate the loop and output the current global optimum. The current global optimum corresponds to the optimal array arrangement to be solved, and the corresponding optimal special array arrangement vector is l = [l1, l2, ..., l N The direction-finding accuracy of the optimal array arrangement obtained by performing the above steps is compared and evaluated with that of a uniform linear array arrangement with the same number of array elements. If the direction-finding accuracy of the optimal array is lower than that of a uniform linear array with the same number of array elements, it is determined to be a failure. In this case, the maximum delay number is changed within the set range. Then return to step two; otherwise, output the optimal array arrangement result. This invention can select the optimal array structure for specific geometric shapes and key cargo placement positions in certain scenarios, achieving high-precision direction-of-arrival estimation with extended aperture, while reducing costs.
[0067] To verify that the array element arrangement designed in this paper is the optimal method under the given conditions, the direction finding simulation results using this array element arrangement are compared with the direction finding accuracy of other array element arrangements that were not selected during QPSO update iteration under the same conditions. The following computer simulation experiment is conducted.
[0068] For ease of description, the optimal special array arrangement method based on the discrete quantum particle swarm algorithm involved in the figure is referred to as "the array element arrangement method designed in this invention", and the other array element arrangement combinations that were not selected during QPSO update iteration are referred to as "comparison array element arrangement". All other parameters are the same as those of the method designed in this invention.
[0069] The specific simulation parameters for the model are set as follows: For the non-uniform array to be optimized, a lower bound for the maximum delay number is set. Upper Realm Given that there are 10 actual array elements, the position vector of the forbidden array elements is b = [3, 4, 5, 6, 7], f0 = 1, and a = 10. When the number of signal sources is set to 5, the direction of arrival is [30, 10, 0, -20, -50], in degrees; when the number of signal sources is set to 11, the direction of arrival is [70, 60, 45, 30, 10, 0, -20, -35, -50, -65, -80], in degrees. The characteristic index of the impulse noise is α = 1.8, the maximum number of snapshots is set to K = 100, and the scanning interval of the MUSIC algorithm is 0.05°.
[0070] The parameters of the QPSO method designed in this embodiment are set as follows: the population size of the quantum particle swarm is N = 100, the maximum number of iterations is G = 200, and the maximum and minimum quantum velocities of the quantum particles are defined as v. max =10, v min =-10, variation factor η1=0.8, selection constants c1=2, c2=2.
[0071] From simulation Figure 2 , Figure 3 , Figure 4 and Figure 5 Simulation results show that the array element arrangement designed in this embodiment has significant advantages in direction-finding accuracy. It can better achieve the maximum effective expansion of the array aperture under constrained conditions while ensuring direction-finding accuracy. Simulation results... Figure 6 and Figure 7 Simulation results show that the maximum sidelobe level obtained by the invented discrete quantum particle swarm optimal array arrangement method is lower than that of the other comparative arrays. The quantum particle swarm search mechanism has superior global convergence characteristics, overcomes the disadvantage of particle swarm algorithms being prone to getting trapped in local optima, obtains a lower maximum relative sidelobe level, saves costs, and ensures the performance of the optimal special array direction finding.
[0072] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. An optimal arrangement method for a non-uniform linear array used for direction finding, characterized in that, include: Based on the preset optimal antenna array arrangement model, the initial position, velocity, and initial local optimal position of the quantum particle are generated; Based on the preset optimal antenna array arrangement model, a first fitness function is constructed based on the minimum spacing criterion and the minimum maximum relative sidelobe level. The first fitness function is: in, It is the proportioning constant. For the number of intervals, Here is the weighting constant. This is the proportionality coefficient. For the first The generation The position of a quantum particle; Based on the first fitness function, the initial global optimal position of the quantum particle is obtained; Obtaining the initial globally optimal position of a quantum particle includes: The position of the quantum particle is substituted into the first fitness function to obtain the fitness function of the quantum particle. The fitness function of the quantum particle is evaluated to obtain the initial global optimal position. Based on the initial local optimal position and the initial global optimal position, the velocity and position of the quantum particle are updated to obtain the global optimal position; Obtaining the globally optimal position includes: The fitness value corresponding to the new position of the updated quantum particle is calculated, the local optimal position of the quantum particle is updated, and the updated global optimal position is obtained. Determine whether the update of the quantum particle has reached the preset maximum number of iterations. If not, continue to update the velocity and position of the quantum particle. If it has, terminate the loop and output the current global optimal position. Based on the globally optimal position, the optimal antenna array arrangement result is obtained; Obtaining the optimal antenna array arrangement results includes: The direction-finding accuracy of the array arrangement corresponding to the global optimal position is compared and evaluated with that of a uniform linear array with the same number of array elements. If the direction-finding accuracy of the corresponding array arrangement is lower than that of a uniform linear array with the same number of array elements, i.e., the root mean square error is large, it is determined to be a failure. At this time, the maximum delay number is randomly changed within a set range, and the first fitness function based on the minimum spacing criterion and the minimum maximum relative sidelobe level is reconstructed. Otherwise, the corresponding array arrangement is regarded as the optimal antenna array arrangement result.
2. The optimal arrangement method for a non-uniform linear array for direction finding according to claim 1, characterized in that, The initial position, velocity, and initial local optimum of the quantum particle are generated by: An optimal arrangement model for the preset antenna array based on the minimum spacing criterion and the minimum maximum relative sidelobe level is constructed. The parameters of the quantum particle swarm search mechanism corresponding to the optimal arrangement model of the preset antenna array are determined, and the initial position, velocity, and local optimal position of the quantum particles are generated.
3. The optimal arrangement method for a non-uniform linear array for direction finding according to claim 1, characterized in that, Updating the velocity and position of quantum particles includes: The velocity of the quantum particle is updated based on the initial local optimal position and the initial global optimal position; The position is updated based on the updated velocity of the quantum particle.