A method and system for estimating direction of arrival (DOA) of a minimum redundant linear array based on the quantum giant trevally mechanism.

Abstract

This invention provides a method and system for direction-of-arrival (DOA) estimation of minimum redundancy linear arrays based on the quantum giant trevally mechanism, belonging to the field of array signal processing. To address the problem of drastic performance degradation of minimum redundancy linear arrays under harsh conditions of impulse noise, this invention proposes using the mean square error of DOA estimation and the probability of successful estimation as core optimization indicators. This method effectively improves the performance degradation problem of arrays under impulse noise by constructing a mapping relationship between the positions of minimum redundancy linear array elements and DOA estimation performance, significantly enhancing the accuracy and robustness of the direction-finding system. The quantum swarm intelligence optimization method designed in this invention provides a promising solution path for the optimization problem through a global search strategy and fitness function design. This invention not only overcomes the applicability and performance bottlenecks of traditional methods under impulse noise environments but also has significant theoretical and practical application value for promoting the engineering application of array technology in high-precision direction-finding.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically, to a method and system for estimating the direction of arrival (DOA) of a minimum redundancy linear array based on the quantum giant trevally mechanism. Background Technology

[0002] Array signal processing technology refers to the use of multiple sensors arranged in a specific geometric configuration to enhance, separate, locate, and identify signals through multi-point sampling in space, accurately extracting the characteristic parameters of target signals while minimizing the impact of various noises and interferences in the environment. Direction of Arrival (DOA) estimation has become a research focus in the field of array signal processing. Through decades of continuous innovation and improvement, it has now deeply penetrated into diverse fields such as sonar, modern communication systems, intelligent transportation, and target detection. The performance of DOA estimation is not only limited by the array's geometry but also tightly coupled to the specific algorithm implementation of the chosen signal processing strategy. Traditional uniform linear arrays limit aperture expansion due to redundant element arrangement, resulting in limited resolution and degrees of freedom. Minimum redundancy linear arrays, through refined reconstruction of element arrangement, push the number of non-redundant baselines to the theoretical upper limit while maintaining a finite physical element size. This strategy not only expands the effective aperture but also simultaneously reduces hardware overhead and computational complexity, and is widely regarded as one of the core paradigms in the field of sparse array research. However, the non-uniform structure of minimum redundancy linear arrays presents new technical challenges for DOA estimation: First, sparsity leads to the loss of array manifold, disrupting the statistical properties of traditional subspace algorithms and exacerbating estimation ambiguity and error sensitivity; second, non-uniform spacing causes the covariance matrix to lose its Toeplitz property, requiring matrix reconstruction or sparse recovery techniques to adapt to classical spatial spectrum algorithms; third, the design of minimum redundancy linear arrays requires a trade-off between aperture expansion, element count, and sidelobe suppression, placing higher demands on noise robustness, multi-signal resolution, and real-time performance. Therefore, researching minimum redundancy linear array DOA estimation methods that can maintain high performance under harsh environments with impulsive noise has significant theoretical implications and greater practical value.

[0003] Currently, in the problem of direction-of-arrival (DOA) estimation for minimum redundancy linear arrays, the technical complexity of finding the optimal non-uniform element placement increases exponentially with the number of array elements. Uneven element distribution leads to unsatisfactory performance in certain angular regions. When the element spacing is too close, mutual coupling effects intensify, causing received signal distortion. The non-uniform structure makes the estimation of the sample covariance matrix sensitive to errors in harsh scenarios. In actual multipath propagation, the estimated matrix degenerates, and its rank decreases. Therefore, improving the DOA estimation performance of minimum redundancy linear arrays is of great significance, especially under extreme conditions.

[0004] According to existing technical literature, the article "Research on DOA Estimation Algorithm for Large-Scale MIMO-OFDM System Based on MUSIC" published by Ma Li et al. in Communication World (1006-4222 (2025) 01-0001-03) mentions that the MUSIC algorithm is used to estimate DOA in a uniform linear receiving antenna array model. This shows that the MUSIC algorithm has ultra-high resolution and accuracy. However, its covariance matrix eigenvalue decomposition is extremely sensitive to abnormal pulses, making it difficult to maintain direction finding accuracy in the context of impulse noise. In their paper "DOA Estimation of Minimum Redundancy Linear Array" published in Firepower and Command Control (002-0640 (2012) 10-0010-04), Zhang Liqiang et al. addressed the limitations of uniform linear arrays in terms of resolution and degrees of freedom by introducing array redundancy to optimize the array element configuration. By comparing with uniform linear arrays, minimum redundancy linear arrays utilize non-uniform array elements to virtualize array element apertures, enrich spatial sampling points, improve spatial resolution, and reduce mean square error. However, their absolute direction finding accuracy is still insufficient, and it is difficult to achieve accurate direction finding in impact noise environments. In their paper "DOA Estimation Algorithm Based on Spatial Smooth Sparse Reconstruction" published in the Journal of Electronics and Information Technology (1009-5896 (2016) 01-0168-06), Cai Jingjing et al. used Khatri-Rao product for sparse reconstruction to estimate DOA. By improving the degree of freedom of the virtual array, they broke through the limitation that the number of information sources cannot exceed the number of array elements in the traditional method. However, its mathematical structure and algorithm implementation depend on the regular array element layout of the uniform linear array.

[0005] The results of existing literature search indicate that the performance degradation of existing minimum redundancy linear arrays is a serious problem that needs to be solved for wave direction of arrival estimation in real-world scenarios, especially under some extreme conditions, such as strong impact noise environments. Summary of the Invention

[0006] The technical problem to be solved by this invention is:

[0007] To address the problem of drastic performance degradation of minimum redundancy linear arrays under harsh conditions of impact noise.

[0008] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0009] This invention provides a method for estimating the direction of arrival (DOA) of a minimum redundancy linear array based on the quantum giant trevally mechanism, comprising the following steps:

[0010] S100. Establish an array direction finding model based on a minimum redundancy linear array under impact noise, and obtain the fractional low-order covariance matrix and its steering vector matrix of the virtual linear array based on the array direction finding model.

[0011] Step S200: Obtain the maximum likelihood equation for the direction of arrival estimation under impact noise based on the fractional low-order covariance matrix and steering matrix of the virtual linear array.

[0012] Step S300: Initialize the quantum giant trevally population and construct a fitness function. Calculate the fitness value of the quantum giant trevally after initialization and update the optimal fitness and the position of the optimal quantum giant trevally. The actual position corresponding to the optimal quantum position is the estimated direction angle vector that maximizes the maximum likelihood function value.

[0013] Step S400: Execute the quantum evolution rules of the quantum giant trevally mechanism, including the broad search phase, the region selection phase, and the attack phase of the quantum giant trevally based on the Levy search strategy;

[0014] Step S500: Map the newly generated quantum position of each quantum giant trevally to the position of the quantum giant trevally according to the mapping rule, calculate the fitness value of the corresponding position, and update its global optimal quantum position;

[0015] Step S600: Determine if the number of iterations is equal to the maximum number of iterations. If not, return to step S400. If it is, terminate the loop iteration, output the best fitness and the quantum position of the best-fit quantum giant trevally. After mapping and transformation by the mapping rule, the position is the estimated value of DOA.

[0016] Furthermore, in step S100, it is assumed that there is a shock noise environment. The minimum redundant linear array composed of n elements, with the first element from the left as the reference element, has: Each wavelength is The narrowband signal from the incident angle of the signal source Incident on the array, let the minimum spacing between array elements be... ;

[0017] The arrangement of the array elements satisfies the following properties: , For the first The absolute position of each array element relative to the reference array element, the th Each array element and the first The correlation delay between individual elements satisfy , For the first The position of each array element For the first The position of each array element, the difference in array element position ;

[0018] The optimal minimum redundancy linear array satisfies the following property: it does not exist. , This represents the positional difference between the w-th and z-th array elements; , Representing the The positional difference between the first and second array elements, For the maximum relevant delay; when It is a continuous set of natural numbers;

[0019] A non-optimal minimum redundancy linear array satisfies the following property: it exists. And the positional differences are small; the positional difference of the last array element satisfies ;when If is a set of consecutive natural numbers except for the common ones, then The output of the time array is:

[0020]

[0021] In the formula, It is the array receive vector. It is the first Individual Receive vector at any time; It is the array manifold matrix corresponding to the minimum redundant linear array, where The steering vector for the Nth direction signal; yes The signal vector at time step, where For the Nth signal source in The complex envelope of time; yes The impulse noise vector at time step, where In order to be in The impulse noise received by the Mth array element at time M, the Signals in each direction The guide vector in the direction is ;

[0022] The fractional low-order covariance matrix of the minimum redundant linear matrix is ​​calculated as follows: The first of the matrix Line number The elements of the column are ,in and They represent Time of the first The and the first The data received by each array element The parameters are the fractional lower-order moment covariance matrix. The range is , For characteristic index, It is the expectation function. It is about finding conjugate;

[0023] When the array receives The next quick shot, then The estimated value of the limited snapshot data is: ,in and They represent the first The and the first The element received the first Secondary snapshot data; The relationship between the minimum redundancy array and the virtual linear array is used to design... ,in, This represents the lower-order covariance of the fraction at a delay of 0 in the virtual linear array. The fractional low-order covariance represents the received signal of the i-th array element; , The fractional low-order covariance matrix for:

[0024]

[0025] Based on the maximum correlation delay The number of elements of the virtual linear array is obtained as follows Then the fractional lower-order covariance matrix of the virtual linear array for:

[0026] .

[0027] Further, in step S200, the maximum likelihood equation is:

[0028]

[0029] In the formula, It is the maximum likelihood function value. , It is a matrix trace operation. It is the array steering matrix of a virtual uniform linear array. It is the Nth angle of incidence. The guiding vector; The corresponding steering vector is , It is the conjugate transpose operation. It is taking the inverse of the matrix. yes The mapping matrix.

[0030] Further, in step S300, the following are included:

[0031] S310. Initialize the quantum position of the quantum giant trevally and set the parameters of the mechanism: Set the population size of the quantum giant trevally to... The maximum number of iterations is Number of iterations , No. The generation The quantum position of a giant trevally is mapped to a position. The mapping rule is ,in It is the first The generation Only giant trevally The quantum position of a dimension , , For the largest dimension, , and They represent and The dimension, and These represent the upper and lower boundaries of the search space, respectively.

[0032] S320, Calculate the first The generation Location of the quantum giant trevally The fitness of the giant trevally is used to evaluate the performance of potential solutions by calculating the fitness value of the giant trevally based on the fitness function.

[0033] Design based on maximum likelihood equation The generation Fitness function of quantum giant trevally position :

[0034]

[0035] S330. Substitute the positions of all initialized quantum giant trevally into the fitness function to calculate their fitness values, and then... The fitness of the quantum giant trevally with the highest fitness value is stored in a variable. In, its quantum position is stored in In China; among them Defined as storing the first To find the optimal fitness value, define a vector. Record all trevally until the [number missing]th [number missing]. The globally optimal quantum position found up to the next iteration. For the first The generation The optimal quantum position in dimensionality, and the corresponding mapping state is the globally optimal position. , For the first The generation The globally optimal position of the dimension.

[0036] Further, in step S400,

[0037] The extensive search phase of the quantum giant trevally was completed based on the Levy search strategy. The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension for:

[0038]

[0039] In the formula, and All values ​​are taken from Random numbers between and They represent the quantum giant trevally. The maximum and minimum values ​​of a quantum position. It is the normalized Levy flight function;

[0040] During the region selection phase, the quantum giant trevally locates the region with the highest food density and richest resources within the selected search space. The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension for:

[0041]

[0042] In the formula, , and All The constants between, and All values ​​are within Random numbers between It is the first All giant trevally The average value of the quantum positions in the dimensional space;

[0043] During the attack phase, the first The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension for:

[0044]

[0045] In the formula, , and These represent the angle of incidence and the angle of refraction, respectively. yes Random numbers between and These represent the absolute refractive indices of air and water, respectively. Is the value in Random numbers between;

[0046] According to the The generation Only one giant trevally The generation of the corresponding quantum rotation angle in the dimensional quantum isotope. The generation Only one giant trevally A quantum position is defined by the following formula for updating its quantum position:

[0047]

[0048] In the formula, It is the first The first individual giant trevally Quantum position The updated version Each stage , No. The first generation Quantum position.

[0049] Further, in step S500, the first The generation Phase 1 Only one giant trevally Quantum position according to Mapped to the first Phase 1 The generation The first individual giant trevally generated Quantum position , , ; and calculate the first Location of newly generated giant trevally individuals fitness function ,like ,but , ,otherwise , , , Sort and update the fitness function values ​​up to the first one. The optimal quantum position is .

[0050] The direction-of-arrival estimation system for a minimum redundancy linear array based on the quantum giant trevally mechanism has a program module corresponding to the above steps, and executes the steps in the above method for estimating the direction of arrival of a minimum redundancy linear array based on the quantum giant trevally mechanism when running.

[0051] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement steps of a direction-of-arrival estimation method for a minimum redundancy linear array based on the quantum giant trevally mechanism.

[0052] Compared with the prior art, the beneficial effects of the present invention are:

[0053] (1) This invention introduces the minimum redundancy linear array into the DOA estimation scenario, which can significantly expand the effective synthetic aperture of the array while keeping the number of physical array elements limited, thereby improving the spatial resolution capability. Simulation results show that it improves the shortcomings of traditional algorithms in the failure of direction finding due to impact noise and poor real-time performance.

[0054] (2) Under the background of impact noise, this invention relies on the fractional low-order moment covariance matrix constructed by the minimum redundant linear array, and combines the giant trevally mechanism and the quantum rotating gate update strategy to design a novel giant trevally mechanism. Simulation results show that it can achieve a lower root mean square error than other traditional algorithms under the same signal-to-noise ratio, improve global search efficiency, convergence speed and complex problem handling ability, and at the same time reduce the difficulty of parameter tuning.

[0055] (3) In the impulse noise direction of arrival estimation system, simulation results show that when the number of information sources is less than the number of array elements, it maintains good real-time performance and adaptability, and has a wider range of applications. Attached Figure Description

[0056] Figure 1 This is a flowchart of the direction-of-arrival estimation method for a minimum redundancy linear array based on the quantum giant trevally mechanism in an embodiment of the present invention;

[0057] Figure 2 This is a flowchart illustrating the quantum giant trevally mechanism in an embodiment of the present invention;

[0058] Figure 3 This is a comparison diagram of two direction-of-arrival estimation methods for two independent signal sources under impact noise in an embodiment of the present invention.

[0059] Figure 4 This is a schematic diagram of direction-of-arrival estimation when the number of signal sources is greater than the number of array elements under impulsive noise in an embodiment of the present invention;

[0060] Figure 5 This is a comparison of the root mean square error and generalized signal-to-noise ratio curves under different direction-finding methods for two independent signal sources under impulse noise in this embodiment of the invention.

[0061] Figure 6 This is a comparison of the relationship between the success probability of direction finding and the generalized signal-to-noise ratio under different direction finding methods for two independent signal sources under impulsive noise in an embodiment of the present invention. Detailed Implementation

[0062] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0063] Specific Implementation Plan 1: Combining Figure 1 and Figure 2 As shown, this invention provides a method for estimating the direction of arrival (DOA) of a minimum redundancy linear array based on the quantum giant trevally mechanism, comprising the following steps:

[0064] Step S100: Establish an array direction finding model based on a minimum redundancy linear array under impact noise, and obtain the fractional low-order covariance matrix and steering vector matrix of the virtual linear array based on the array direction finding model.

[0065] Assuming there is a minimum redundant linear array under impact noise conditions, by It consists of several array elements, with the first array element on the left as the reference array element. Each wavelength is The narrowband signal from the incident angle of the signal source Incident on the array, let the minimum spacing between array elements be... ;

[0066] The arrangement of the array elements satisfies the following properties: , For the first The absolute position of each array element relative to the reference array element, the th Each array element and the first The correlation delay between individual elements satisfy ,in For the first The position of each array element For the first The position of each array element, the difference in array element position ;

[0067] The optimal minimum redundancy linear array satisfies the following property: it does not exist. , This represents the positional difference between the w-th and z-th array elements; , Representing the The positional difference between the first and second array elements, For the maximum relevant delay; when It is a continuous set of natural numbers, belonging to one of the properties of the optimal minimum redundancy array, which means that the difference between all non-zero array elements exactly covers all integers from 1 to the maximum distance, without any gaps, that is, the difference set is hole-free;

[0068] A non-optimal minimum redundancy linear array satisfies the following property: it exists. Furthermore, the number of identical positional differences is small, meaning there are a few duplicates in the difference set, but the overall virtual element coverage remains high, differing from the optimal minimum redundancy array only in redundancy; the positional difference of the last element satisfies... It should be noted that this inequality should be understood as an engineering description, used to express that the position of the largest element is larger in a non-optimal array; when If is a set of consecutive natural numbers except for the common ones, then The output of the time array is:

[0069]

[0070] In the formula, It is the array receive vector. It is the first Individual Receive vector at any time; It is the array manifold matrix corresponding to the minimum redundant linear array, where The steering vector for the Nth direction signal; yes The signal vector at time step, where For the Nth signal source in The complex envelope of time; yes The impulse noise vector at time step, where For the Mth array element in The impact noise received at time 1, the first Signals in each direction The guide vector in the direction is ;

[0071] The fractional low-order covariance matrix of the minimum redundant linear matrix is ​​calculated as follows: The first of the matrix Line number The elements of the column are ,in and They represent Time of the first The and the first The data received by each array element The parameters are the fractional lower-order moment covariance matrix. The range is , For characteristic index, It is the expectation function. It is about finding conjugate;

[0072] When the array receives The next quick shot, then The estimated value of the limited snapshot data is: ,in and They represent the first The and the first The element received the first Secondary snapshot data; The relationship between the minimum redundancy array and the virtual linear array is used to design... ,in, This represents the lower-order covariance of the fraction at a delay of 0 in the virtual linear array. The fractional low-order covariance represents the received signal of the i-th array element; , The fractional low-order covariance matrix for:

[0073]

[0074] Based on the maximum correlation delay The number of elements of the virtual linear array is obtained as follows Then the fractional lower-order covariance matrix of the virtual linear array for:

[0075]

[0076] Step S200: Obtain the maximum likelihood equation for the direction of arrival estimation under impact noise based on the fractional low-order covariance matrix and steering matrix of the virtual linear array.

[0077] The maximum likelihood equation is:

[0078]

[0079] In the formula, It is the maximum likelihood function value. , It is a matrix trace operation. It is the array steering matrix of a virtual uniform linear array. It is the Nth angle of incidence. The guiding vector; The corresponding steering vector is , It is the conjugate transpose operation. It is taking the inverse of the matrix. yes The mapping matrix;

[0080] Step S300: Initialize the quantum giant trevally population and construct a fitness function. Calculate the fitness value of the quantum giant trevally after initialization and update the optimal fitness and the position of the optimal quantum giant trevally. The actual position corresponding to the optimal quantum position is the estimated direction angle vector that maximizes the maximum likelihood function value.

[0081] S310. Initialize the quantum position of the quantum giant trevally and set the parameters of the mechanism: Set the population size of the quantum giant trevally to... The maximum number of iterations is Iteration number label , No. The generation The quantum position of a giant trevally is mapped to a position. The specific mapping rules are as follows: ,in It is the first The generation Only giant trevally The quantum position of a dimension , , For the largest dimension, , and They represent and The dimension, and These represent the upper and lower boundaries of the search space, respectively.

[0082] S320, Calculate the first The generation Location of the quantum giant trevally Adaptability, The fitness value of the giant trevally is calculated based on the fitness function to evaluate the performance of potential solutions;

[0083] Design based on maximum likelihood equation The generation Fitness function of quantum giant trevally position :

[0084]

[0085] S330. Substitute the positions of all initialized quantum giant trevally into the fitness function to calculate their fitness values, and then... The fitness of the quantum giant trevally with the highest fitness value is stored in a variable. In, its quantum position is stored in In China; among them Defined as storing the first To find the optimal fitness value, define a vector. Record all trevally until the [number missing]th [number missing]. The globally optimal quantum position found up to the next iteration. For the first The generation The optimal quantum position in dimensionality, and the corresponding mapping state is the globally optimal position. , For the first The generation The global optimal position of the dimension;

[0086] Step S400: Execute the quantum evolution rules of the quantum giant trevally mechanism;

[0087] The extensive search phase of the quantum giant trevally was completed using the Levy search strategy. The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension for:

[0088]

[0089] In the formula, and All values ​​are taken from Random numbers between and They represent the quantum giant trevally. The maximum and minimum values ​​of a quantum position. It is the normalized Levy flight function;

[0090] During the region selection phase, the quantum giant trevally locates the region with the highest food density and richest resources within the selected search space. The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension The formula is:

[0091]

[0092] In the formula, , and All The constants between, and All values ​​are taken from Random numbers between It is the first All giant trevally The average value of the quantum positions in the dimensional space;

[0093] During the attack phase, the trevally chases its prey. To simulate the behavior of the quantum giant trevally in chasing and attacking its prey, it is assumed that the quantum giant trevally is affected by visual distortion. The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension The formula is:

[0094]

[0095] In the formula, , and These represent the angle of incidence and the angle of refraction, respectively. yes Random numbers between and These represent the absolute refractive indices of air and water, respectively. Is the value in The random numbers between these numbers refer to the different senses of motion of the quantum giant trevally during the development process;

[0096] According to the The generation Only one giant trevally The generation of the corresponding quantum rotation angle in the dimensional quantum isotope. The generation Only one giant trevally A quantum position is defined by the following formula for updating its quantum position:

[0097]

[0098] In the formula, It is the first The first individual giant trevally Quantum position The updated version Each stage , No. The first generation Quantum position;

[0099] Step S500: Map the newly generated quantum position of each quantum giant trevally to the position of the quantum giant trevally according to the mapping rule, calculate the fitness value of the corresponding position, and update its global optimal quantum position;

[0100] The first The generation Phase 1 Only one giant trevally Quantum position according to Mapped to the first Phase 1 The generation The first individual giant trevally generated Quantum position , , ; and calculate the first Location of newly generated giant trevally individuals fitness function ,like ,but , ,otherwise , , , Sort and update the fitness function values ​​up to the first one. The optimal quantum position is ;

[0101] Step S600: Determine the number of iterations. Is it equal to the maximum number of iterations? If it is not achieved, then Return to step S400; if the optimal fitness is achieved, terminate the iteration and output the best fitness. And the quantum position of the quantum giant trevally with optimal fitness. After being mapped and transformed into position according to the mapping rules This is the estimated value of DOA.

[0102] Specific implementation scheme two: The present invention provides a direction-of-arrival estimation system for a minimum redundancy linear array based on the quantum giant trevally mechanism. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned direction-of-arrival estimation method for a minimum redundancy linear array based on the quantum giant trevally mechanism when running.

[0103] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0104] Specific Implementation Scheme 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement, when called by a processor, a method for estimating the direction of arrival of a minimum redundant linear array based on the quantum giant trevally mechanism.

[0105] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0106] Simulation Experiment

[0107] For ease of description, the direction-of-arrival estimation method for the minimum redundancy linear array based on the quantum giant trevally mechanism designed in this invention is denoted as QGTO, the pigeon swarm optimization method is denoted as PIO, and its parameter settings are based on "Multiple UAVs mission assignment based on modified Pigeon-inspired optimization algorithm" published by Ran Hao et al. in the "Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference". The particle swarm optimization method is denoted as PSO, and its parameter settings are based on "Solving Weapon-Target Assignment Problem using Discrete Particle Swarm Optimization" published by Xiangping Zeng et al. in the "2006 6th World Congress on Intelligent Control and Automation". The specific parameter settings for the simulation model are as follows: the number of elements of the minimum redundancy linear array. The array element position unit is taken The array element position set is The number of virtual array elements of a virtual uniform linear array Set the number of information sources. , Set the number of information sources , The spatial noise is additive impulse noise, with a generalized signal-to-noise ratio of 10dB and a maximum number of snapshots. The parameters for QGTO are set as follows: population size is... The search space is Maximum number of iterations , , , and These represent the absolute refractive indices of air and water, respectively.

[0108] Figure 3 Comparison diagrams of QGTO and MUSIC direction finding for two independent signal sources under impulse noise are presented. At this time, the two independent signal sources respectively... Spatial noise incident on a minimum redundancy linear array Distribution characteristic index The signal strength is 1.6, the generalized signal-to-noise ratio is 10dB, and the maximum number of snapshots is [missing information]. The MUSIC scan interval is 0.1°, and the Monte Carlo experiment is performed 30 times. A schematic diagram comparing the direction finding of QGTO and MUSIC is simulated. Figure 3 As can be seen, the MUSIC method is no longer able to perform high-precision direction finding, while QGTO can not only accurately estimate the number of sources, but also achieve high-precision DOA estimation.

[0109] Figure 4 The number of signal sources under impulse noise is given. A schematic diagram of QGTO direction-of-arrival estimation. At this time, the six sources respectively... Spatial noise incident on a minimum redundancy linear array Distribution characteristic index The signal strength is 1.6, the generalized signal-to-noise ratio is 10dB, and the maximum number of snapshots is [missing information]. The Monte Carlo experiment was performed 30 times. A schematic diagram illustrating the relationship between the number of sources and the estimated direction of arrival was generated from the simulation. Figure 4 As can be seen, when the number of information sources exceeds the number of array elements, QGTO can still maintain strong robustness and accurately estimate DOA.

[0110] Figure 5 and Figure 6 The impact of generalized signal-to-noise ratio (SNR) on the direction-finding accuracy and estimation success probability of three direction-finding methods (PSO, PIO, and QGTO) under impulse noise is presented. At this point, two independent signal sources are respectively... Incident on a minimally redundant linear array, the population size of PSO, PIO, and QGTO is 100, with spatial noise. Distribution characteristic index The maximum number of snapshots is 1.6. The Monte Carlo simulation was performed 30 times. A successful estimation was defined as one where the error between the estimated value and the target value was less than 2.5°. (From simulation...) Figure 5 and 6 It can be seen that, under the background of impact noise, the QGTO method designed in this invention can effectively complete the direction of arrival estimation in harsh environments.

[0111] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for estimating the direction of arrival (DOA) of a minimum redundancy linear array based on the quantum giant trevally mechanism, characterized in that, Includes the following steps: S100. Establish an array direction finding model based on a minimum redundancy linear array under impact noise, and obtain the fractional low-order covariance matrix and its steering vector matrix of the virtual linear array based on the array direction finding model. Step S200: Obtain the maximum likelihood equation for the direction of arrival estimation under impact noise based on the fractional low-order covariance matrix and steering matrix of the virtual linear array. Step S300: Initialize the quantum giant trevally population and construct a fitness function. Calculate the fitness value of the quantum giant trevally after initialization and update the optimal fitness and the position of the optimal quantum giant trevally. The actual position corresponding to the optimal quantum position is the estimated direction angle vector that maximizes the maximum likelihood function value. Step S400: Execute the quantum evolution rules of the quantum giant trevally mechanism, including the broad search phase, the region selection phase, and the attack phase of the quantum giant trevally based on the Levy search strategy; Step S500: Map the newly generated quantum position of each quantum giant trevally to the position of the quantum giant trevally according to the mapping rule, calculate the fitness value of the corresponding position, and update its global optimal quantum position; Step S600: Determine if the number of iterations is equal to the maximum number of iterations. If not, return to step S400. If it is, terminate the loop iteration, output the best fitness and the quantum position of the best-fit quantum giant trevally. After mapping and transformation by the mapping rule, the position is the estimated value of DOA.

2. The method for estimating the direction of arrival of a minimum redundant linear array based on the quantum giant trevally mechanism according to claim 1, characterized in that: In step S100, it is assumed that there is an impact noise environment. The minimum redundant linear array composed of n elements, with the first element from the left as the reference element, has: Each wavelength is The narrowband signal from the incident angle of the signal source Incident on the array, let the minimum spacing between array elements be... ; The arrangement of the array elements satisfies the following properties: , For the first The absolute position of each array element relative to the reference array element, the th Each array element and the first The correlation delay between individual elements satisfy , For the first The position of each array element For the first The position of each array element, the difference in array element position ; The optimal minimum redundancy linear array satisfies the following property: it does not exist. , This represents the positional difference between the w-th and z-th array elements; , Representing the The positional difference between the first and second array elements, For the maximum relevant delay; when It is a continuous set of natural numbers; A non-optimal minimum redundancy linear array satisfies the following property: it exists. And the positional differences are small; the positional difference of the last array element satisfies ;when If is a set of consecutive natural numbers except for the common ones, then The output of the time array is: In the formula, It is the array receive vector. It is the first Individual Receive vector at any time; It is the array manifold matrix corresponding to the minimum redundant linear array, where The steering vector for the Nth direction signal; yes The signal vector at time step, where For the Nth signal source in The complex envelope of time; yes The impulse noise vector at time step, where In order to be in The impulse noise received by the Mth array element at time M, the Signals in each direction The guide vector in the direction is ; The fractional low-order covariance matrix of the minimum redundant linear matrix is ​​calculated as follows: The first of the matrix Line number The elements of the column are ,in and They represent Time of the first The and the first The data received by each array element The parameters are the fractional lower-order moment covariance matrix. The range is , For characteristic index, It is the expectation function. It is about finding conjugate; When the array receives The next quick shot, then The estimated value of the limited snapshot data is: ,in and They represent the first The and the first The element received the first Secondary snapshot data; The relationship between the minimum redundancy array and the virtual linear array is used to design... ,in, This represents the lower-order covariance of the fraction at a delay of 0 in the virtual linear array. The fractional low-order covariance represents the received signal of the i-th array element; , The fractional low-order covariance matrix for: Based on the maximum correlation delay The number of elements of the virtual linear array is obtained as follows Then the fractional lower-order covariance matrix of the virtual linear array for: 。 3. The method for estimating the direction of arrival of a minimum redundant linear array based on the quantum giant trevally mechanism according to claim 2, characterized in that: In step S200, the maximum likelihood equation is: In the formula, It is the maximum likelihood function value. , It is a matrix trace operation. It is the array steering matrix of a virtual uniform linear array. It is the Nth angle of incidence. The guiding vector; The corresponding steering vector is , It is the conjugate transpose operation. It is taking the inverse of the matrix. yes The mapping matrix.

4. The method for estimating the direction of arrival of a minimum redundant linear array based on the quantum giant trevally mechanism according to claim 3, characterized in that: Step S300 includes, S310. Initialize the quantum position of the quantum giant trevally and set the parameters of the mechanism: Set the population size of the quantum giant trevally to... The maximum number of iterations is Number of iterations , No. The generation The quantum position of a giant trevally is mapped to a position. The mapping rule is ,in It is the first The generation Only giant trevally The quantum position of a dimension , , For the largest dimension, , and They represent and The dimension, and These represent the upper and lower boundaries of the search space, respectively. S320, Calculate the first The generation Location of the quantum giant trevally The fitness of the giant trevally is used to evaluate the performance of potential solutions by calculating the fitness value of the giant trevally based on the fitness function. Design based on maximum likelihood equation The generation Fitness function of quantum giant trevally position : S330. Substitute the positions of all initialized quantum giant trevally into the fitness function to calculate their fitness values, and then... The fitness of the quantum giant trevally with the highest fitness value is stored in a variable. In the middle, its quantum position is stored In China; among them Defined as storing the first To find the optimal fitness value, define a vector. Record all trevally until the [number missing]th [number missing]. The globally optimal quantum position found up to the next iteration. For the first The generation The optimal quantum position in dimensionality, and the corresponding mapping state is the globally optimal position. , For the first The generation The globally optimal position of the dimension.

5. The method for estimating the direction of arrival of a minimum redundant linear array based on the quantum giant trevally mechanism according to claim 4, characterized in that: In step S400, The extensive search phase of the quantum giant trevally was completed based on the Levy search strategy. The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension for: In the formula, and All values ​​are taken from Random numbers between and They represent the quantum giant trevally. The maximum and minimum values ​​of a quantum position. It is the normalized Levy flight function; During the region selection phase, the quantum giant trevally locates the region with the highest food density and richest resources within the selected search space. The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension for: In the formula, , and All The constants between, and All values ​​are within Random numbers between It is the first All giant tuna The average value of the quantum positions in the dimensional space; During the attack phase, the first The generation The first quantum position of the giant trevally The quantum rotation angle corresponding to the dimension for: In the formula, , and These represent the angle of incidence and the angle of refraction, respectively. yes Random numbers between and These represent the absolute refractive indices of air and water, respectively. Is the value in Random numbers between; According to the The generation Only one giant trevally The generation of the corresponding quantum rotation angle in the dimensional quantum isotope. The generation Only one giant trevally A quantum position is defined by the following formula for updating its quantum position: In the formula, It is the first The first individual giant trevally Quantum position The updated version Each stage , No. The first generation Quantum position.

6. The method for estimating the direction of arrival of a minimum redundant linear array based on the quantum giant trevally mechanism according to claim 5, characterized in that: In step S500, the first The generation Phase 1 Only one giant trevally Quantum position according to Mapped to the first Phase 1 The generation The first individual giant trevally generated Quantum position , , ; and calculate the first Location of newly generated giant trevally individuals fitness function ,like ,but , ,otherwise , , , Sort and update the fitness function values ​​up to the first one. The optimal quantum position is .

7. A direction-of-arrival estimation system for a minimum redundancy linear array based on the quantum giant trevally mechanism, characterized in that: The system has a program module corresponding to the steps of any one of claims 1-6 above, and executes the steps in the above-described method for estimating the direction of arrival of a minimum redundant linear array based on the quantum giant trevally mechanism when it is run.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the direction-of-arrival estimation method for a minimum redundant linear array based on the quantum giant trevally mechanism as described in any one of claims 1-6.

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