Circular array direction of arrival estimation method based on quantum stick insect mechanism and sigmoid kernel relative entropy

Abstract

The application provides a circular array direction of arrival estimation method based on a quantum stick insect mechanism and a Sigmoid kernel related entropy, fuses a quantum optimization method into a stick insect bionic mechanism calculation method, obtains a calculation method of the quantum stick insect mechanism, and improves the convergence performance of the stick insect algorithm. A cross-correlation entropy covariance matrix based on a Sigmoid kernel function is constructed by using received information data, a low-order matrix based on the Sigmoid kernel related entropy is obtained, the deficiency that the second order and above are weak in anti-impact noise ability is eliminated, and the maximum likelihood equation based on the Sigmoid kernel related entropy is solved in a search interval by using the designed quantum stick insect mechanism. The problem of large calculation amount of multi-dimensional nonlinear optimization involved in the maximum likelihood method is solved, the search efficiency is improved, the estimation accuracy of the direction of arrival in an impact noise environment is also improved, and the quantum stick insect mechanism designed based on quantum coding and a simulated quantum evolution equation has a faster convergence speed, so that the global optimal solution of the estimated two-dimensional direction of arrival can be quickly obtained.

Description

Technical Field

[0001] This invention relates to a maximum likelihood direction-of-arrival estimation method for circular arrays based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy under impulsive noise conditions, belonging to the field of array signal processing. Background Technology

[0002] Direction of Arrival (DOA) estimation studies the direction of arrival of spatial signals. It is a crucial concept in spatial spectrum estimation theory and a key technology in array signal processing, widely applied in communications, sonar, and radar. Traditional DOA estimation methods include noise subspace algorithms (represented by MUSIC) and signal subspace algorithms (represented by ESPRIT rotation-invariant subspace). These algorithms are based on eigenvalue decomposition. For solving two-dimensional circular array problems, a large number of snapshots is often required to achieve good estimation performance, resulting in low real-time performance, high computational cost, and the need to sacrifice array aperture for coherent sources. Furthermore, traditional spatial spectrum estimation methods degrade or even fail under impulsive noise, low signal-to-noise ratio, and small snapshot numbers. Therefore, designing a fast and efficient DOA estimation method for circular arrays under impulsive noise conditions is essential.

[0003] A review of existing literature revealed that Zhang Hui et al., in their paper "A Space-Time Two-Dimensional Direction-of-Arrival Estimation Algorithm Based on a Uniform Circular Array" published in *Signal Processing*, utilized mode excitation techniques to transform the received data. Then, they used the cross-correlation between the transformed data to further map the data to the space-time domain, constructing a pair of space-time DOA matrix bundles. The wave angle was calculated using the generalized eigenvalues ​​of the matrix bundles. However, a relatively large number of snapshots and a high signal-to-noise ratio are still required to achieve satisfactory results, and its accuracy needs further improvement. Wang Hongqiu, in her paper "Research on Maximum Likelihood Direction-of-Arrival Estimation Algorithm Based on Alternating Projection," employed a maximum likelihood algorithm based on alternating projection to conduct two-dimensional direction-finding simulations under Gaussian noise. Although direction finding could be achieved with small snapshots and low signal-to-noise ratios, the inherent limitations of the alternating projection method, its over-reliance on initial value selection, resulted in relatively poor algorithm effectiveness and robustness, especially under impulse noise, where performance degradation was more severe. In their paper "Direction of Arrival Estimation Based on Improved ESPRIT Algorithm" published in *Modern Electronics Technology*, Li Shan et al. mentioned using spatial smoothing techniques on the ESPRIT algorithm to avoid the impact of inaccurate noise variance estimation. They then transformed the uniform circular array into a virtual uniform linear array using a mode transformation matrix before processing. Although the improved algorithm exhibits some performance enhancement, it still requires a large number of snapshots and a high signal-to-noise ratio to ensure accuracy, direction-finding precision, impulse noise reduction, and decoherence capabilities. Furthermore, it cannot simultaneously estimate azimuth and elevation angles, limiting its application scope and leaving significant room for improvement.

[0004] Furthermore, existing literature indicates that most two-dimensional direction-finding methods based on uniform circular arrays employ subspace decomposition-based methods. These methods not only perform poorly at low signal-to-noise ratios but also require decoherence processing when dealing with coherent sources, making the process cumbersome and often sacrificing some effective array elements, resulting in a loss of array aperture. Moreover, existing literature assumes that the noise encountered is predominantly Gaussian noise. However, noise in signal transmission often does not follow a Gaussian distribution, such as sea clutter and atmospheric noise, which are highly impactful. While these noises can be modeled using an alpha-stable distribution, their mismatch with Gaussian noise models renders traditional algorithms based on second-order or higher-order cumulants ineffective. Therefore, decoherent, fast-frame, high-precision, and robust DOA estimation for azimuth and elevation angles under impact noise environments is a crucial research topic. Summary of the Invention

[0005] The purpose of this invention is to address the challenge of rapidly estimating the direction of arrival (DOA) of a circular array under conditions of impulsive noise, small snapshots, and coherent sources. A more effective and robust DOA estimation method for circular arrays based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy is designed. This invention integrates quantum optimization methods into the stick insect-inspired computational method, resulting in a quantum stick insect mechanism computational method that further improves the convergence performance of the stick insect algorithm. Specifically, a cross-correlation entropy covariance matrix based on the Sigmoid kernel function is constructed using the received information data to obtain a low-order matrix based on the Sigmoid kernel correlation entropy. This also eliminates the weakness of second-order and higher-order moments in resisting impulsive noise. Then, the designed quantum stick insect mechanism is used to solve the maximum likelihood equation based on the Sigmoid kernel correlation entropy within the search interval. This study solves the problem of high computational cost in multidimensional nonlinear optimization involving the maximum likelihood method, improving its search efficiency and the estimation accuracy of wave direction in impact noise environments. At the same time, the quantum stick insect mechanism designed based on quantum coding and simulated quantum evolution equations has a faster convergence speed and can quickly obtain the global optimal solution of the estimated two-dimensional wave direction of arrival.

[0006] The objective of this invention is achieved as follows: The steps are as follows:

[0007] Step 1: Establish a uniform circular array sampling model under impact noise environment and acquire snapshot data received by the array;

[0008] Step 2: Construct a low-order matrix based on the Sigmoid kernel correlation entropy using the data received from the array, and then obtain the maximum likelihood estimation equation based on the Sigmoid kernel correlation entropy;

[0009] Step 3: Initialize the population information of the quantum stick insect mechanism and the quantum position and corresponding mapping position of each quantum stick insect population;

[0010] Step 4: Calculate the fitness value of the quantum stick insect population using the fitness function to obtain the initial global optimal quantum position and historical optimal quantum position space set;

[0011] Step 5: According to the quantization rules, use a simulated quantum rotation gate to update the quantum position and corresponding mapped state position of each quantum stick insect population, as well as the global optimal quantum position and historical optimal quantum position space set of the population;

[0012] Step 6: Based on the updated fitness function value, determine the next evolutionary trend of each subpopulation, and update the population size and growth rate information;

[0013] Step 7: Consider the impact of interpopulation competition on the evolutionary trend;

[0014] Step 8: When the size of a subpopulation is too small or its population growth rate exceeds the normal range, the subpopulation needs to be eliminated and a new subpopulation generated to replace it. This indicates that the current stick insect population has been eliminated due to poor adaptability to the environment.

[0015] Step 9: Determine if the maximum number of iterations T has been reached. max If the maximum number of iterations is not reached, let t = t + 1 and return to step five to continue iterating; if the maximum number of iterations is reached, select the current global optimal quantum position's mapping position as the final result and output the mapping state position corresponding to the current optimal quantum position.

[0016] Furthermore, step one specifically includes: assuming N narrowband far-field sources are located at azimuth angles... Pitch angle The incident light is directed onto a uniform circular array of radius r composed of M array elements. If the incident wavelength is λ, then the mathematical model for the k-th snapshot data received by the array is: Where k = 1, 2, ..., K, K is the maximum number of snapshots, and y(k) = [y1(k), y2(k), ..., y M (k)] T This is the snapshot data vector received by the M×1 dimensional array, where the superscript T denotes transpose. Let θ be an M×N dimensional manifold matrix, where θ = [θ1, θ2, ..., θ N ]and These are the azimuth vector and elevation vector of the signal source, respectively. It is the first of the manifold matrix There are 1 guide vector, among which s(k) is an N×1 dimensional signal vector, and n(k) is an M×1 dimensional impulse noise vector that follows a stable SαS distribution.

[0017] Furthermore, step two specifically includes: constructing a low-order moment matrix based on the Sigmoid kernel correlation entropy using the received data. That OK Column elements Represented as, In the formula and These represent the k-th snapshot signal data vector received, respectively. peacekeeping Dimensional signal, (·) * E(·) represents the conjugate operation, and E(·) represents taking the expected value of the variable within the parentheses. For the Sigmoid function, b is an amplitude adjustment parameter of the input data, and c is a displacement parameter that controls the mapping;

[0018] The orthogonal projection matrix of a uniform circular array is (·) H The conjugate transpose operation is represented by (·). -1 This represents the inverse operation. Therefore, for the two-dimensional direction-of-arrival estimation problem based on the azimuth and elevation angles of a uniform circular array, the designed maximum likelihood equation based on the Sigmoid kernel correlation entropy is as follows: Where tr(·) is the trace function of a matrix, which can be further expressed as

[0019] Furthermore, step three specifically includes: First, setting the number of subpopulations of the quantum stick insect population to N. p Each subpopulation has a spatial dimension of 2N, and the maximum number of iterations is T. max ; Define evolutionary trend as initialization All elements are 0, i = 1, 2, ..., N p , The evolutionary trend of the i-th quantum stick insect population in the t-th generation is represented by the set of the number of individuals in all subpopulations. The initial number of individuals in the i-th quantum stick insect population is: Define the population growth rate of quantum stick insects in generation t as in This represents the population growth rate of the i-th quantum stick insect population in the t-th generation, where i = 1, 2, ..., N. p ;

[0020] For Np The quantum positions of a quantum stick insect population are randomly initialized within the quantum domain [0, 1]. The quantum position of the i-th subpopulation in the t-th generation is defined as... in Let t represent the nth-dimensional quantum position of the i-th quantum stick insect population in the t-th generation, where t represents the iteration number, initialized to 1, and i = 1, 2, ..., N. p , n = 1, 2, ..., 2N; the population position of the i-th quantum stick insect population in the t-th generation. For quantum position The corresponding mapped state positions have the following mapping relationship: in This represents the lower bound of the nth dimension variable. This represents the upper boundary of the nth dimension variable, where i = 1, 2, ..., N. p , n=1,2,...,2N.

[0021] Furthermore, step four specifically includes: calculating the fitness value of the mapped state position of each quantum stick insect population, and setting the i-th mapped state position of generation t. Substituting into the fitness function expression, the fitness function expression for the mapped state position of the i-th quantum stick insect population in the t-th generation is: Record the position of the mapped state with the smallest fitness value in the entire population at generation t, and denote its corresponding quantum position as the globally optimal quantum population position. Its mapped state position is denoted as Record the first with the smallest fitness value The quantum positions corresponding to the mapped positions form the optimal quantum position space. in The corresponding space represented by its mapped state position is in Simultaneously select before The quantum position with the lowest fitness is used as the set of historically best quantum positions to guide the evolutionary direction of the population.

[0022] Furthermore, step five specifically includes: setting the quantum rotation angle of the i-th quantum stick insect population in the t-th generation as the evolutionary trend corresponding to that subpopulation. The quantum rotation angle for generating the i-th quantum stick insect population of the (t+1)-th generation is: For the nth quantum position of the i-th quantum stick insect population in the (t+1)-th generation, the update equation using the simulated quantum rotation gate is: The nth-dimensional mapping state position of the i-th quantum stick insect population in the (t+1)-th generation is obtained through the mapping equation. Calculate the fitness value of the mapped state position of this subpopulation. The quantum position corresponding to the smaller fitness value is selected as the globally optimal quantum position of the (t+1)th generation quantum stick insect population, denoted as […]. The mapped state position of its globally optimal quantum position is denoted as Update the optimal quantum position space, also taking the first sorted position. Each fitness value is compared with the fitness values ​​of the quantum positions in the previous best quantum position space, and the quantum position with the smallest fitness is retained. The quantum positions serve as the updated historical best quantum position space. Its corresponding mapped state position space is then updated to H. t+1 .

[0023] Furthermore, step six specifically includes: the first case is: the fitness value of the i-th quantum stick insect population after the update is less than the fitness value of the previous generation, that is... Update on growth rate The corresponding change in the number of individuals in the subpopulation is After updating the growth rate and number of individuals, the evolutionary trend needs to be updated. The updated population evolution trend formula is: in Used to find the (t+1)th generation closest The historical best quantum position, α is the influence coefficient of the closest best quantum position on the current population. This represents a mutation in certain dimensions of the population. The number of dimensions experiencing mutations is determined by using a uniform distribution between 0 and 2N, combined with rounding down. Then, the specific dimension experiencing the mutation is determined by a random permutation of integers, assigned a value of 1, and the rest are set to 0, resulting in a 2N-dimensional vector η. σ is an adjustment coefficient, and the symbol "☉" indicates the product of corresponding elements of two vectors. L represents a 2N-dimensional random vector generated using a standard normal distribution;

[0024] The second scenario is: the update of the i-th quantum stick insect population does not yield better results, that is... The evolutionary trend of the i-th subpopulation in generation t+1 is updated as follows: The symbol “☉” is defined to represent the product of corresponding elements of two vectors, r i t+1 This represents a 2N-dimensional random vector generated using uniformly distributed random numbers (0, 1). It is used to find the (t+1)th generation. closest The historical best quantum position, This represents a 2N-dimensional random vector generated using a standard normal distribution. Initially, Where τ is the proportionality coefficient. And when t≥2, W t+1 =uW t u is the iteration coefficient;

[0025] Furthermore, the i-th subpopulation has a certain probability of remaining in a relatively poor state after the update, assuming the probability of remaining in a poor state is... Then it is compared with a random number from 0 to 1 generated by a uniform distribution; if it is greater than it, it is determined that the relatively poor situation will continue; otherwise, it will not continue; if it is determined that the quantum stick insect population will continue to maintain this relatively poor situation, then its growth rate will change to The population size changes as follows If it is determined that the population will no longer be maintained, then the previous growth rate and the number of individuals in the population will remain unchanged until the next update.

[0026] Furthermore, step seven specifically includes: defining It is the quantum position of the i-th quantum stick insect population in the (t+1)-th generation. For the corresponding mapped state position, From other N p The quantum position of the j-th quantum stick insect population randomly selected from the -1 subpopulations, also... Given the corresponding mapped state position; calculate the Euclidean distance between the mapped state positions of the two subpopulations, and the given threshold D for the (t+1)th generation. t+1 Comparison, among which ε is the adjustment coefficient, T max The maximum number of iterations; if It is assumed that there is competition between the two; for the i-th quantum stick insect population, the number of individuals in the population will also be affected, and the corresponding number of individuals will be updated again. The subsequent evolutionary trend of the population will also be updated accordingly.

[0027] Compared with the prior art, the beneficial effects of the present invention are: (1) It addresses the complex electromagnetic environment in practical applications and the actual need for uniform circular array direction of arrival estimation under low signal-to-noise ratio, small snapshot, and impact noise backgrounds. When using traditional methods, the robustness and accuracy are often difficult to meet the requirements of practical applications. The maximum likelihood equation based on Sigmoid kernel correlation entropy designed in this invention can effectively eliminate the influence of impact noise, and under low signal-to-noise ratio and small snapshot conditions, it can still effectively estimate the direction of arrival of coherent sources due to the characteristics of the maximum likelihood method. (2) By combining quantum optimization theory with stick insect biomimetic mechanism, and through quantum coding and simulated quantum rotating gate improved calculation methods, the designed objective function can be solved quickly and with high precision. Furthermore, it can improve the accuracy and robustness of the solution while reducing the amount of computation, solving the shortcomings of existing maximum likelihood direction of arrival estimation methods, which have large computational load and long time consumption. This makes the direction of arrival estimation results have better robustness and convergence. Attached Figure Description

[0028] Figure 1 Schematic diagram of a circular array direction-of-arrival estimation method based on quantum stick insect mechanism and Sigmoid kernel correlation entropy;

[0029] Figure 2 Schematic diagram of two-dimensional direction of arrival estimation results under impact noise with low signal-to-noise ratio and small snapshots;

[0030] Figure 3 Schematic diagram of 50th direction of arrival estimation for two coherent sources under weak impulse noise;

[0031] Figure 4 Schematic diagram of the 50th direction of arrival estimation of two coherent sources under strong impulsive noise;

[0032] Figure 5 Comparison of the success probabilities of two direction-of-arrival estimation methods. Detailed Implementation

[0033] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0034] The overall flow of the circular array wave direction of arrival estimation method of this invention is as follows: Figure 1 As shown, the technical solution of the present invention includes the following steps:

[0035] Step 1: Establish a uniform circular array sampling model under impact noise environment and obtain the snapshot data received by the array.

[0036] Assume N narrowband far-field sources are located at azimuth angles. Pitch angle The incident light is directed onto a uniform circular array of radius r composed of M array elements. If the incident wavelength is λ, then the mathematical model for the k-th snapshot data received by the array is: Where k = 1, 2, ..., K, K is the maximum number of snapshots, and y(k) = [y1(k), y2(k), ..., y M (k)] T This is the snapshot data vector received by the M×1 dimensional array, where the superscript T denotes transpose. Let θ be an M×N dimensional manifold matrix, where θ = [θ1, θ2, ..., θ N ]and These are the azimuth vector and elevation vector of the signal source, respectively. It is the first of the manifold matrix There are 1 guide vector, among which s(k) is an N×1 dimensional signal vector, and n(k) is an M×1 dimensional impulse noise vector that follows a stable SαS distribution.

[0037] Step 2: Construct a low-order matrix based on the Sigmoid kernel correlation entropy using the data received from the array, and then obtain the maximum likelihood estimation equation based on the Sigmoid kernel correlation entropy.

[0038] Construct a low-order moment matrix based on the Sigmoid kernel correlation entropy using the received data. That OK Column elements Represented as, In the formula and These represent the k-th snapshot signal data vector received, respectively. peacekeeping Dimensional signal, (·) * E(·) represents the conjugate operation, and E(·) represents taking the expected value of the variable within the parentheses. Here, b is an amplitude adjustment parameter for the input data, and c is a displacement parameter that controls the mapping.

[0039] The orthogonal projection matrix of a uniform circular array is (·) H The conjugate transpose operation is represented by (·). -1 This represents the inverse operation. Therefore, for the two-dimensional direction-of-arrival estimation problem based on the azimuth and elevation angles of a uniform circular array, the designed maximum likelihood equation based on the Sigmoid kernel correlation entropy is as follows: Where tr(·) is the trace function of a matrix, which can be further expressed as

[0040] Step 3: Initialize the population information of the quantum stick insect mechanism and the quantum position and corresponding mapping position of each quantum stick insect population.

[0041] First, the number of subpopulations of the quantum stick insect population is set to N. p Each subpopulation has a spatial dimension of 2N, and the maximum number of iterations is T. max Evolutionary trend is defined as... Because it was the first generation, it lacked the experience to guide its evolution, so it was initialized. All elements are 0, i = 1, 2, ..., N p , Let represent the evolutionary trend of the i-th quantum stick insect population in the t-th generation. The set of the number of individuals in all subpopulations is defined as . The initial number of individuals in the i-th quantum stick insect population is: Define the population growth rate of quantum stick insects in generation t as in This represents the population growth rate of the i-th quantum stick insect population in the t-th generation, where i = 1, 2, ..., N. p .

[0042] For N p The quantum positions of a quantum stick insect population are randomly initialized within the quantum domain [0, 1]. The quantum position of the i-th subpopulation in the t-th generation is defined as... in Let t represent the nth-dimensional quantum position of the i-th quantum stick insect population in the t-th generation, where t represents the iteration number, initialized to 1, and i = 1, 2, ..., N. p Let n = 1, 2, ..., 2N. The population position of the i-th quantum stick insect population in generation t. For quantum position The corresponding mapped state positions have the following mapping relationship: in This represents the lower bound of the nth dimension variable. This represents the upper boundary of the nth dimension variable, where i = 1, 2, ..., N. p , n=1,2,...,2N.

[0043] Step 4: Calculate the fitness value of the quantum stick insect population using the fitness function to obtain the initial global optimal quantum position and historical optimal quantum position space set.

[0044] Calculate the fitness value of the mapped state position for each quantum stick insect population, and set the i-th mapped state position in generation t. Substituting into the fitness function expression, the fitness function expression for the mapped state position of the i-th quantum stick insect population in the t-th generation is: Record the position of the mapped state with the smallest fitness value in the entire population at generation t, and denote its corresponding quantum position as the globally optimal quantum population position. Its mapped state position is denoted as Record the first with the smallest fitness value The quantum positions corresponding to the mapped positions form the optimal quantum position space. in The corresponding space represented by its mapped state position is in Simultaneously select before The quantum position with the lowest fitness is used as the set of historically best quantum positions to guide the evolutionary direction of the population.

[0045] Step 5: According to the quantization rules, use a simulated quantum rotation gate to update the quantum position and corresponding mapped state position of each quantum stick insect population, as well as the global optimal quantum position and historical optimal quantum position space set of the population.

[0046] The quantum rotation angle of the i-th quantum stick insect population in generation t represents the evolutionary trend of that population. Therefore, the quantum position of each quantum stick insect population is updated using a simplified simulated quantum rotation gate. The quantum rotation angle for generating the i-th quantum stick insect population in the (t+1)-th generation is set to... Then, for the nth quantum position of the i-th quantum stick insect population in the (t+1)-th generation, the update equation using the simulated quantum rotation gate is: Simultaneously, the nth-dimensional mapping state position of the i-th quantum stick insect population in the (t+1)-th generation is obtained through the mapping equation. Next, the fitness value of the mapped state position of the subpopulation is calculated. Finally, the fitness values ​​of all subpopulations are sorted in ascending order, and the minimum value is compared with the fitness value of the globally optimal quantum position of the previous generation. The quantum position corresponding to the smaller fitness value is ultimately selected as the globally optimal quantum position of the (t+1)th generation quantum stick insect population, denoted as […]. The mapped state position of its globally optimal quantum position is denoted as Update the optimal quantum position space, also taking the first sorted position. Each fitness value is compared with the fitness values ​​of the quantum positions in the previous best quantum position space, and the quantum position with the smallest fitness is retained. The quantum positions serve as the updated historical best quantum position space. Its corresponding mapped state position space is then updated to H. t+1 .

[0047] Step 6: Based on the updated fitness function value, determine the future evolutionary trend of each subpopulation, and update the population size and growth rate information.

[0048] The evolutionary direction of the quantum stick insects is a matter of autonomous decision-making, utilizing characteristics such as population growth models, convergent evolution, and path dependence. It is mainly discussed in two cases, with each quantum stick insect population taking different evolutionary actions under different circumstances. The determination of which case it belongs to is based on the updated fitness function value.

[0049] The first scenario is: the fitness value of the i-th quantum stick insect population after the update is less than the fitness value of the previous generation, i.e. This means improved fitness. Such a change will affect the current population growth rate, the number of individuals in the population, and future evolutionary trends. Regarding the update of the growth rate... The corresponding change in the number of individuals in the subpopulation is After updating the growth rate and number of individuals, the evolutionary trend needs to be updated. Evolutionary trends are influenced by three factors. The first is that the population will converge to the vicinity of the optimal quantum position. Therefore, using... Zhongyu The closest quantum position to guide The first aspect is the evolution of the population, which facilitates the exploration of different local optima. The second aspect is the continuation of the evolutionary trend. If the fitness value obtained after the movement is better, the movement trend continues. The third aspect is mutation within the population. Mutation increases the uncertainty of evolution. Based on the above three aspects, the updated population evolutionary trend formula is: in Used to find the (t+1)th generation closest The historical best quantum position, α is the influence coefficient of the closest best quantum position on the current population, which is usually less than 1. This represents a mutation in the population along certain dimensions. The number of dimensions experiencing mutations is determined by using a uniform distribution between 0 and 2N, combined with rounding down. Then, the specific dimension experiencing the mutation is determined by a random permutation of integers, assigned a value of 1, and the rest are set to 0, resulting in a 2N-dimensional vector η. σ is an adjustment coefficient, and the symbol "☉" indicates the product of corresponding elements of two vectors. L represents a 2N-dimensional random vector generated using a standard normal distribution.

[0050] The second scenario is: the update of the i-th quantum stick insect population does not yield better results, that is... This means the fitness value deteriorates. The population will no longer maintain its original evolutionary trend, but will instead tend towards the closest historical optimal quantum position, generating an unpredictable perturbation as a consequence of the uncertainty brought about by breaking the existing trend. Therefore, the evolutionary trend of the i-th subpopulation in generation t+1 is updated as follows: The symbol “☉” is defined to represent the product of corresponding elements of two vectors, r i t+1 This represents a 2N-dimensional random vector generated using uniformly distributed random numbers (0, 1). It is used to find the (t+1)th generation. closest The historical best quantum position, This represents a 2N-dimensional random vector generated using a standard normal distribution. Initially, Where τ is the proportionality coefficient. And when t≥2, W t+1 =uW t , where u is the iteration coefficient.

[0051] Furthermore, the i-th subpopulation has a certain probability of remaining in a relatively poor state after the update, so this needs to be assessed. Let's assume the probability of remaining in a poor state is... Then it is compared with a random number from 0 to 1 generated by a uniform distribution. If it is greater than the random number, it is determined that the relatively poor situation will continue; otherwise, it will not continue. If it is determined that the quantum stick insect population will continue to maintain this relatively poor situation, then its growth rate will change to... The population size changes as follows If it is determined that the population will no longer be maintained, then the previous growth rate and the number of individuals in the population will remain unchanged until the next update.

[0052] Step 7: Consider the impact of interpopulation competition on the evolutionary trend.

[0053] Define based on the potential population competition relationships between subpopulations. It is the quantum position of the i-th quantum stick insect population in the (t+1)-th generation. For the corresponding mapped state position, From other N p The quantum position of the j-th quantum stick insect population randomly selected from the -1 subpopulations, also... This corresponds to the mapped state position. Then, it's necessary to calculate the Euclidean distance between the mapped state positions of the two subpopulations, relative to the given threshold D for the (t+1)th generation. t+1 Comparison, among which ε is the adjustment coefficient, T max This represents the maximum number of iterations. If... Therefore, it is assumed that there is competition between the two. Consequently, the population size of the i-th quantum stick insect population will also be affected, and the corresponding population size will be updated again. The subsequent evolutionary trend of the population will also be updated accordingly.

[0054] Step 8: When a subpopulation is too small or its population growth rate exceeds the normal range, the subpopulation needs to be eliminated and a new subpopulation generated to replace it. This indicates that the current stick insect population has been eliminated due to poor adaptability to the environment.

[0055] Step 9: Determine if the maximum number of iterations T has been reached. max If the maximum number of iterations is not reached, let t = t + 1 and return to step five to continue iterating; if the maximum number of iterations is reached, select the current global optimal quantum position's mapping position as the final result and output the mapping state position corresponding to the current optimal quantum position.

[0056] For ease of explanation, the circular array maximum likelihood direction-of-arrival (DOA) estimation method based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy will be abbreviated as QPPE-SCE-ML, while the contrasting circular array DOA estimation method based on fractional low-order matrices (MUSIC) will be abbreviated as FLOM-MUSIC. In the simulation experiment, two signal sources are incident on a uniform circular array from the directions {250°, 30°} and {100°, 10°}, respectively. The simulation parameters are designed as follows: number of antenna array elements M = 16, number of signal sources N = 2, parameters b = 0.5, c = 1, maximum number of iterations L = 400, and the number of quantum stick insect subpopulations N... p =80, initialize the population growth rate of the i-th quantum stick insect population as Historical best number of quantum positions Adjustment coefficient σ = 2, proportional coefficient τ = 0.1, iteration coefficient u = 0.99, influence coefficient α = 0.2, and maintenance probability. The adjustment coefficient ε = 0.99, and the simulation was completed under an impact noise environment.

[0057] Figure 2 In the figure, two coherent sources are incident from the directions {250°, 30°} and {100°, 10°}, respectively. This is a schematic diagram of direction of arrival estimation under the background of impulse noise, with a generalized signal-to-noise ratio of 5dB and a snapshot number of 50.

[0058] Figure 3 In the simulation, two coherent sources are incident from {250°, 30°} and {100°, 10°} directions, respectively. The impulse noise characteristic index is 1.5, the generalized signal-to-noise ratio is 10dB, the snapshot number is 150, and the number of experiments is 50. Figure 3 As can be seen, the direction finding performance is quite satisfactory, with a small deviation between the estimated and actual values. Therefore, the designed QPPE-SCE-ML can perform effective DOA estimation in a weak impulse noise environment.

[0059] Figure 4 In the simulation, two coherent sources are incident from {250°, 30°} and {100°, 10°} directions, respectively. The impulse noise characteristic index is 0.95, the generalized signal-to-noise ratio is 10dB, the number of snapshots is 150, and the number of experiments is 50. Figure 4 As can be seen, the deviation between the estimated value and the true value is small, with only a few isolated points showing a certain degree of deviation. Therefore, the designed QPPE-SCE-ML can effectively estimate DOA in environments with strong impact noise.

[0060] Figure 5 In the simulation, two coherent signal sources are incident from {250°, 30°} and {100°, 10°} directions, respectively. The QPPE-SCE-ML algorithm of this invention and the classic FLOM-MUSIC algorithm are simultaneously processed and compared. The impulse noise characteristic index is 1.5, the generalized signal-to-noise ratio is 10dB, and the estimation result is considered successful if the deviation does not exceed 2°. The number of trials is 50. From the simulation... Figure 5 Experimental results show that the designed QPPE-SCE-ML method has significant advantages under impulsive noise and a small number of snapshots, and can perform direction-of-arrival (DOA) estimation well in harsh environments. In contrast, the FLOM-MUSIC algorithm cannot adapt to this environment. Therefore, this demonstrates that the invented QPPE-SCE-ML method can still perform effective DOA estimation under poor conditions such as small snapshots and impulsive noise.

Claims

1. A method for estimating the direction of arrival (DOA) of a circular array based on the quantum stick insect mechanism and the Sigmoid kernel correlation entropy, characterized in that... The steps are as follows: Step 1: Establish a uniform circular array sampling model under impact noise environment and acquire snapshot data received by the array; Step 2: Construct a low-order matrix based on the Sigmoid kernel correlation entropy using the data received from the array. This leads to the maximum likelihood estimation equation based on the Sigmoid kernel correlation entropy; Low-order moment matrix based on Sigmoid kernel correlation entropy of OK Column elements for: in, and These represent the k-th snapshot signal data vector received, respectively. peacekeeping Dimensional signal, (·) * E(·) represents the conjugate operation, and E(·) represents taking the expected value of the variable within the parentheses. For the Sigmoid function, b is an amplitude adjustment parameter of the input data, and c is a displacement parameter that controls the mapping; Step 3: Initialize the population information of the quantum stick insect mechanism and the quantum position and corresponding mapping position of each quantum stick insect population; Step 4: Calculate the fitness value of the quantum stick insect population using the fitness function to obtain the initial global optimal quantum position and historical optimal quantum position space set; Step 5: According to the quantization rules, use a simulated quantum rotation gate to update the quantum position and corresponding mapped state position of each quantum stick insect population, as well as the global optimal quantum position and historical optimal quantum position space set of the population; Step 6: Based on the updated fitness function value, determine the next evolutionary trend of each subpopulation, and update the population size and growth rate information; Step 7: Consider the impact of interpopulation competition on the evolutionary trend; Step 8: When the size of a subpopulation is too small or its population growth rate exceeds the normal range, the subpopulation needs to be eliminated and a new subpopulation generated to replace it. This indicates that the current stick insect population has been eliminated due to poor adaptability to the environment. Step 9: Determine if the maximum number of iterations T has been reached. max If the maximum number of iterations is not reached, let t = t + 1 and return to step five to continue iterating; if the maximum number of iterations is reached, select the current global optimal quantum position as the final result and output the mapping state position corresponding to the current optimal quantum position.

2. The method for estimating the direction of arrival of a circular array based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy according to claim 1, characterized in that, Step one specifically includes: assuming N narrowband far-field sources are located at azimuth angles... Pitch angle The incident light is directed onto a uniform circular array of radius r composed of M array elements. If the incident wavelength is λ, then the mathematical model for the k-th snapshot data received by the array is: Where k = 1, 2, ..., K, K is the maximum number of snapshots, and y(k) = [y1(k), y2(k), ..., y M (k)] T This is the snapshot data vector received by the M×1 dimensional array, where the superscript T denotes transpose. Let θ be an M×N dimensional manifold matrix, where θ = [θ1, θ2, ..., θ N ]and These are the azimuth and elevation vectors of the signal source, respectively. It is the first of the manifold matrix There are 1 guide vector, among which s(k) is an N×1 dimensional signal vector, and n(k) is an M×1 dimensional impulse noise vector that follows a stable SαS distribution.

3. The method for estimating the direction of arrival of a circular array based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy according to claim 1, characterized in that, The orthogonal projection matrix of a uniform circular array is (·) H The conjugate transpose operation is represented by (·). -1 This represents the inverse operation. Therefore, for the two-dimensional direction-of-arrival estimation problem based on the azimuth and elevation angles of a uniform circular array, the designed maximum likelihood equation based on the Sigmoid kernel correlation entropy is as follows: Where tr(·) is the trace function of a matrix, which can be further expressed as 4. The method for estimating the direction of arrival of a circular array based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy according to claim 1, characterized in that, Step three specifically includes: First, setting the number of subpopulations of the quantum stick insect population to N. p Each subpopulation has a spatial dimension of 2N, and the maximum number of iterations is T. max ; Define evolutionary trend as initialization All elements are 0, i = 1, 2, ..., N p , The evolutionary trend of the i-th quantum stick insect population in the t-th generation is represented by the set of the number of individuals in all subpopulations. The initial number of individuals in the i-th quantum stick insect population is: Define the population growth rate of quantum stick insects in generation t as in This represents the population growth rate of the i-th quantum stick insect population in the t-th generation, where i = 1, 2, ..., N. p ; For N p The quantum positions of a quantum stick insect population are randomly initialized within the quantum domain [0, 1]. The quantum position of the i-th subpopulation in the t-th generation is defined as... in Let t represent the nth-dimensional quantum position of the i-th quantum stick insect population in the t-th generation, where t represents the iteration number, initialized to 1, and i = 1, 2, ..., N. p , n = 1, 2, ..., 2N; the population position of the i-th quantum stick insect population in the t-th generation. For quantum position The corresponding mapped state positions have the following mapping relationship: in This represents the lower bound of the nth dimension variable. This represents the upper boundary of the nth dimension variable, where i = 1, 2, ..., N. p , n=1,2,...,2N.

5. The method for estimating the direction of arrival of a circular array based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy according to claim 1, characterized in that, Step four specifically includes: calculating the fitness value of the mapped state position for each quantum stick insect population, and setting the i-th mapped state position in generation t. Substituting into the fitness function expression, the fitness function expression for the mapped state position of the i-th quantum stick insect population in the t-th generation is: Record the position of the mapped state with the smallest fitness value in the entire population at generation t, and denote its corresponding quantum position as the globally optimal quantum population position. Its mapped state position is denoted as Record the first with the smallest fitness value The quantum positions corresponding to the mapped positions form the optimal quantum position space. in The corresponding space represented by its mapped state position is in Simultaneously select before The quantum position with the lowest fitness is used as the set of historically best quantum positions to guide the evolutionary direction of the population.

6. The method for estimating the direction of arrival of a circular array based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy according to claim 1, characterized in that, Step five specifically includes: setting the quantum rotation angle of the i-th quantum stick insect population in generation t, which represents the evolutionary trend of that subpopulation. The quantum rotation angle for generating the i-th quantum stick insect population of the (t+1)-th generation is: For the nth quantum position of the i-th quantum stick insect population in the (t+1)-th generation, the update equation using the simulated quantum rotation gate is: i = 1, 2, ..., N p n = 1, 2, ..., 2N; the nth-dimensional mapped state position of the i-th quantum stick insect population in the (t+1)-th generation is obtained through the mapping equation. Calculate the fitness value of the mapped state position of this subpopulation. The quantum position corresponding to the smaller fitness value is selected as the globally optimal quantum position of the (t+1)th generation quantum stick insect population, denoted as […]. The mapped state position of its globally optimal quantum position is denoted as Update the optimal quantum position space, also taking the first sorted position. Each fitness value is compared with the fitness values ​​of quantum positions in the previous historical best quantum position space, and the top K quantum positions with the lowest fitness values ​​are retained as the updated historical best quantum position space. Its corresponding mapped state position space is then updated to H. t+1 .

7. The method for estimating the direction of arrival of a circular array based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy according to claim 1, characterized in that, Step six specifically includes: The first case is: the fitness value of the i-th quantum stick insect population after the update is less than the fitness value of the previous generation, that is... Update on growth rate The corresponding change in the number of individuals in the subpopulation is After updating the growth rate and number of individuals, the evolutionary trend needs to be updated. The updated population evolution trend formula is: in Used to find the (t+1)th generation closest The historical best quantum position, α is the influence coefficient of the closest best quantum position on the current population. This represents a mutation in certain dimensions of the population. The number of dimensions experiencing mutations is determined by using a uniform distribution between 0 and 2N, combined with rounding down. Then, the specific dimension experiencing the mutation is determined by a random permutation of integers, assigned a value of 1, and the rest are set to 0, resulting in a 2N-dimensional vector η. σ is an adjustment coefficient, and the symbol "☉" indicates the product of corresponding elements of two vectors. L represents a 2N-dimensional random vector generated using a standard normal distribution; The second scenario is: the update of the i-th quantum stick insect population does not yield better results, that is... The evolutionary trend of the i-th subpopulation in generation t+1 is updated as follows: The symbol "☉" is defined to represent the product of corresponding elements of two vectors, r i t+1 This represents a 2N-dimensional random vector generated using uniformly distributed random numbers (0, 1). It is used to find the (t+1)th generation. closest The historical best quantum position, This represents a 2N-dimensional random vector generated using a standard normal distribution; initially, Where τ is the proportionality coefficient. And when t≥2, W t+1 =uW t u is the iteration coefficient; Furthermore, the i-th subpopulation has a certain probability of remaining in a relatively poor state after the update, assuming the probability of remaining in a poor state is... Then it is compared with a random number from 0 to 1 generated by a uniform distribution; if it is greater than it, it is determined that the relatively poor situation will continue; otherwise, it will not continue; if it is determined that the quantum stick insect population will continue to maintain this relatively poor situation, then its growth rate will change to The population size changes as follows If it is determined that the population will no longer be maintained, then the previous growth rate and the number of individuals in the population will remain unchanged until the next update.

8. The method for estimating the direction of arrival of a circular array based on the quantum stick insect mechanism and Sigmoid kernel correlation entropy according to claim 1, characterized in that, Step seven specifically includes: definition It is the quantum position of the i-th quantum stick insect population in the (t+1)-th generation. For the corresponding mapped state position, From other N p The quantum position of the j-th quantum stick insect population randomly selected from the -1 subpopulations, also... Given the corresponding mapped state position; calculate the Euclidean distance between the mapped state positions of the two subpopulations, and the given threshold D for the (t+1)th generation. t+1 Comparison, among which ε is the adjustment coefficient, T max The maximum number of iterations; if It is assumed that there is competition between the two; for the i-th quantum stick insect population, the number of individuals in the population will also be affected, and the corresponding number of individuals will be updated again. The subsequent evolutionary trend of the population will also be updated accordingly.

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