A distributed array doa estimation method and system

Abstract

The application discloses a kind of distributed array DOA estimation method and system, by combining traditional coronavirus population immunity search mechanism with quantum computing theory, a kind of quantum coronavirus population immunity search mechanism is designed, the amount of calculation is reduced using complex Givens rotation transformation, the optimal solution of target function is searched in the search range given and the optimal matrix corresponding thereto, blind source separation is realized.Utilizing the designed quantum coronavirus population immunity search mechanism, the optimal solution of target function and the optimal matrix corresponding thereto in the range are searched, blind source separation is realized.Then the partial calibration array multi-observation signal constructed is input into the new blind source separation algorithm, the recovery of phase deviation between subarrays is realized.Finally, under the condition that the phase deviation between subarrays is recovered, the Root-Music algorithm is introduced to realize the high-precision direction finding of distributed array under the condition of low signal-to-noise ratio and small snapshot number.Under the condition of small snapshot number, low signal-to-noise ratio and multiple targets, effective error correction and DOA estimation can still be realized, with the advantages of fast convergence speed, high precision, stable performance and the like.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing, specifically relating to a distributed array DOA estimation method and system. Background Technology

[0002] Direction finding, also known as direction of arrival (DOA) estimation, has always been a hot research topic in the field of array signal processing, with wide applications in communication, radar, and sonar systems. Distributed arrays are special sparse arrays that divide an antenna array into multiple small-aperture subarrays and distribute them widely. Unlike the non-coherent processing of traditional array signals, distributed arrays perform coherent processing on these distributed subarray signals to achieve the equivalent array aperture using a small number of array elements. This approach offers advantages such as high flexibility and degree of freedom. The key to achieving coherent processing between subarrays is precise synchronization between the arrays. This ensures a clear correlation between all antenna arrays, eliminates the influence of array errors, and achieves precise array synchronization—a task known as "error correction." However, current error correction methods struggle to guarantee precise synchronization when the number of snapshots is small and the signal-to-noise ratio is low. Consequently, they cannot guarantee high-precision direction finding for distributed arrays in high-dynamic scenarios. Furthermore, even if precise synchronization can be guaranteed, existing direction finding methods still suffer from performance dependence on parameter settings and sufficient observation data, indicating that method performance needs improvement.

[0003] A review of existing literature revealed that Xu Hongbo et al., in their paper "A Method for Estimating Direction of Arrival (DOA) of Distributed Arrays" published in the *Journal of Astronautics* (2012, Vol. 33, No. 12, pp. 1801-1805), performed DOA estimation on each virtual subarray separately and then fused the results to obtain the final azimuth estimation. However, this method did not perform coherent processing on the received signals of each subarray, thus failing to achieve spatial resolution corresponding to the entire array aperture. Xiang Hong et al., in their paper "DOA Estimation of Distributed Arrays Using Single-Snapshot Data" published in the *Journal of Electronics and Information Technology* (2016, Vol. 38, No. 11, pp. 2767-2773), proposed a 1D DOA estimation algorithm based on the state-space equilibrium method. This method can obtain high-precision DOA estimation for distributed arrays. However, this method requires constructing a Hankle matrix using single-snapshot data for each subarray element of the distributed array. The estimation accuracy is affected by the parameter settings in the constructed Hankle matrix; improper parameter settings degrade the method's performance. In their paper "Direction finding in partly calibrated arrays exploiting the whole array aperture" published in IEEE Transactions on Aerospace and Electronic Systems (2023, Vol. 59, No. 4, e12741), Guangbin Zhang et al. proposed a distributed array direction finding method based on blind source separation. First, they introduced the Joint Approximate Diagonalization of Eigen-matrices (JADE) algorithm to recover the phase deviation between subarrays. Then, they considered matched filtering and nonlinear least squares methods for azimuth estimation. This method can achieve high-resolution direction finding of targets corresponding to the entire array aperture in highly dynamic scenarios by recovering the phase deviation between subarrays. However, the JADE algorithm used in this method is prone to getting trapped in local optima. The method does not consider the impact of low signal-to-noise ratio on the recovery of phase deviation between subarrays. In addition, the azimuth estimation accuracy of matched filtering is low in multi-target scenarios, and the azimuth estimation accuracy of nonlinear least squares is easily affected by the iteration step size, requiring an additional search algorithm to determine the iteration step size. Improperly set iteration step size degrades the method's performance.

[0004] Existing literature indicates that significant progress has been made in the research of distributed array direction finding methods. However, these methods are prone to getting trapped in local optima, exhibit poor robustness, and require improvement in phase deviation recovery accuracy and direction finding accuracy between subarrays under low signal-to-noise ratio and multi-target conditions. Furthermore, the performance of these methods is highly dependent on parameter settings; improper parameter settings can degrade performance. Summary of the Invention

[0005] The purpose of this invention is to overcome the engineering challenges faced by traditional distributed array direction finding methods, such as low accuracy in recovering phase difference between subarrays and low direction finding accuracy under low signal-to-noise ratio conditions, and the fact that the performance of the method depends on parameter settings. This invention provides a distributed array DOA estimation method and system.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A method for estimating the DOA of a distributed array includes the following steps:

[0008] Step 1: Obtain snapshot sampling data of the received signal from each subarray in the distributed array;

[0009] Step 2: Whiten the sampled data received by the subarray, and construct the objective function based on the cost function of the JADE algorithm;

[0010] Step 3: Construct and calculate the fitness of quantum cases to determine the globally optimal quantum position;

[0011] Step 4: Update the quantum position of each quantum case in the quantum case population;

[0012] Step 5: Map the updated quantum case's quantum position to the quantum case position, calculate the fitness value of the new quantum case position according to the fitness function, and then update the global optimal quantum position;

[0013] Step Six: Complete the quantum case state transition based on the fitness value of the new quantum case location;

[0014] Step 7: Determine if the iterative model has reached its maximum number of iterations; if not, return to step 4 to iterate again; otherwise, output the global optimal position and its corresponding optimal matrix, and then obtain the estimated matrix of the mixture matrix to recover the source signal.

[0015] Step 8: Normalize the recovered source signal and then estimate the phase deviation between subarrays;

[0016] Step 9: Substitute the estimated inter-subarray phase deviation into the Root-Music algorithm to achieve DOA estimation based on distributed arrays.

[0017] Furthermore, step one specifically includes:

[0018] Consider using in a two-dimensional plane A linear distributed array is used for detection, and each subarray has Each array element, The total number of array elements is expressed as ;

[0019] Construct a planar Cartesian coordinate system, with the reference element position of the first subarray as the origin, and use coordinates to represent the relative positions of the arrays. The position of the first element of each subarray is represented as... ,in, Then the first The spatial relationship between each subarray and the first subarray is expressed as follows: If the platform movement causes an angular deviation between the array's orientation and the horizontal direction, then the first... The angular deviation of each subarray is represented as ;

[0020] Within the subarray, the first The first of the sub-arrays The relative spatial position of each array element to the first array element is represented as follows: ,in, , , Then the array manifold within the subarray is ;

[0021] No. The first of the sub-arrays Individual elements and the first The distance between each array element is , Then the first The element spacing vector of each subarray is ;

[0022] Consider the case where each subarray is a uniform linear array with the same number of elements. And the spacing between each subarray element is ,but , The array manifold of each subarray is ;

[0023] The aperture of the entire distributed array is represented as In dynamic scenarios, platform movement causes unknown positional errors between subarrays. Relative Positional Relationships of Subarrays From precisely known to unknown and the first The unknown angular deviation of the individual array ;

[0024] Construct a distributed array far-field model, considering the placement of all subarrays in... In the case of the axis, the first The position of the first element of each subarray is represented as... ,in , Then the first The spatial relationship between each subarray and the first subarray is expressed as follows: And the arrangement of the subarrays is as follows ,Right now However, without considering the effect of angular deviation, that is ;

[0025] A far-field narrowband signal from the direction Incident on the distributed array; the first The subarray receives the first The sampled data for the second snapshot is as follows:

[0026]

[0027] in, For the first The individual formations The 3D array receives data vectors. for 3D signal vector For the first The individual formations Vaticaned Gaussian noise signal vector , This represents the maximum number of snapshots. For the first The individual formations The dimensional guidance matrix is ​​represented as:

[0028]

[0029]

[0030] in , ,and Indicates the first Each subarray is for the direction of arrival. The array steering vector of the incident narrowband signal, where Indicates the first The phase deviation of each subarray relative to the first subarray. Indicates the first Within the formation The phase deviation of each array element relative to the first array element. , It is a plural unit. The wavelength of the target signal incident on the distributed array.

[0031] Furthermore, step two specifically includes:

[0032] Whitening of sampled data, specifically, involves... A linear transformation is performed to obtain the whitening signal. , For the whitening matrix; calculate Sampling covariance matrix ,right Perform eigenvalue decomposition, i.e. , where the orthogonal matrix Depend on The eigenvectors are composed of a diagonal matrix. The whitening matrix is ​​composed of eigenvalues ​​corresponding to the eigenvectors. The solution method is as follows: when At that time, The eigenvalues ​​in the matrix are sorted from largest to smallest, and the sorted eigenvalues ​​form a matrix. ,Pick middle The average of the smaller eigenvalues ,in for No. Line number If the column elements are defined, then the white noise covariance matrix is ​​estimated as follows: , It is the identity matrix. middle Larger eigenvalues ​​in The corresponding eigenvectors form a matrix Then the whitening matrix is:

[0033]

[0034] in This represents taking the first few elements of a matrix. Before the journey Composed of columns 3D matrix;

[0035] Calculate the whitening signal 4-dimensional cumulant matrix Defined as:

[0036]

[0037] in For any element that is 1, and all other elements that are 0 Wikipedia basis matrix The Line number Column elements, A fourth-order cumulant matrix The Line number Column elements, for The Middle and The fourth-order cumulants of the four components are:

[0038]

[0039] in This represents taking the conjugate value of the complex number. and Representing matrices respectively The Line number Column, No. Line number Column element, first Line number Column and number Line number Column elements, , and Representing matrices respectively The Line number Column and number Line number Column elements, , , , , ;

[0040] Take only one basis matrix This can easily lead to insufficient information in fourth-order cumulants, therefore the basis matrix is... By placing the 1 element in different positions, a set of basis matrices can be constructed. The number of matrices in the basis matrix group is One; construct the objective function based on the cost function of the JADE algorithm, that is:

[0041]

[0042] We need to find the objective function Minimize the matrix ,in This is to extract the sum of squares of the diagonal elements of the matrix.

[0043] Furthermore, step three specifically includes:

[0044] The number of individuals in the quantum case population is The maximum number of iterations for the entire population is , Represents the number of iterations. Representing the spatial dimension of each quantum case, the first one is randomly initialized. The quantum position of each quantum case is , , ;No. The quantum position of a quantum case is then mapped back to the position of the quantum case. The mapping rule is:

[0045]

[0046] in , For the position of quantum case number Upper limit of dimensional variables, For the position of quantum case number Lower bound of dimensional variable ;

[0047] The complex Givens rotation transformation can be expressed as a product of a series of rotation matrices, i.e. ,in This reduces the amount of computation.

[0048]

[0049] That is, a rotation matrix. represent 3D identity matrix represent 3D identity matrix represent 3D identity matrix , The maximum dimension of the separating matrix. and These represent the row and column numbers of the element containing the rotation angle in the rotation matrix, respectively, and the labels are... represent The rotation matrix indices arranged from left to right on the right side of the equals sign, i.e. It is the first one arranged from left to right on the right side of the equal sign. The magnitude of the rotation matrix and the rotation angle. ,and , and It is the first one arranged from left to right on the right side of the equal sign. The three phase rotation angles of the rotation matrix;

[0050] Rotation angle information of the rotation matrix

[0051]

[0052] As the first The generation The location information of a quantum case, that is, by as well as Then we get the first The location of a quantum case The corresponding matrix Based on the above process and objective function, the first... The generation The fitness value of each quantum case is calculated according to the following fitness function;

[0053]

[0054] The fitness value of each quantum case is calculated based on the fitness function, and the positions are sorted according to the fitness value. The quantum position with the smallest fitness value in the quantum case population up to the current generation is found, and the position up to the [number missing]th quantum case is determined. Replace its global optimal quantum position .

[0055] Furthermore, step four specifically includes:

[0056] A random number of quantum cases are randomly selected from the quantum case population to form a quantum infection case population. Then, a random number of quantum cases are randomly selected from the remaining quantum cases to form a quantum susceptible case population. Then, a random number of quantum cases are randomly selected from the remaining quantum cases to form a quantum immune population. ; Initialize the age of the quantum case population, i.e., the first The age of the quantum cases is , The oldest age is Number of outbreaks ;

[0057] No. The quantum position of each quantum case will be related to the probability of infection. Randomly selected and updated, this will generate Random numbers that follow a uniform distribution ,like Furthermore, if quantum infection cases exist, the quantum position is updated using a simulated quantum rotation gate. The r-th dimension quantum rotation angle of the quantum case is updated as follows:

[0058]

[0059] in, Also for Random numbers that follow a uniform distribution. and As a learning factor, The individual labels randomly selected from the quantum infection case population are... Number of outbreaks Then the first The first quantum case The quantum position is updated to:

[0060]

[0061] like And if there are cases of quantum susceptibility, then the first The r-th dimension quantum rotation angle of the quantum case is updated as follows:

[0062]

[0063] in The individual labels randomly selected from the quantum susceptible case population are... Then the first The first quantum case The quantum position is updated to:

[0064]

[0065] like And there are cases of quantum immunity, the first The r-th dimension quantum rotation angle of the quantum case is updated as follows:

[0066]

[0067] The individual labels randomly selected from the quantum immune case population are... Then the first The first quantum case The quantum position is updated to:

[0068]

[0069] like Then the first The first quantum case The quantum position is updated to .

[0070] Furthermore, step five specifically includes:

[0071] The updated number The first quantum case Quantum position Mapped to the first The first quantum case Dimensional position ,Right now According to the fitness function Calculate the first The fitness value of the newly generated position of each quantum case is used, and then a greedy selection strategy is used to select the quantum position of the quantum case, that is, if ,but , If the first In the quantum infection case population, a single quantum case represents a significant portion of the total quantum infection case population. ;

[0072] After the greedy selection, sort the quantum cases according to their fitness values, find the quantum case with the smallest fitness value and record its quantum position, which is the global best quantum position so far. Update this to the global best quantum position. The mapping to the global optimal position is .

[0073] Furthermore, step six specifically includes:

[0074] if , And the If a quantum case is in a population of quantum susceptible cases, then this quantum case transforms into a quantum infected case and is set... =1;

[0075] if And the If a quantum case is present in the quantum infection case population, then this quantum case transforms into a quantum immune case and is set... =0;

[0076] if If this quantum case dies, a new quantum case will be born. This case was then placed into a quantum-susceptible population. for The numbers are random numbers that follow a uniform distribution.

[0077] Furthermore, step eight specifically includes:

[0078] For the recovered source signal Perform normalization, and then estimate the phase deviation between subarrays. ,in For the first The received sampled data of each subarray is obtained as the first Path separation signal, , .

[0079] Furthermore, step nine specifically includes:

[0080] According to the The sampled data received by each subarray Construct the covariance matrix ,right Perform eigenvalue decomposition, i.e. , where the orthogonal matrix Depend on The eigenvectors are composed of a diagonal matrix. It consists of eigenvalues ​​corresponding to the eigenvectors, for Sort the eigenvalues ​​in the dataset from smallest to largest. middle Smaller eigenvalues ​​in The corresponding eigenvectors form the noise subspace matrix. ; build 3D polynomial coefficient matrix;

[0081]

[0082] And by Extracting polynomial coefficients, by The main diagonal is moved to the 1st The polynomial coefficients are obtained by summing the elements along the diagonal. Then, they form a polynomial coefficient vector;

[0083]

[0084] in Indicates moving upwards. This indicates a downward shift; for the polynomial formed by the coefficient vectors of this polynomial, find the root and identify the polynomial whose modulus is closest to 1. root values Then by The obtained number The estimated angles of each subarray are:

[0085]

[0086] in If we are solving for the phase angle function, then from The estimated angle of the entire distributed array is obtained as follows: , Ultimately by The DOA estimation results obtained from the polynomial coefficient matrix are as follows: ,in .

[0087] A computer device / apparatus / system includes a memory, a processor, and a computer program stored in the memory, characterized in that: the processor executes the computer program to implement the steps of a distributed array DOA estimation method.

[0088] The beneficial effects of this invention are as follows:

[0089] (1) The traditional JADE algorithm is prone to getting trapped in local optima and has low accuracy in recovering phase deviation between subarrays under low signal-to-noise ratio conditions, which in turn affects the DOA estimation accuracy of distributed arrays. The present invention designs a quantum coronavirus herd immunity search mechanism, which optimizes the objective function established based on the cost function of the JADE algorithm. The optimization accuracy is higher, the robustness is stronger, and the accuracy of recovering phase deviation between subarrays is improved.

[0090] (2) In the case of multiple targets and low signal-to-noise ratio, the accuracy of the traditional method for azimuth estimation still needs to be improved. The performance of the method is affected by the parameter settings. If the parameters are not set properly, the performance of the method will deteriorate. This invention combines the Root-Music algorithm with the error correction method of distributed arrays, which solves the problem that the performance of the Root-Music algorithm depends on a large amount of observation data. At the same time, it also solves the problem of performance degradation of traditional methods in the case of multiple targets or low signal-to-noise ratio, and realizes high-precision DOA estimation of distributed arrays in the case of small number of snapshots, multiple targets and low signal-to-noise ratio.

[0091] (3) The present invention designs a novel quantum coronavirus herd immunity search mechanism as an evolution strategy, which combines quantum computing theory with the traditional coronavirus herd immunity search mechanism. It uses single-chain quantum coding and simulated quantum rotation gate to design a new quantum position update equation, which can then solve the objective function equation quickly and with high precision. Compared with the traditional coronavirus herd immunity search mechanism, the designed method has a faster convergence speed and higher convergence accuracy. Attached Figure Description

[0092] Figure 1 This is a flowchart of a distributed array DOA estimation method based on the quantum coronavirus herd immunity search mechanism.

[0093] Figure 2 This is a schematic diagram of the positional error of a distributed array.

[0094] Figure 3 It is a distributed array model.

[0095] Figure 4 The graph shows a comparison of the convergence performance of the two search mechanisms.

[0096] Figure 5 The graph shows a comparison of the signal separation accuracy of the two methods as a function of the signal-to-noise ratio.

[0097] Figure 6 The graph shows a comparison of the root mean square error (RMSE) of the two methods as a function of the signal-to-noise ratio. Detailed Implementation

[0098] The present invention will now be further described with reference to the accompanying drawings.

[0099] In the description of this invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

[0100] 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.

[0101] Specific Implementation Plan 1: Combining Figure 1 As shown, this invention provides a distributed array DOA estimation method, comprising the following steps:

[0102] Step 1: Obtain snapshot data of the received signal from each subarray in the distributed array, specifically as follows:

[0103] Consider using in a two-dimensional plane A linear distributed array is used for detection, and each subarray has Each array element, The total number of array elements is expressed as ;

[0104] Construct a planar Cartesian coordinate system, with the reference element position of the first subarray as the origin, and use coordinates to represent the relative positions of the arrays. The position of the first element of each subarray is represented as... ,in, Then the first The spatial relationship between each subarray and the first subarray is expressed as follows: If the platform movement causes an angular deviation between the array's orientation and the horizontal direction, then the first... The angular deviation of each subarray is represented as ;

[0105] Within the subarray, the first The first of the sub-arrays The relative spatial position of each array element to the first array element is represented as follows: ,in, , , Then the array manifold within the subarray is .

[0106] No. The first of the sub-arrays Individual elements and the first The distance between each array element is , Then the first The element spacing vector of each subarray is .

[0107] Consider the case where each subarray is a uniform linear array with the same number of elements. And the spacing between each subarray element is ,but , The array manifold of each subarray is .

[0108] The aperture of the entire distributed array is represented as In dynamic scenarios, platform movement causes unknown positional errors between subarrays. Relative Positional Relationships of Subarrays From precisely known to unknown and the first The unknown angular deviation of the individual array .

[0109] Construct a distributed array far-field model, considering the placement of all subarrays in... In the case of the axis, the first The position of the first element of each subarray is represented as... ,in , Then the first The spatial relationship between each subarray and the first subarray is expressed as follows: And the arrangement of the subarrays is as follows ,Right now However, without considering the effect of angular deviation, that is .

[0110] A far-field narrowband signal from the direction Incident on the distributed array. The subarray receives the first The sampled data for the second quick snapshot is

[0111]

[0112] in For the first The individual formations The 3D array receives data vectors. for 3D signal vector For the first The individual formations Vaticaned Gaussian noise signal vector , This represents the maximum number of snapshots. For the first The individual formations The dimensional guidance matrix is ​​represented as

[0113]

[0114]

[0115] in , ,and Indicates the first Each subarray is for the direction of arrival. The array steering vector of the incident narrowband signal, where Indicates the first The phase deviation of each subarray relative to the first subarray. Indicates the first Within the formation The phase deviation of each array element relative to the first array element. , It is a plural unit. The wavelength of the target signal incident on the distributed array.

[0116] Step two involves whitening the sampled data received by the subarray and constructing the objective function based on the cost function of the JADE algorithm. Specifically, this includes...

[0117] Whitening of sampled data, specifically, involves... A linear transformation is performed to obtain the whitening signal. , This is the whitening matrix. Calculate... Sampling covariance matrix ,right Perform eigenvalue decomposition, i.e. , where the orthogonal matrix Depend on The eigenvectors are composed of a diagonal matrix. The whitening matrix is ​​composed of eigenvalues ​​corresponding to the eigenvectors. The solution method is as follows: when At that time, The eigenvalues ​​in the matrix are sorted from largest to smallest, and the sorted eigenvalues ​​form a matrix. ,Pick middle The average of the smaller eigenvalues ,in for No. Line number If the column elements are defined, then the white noise covariance matrix is ​​estimated as follows: , It is the identity matrix. middle Larger eigenvalues ​​in The corresponding eigenvectors form a matrix Then the whitening matrix is

[0118]

[0119] in This represents taking the first few elements of a matrix. Before the journey Composed of columns 3D matrix.

[0120] Calculate the whitening signal 4-dimensional cumulant matrix Defined as

[0121]

[0122] in For any element that is 1, and all other elements that are 0 Wikipedia basis matrix The Line number Column elements, A fourth-order cumulant matrix The Line number Column elements, for The Middle and The fourth-order cumulant of the four components, i.e.

[0123]

[0124] in This represents taking the conjugate value of the complex number. and Representing matrices respectively The Line number Column, No. Line number Column element, first Line number Column and number Line number Column elements, , and Representing matrices respectively The Line number Column and number Line number Column elements, , , , , .

[0125] Take only one basis matrix This can easily lead to insufficient information in fourth-order cumulants, therefore the basis matrix is... By placing the 1 element in different positions, a set of basis matrices can be constructed. The number of matrices in the basis matrix group is One. Construct the objective function based on the cost function of the JADE algorithm, i.e.

[0126]

[0127] We need to find the objective function Minimize the matrix ,in This is to extract the sum of squares of the diagonal elements of the matrix.

[0128] Step 3 involves constructing and calculating the fitness of quantum cases to determine the globally optimal quantum position, specifically including:

[0129] The number of individuals in the quantum case population is The maximum number of iterations for the entire population is , Represents the number of iterations. Representing the spatial dimension of each quantum case, the first is randomly initialized. The quantum position of each quantum case is , , ;No. The quantum position of a quantum case is then mapped back to the position of the quantum case. The mapping rule is

[0130]

[0131] in , For the position of quantum case number Upper limit of dimensional variables, For the position of quantum case number Lower bound of dimensional variable .

[0132] The complex Givens rotation transformation can be represented as a product of a series of rotation matrices, i.e. ,in This reduces the amount of computation.

[0133]

[0134] That is, a rotation matrix. represent 3D identity matrix represent 3D identity matrix represent 3D identity matrix , The maximum dimension of the separating matrix. and These represent the row and column numbers of the element containing the rotation angle in the rotation matrix, respectively, and the labels are... represent The rotation matrix indices arranged from left to right on the right side of the equals sign, i.e. It is the first one arranged from left to right on the right side of the equal sign. The magnitude of the rotation matrix and the rotation angle. ,and , and It is the first one arranged from left to right on the right side of the equal sign. The three phase rotation angles of the rotation matrix.

[0135] Rotation angle information of the rotation matrix

[0136]

[0137] As the first The generation The location information of a quantum case, that is, by as well as You can get the first The location of a quantum case The corresponding matrix Based on the above process and objective function, the first... The generation The fitness value of a quantum case can be calculated using the following fitness function.

[0138]

[0139] The fitness value of each quantum case is calculated based on the fitness function, and the positions are sorted according to the fitness value. The quantum position with the smallest fitness value in the quantum case population up to the current generation is found, and the position up to the [number missing]th quantum case is determined. Replace its global optimal quantum position ;

[0140] Step four, update the quantum position of each quantum case in the quantum case population, specifically including,

[0141] A random number of quantum cases are randomly selected from the quantum case population to form a quantum infection case population. Then, a random number of quantum cases are randomly selected from the remaining quantum cases to form a quantum susceptible case population. Then, a random number of quantum cases are randomly selected from the remaining quantum cases to form a quantum immune population. Initialize the age of the quantum case population, i.e., the [number]th [case]. The age of the quantum cases is , The oldest age is Number of outbreaks .

[0142] No. The quantum position of each quantum case will be related to the probability of infection. Randomly selected and updated, this will generate Random numbers that follow a uniform distribution ,like Furthermore, if quantum infection cases exist, the quantum position is updated using a simulated quantum rotation gate. The r-th dimension quantum rotation angle of the quantum case is updated to...

[0143]

[0144] in, Also for Random numbers that follow a uniform distribution. and As a learning factor, The individual labels randomly selected from the quantum infection case population are... Number of outbreaks Then the first The first quantum case The quantum position can be updated to

[0145]

[0146] like And if there are cases of quantum susceptibility, then the first The r-th dimension quantum rotation angle of the quantum case is updated to...

[0147]

[0148] in The individual labels randomly selected from the quantum susceptible case population are... Then the first The first quantum case The quantum position can be updated to

[0149]

[0150] like And there are cases of quantum immunity, the first The r-th dimension quantum rotation angle of the quantum case is updated to...

[0151]

[0152] The individual labels randomly selected from the quantum immune case population are... Then the first The first quantum case The quantum position can be updated to

[0153]

[0154] like Then the first The first quantum case The quantum position is updated to .

[0155] Step 5 involves mapping the updated quantum case's quantum position to a quantum case position, calculating the fitness value of the new quantum case position based on the fitness function, and then updating the globally optimal quantum position. Specifically, this includes...

[0156] The updated number The first quantum case Quantum position Mapped to the first The first quantum case Dimensional position ,Right now According to the fitness function Calculate the first The fitness value of the newly generated position of each quantum case is used, and then a greedy selection strategy is used to select the quantum position of the quantum case, that is, if ,but , If the first In the quantum infection case population, a single quantum case represents a significant portion of the total quantum infection case population. .

[0157] After the greedy selection, sort the quantum cases according to their fitness values, find the quantum case with the smallest fitness value and record its quantum position, which is the global best quantum position so far. Update this to the global best quantum position. The mapping to the global optimal position is .

[0158] Step six: Complete the quantum case state transition based on the fitness value of the new quantum case location, specifically including:

[0159] if , And the If a quantum case is in a population of quantum susceptible cases, then this quantum case transforms into a quantum infected case and is set... =1;

[0160] if And the If a quantum case is present in the quantum infection case population, then this quantum case transforms into a quantum immune case and is set... =0;

[0161] if If this quantum case dies, a new quantum case will be born. This case was then placed into a quantum-susceptible population. for The numbers are random numbers that follow a uniform distribution.

[0162] Step 7: Determine if the iterative model has reached its maximum number of iterations. If not achieved, then If the result is positive, return to step four and continue iterating; otherwise, output the globally optimal position. and its corresponding optimal matrix This leads to the hybrid matrix. estimation matrix The source signal was recovered. ,in This represents the pseudo-inverse matrix of the matrix.

[0163] Step eight involves normalizing the recovered source signal and then estimating the phase deviation between subarrays, specifically including...

[0164] For the recovered source signal Perform normalization, and then estimate the phase deviation between subarrays. ,in For the first The received sampled data of each subarray is obtained as the first Path separation signal, , .

[0165] Step nine: Substitute the estimated inter-subarray phase deviation into the Root-Music algorithm to achieve DOA estimation based on the distributed array.

[0166] According to the The sampled data received by each subarray Construct the covariance matrix ,right Perform eigenvalue decomposition, i.e. , where the orthogonal matrix Depend on The eigenvectors are composed of a diagonal matrix. It consists of eigenvalues ​​corresponding to the eigenvectors, for Sort the eigenvalues ​​in the dataset from smallest to largest. middle Smaller eigenvalues ​​in The corresponding eigenvectors form the noise subspace matrix. Build dimensional polynomial coefficient matrix

[0167]

[0168] And by Extracting polynomial coefficients, by The main diagonal is moved to the 1st The polynomial coefficients are obtained by summing the elements along the diagonal. Then, they form a polynomial coefficient vector.

[0169]

[0170] in Indicates moving upwards. This indicates a downward shift. Find the roots of the polynomial formed by the coefficient vectors of this polynomial, and identify the polynomial whose modulus is closest to 1. root values Then by The obtained number The estimated angle of each subarray is:

[0171]

[0172] in If we are solving for the phase angle function, then from The estimated angle of the entire distributed array is obtained as follows: , Ultimately by The DOA estimation results obtained from the polynomial coefficient matrix are as follows: ,in .

[0173] Specific Implementation Method Two: Combining Figure 1 As shown, the present invention provides a distributed array DOA estimation system, which has a program module corresponding to the above steps, and executes the steps in the above distributed array DOA estimation method when running.

[0174] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0175] Specific Implementation Method 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement the steps of a distributed array DOA estimation method when called by a processor.

[0176] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0177] Simulation Experiment

[0178] The parameters for the distributed array model are set as follows: the number of subarrays in the distributed array is... Each subarray is Each array element is a uniform linear array, and the wavelength of the target signal incident on the distributed array is... The spacing between each subarray element is 1. The entire distributed array aperture Number of sources , , ,in for Random numbers that follow a uniform distribution, snapshot number , .

[0179] For ease of description, the quantum coronavirus herd immunity search mechanism will be abbreviated as QCHIO, and the coronavirus herd immunity search mechanism will be abbreviated as CHIO. The QCHIO parameters are set as follows: , , , , , , .

[0180] For CHIO parameter settings, see "Coronavirus herd immunity optimizer (CHIO)" published in Neural Computing and Applications by Mohammed Azmi Al-Betar et al. Other parameters, such as population size and number of iterations, are the same as those in QCHIO.

[0181] Combination Figure 4 As shown, Figure 4 The curves showing the change of the objective function values ​​of QCHIO and CHIO with the number of iterations are compared. The maximum number of iterations is set to 200, the population size is set to 20, and the simulation results are the average of 50 independent experiments. Compared with CHIO, it can be seen that QCHIO exhibits superior convergence performance, ensuring faster convergence accuracy while achieving higher convergence accuracy.

[0182] For ease of description, the QCHIO-based inter-subarray phase offset recovery method will be abbreviated as QCHIO-BSS, and the JADE-based inter-subarray phase offset recovery method will be abbreviated as BSS. The correlation coefficient will be selected. To evaluate the performance of source signal recovery methods, the closer the correlation coefficient is to 1, the closer the recovered source signal is to the original signal, and the higher the accuracy of the method. This represents the recovered source signal.

[0183] Combination Figure 5 As shown, Figure 5 The graphs show the signal separation accuracy of QCHIO-BSS and BSS as a function of signal-to-noise ratio. The experimental results at the same signal-to-noise ratio are the average of 100 independent runs. It can be seen that QCHIO-BSS can achieve better source signal recovery than BSS, thereby improving the recovery accuracy of phase deviation between subarrays.

[0184] For ease of description, the QCHIO-based distributed array DOA estimation method is abbreviated as QCHIO-BSS-Root-Music, and the matched-filter-based distributed array DOA estimation method is abbreviated as BSS-MF. The parameter settings for BSS-MF can be found in "Direction finding in partly calibrated arrays exploiting the whole arrayaperture" published by Guangbin Zhang et al. in *IEEE Transactions on Aerospace and Electronic Systems*. Root mean square error is selected. As an indicator for evaluating the accuracy of DOA estimation methods, among which, For the number of experiments, For the first The results of the second experiment on orientation estimation. This represents the true value of the target orientation.

[0185] Combination Figure 6 The figure shows a comparison of the DOA estimation accuracy of the QCHIO-BSS-Root-Music and BSS-MF methods as a function of signal-to-noise ratio. At the same signal-to-noise ratio... It can be seen that, compared to BSS-MF, QCHIO-BSS-Root-Music achieves higher DOA estimation accuracy under low signal-to-noise ratio conditions.

[0186] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for estimating the DOA of a distributed array, characterized in that, Includes the following steps: Step 1: Obtain snapshot sampling data of the received signal from each subarray in the distributed array; Step 2: Whiten the sampled data received by the subarray, and construct the objective function based on the cost function of the JADE algorithm; Step 3: Construct and calculate the fitness of quantum cases to determine the globally optimal quantum position; Step 4: Update the quantum position of each quantum case in the quantum case population; Step 5: Map the updated quantum case's quantum position to the quantum case position, calculate the fitness value of the new quantum case position according to the fitness function, and then update the global optimal quantum position; Step Six: Complete the quantum case state transition based on the fitness value of the new quantum case location; Step 7: Determine if the iterative model has reached its maximum number of iterations; if not, return to step 4 to iterate again; otherwise, output the global optimal position and its corresponding optimal matrix, and then obtain the estimated matrix of the mixture matrix to recover the source signal. Step 8: Normalize the recovered source signal and then estimate the phase deviation between subarrays; Step 9: Substitute the estimated inter-subarray phase deviation into the Root-Music algorithm to achieve DOA estimation based on distributed arrays.

2. The distributed array DOA estimation method according to claim 1, characterized in that: Step one specifically includes: Consider using in a two-dimensional plane A linear distributed array is used for detection, and each subarray has Each array element, The total number of array elements is expressed as ; Construct a planar Cartesian coordinate system, with the reference element position of the first subarray as the origin, and use coordinates to represent the relative positions of the arrays. The position of the first element of each subarray is represented as... ,in, Then the first The spatial relationship between each subarray and the first subarray is expressed as follows: If the platform movement causes an angular deviation between the array's orientation and the horizontal direction, then the first... The angular deviation of each subarray is represented as ; Within the subarray, the first The first of the sub-arrays The relative spatial position of each array element to the first array element is represented as follows: ,in, , , Then the array manifold within the subarray is ; No. The first of the sub-arrays Each element and the first The distance between each array element is , Then the first The element spacing vector of each subarray is ; Consider the case where each subarray is a uniform linear array with the same number of elements. And the spacing between each subarray element is ,but , The array manifold of each subarray is ; The aperture of the entire distributed array is represented as In dynamic scenarios, platform movement causes unknown positional errors between subarrays. Relative Positional Relationships of Subarrays From precisely known to unknown and the first The unknown angular deviation of the individual array ; Construct a distributed array far-field model, considering the placement of all subarrays in... In the case of the axis, the first The position of the first element of each subarray is represented as... ,in , Then the first The spatial relationship between each subarray and the first subarray is expressed as follows: And the arrangement of the subarrays is as follows ,Right now However, without considering the effect of angular deviation, that is ; A far-field narrowband signal from the direction Incident on the distributed array; the first The subarray receives the first The sampled data for the second snapshot is as follows: in, For the first The individual formations The 3D array receives data vectors. for 3D signal vector For the first The individual formations Vaticaned Gaussian noise signal vector , This represents the maximum number of snapshots. For the first The individual formation The dimensional guidance matrix is ​​represented as: in, , ,and Indicates the first Each subarray is for the direction of arrival. The array steering vector of the incident narrowband signal, where Indicates the first The phase deviation of each subarray relative to the first subarray. Indicates the first Within the formation The phase deviation of each array element relative to the first array element. , It is a plural unit. The wavelength of the target signal incident on the distributed array.

3. The distributed array DOA estimation method according to claim 2, characterized in that: Step two specifically includes: The specific method for whitening the sampled data is to... A linear transformation is performed to obtain the whitening signal. , For the whitening matrix; calculate Sampling covariance matrix ,right Perform eigenvalue decomposition, i.e. , where the orthogonal matrix Depend on The eigenvectors are composed of a diagonal matrix. The whitening matrix is ​​composed of eigenvalues ​​corresponding to the eigenvectors. The solution method is as follows: when At that time, The eigenvalues ​​in the matrix are sorted from largest to smallest, and the sorted eigenvalues ​​form a matrix. ,Pick middle The average of the smaller eigenvalues ,in for No. Line 1 If the column elements are defined, then the white noise covariance matrix is ​​estimated as follows: , It is the identity matrix. middle Larger eigenvalues ​​in The corresponding eigenvectors form a matrix Then the whitening matrix is: in This represents taking the first few elements of a matrix. Before the journey Composed of columns 3D matrix; Calculate the whitening signal 4-dimensional cumulant matrix Defined as: in For any element that is 1 and all other elements that are 0 Wikipedia basis matrix The Line 1 Column elements, A fourth-order cumulant matrix The Line 1 Column elements, for The Middle and The fourth-order cumulants of the four components are: in This represents taking the conjugate value of the complex number. and Representing matrices respectively The Line 1 Column, No. Line 1 Column element, first Line 1 Column and number Line 1 Column elements, , and Representing matrices respectively The Line 1 Column and number Line 1 Column elements, , , , , ; Take only one basis matrix This can easily lead to insufficient information in fourth-order cumulants, therefore the basis matrix is... By placing the 1 element in different positions, a set of basis matrices can be constructed. The number of matrices in the basis matrix group is One; construct the objective function based on the cost function of the JADE algorithm, that is: We need to find the objective function Minimized matrix ,in This is to extract the sum of squares of the diagonal elements of the matrix.

4. The distributed array DOA estimation method according to claim 1, characterized in that: Step three specifically includes: The number of individuals in the quantum case population is The maximum number of iterations for the entire population is , Represents the number of iterations. Representing the spatial dimension of each quantum case, the first one is randomly initialized. The quantum position of each quantum case is , , ;No. The quantum position of a quantum case is then mapped back to the position of the quantum case. The mapping rule is: in , For the position of quantum case number Upper limit of dimensional variables, For the position of quantum case number Lower bound of dimensional variable ; The complex Givens rotation transformation can be expressed as a product of a series of rotation matrices, i.e. ,in This reduces the amount of computation. That is, a rotation matrix. represent 3D identity matrix represent 3D identity matrix represent 3D identity matrix , The maximum dimension of the separating matrix. and These represent the row and column numbers of the element containing the rotation angle in the rotation matrix, respectively, and the labels are... represent The rotation matrix indices arranged from left to right on the right side of the equals sign, i.e. It is the first one arranged from left to right on the right side of the equal sign. The magnitude of the rotation matrix and the rotation angle. ,and , and It is the first one arranged from left to right on the right side of the equal sign. The three phase rotation angles of the rotation matrix; Rotation angle information of the rotation matrix As the first The generation The location information of a quantum case, that is, by as well as Then we get the first The location of a quantum case The corresponding matrix Based on the above process and objective function, the first... The generation The fitness value of each quantum case is calculated according to the following fitness function; The fitness value of each quantum case is calculated based on the fitness function, and the positions are sorted according to the fitness value. The quantum position with the smallest fitness value in the quantum case population up to the current generation is found, and the position up to the [number missing]th quantum case is determined. Replace its global optimal quantum position .

5. The distributed array DOA estimation method according to claim 4, characterized in that: Step four specifically includes: A random number of quantum cases are randomly selected from the quantum case population to form a quantum infection case population. Then, a random number of quantum cases are randomly selected from the remaining quantum cases to form a quantum susceptible case population. Then, a random number of quantum cases are randomly selected from the remaining quantum cases to form a quantum immune population. ; Initialize the age of the quantum case population, i.e., the first The age of the quantum cases is , The oldest age is Number of COVID-19 outbreaks ; No. The quantum position of each quantum case will be related to the probability of infection. Randomly selected and updated, this will generate Random numbers that follow a uniform distribution ,like Furthermore, if quantum infection cases exist, the quantum position is updated using a simulated quantum rotation gate. The r-th dimension quantum rotation angle of the quantum case is updated as follows: in, Also for Random numbers that follow a uniform distribution. and As a learning factor, The individual labels randomly selected from the quantum infection case population are... Number of COVID-19 outbreaks Then the first The first quantum case The quantum position is updated to: like And if there are cases of quantum susceptibility, then the first The r-th dimension quantum rotation angle of the quantum case is updated as follows: in The individual labels randomly selected from the quantum susceptible case population are... Then the first The first quantum case The quantum position is updated to: like And there are cases of quantum immunity, the first The r-th dimension quantum rotation angle of the quantum case is updated as follows: The individual labels randomly selected from the quantum immune case population are... Then the first The first quantum case The quantum position is updated to: like Then the first The first quantum case The quantum position is updated to .

6. The distributed array DOA estimation method according to claim 5, characterized in that: Step five specifically includes: The updated number The first quantum case Quantum position Mapped to the first The first quantum case Dimensional position ,Right now According to the fitness function Calculate the first The fitness value of the newly generated position of each quantum case is used, and then a greedy selection strategy is used to select the quantum position of the quantum case, that is, if ,but , If the first In the quantum infection case population, a single quantum case represents a significant portion of the total quantum infection case population. ; After the greedy selection, sort the quantum cases according to their fitness values, find the quantum case with the smallest fitness value and record its quantum position, which is the global best quantum position so far. Update this to the global best quantum position. The mapping to the global optimal position is .

7. A distributed array DOA estimation method according to claim 6, characterized in that: Step six specifically includes: if , And the If a quantum case is in a population of quantum susceptible cases, then this quantum case transforms into a quantum infected case and is set... =1; if And the If a quantum case is present in the quantum infection case population, then this quantum case transforms into a quantum immune case and is set... =0; if If this quantum case dies, a new quantum case will be born. This case was then placed into a quantum-susceptible population. for The numbers are random numbers that follow a uniform distribution.

8. A distributed array DOA estimation method according to claim 2, characterized in that: Step eight specifically includes: For the recovered source signal Perform normalization, and then estimate the phase deviation between subarrays. ,in For the first The received sampled data of each subarray is obtained as the first Path separation signal, , , express Each far-field narrowband signal corresponds to A separate signal.

9. A distributed array DOA estimation method according to claim 8, characterized in that: Step nine specifically includes: According to the The sampled data received by each subarray Construct the covariance matrix ,right Perform eigenvalue decomposition, i.e. , where the orthogonal matrix Depend on The eigenvectors are composed of a diagonal matrix. It consists of eigenvalues ​​corresponding to the eigenvectors, for Sort the eigenvalues ​​in the dataset from smallest to largest. middle Smaller eigenvalues ​​in The corresponding eigenvectors form the noise subspace matrix. ; build Multidimensional polynomial coefficient matrix: And by Extracting polynomial coefficients, by The main diagonal is moved to the 1st The polynomial coefficients are obtained by summing the elements along the diagonal. Then, the polynomial coefficient vector is formed: in Indicates moving upwards. This indicates a downward shift; for the polynomial formed by the coefficient vectors of this polynomial, find the root and identify the polynomial whose modulus is closest to 1. root values Then by The obtained number The estimated angles of each subarray are: in If we are solving for the phase angle function, then from The estimated angle of the entire distributed array is obtained as follows: , Ultimately by The DOA estimation results obtained from the polynomial coefficient matrix are as follows: ,in .

10. A system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 9.

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