A few-channel switching direction finding method based on blind source separation
By employing a few-channel switching direction finding method based on blind source separation, and utilizing a uniform circular array and signal matrix processing, the accuracy and real-time performance issues of existing direction finding schemes in complex environments are resolved, achieving high-precision and interference-resistant direction finding results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-05-26
- Publication Date
- 2026-07-21
AI Technical Summary
Existing multi-channel direction finding schemes lack sufficient direction finding accuracy in complex airborne environments, have weak anti-interference capabilities, and have complex channel switching logic, failing to meet the high precision and real-time requirements of aviation search and rescue.
A few-channel switching direction finding method based on blind source separation is adopted. By uniform circular array setup, array element switching, signal matrix preprocessing, blind source separation and array manifold matrix calibration, the total array manifold matrix is constructed for direction of arrival estimation.
It improves direction finding accuracy and robustness, enhances noise interference resistance, simplifies channel switching logic, and meets the high precision and real-time requirements of aerial search and rescue.
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Figure CN122260219B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of emergency search and rescue direction finding technology, and in particular to a few-channel switching direction finding method based on blind source separation. Background Technology
[0002] In emergency search and rescue operations, obtaining direction-finding information of the target is a prerequisite for carrying out subsequent rescue work. Among them, airborne platform direction-finding technology has been widely used in scenarios such as aerial search and rescue and emergency communications due to its advantages such as simple equipment deployment, low implementation cost, wide coverage, and fast response speed.
[0003] In the field of airborne platform direction finding, traditional direction finding schemes typically adopt a "full-element, full-channel" architecture design, which means configuring the same number of receiving channels as the number of elements in the antenna array, with each element corresponding to an independent receiving channel. Traditional direction finding schemes can directly acquire signal data from all antenna elements, thereby obtaining a complete signal covariance matrix. Direction finding calculations can be performed without multiple signal switching and covariance matrix reconstruction, giving them an advantage in direction finding accuracy compared to multi-channel direction finding systems.
[0004] However, traditional direction finding solutions suffer from problems such as bulky equipment, limited installation flexibility, and high cost. To overcome these issues, engineers have proposed a few-channel direction finding solution, attempting to reduce the number of receiving channels while maintaining a certain direction finding performance, thereby achieving equipment miniaturization and cost reduction. This would balance direction finding performance and equipment feasibility. However, existing few-channel direction finding solutions have significant technical shortcomings and cannot meet the needs of complex application scenarios such as airborne platforms, specifically:
[0005] First, the direction-finding accuracy is limited, and the anti-interference capability is weak. The application environment of airborne platforms is complex, with severe noise interference, multipath propagation interference, and other interference factors. Existing few-channel direction-finding algorithms have weak ability to suppress these interference factors and are easily affected by interference factors in complex airborne environments, leading to a decrease in the accuracy of covariance matrix reconstruction. This, in turn, results in large errors in the direction-finding results, making it difficult to meet the high-precision target positioning requirements of aerial search and rescue, and may even lead to delays or failures in search and rescue operations. Especially in low signal-to-noise ratio environments, the direction-finding performance of existing few-channel direction-finding algorithms will be further reduced, making it impossible to effectively distinguish target signals from interference signals, and making it difficult to achieve accurate positioning of search and rescue targets. At the same time, the antenna array of airborne platforms is prone to mutual coupling problems between array elements, resulting in a deviation between the actual array manifold and the theoretical array manifold, which will further exacerbate the accuracy loss of existing few-channel direction-finding algorithms.
[0006] Secondly, the channel switching logic is complex and involves numerous switching operations. Existing few-channel direction finding solutions require multiple switching of receiving channels to collect signal data from different antenna array elements, followed by stitching and reconstruction of this data to obtain a complete covariance matrix for direction finding calculation. However, the channel switching process lacks optimization, resulting in complex switching logic and excessive switching operations. This not only increases the time cost of signal acquisition and reduces the direction finding response speed, but may also further affect direction finding accuracy due to signal loss and synchronization errors during channel switching. This makes it unsuitable for the dual requirements of real-time and accuracy in direction finding for aerial search and rescue operations. Furthermore, the complex switching logic increases the cost and implementation difficulty of equipment engineering.
[0007] Therefore, it is necessary to propose a solution to improve one or more problems existing in the above-mentioned related technical solutions.
[0008] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention
[0009] This application provides a few-channel switching direction finding method based on blind source separation, which includes the following steps:
[0010] The uniform circular array is set to a few-channel receiving mode, and at each array element switch, the corresponding array element group is used to simultaneously receive signals from multiple rescue targets to form the corresponding original signal matrix.
[0011] Each original signal matrix is preprocessed to obtain the standard signal matrix corresponding to each array element switching;
[0012] Blind source separation is performed on each standard signal matrix using the joint approximate diagonalization algorithm of the feature matrix, resulting in the corresponding separation matrix and separated signal matrix.
[0013] The generalized inverse matrix of each separation matrix is taken as the corresponding array manifold matrix, and the waveform correlation coefficient between the separation signal vector of each row of each separation signal matrix and the separation signal vector of all rows of all other separation signal matrices is calculated.
[0014] Based on all waveform correlation coefficients, cluster registration is performed on each separated signal matrix to construct the permutation matrix corresponding to each array element switching. Then, each permutation matrix is used to align the corresponding array manifold matrix to obtain the aligned array manifold matrix corresponding to each array element switching.
[0015] Arbitrarily select one array element from all array elements as the reference array element, and arbitrarily select an aligned array manifold matrix containing the reference array element as the base matrix.
[0016] Using the reference matrix, construct the diagonal parameter transformation matrix corresponding to each of the remaining aligned array manifold matrices, and use each diagonal parameter transformation matrix to perform amplitude calibration on the corresponding aligned array manifold matrix to obtain the calibration array manifold matrix corresponding to each array element switch;
[0017] Based on the physical order of all array elements in the uniform circular array, all calibration array manifold matrices are merged into a total array manifold matrix, and the direction of arrival is estimated for each rescue target using the total array manifold matrix.
[0018] Furthermore, each original signal matrix includes a binary phase shift keying signal, a linear frequency modulation signal, and a single-carrier signal.
[0019] Further, the steps of preprocessing each original signal matrix to obtain the standard signal matrix corresponding to each element switching include:
[0020] Each original signal matrix is subjected to mean-removal processing to obtain the zero-mean signal matrix corresponding to each array element switch;
[0021] The expression for the zero-mean signal matrix is:
[0022] (1)
[0023] in, Indicates the first The zero-mean signal matrix corresponding to the secondary array element switching , express 3D real space, This indicates the total number of array elements during each array element switch. This indicates the number of all sampling points during each array element switch. Indicates the first The secondary array element switches correspond to the original signal matrix. , express A column vector of all 1s Indicates transpose;
[0024] According to the array element switching order, all zero-mean signal matrices are vertically spliced to obtain the intermediate signal matrix, and the sample covariance matrix is calculated using the intermediate signal matrix.
[0025] The expression for the sample covariance matrix is:
[0026] (2)
[0027] in, Represents the sample covariance matrix. Represents the intermediate signal matrix. This represents the conjugate transpose of the intermediate signal matrix;
[0028] Perform eigenvalue decomposition on the sample covariance matrix and sort all the obtained eigenvalues in descending order;
[0029] The expression for eigenvalue decomposition of the sample covariance matrix is as follows:
[0030] (3)
[0031] in, This represents the eigenvector obtained by eigenvalue decomposition of the sample covariance matrix. This represents the diagonal matrix of eigenvalues obtained by eigenvalue decomposition of the sample covariance matrix. , Represents a diagonal matrix function. The eigenvalue decomposition of the sample covariance matrix is represented by the eigenvalue decomposition of the sample covariance matrix. eigenvalues, , This indicates the total number of array element switching. This represents the conjugate transpose of the eigenvectors obtained by eigenvalue decomposition of the sample covariance matrix;
[0032] The number of all rescue targets can be determined using information theory criteria or eigenvalue thresholding.
[0033] Based on the total number of all rescue targets, all feature values sorted in descending order are divided into two groups. The first group includes the previous... The second group includes the following feature values. There are 10 characteristic values. All characteristic values in the first group are used as signal characteristic values, and all characteristic values in the second group are used as noise characteristic values. The total number of signal characteristic values is equal to the total number of rescue targets.
[0034] The average of all noise features is used as the global noise variance estimate.
[0035] The expression for the global noise variance estimate is:
[0036] (4)
[0037] in, This represents the estimated global noise variance. Indicates the first One eigenvalue;
[0038] Each zero-mean signal matrix is whitened using the global noise variance estimate to obtain the standard signal matrix corresponding to each element switching.
[0039] Furthermore, the steps of whitening each zero-mean signal matrix using the global noise variance estimate to obtain the standard signal matrix corresponding to each element switch include:
[0040] Calculate the covariance matrix corresponding to each array element switch using the zero-mean signal matrix corresponding to each array element switch.
[0041] The expression for the covariance matrix is:
[0042] (5)
[0043] in, Indicates the first The covariance matrix corresponding to the next element switching is changed. Indicates the first The conjugate transpose of the zero-mean signal matrix corresponding to the element switching;
[0044] Denoise each covariance matrix using the global noise variance estimate to obtain the partial covariance matrix corresponding to each element switching.
[0045] The expression for the partial covariance matrix is as follows:
[0046] (6)
[0047] in, Indicates the first The partial covariance matrix corresponding to the element switching of the next array element Represents the identity matrix;
[0048] Eigenvalue decomposition is performed on each part of the covariance matrix, and the corresponding whitening matrix is constructed using the obtained eigenvalue decomposition results.
[0049] The expression for eigenvalue decomposition of a partial covariance matrix is as follows:
[0050] (7)
[0051] in, Indicates the first The eigenvectors are obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching. Indicates the first The eigenvalue diagonal matrix is obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching. Indicates the first The conjugate transpose of the eigenvectors obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching of the second array;
[0052] The expression for the whitening matrix is:
[0053] (8)
[0054] in, Indicates the first The whitening matrix corresponding to the secondary array element switching;
[0055] Each whitening matrix is multiplied by its corresponding zero-mean signal matrix to obtain the standard signal matrix corresponding to each element switching.
[0056] The expression for the standard signal matrix is:
[0057] (9)
[0058] in, Indicates the first The standard signal matrix corresponding to the switching of secondary array elements.
[0059] Furthermore, the steps of performing blind source separation on each standard signal matrix using the characteristic matrix joint approximate diagonalization algorithm to obtain the corresponding separation matrix and separated signal matrix include:
[0060] Calculate a set of fourth-order cumulant matrices for each standard signal matrix. Each fourth-order cumulant matrix in the same set corresponds to a row of standard signal vectors in the corresponding standard signal matrix.
[0061] The joint approximate diagonalization algorithm of the characteristic matrix is used to perform joint approximate diagonalization on each group of fourth-order cumulant matrices to obtain the orthogonal rotation matrix corresponding to each array element switch, and to minimize the sum of the squares of the moduli of all transformation matrices obtained by performing similarity transformation on the corresponding group of fourth-order cumulant matrices through each orthogonal rotation matrix.
[0062] Multiply each orthogonal rotation matrix by its corresponding whitening matrix to obtain the separation matrix for each element switching;
[0063] The expression for the separation matrix is:
[0064] (10)
[0065] in, Indicates the first The secondary array element switches correspond to the separation matrix. Indicates the first The whitening matrix corresponding to the next element switching is used. Indicates the first The conjugate transpose of the orthogonal rotation matrix corresponding to the element switching;
[0066] Each separation matrix is multiplied by its corresponding zero-mean signal matrix to obtain the separation signal matrix corresponding to each element switching.
[0067] The expression for the separated signal matrix is:
[0068] (11)
[0069] in, Indicates the first The secondary array element switching corresponds to the separation signal matrix. , Indicates the first The standard signal matrix corresponding to the switching of secondary array elements. Indicates the first The zero-mean signal matrix corresponding to the switching of the secondary array elements.
[0070] Furthermore, the expression for the array manifold matrix is:
[0071] (12)
[0072] in, Indicates the first The array manifold matrix corresponding to the next array element switching. Represents the generalized inverse operation;
[0073] The expression for the waveform correlation coefficient is:
[0074] (13)
[0075] in, Indicates the first The first element switching of the secondary array The line-separated signal vector and the first The first element switching of the secondary array The waveform correlation coefficient between the line-separated signal vectors Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The value of each sampling point, Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The value of each sampling point, Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The complex conjugate of the values at each sampling point This represents the modulo operation. Indicates the first The first element switching of the secondary array The total energy of the line-separated signal vector. Indicates the first The first element switching of the secondary array The total energy of the row-separated signal vector.
[0076] Furthermore, based on all waveform correlation coefficients, the steps of clustering and registering each separated signal matrix to construct the permutation matrix corresponding to each element switching include:
[0077] Based on all waveform correlation coefficients, cluster and register all the separate signal vectors with the same waveform correlation coefficient from all the separate signal matrices to determine the separate signal vector corresponding to each rescue target at each array element switch;
[0078] The order of all separated signal vectors in the separated signal matrix corresponding to the first array element switch is used as a reference standard, and the corresponding permutation matrix is constructed according to the clustering registration results corresponding to each array element switch.
[0079] Furthermore, the steps of aligning the corresponding array manifold matrix with each permutation matrix to obtain the aligned array manifold matrix for each element switching include:
[0080] Each permutation matrix is used to align the corresponding array manifold matrix in the column dimension to obtain the aligned array manifold matrix corresponding to each array element switch.
[0081] The expression for the aligned array manifold matrix is:
[0082] (14)
[0083] in, Indicates the first The alignment array manifold matrix corresponding to the secondary array element switching Indicates the first The array manifold matrix corresponding to the next array element switching. Indicates the first The permutation matrix corresponding to the next element is switched. This indicates transpose.
[0084] Furthermore, using the reference matrix, the diagonal parameter transformation matrix corresponding to each of the remaining aligned array manifold matrices is constructed, and the amplitude calibration of the corresponding aligned array manifold matrix is performed using each diagonal parameter transformation matrix to obtain the calibration array manifold matrix corresponding to each element switch. The steps include:
[0085] Based on the signal relationship between the reference matrix and all other aligned array manifold matrices, construct the diagonal parameter transformation matrix corresponding to the aligned array manifold matrix for each element switching;
[0086] The expression for the diagonal parametric transformation matrix is:
[0087] (15)
[0088] in, Indicates the first The diagonal parameter transformation matrix corresponding to the alignment array manifold matrix during secondary array element switching. Represents a diagonal matrix function. Indicates the first When switching secondary array elements, the first The calibration transform coefficients of the original signal vector, , Indicates the first When switching secondary array elements, the first The calibration transform coefficients of the original signal vector, This represents the total number of the original signal vectors. Represents the first corresponding to the reference matrix Each array element is paired with the first The response value of each original signal vector. Indicates the first The alignment array manifold matrix corresponding to the second element switching is the first... Each array element is paired with the first The response value of each original signal vector;
[0089] The expression for the calibration array manifold matrix is:
[0090] (16)
[0091] in, Indicates the first The calibration array manifold matrix corresponding to the secondary array element switching Indicates the first The alignment array manifold matrix corresponding to the element switching.
[0092] Furthermore, the steps of fusing all calibration array manifold matrices into a total array manifold matrix based on the physical order of all elements in the uniform circular array, and then using the total array manifold matrix to estimate the direction of arrival for each rescue target include:
[0093] Based on the number of all array elements and the number of all rescue targets in the uniform circular array, create an all-zero matrix. The total number of rows in the all-zero matrix is equal to the number of all array elements, and the total number of columns in the all-zero matrix is equal to the number of all rescue targets. Establish a corresponding counter for each array element.
[0094] The response vector of each row in each calibration array manifold matrix is accumulated into the corresponding row of the all-zero matrix, and the counter value of the corresponding array element is incremented by 1.
[0095] Traverse all array elements. If the value of the counter corresponding to a certain array element is greater than zero, then divide all the accumulated response vectors in the corresponding row of the all-zero matrix by the accumulated number to obtain the average response vector of that array element.
[0096] After traversal, all average response vectors are vertically concatenated to form a total array manifold matrix. Each row in the total array manifold matrix represents the average response vector of the corresponding array element to all rescue targets.
[0097] By using all the response vectors of the corresponding column in the total array manifold matrix, the direction of arrival of the corresponding rescue target is estimated, and the direction of arrival of the wave for each rescue target is obtained.
[0098] This application provides a few-channel switching direction finding method based on blind source separation, which has at least the following advantages:
[0099] (1) This application introduces an array element switching mechanism to calculate the sample covariance matrix and the global noise variance estimate in sequence, and uses the global noise variance estimate to whiten each zero-mean signal matrix to obtain the standard signal matrix corresponding to each array element switching, thereby solving the problem that the existing few-channel direction finding algorithm is susceptible to noise interference in complex airborne environments and realizing effective noise estimation.
[0100] (2) This application uses the Joint Approximate Diagonalization of Eigenmatrices (JADE) algorithm to perform blind source separation on each standard signal matrix, thereby obtaining the separation matrix and separation signal matrix corresponding to each array element switching, and thus obtaining the corresponding array manifold matrix and all waveform correlation coefficients. Signal alignment is performed on all array manifold matrices to obtain the calibration array manifold matrix corresponding to each array element switching, thereby effectively improving the direction finding accuracy, angle resolution and robustness of the few-channel direction finding system. Attached Figure Description
[0101] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.
[0102] Figure 1 This illustration shows the steps of a few-channel switching direction finding method based on blind source separation in an exemplary embodiment of this application;
[0103] Figure 2This diagram illustrates how a uniform circular array is used to receive data from different array elements in a time-division multiplexing manner and perform direction-of-arrival estimation in an exemplary embodiment of this application. Detailed Implementation
[0104] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided to make this application more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
[0105] Furthermore, the accompanying drawings are merely illustrative of this application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.
[0106] The following will provide a more detailed description of a few-channel switching direction finding method based on blind source separation proposed in the embodiments of this application.
[0107] This application proposes a few-channel switching direction finding method based on blind source separation, such as... Figure 1 and Figure 2 As shown, the method may include the following steps:
[0108] In this embodiment, step S101 involves setting the uniform circular array to a few-channel receiving mode, and simultaneously receiving multiple rescue target signals using the corresponding array element group each time the array elements are switched, thus forming the corresponding original signal matrix.
[0109] Furthermore, each original signal matrix includes a binary phase shift keying signal, a linear frequency modulation signal, and a single-carrier signal.
[0110] Furthermore, Figure 2 The diagram shows that during each element switch of a uniform circular array, the corresponding array element group simultaneously receives signals from multiple rescue targets. The data from different array element groups is received in a time-division manner by a radio frequency switch, and the data from all array element groups during element switches are processed through a limited receiving channel. Finally, the direction of arrival is estimated for each rescue target.
[0111] Step S102 of this embodiment: Preprocess each original signal matrix to obtain the standard signal matrix corresponding to each element switching. Preprocessing can reduce the amount of computation in subsequent steps, improve the calculation speed, and at the same time reduce noise and improve accuracy. Step S102 of this embodiment may include the following sub-steps:
[0112] Sub-step S1021: Perform mean-removal processing on each original signal matrix to obtain the zero-mean signal matrix corresponding to each array element switch.
[0113] Furthermore, the expression for the zero-mean signal matrix is:
[0114] (1)
[0115] in, Indicates the first The zero-mean signal matrix corresponding to the secondary array element switching , express 3D real space, This indicates the total number of array elements during each array element switch. This indicates the number of all sampling points during each array element switch. Indicates the first The secondary array element switches correspond to the original signal matrix. , express A column vector of all 1s This indicates transpose.
[0116] Sub-step S1022: According to the array element switching order, vertically concatenate all zero-mean signal matrices to obtain an intermediate signal matrix, and use the intermediate signal matrix to calculate the sample covariance matrix. This sub-step is a conventional technique in this field and will not be described in detail in this embodiment.
[0117] Furthermore, the expression for the sample covariance matrix is:
[0118] (2)
[0119] in, Represents the sample covariance matrix. Represents the intermediate signal matrix. This represents the conjugate transpose of the intermediate signal matrix.
[0120] Sub-step S1023: Perform eigenvalue decomposition on the sample covariance matrix and sort all the obtained eigenvalues in descending order.
[0121] Furthermore, the expression for eigenvalue decomposition of the sample covariance matrix is as follows:
[0122] (3)
[0123] in, This represents the eigenvector obtained by eigenvalue decomposition of the sample covariance matrix. This represents the diagonal matrix of eigenvalues obtained by eigenvalue decomposition of the sample covariance matrix. , Represents a diagonal matrix function. The eigenvalue decomposition of the sample covariance matrix is represented by the eigenvalue decomposition of the sample covariance matrix. eigenvalues, , This indicates the total number of array element switching. This represents the conjugate transpose of the eigenvectors obtained by eigenvalue decomposition of the sample covariance matrix.
[0124] Sub-step S1024: Determine the number of all rescue targets using information theory criteria or eigenvalue thresholding. Sub-step S1024 is a conventional technique in this field and will not be described in detail in this embodiment.
[0125] Sub-step S1025: Based on the number of all rescue targets, divide all feature values after descending order into two groups. The first group includes the previous... The second group includes the following feature values. There are 10 characteristic values. All characteristic values in the first group are used as signal characteristic values, and all characteristic values in the second group are used as noise characteristic values. The number of all signal characteristic values is equal to the number of all rescue targets.
[0126] Sub-step S1026: Use the average of all noise features as the global noise variance estimate.
[0127] Furthermore, the expression for the global noise variance estimate is:
[0128] (4)
[0129] in, This represents the estimated global noise variance. Indicates the first Each feature value.
[0130] Sub-step S1027: Whitening is performed on each zero-mean signal matrix using the global noise variance estimate to obtain the standard signal matrix corresponding to each element switching. Sub-step S1027 serves to reduce noise and improve accuracy. The processing procedure of sub-step S1027 is as follows:
[0131] The first step is to calculate the covariance matrix corresponding to each array element switch using the zero-mean signal matrix.
[0132] Furthermore, the expression for the covariance matrix is:
[0133] (5)
[0134] in, Indicates the first The covariance matrix corresponding to the next element switching is changed. Indicates the first The conjugate transpose of the zero-mean signal matrix corresponding to the switching of secondary array elements.
[0135] The second step is to use the global noise variance estimate to denoise each covariance matrix to obtain the partial covariance matrix corresponding to each element switching.
[0136] Furthermore, the expression for the partial covariance matrix is as follows:
[0137] (6)
[0138] in, Indicates the first The partial covariance matrix corresponding to the element switching of the next array element Represents the identity matrix.
[0139] The third step is to perform eigenvalue decomposition on each part of the covariance matrix and construct the corresponding whitening matrix using the obtained eigenvalue decomposition results.
[0140] Furthermore, the expression for eigenvalue decomposition of a portion of the covariance matrix is as follows:
[0141] (7)
[0142] in, Indicates the first The eigenvectors are obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching. Indicates the first The eigenvalue diagonal matrix is obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching. Indicates the first The conjugate transpose of the eigenvectors obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching.
[0143] Furthermore, the expression for the whitening matrix is:
[0144] (8)
[0145] in, Indicates the first The whitening matrix corresponding to the next element switching.
[0146] The fourth step is to multiply each whitening matrix by its corresponding zero-mean signal matrix to obtain the standard signal matrix corresponding to each element switching.
[0147] Furthermore, the expression for the standard signal matrix is:
[0148] (9)
[0149] in, Indicates the first The standard signal matrix corresponding to the switching of secondary array elements.
[0150] Step S103 of this embodiment: Blind source separation is performed on each standard signal matrix using the characteristic matrix joint approximate diagonalization algorithm, resulting in the corresponding separation matrix and separated signal matrix. Step S103 of this embodiment may include the following sub-steps:
[0151] Sub-step S1031: Calculate a set of fourth-order cumulant matrices for each standard signal matrix. Each fourth-order cumulant matrix in the same set corresponds to a row of standard signal vectors in the corresponding standard signal matrix.
[0152] Sub-step S1032: Utilize the joint approximate diagonalization algorithm of the eigenma matrix to perform joint approximate diagonalization on each group of fourth-order cumulant matrices, obtaining the orthogonal rotation matrix corresponding to each element switching. This ensures that the sum of the squared moduli of the off-diagonal elements of all transformation matrices obtained after performing similarity transformations on the corresponding group of fourth-order cumulant matrices using each orthogonal rotation matrix is minimized. This sub-step is a conventional technique in this field and will not be elaborated upon in this embodiment.
[0153] Sub-step S1033: Multiply each orthogonal rotation matrix by the corresponding whitening matrix to obtain the separation matrix corresponding to each element switching.
[0154] Furthermore, the expression for the separation matrix is:
[0155] (10)
[0156] in, Indicates the first The secondary array element switches correspond to the separation matrix. Indicates the first The whitening matrix corresponding to the next element switching is used. Indicates the first The conjugate transpose of the orthogonal rotation matrix corresponding to the element switching.
[0157] Sub-step S1034: Multiply each separation matrix by its corresponding zero-mean signal matrix to obtain the separation signal matrix corresponding to each array element switching.
[0158] Furthermore, the expression for the separated signal matrix is:
[0159] (11)
[0160] in, Indicates the first The secondary array element switching corresponds to the separation signal matrix. , Indicates the first The standard signal matrix corresponding to the switching of secondary array elements. Indicates the first The zero-mean signal matrix corresponding to the switching of the secondary array elements.
[0161] In step S104 of this embodiment, the generalized inverse matrix of each separation matrix is used as the corresponding array manifold matrix, and the waveform correlation coefficient between the separation signal vector of each row of each separation signal matrix and the separation signal vector of all rows of all other separation signal matrices is calculated.
[0162] Furthermore, the expression for the array manifold matrix is:
[0163] (12)
[0164] in, Indicates the first The array manifold matrix corresponding to the next array element switching. This represents the generalized inverse operation.
[0165] Furthermore, the expression for the waveform correlation coefficient is:
[0166] (13)
[0167] in, Indicates the first The first element switching of the secondary array The line-separated signal vector and the first The first element switching of the secondary array The waveform correlation coefficient between the line-separated signal vectors Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The value of each sampling point, Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The value of each sampling point, Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The complex conjugate of the values at each sampling point This represents the modulo operation. Indicates the first The first element switching of the secondary array The total energy of the line-separated signal vector. Indicates the first The first element switching of the secondary array The total energy of the row-separated signal vector.
[0168] In this embodiment, total energy refers to the sum of the squares of the values of the separated signal vector at all sampling points.
[0169] Step S105 of this embodiment: Based on all waveform correlation coefficients, cluster registration is performed on each separated signal matrix to construct the permutation matrix corresponding to each array element switch. Then, each permutation matrix is used to align the corresponding array manifold matrix, resulting in the aligned array manifold matrix corresponding to each array element switch. Step S105 of this embodiment may include the following sub-steps:
[0170] Sub-step S1051: Based on all waveform correlation coefficients, cluster and register all separated signal vectors with the same waveform correlation coefficient from all separated signal matrices to determine the separated signal vector corresponding to each rescue target at each array element switch. This sub-step is a conventional technique in this field and will not be described in detail in this embodiment.
[0171] Sub-step S1052: Using the order of all separated signal vectors in the separated signal matrix corresponding to the first array element switch as a reference standard, and constructing the corresponding permutation matrix according to the clustering registration results corresponding to each array element switch. This sub-step is a conventional technique in this field and will not be described in detail in this embodiment.
[0172] Sub-step S1053: Align the corresponding array manifold matrix with signals in the column dimension using each permutation matrix to obtain the aligned array manifold matrix corresponding to each array element switch.
[0173] Furthermore, the expression for the aligned array manifold matrix is:
[0174] (14)
[0175] in, Indicates the first The alignment array manifold matrix corresponding to the secondary array element switching Indicates the first The array manifold matrix corresponding to the next array element switching. Indicates the first The permutation matrix corresponding to the next element is switched. This indicates transpose.
[0176] In this embodiment, step S106 is as follows: arbitrarily select one array element from all array elements as a reference array element, and arbitrarily select an aligned array manifold matrix containing the reference array element as a base matrix.
[0177] Step S107 of this embodiment: Using the reference matrix, construct the diagonal parameter transformation matrix corresponding to each of the remaining aligned array manifold matrices, and perform amplitude calibration on the corresponding aligned array manifold matrix using each diagonal parameter transformation matrix to obtain the calibration array manifold matrix corresponding to each element switch. Step S107 of this embodiment may include the following sub-steps:
[0178] Sub-step S1071: Based on the signal relationship between the reference matrix and all other aligned array manifold matrices, construct the diagonal parameter transformation matrix corresponding to the aligned array manifold matrix for each element switching.
[0179] Furthermore, the expression for the diagonal parametric transformation matrix is:
[0180] (15)
[0181] in, Indicates the first The diagonal parameter transformation matrix corresponding to the alignment array manifold matrix during secondary array element switching. Represents a diagonal matrix function. Indicates the first When switching secondary array elements, the first The calibration transform coefficients of the original signal vector, , Indicates the first When switching secondary array elements, the first The calibration transform coefficients of the original signal vector, This represents the total number of the original signal vectors. Represents the first corresponding to the reference matrix Each array element is paired with the first The response value of each original signal vector. Indicates the first The alignment array manifold matrix corresponding to the second element switching is the first... Each array element is paired with the first The response value of the original signal vector. Here, the response value refers to the complex gain of the array elements of the reference matrix with respect to the original signal vector.
[0182] Sub-step S1072: Perform amplitude calibration on the corresponding aligned array manifold matrix using each diagonal parameter transformation matrix to obtain the calibration array manifold matrix corresponding to each array element switch.
[0183] Furthermore, the expression for the calibration array manifold matrix is:
[0184] (16)
[0185] in, Indicates the first The calibration array manifold matrix corresponding to the secondary array element switching Indicates the first The alignment array manifold matrix corresponding to the element switching.
[0186] Step S108 of this embodiment: Based on the physical order of all array elements in the uniform circular array, all calibration array manifold matrices are merged into a total array manifold matrix, and the direction of arrival is estimated for each rescue target using the total array manifold matrix. By constructing the total array manifold matrix, better estimation results can be obtained subsequently. Step S108 of this embodiment may include the following sub-steps:
[0187] Sub-step S1081: Based on the number of all array elements and the number of all rescue targets in the uniform circular array, create an all-zero matrix. The total number of rows in the all-zero matrix is equal to the number of all array elements, and the total number of columns in the all-zero matrix is equal to the number of all rescue targets. Establish a corresponding counter for each array element.
[0188] Sub-step S1082: Accumulate the response vector of each row in each calibration array manifold matrix to the corresponding row of the all-zero matrix, and increment the counter value of the corresponding array element by 1.
[0189] Sub-step S1083: Traverse all array elements. If the value of the counter corresponding to a certain array element is greater than zero, then divide all the accumulated response vectors in the corresponding row of the all-zero matrix by the accumulated number to obtain the average response vector of that array element.
[0190] After traversal, all average response vectors are vertically concatenated to form a total array manifold matrix. Each row in the total array manifold matrix represents the average response vector of the corresponding array element to all rescue targets.
[0191] Sub-step S1084: Using all the response vectors of the corresponding column in the total array manifold matrix, estimate the direction of arrival for the corresponding rescue target to obtain the direction of arrival for each rescue target. This sub-step is a conventional technique in this field and will not be described in detail in this embodiment.
[0192] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified.
[0193] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.
[0194] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application.
[0195] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.
Claims
1. A few-channel switching direction finding method based on blind source separation, characterized in that, The method includes the following steps: The uniform circular array is set to a few-channel receiving mode, and at each array element switch, the corresponding array element group is used to simultaneously receive signals from multiple rescue targets to form the corresponding original signal matrix. Each of the original signal matrices is preprocessed to obtain the standard signal matrix corresponding to each array element switching; Blind source separation is performed on each of the standard signal matrices using the characteristic matrix joint approximate diagonalization algorithm to obtain the corresponding separation matrix and separation signal matrix; The generalized inverse matrix of each separation matrix is taken as the corresponding array manifold matrix, and the waveform correlation coefficient between the separation signal vector of each row of each separation signal matrix and the separation signal vector of all rows of all other separation signal matrices is calculated. Based on all the waveform correlation coefficients, cluster registration is performed on each of the separated signal matrices to construct the permutation matrix corresponding to each array element switching. Then, each of the permutation matrices is used to perform signal alignment on the corresponding array manifold matrix to obtain the aligned array manifold matrix corresponding to each array element switching. Arbitrarily select one of the array elements from all array elements as a reference array element, and arbitrarily select one of the alignment array manifold matrices containing the reference array element as a base matrix; Using the reference matrix, a diagonal parameter transformation matrix corresponding to each of the remaining alignment array manifold matrices is constructed, and the corresponding alignment array manifold matrix is calibrated using each diagonal parameter transformation matrix to obtain the calibration array manifold matrix corresponding to each array element switch; Based on the physical order of all the array elements in the uniform circular array, all the calibration array manifold matrices are merged into a total array manifold matrix, and the direction of arrival is estimated for each rescue target using the total array manifold matrix.
2. The few-channel switching direction finding method based on blind source separation according to claim 1, characterized in that, Each of the original signal matrices includes a binary phase shift keying signal, a linear frequency modulated signal, and a single-carrier signal.
3. The few-channel switching direction finding method based on blind source separation according to claim 1, characterized in that, The step of preprocessing each of the original signal matrices to obtain the standard signal matrix corresponding to each element switching includes: Each of the original signal matrices is subjected to mean removal processing to obtain the zero-mean signal matrix corresponding to each array element switch; The expression for the zero-mean signal matrix is: (1) in, Indicates the first The zero-mean signal matrix corresponding to the secondary array element switching , express 3D real space, This indicates the total number of array elements during each array element switch. This indicates the number of all sampling points during each array element switch. Indicates the first The secondary array element switches correspond to the original signal matrix. , express A column vector of all 1s Indicates transpose; According to the array element switching order, all the zero-mean signal matrices are vertically spliced to obtain an intermediate signal matrix, and the sample covariance matrix is calculated using the intermediate signal matrix. The expression for the sample covariance matrix is: (2) in, Represents the sample covariance matrix. Represents the intermediate signal matrix. This represents the conjugate transpose of the intermediate signal matrix; The sample covariance matrix is decomposed into eigenvalues, and all the obtained eigenvalues are sorted in descending order. The expression for eigenvalue decomposition of the sample covariance matrix is as follows: (3) in, This represents the eigenvector obtained by eigenvalue decomposition of the sample covariance matrix. This represents the diagonal matrix of eigenvalues obtained by eigenvalue decomposition of the sample covariance matrix. , Represents a diagonal matrix function. The eigenvalue decomposition of the sample covariance matrix is represented by the eigenvalue decomposition of the sample covariance matrix. 1 eigenvalue, , This indicates the total number of array element switching. This represents the conjugate transpose of the eigenvectors obtained by eigenvalue decomposition of the sample covariance matrix; The number of all rescue targets is determined using information theory criteria or eigenvalue thresholding. Based on the number of all the rescue targets, all the aforementioned feature values, sorted in descending order, are divided into two groups. The first group includes the previous... The second group includes the following feature values. The first group of all the aforementioned feature values is used as signal feature values, and the second group of all the aforementioned feature values is used as noise feature values; the number of all the aforementioned signal feature values is equal to the number of all the aforementioned rescue targets. The average value of all the noise features is used as the global noise variance estimate. The expression for the global noise variance estimate is: (4) in, This represents the estimated global noise variance. Indicates the first One eigenvalue; The global noise variance estimate is used to whiten each of the zero-mean signal matrices to obtain the standard signal matrix corresponding to each array element switch.
4. The few-channel switching direction finding method based on blind source separation according to claim 3, characterized in that, The step of whitening each zero-mean signal matrix using the global noise variance estimate to obtain the standard signal matrix corresponding to each element switching includes: The covariance matrix is calculated using the zero-mean signal matrix corresponding to each array element switch. The expression for the covariance matrix is: (5) in, Indicates the first The covariance matrix corresponding to the next element switching is changed. Indicates the first The conjugate transpose of the zero-mean signal matrix corresponding to the element switching; The global noise variance estimate is used to denoise each covariance matrix to obtain the partial covariance matrix corresponding to each element switching. The expression for the partial covariance matrix is as follows: (6) in, Indicates the first The partial covariance matrix corresponding to the element switching of the next array element Represents the identity matrix; Eigenvalue decomposition is performed on each of the aforementioned partial covariance matrices, and the corresponding whitening matrix is constructed using the obtained eigenvalue decomposition results; The expression for eigenvalue decomposition of the partial covariance matrix is as follows: (7) in, Indicates the first The eigenvectors are obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching. Indicates the first The eigenvalue diagonal matrix is obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching. Indicates the first The conjugate transpose of the eigenvectors obtained by eigenvalue decomposition of the partial covariance matrix corresponding to the element switching of the second array; The expression for the whitening matrix is: (8) in, Indicates the first The whitening matrix corresponding to the secondary array element switching; Each whitening matrix is multiplied by its corresponding zero-mean signal matrix to obtain the standard signal matrix corresponding to each element switching. The expression for the standard signal matrix is: (9) in, Indicates the first The standard signal matrix corresponding to the switching of secondary array elements.
5. The few-channel switching direction finding method based on blind source separation according to claim 1, characterized in that, The step of performing blind source separation on each of the standard signal matrices using the joint approximate diagonalization algorithm of the feature matrix to obtain the corresponding separation matrix and the separated signal matrix includes: Each set of fourth-order cumulant matrices is calculated based on each of the standard signal matrices, and each of the fourth-order cumulant matrices in the same set corresponds to a row of standard signal vectors in the corresponding standard signal matrix. The joint approximate diagonalization algorithm of the characteristic matrix is used to perform joint approximate diagonalization on each group of the fourth-order cumulant matrices to obtain the orthogonal rotation matrix corresponding to each array element switch, and to minimize the sum of the squares of the moduli of all transformation matrices obtained by performing similarity transformation on the corresponding group of the fourth-order cumulant matrices through each orthogonal rotation matrix. Each of the orthogonal rotation matrices is multiplied by its corresponding whitening matrix to obtain the separation matrix corresponding to each element switching. The expression for the separation matrix is: (10) in, Indicates the first The secondary array element switches correspond to the separation matrix. Indicates the first The whitening matrix corresponding to the next element switching is used. Indicates the first The conjugate transpose of the orthogonal rotation matrix corresponding to the element switching; Each separation matrix is multiplied by its corresponding zero-mean signal matrix to obtain the separation signal matrix corresponding to each element switching. The expression for the separated signal matrix is: (11) in, Indicates the first The secondary array element switching corresponds to the separation signal matrix. , Indicates the first The standard signal matrix corresponding to the switching of secondary array elements. Indicates the first The zero-mean signal matrix corresponding to the switching of the secondary array elements.
6. The few-channel switching direction finding method based on blind source separation according to claim 1, characterized in that, The expression for the array manifold matrix is: (12) in, Indicates the first The array manifold matrix corresponding to the secondary array element switching Represents the generalized inverse operation; The expression for the waveform correlation coefficient is: (13) in, Indicates the first The first element switching of the secondary array The line-separated signal vector and the first The first element switching of the secondary array The waveform correlation coefficient between the line-separated signal vectors Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The value of each sampling point, Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The value of each sampling point, Indicates the first The first element switching of the secondary array The line-separated signal vector is in the first position. The complex conjugate of the values at each sampling point This represents the modulo operation. Indicates the first The first element switching of the secondary array The total energy of the line-separated signal vector. Indicates the first The first element switching of the secondary array The total energy of the row-separated signal vector.
7. The few-channel switching direction finding method based on blind source separation according to claim 1, characterized in that, The step of clustering and registering each of the separated signal matrices according to all the waveform correlation coefficients to construct the permutation matrix corresponding to each array element switching includes: Based on all the waveform correlation coefficients, cluster registration is performed on all the separated signal vectors with the same waveform correlation coefficient from all the separated signal matrices to determine the separated signal vector corresponding to each rescue target at each array element switch; The order of all the separated signal vectors in the separated signal matrix corresponding to the first array element switch is used as a reference standard, and the corresponding permutation matrix is constructed according to the clustering registration results corresponding to each array element switch.
8. The few-channel switching direction finding method based on blind source separation according to claim 7, characterized in that, The step of aligning the corresponding array manifold matrix with each of the permutation matrices to obtain the aligned array manifold matrix corresponding to each element switching includes: Each of the permutation matrices is used to perform signal alignment on the corresponding array manifold matrix in the column dimension to obtain the aligned array manifold matrix corresponding to each array element switch. The expression for the aligned array manifold matrix is: (14) in, Indicates the first The alignment array manifold matrix corresponding to the secondary array element switching Indicates the first The array manifold matrix corresponding to the secondary array element switching Indicates the first The permutation matrix corresponding to the next element is switched. This indicates transpose.
9. The few-channel switching direction finding method based on blind source separation according to claim 1, characterized in that, The steps of constructing a diagonal parameter transformation matrix corresponding to each of the remaining aligned array manifold matrices using the reference matrix, and performing amplitude calibration on the corresponding aligned array manifold matrix using each diagonal parameter transformation matrix to obtain the calibration array manifold matrix corresponding to each element switch include: Based on the signal relationship between the reference matrix and all other aligned array manifold matrices, the diagonal parameter transformation matrix corresponding to the aligned array manifold matrix is constructed for each array element switching; The expression for the diagonal parametric transformation matrix is: (15) in, Indicates the first The diagonal parameter transformation matrix corresponding to the alignment array manifold matrix during secondary array element switching. Represents a diagonal matrix function. Indicates the first When switching secondary array elements, the first The calibration transform coefficients of the original signal vector, , Indicates the first When switching secondary array elements, the first The calibration transform coefficients of the original signal vector, This represents the total number of the original signal vectors. Represents the first corresponding to the reference matrix Each array element is paired with the first The response value of each original signal vector. Indicates the first The alignment array manifold matrix corresponding to the second element switching is the first... Each array element is paired with the first The response value of each original signal vector; The expression for the calibration array manifold matrix is: (16) in, Indicates the first The calibration array manifold matrix corresponding to the secondary array element switching Indicates the first The alignment array manifold matrix corresponding to the element switching.
10. The few-channel switching direction finding method based on blind source separation according to claim 1, characterized in that, The step of fusing all the calibration array manifold matrices into a total array manifold matrix according to the physical order of all the array elements in the uniform circular array, and then using the total array manifold matrix to estimate the direction of arrival for each rescue target, includes: Based on the number of all array elements in the uniform circular array and the number of all rescue targets, a zero matrix is created. The total number of rows in the zero matrix is equal to the number of all array elements, and the total number of columns in the zero matrix is equal to the number of all rescue targets. A corresponding counter is established for each array element. The response vector of each row in each of the calibration array manifold matrices is accumulated and added to the corresponding row of the all-zero matrix, while the value of the counter of the corresponding array element is incremented by 1. Traverse all the array elements. If the value of the counter corresponding to a certain array element is greater than zero, then divide all the response vectors accumulated in the corresponding row of the all-zero matrix by the accumulated number to obtain the average response vector of the array element. After traversal, all the average response vectors are vertically concatenated to form the total array manifold matrix, where each row of the total array manifold matrix represents the average response vector of the corresponding array element to all the rescue targets; By using all the response vectors in the corresponding column of the total array manifold matrix, the direction of arrival of the corresponding rescue target is estimated to obtain the direction of arrival of the wave for each rescue target.