An array direction finding method based on the summation and product of projected vector elements

Abstract

This invention discloses an array direction finding method based on the summation and product of projection vector elements, comprising: performing eigenvalue decomposition on the covariance matrix of the array output samples under finite snapshot conditions to obtain estimated signal subspace and noise subspace; projecting the scanning direction vector onto the estimated signal subspace and noise subspace respectively to obtain signal projection vector and noise projection vector; constructing a spatial spectrum function of the signal subspace based on the numerical characteristics of each element of the signal projection vector; constructing two spatial spectrum functions of the noise subspace based on the numerical characteristics of each element of the noise projection vector; and designing the final forms of two objective functions by comprehensively utilizing the spatial spectrum functions of the signal and noise subspaces to further improve angular resolution and maintain high estimation accuracy, while maintaining low computational complexity of the overall algorithm. Through fully exploiting the numerical characteristics of the sample covariance matrix and experimental verification, the proposed algorithm is particularly suitable for low signal-to-noise ratio, small snapshot, and near-source scenarios.

Description

Technical Field

[0001] This invention relates to the field of direction finding in array signal processing, specifically to an array direction finding method based on the summation and product of projected vector elements. By comprehensively utilizing the signal subspace and noise subspace and rationally designing a new objective function, it can achieve high estimation accuracy and high resolution direction finding results, especially in scenarios with low signal-to-noise ratio, small snapshots, and nearby signal sources. Background Technology

[0002] Direction finding is one of the main research directions in array signal processing. Early radars used mechanically rotating antennas for aerial target direction finding. Later, phased array radars used phase shifters to change the phase of the antennas, resulting in low resolution. In 1959, Capon proposed an adaptive beamformer to minimize the average power of the array output while keeping the gain constant in the main lobe direction, significantly improving array direction finding resolution and ushering in the era of high-resolution direction finding. In 1986, Schmidt proposed the Multiple Signal Classification (MUSIC) method using the orthogonality between the signal and noise subspaces. Also in 1986, Roy et al. proposed the Rotationally Invariant Signal Parameter Estimation (ESPRIT) method, utilizing the rotational invariance of array geometry, ushering in the era of super-resolution direction finding.

[0003] However, most existing subspace-based direction-finding methods experience significant performance degradation at low signal-to-noise ratios and with a small number of snapshots, especially when the source angle intervals are small. This is because the signal and noise subspaces partially overlap, leading to a substantial decrease in direction-finding performance. In recent years, methods such as subspace iteration, matrix shrinkage, and diagonal loading have been proposed to further improve the estimation performance of subspace-based algorithms under low signal-to-noise ratio and small snapshot conditions. Algorithms based on matrix shrinkage and diagonal loading scale and shift the eigenvalues ​​of the output sample covariance matrix, but do not change the form of the objective function, resulting in limited performance improvement. Subspace iterative algorithms require iterative calculation of the subspace, which places certain requirements on the initial iteration matrix, leading to high computational complexity. Furthermore, since the form of the objective function remains unchanged, the improvement in resolution and estimation accuracy is limited.

[0004] Based on the above analysis, it is necessary to study new direction finding methods with high resolution and high estimation accuracy, and to design new objective function forms to adapt to the harsh environments in practical applications, so as to further improve the success rate and accuracy of angle estimation. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the problem that most existing subspace-based direction finding methods suffer from a significant drop in direction finding performance due to subspace leakage when the signal-to-noise ratio is low and the number of snapshots is small. This invention provides an array direction finding method based on the summation and product of projected vector elements, which can achieve high estimation accuracy and high resolution direction finding results.

[0006] The objective of this invention is achieved through the following technical solution: By deeply analyzing the numerical characteristics of the sample covariance matrix and fully utilizing the information of the signal subspace and noise subspace, this invention studies the range and variation characteristics of each element of the signal projection vector and noise projection vector, and obtains an array direction finding method based on the summation and product of projection vector elements. Based on the equivalence of the subspace spanned by the signal direction vector and the signal subspace, and the orthogonality of the signal direction vector and noise subspace, the invention first calculates the signal projection vector projected from the scanning direction vector onto the signal subspace, and obtains the spatial spectrum function of the signal subspace based on the signal projection vector; then, it calculates the noise projection vector projected from the scanning direction vector onto the noise subspace, and obtains two different forms of spatial spectrum functions of the noise subspace based on the noise projection vector; combining the spatial spectrum functions of the signal subspace and the noise subspace, two different forms of final spatial spectrum functions are obtained; the final spatial spectrum function with the largest value... The angle corresponding to each maximum value is the estimated source angle.

[0007] In a first aspect, the present invention provides an array direction finding method based on the summation and product of projection vector elements, comprising the following steps:

[0008] Step 1: When the number of data samples received by the array is limited, perform eigenvalue decomposition on the sample covariance matrix to obtain the estimated signal subspace and noise subspace, and determine the relationship between the estimated signal subspace and noise subspace and the real signal subspace and noise subspace.

[0009] Step 2: Project the scanning direction vector onto the estimated signal subspace to obtain the signal projection vector. Combine the results of the estimated signal subspace in Step 1 to determine the range of the magnitude values ​​of each element of the signal projection vector. Based on the summation and product of the elements of the signal projection vector, obtain the spatial spectrum function of the signal subspace.

[0010] Step 3: Project the scanning direction vector onto the estimated noise subspace to obtain the noise projection vector. Combine the results of the noise subspace estimated in Step 1 to determine the range of the magnitude of each element of the noise projection vector and obtain the result of the error of each element of the noise projection vector.

[0011] Step 4: Based on the results of the noise projection vector in Step 3, perform pseudo-peak removal processing based on the summation and product of the noise projection vector elements to obtain two spatial spectrum functions for the noise subspace. The first spatial spectrum function is constructed based on the estimation error of each element of the equalized noise projection vector; the second spatial spectrum function is constructed based on the smoothed spatial spectrum.

[0012] Step 5: By combining the spatial spectrum functions of the signal subspace and noise subspace obtained in Steps 2 and 4, two different forms of the final spatial spectrum function are obtained, further improving the angle resolution and estimation accuracy. The final spatial spectrum function with the largest... The angle corresponding to each maximum value is the estimated source angle.

[0013] Furthermore, in step 1,

[0014] An unrelated far-field narrowband signal from Incident to A uniform linear array Less than The covariance matrix of the array received data Eigenvalue decomposition, and eigenvalues ​​arranged in non-increasing order, i.e. ,forward eigenvalues The corresponding feature vectors constitute the real signal subspace The remaining eigenvalues The corresponding feature vectors constitute the real noise subspace In practical applications, the number of snapshots is limited, and what is obtained is the sample covariance matrix of the received data. For the sample covariance matrix Perform eigenvalue decomposition to obtain the estimated signal subspace. and estimated noise subspace The estimated signal subspace and noise subspace satisfy the following relationship with the true signal subspace and noise subspace:

[0015] ,

[0016] ,

[0017] in, and These are the error matrices for the signal subspace and the noise subspace, respectively. and It is the error vector, and , .

[0018] Furthermore, step 2 includes the following steps:

[0019] Step 21, according to A uniform linear array can be used to obtain arbitrary directional angles. Corresponding scanning direction vector And normalize the scanning direction vector, that is:

[0020]

[0021] Step 22: Set the scanning direction vector Projecting the signal onto the estimated signal subspace yields the signal projection vector. :

[0022] ,

[0023] in, and These represent the conjugate transpose and transpose operations of a matrix or vector, respectively. Based on the definition of the complex vector inner product, the range of the magnitudes of each element of the signal projection vector is as follows:

[0024] ,

[0025] In the formula:

[0026]

[0027] in, and They are vectors and vector The Hermitian angle and pseudo-angle between them, and respectively satisfying and , This indicates the operation of taking the modulus value of a single variable or the modulus value of each element of a vector. Indicates calculation Norm operations;

[0028] Step 23: Based on the signal direction vector, i.e. , The spanned subspace is equivalent to the signal subspace, and the signal direction vector is orthogonal to the noise subspace, thus obtaining the true signal projection vector. satisfy:

[0029]

[0030] In the formula:

[0031]

[0032]

[0033] According to the above formula, when the number of snapshots is small (not exceeding 100), the signal projection vector... of norm The vector that approaches 1 and is obtained by taking the modulus of each element of the signal projection vector. The largest element tends to 1; when the scanning angle is not in the source direction, i.e. hour, The value of decreases, and the vector The smallest element becomes significantly smaller;

[0034] Step 24: Based on the results of the signal projection vectors in steps 22 and 23, increase the source direction, i.e. and non-source directions, i.e. The objective is the difference between the corresponding objective functions. The spatial spectrum function of the signal subspace is constructed as follows:

[0035]

[0036] in, As an exponential factor, it takes a positive number greater than 0, typically 2, and exist It has a maximum value at that time.

[0037] Furthermore, step 3 includes the following steps:

[0038] Step 31: Set the scanning direction vector Projecting onto the estimated noise subspace yields the noise projection vector. :

[0039] ,

[0040] Based on the definition of the inner product of complex vectors, the range of the magnitudes of each element of the noise projection vector is obtained as follows:

[0041]

[0042] Step 32: Arrange the elements of the noise projection vector in non-increasing order of their magnitudes, i.e. Based on the error between the estimated noise subspace and the true noise subspace, and according to the signal direction vector, , Orthogonal to the noise subspace, the noise projection vector located in the source direction satisfies:

[0043]

[0044]

[0045] In the formula:

[0046]

[0047]

[0048] Among them, the error modulus of each element .

[0049] Furthermore, step 4 includes the following steps:

[0050] Step 41: Design the first spatial spectrum function based on the noise projection vector. With the goal of balancing the errors of each element of the noise projection vector, construct the spatial spectrum function of the noise subspace as follows:

[0051]

[0052] in, As an exponential factor, it takes a positive number greater than 0, typically 0.5 or 1. , Indicates rounding down; exist It has a minimum value;

[0053] Step 42: Design a second spatial spectrum function based on the noise projection vector, dividing the noise projection vector into two parts, namely... and ,in For hyperparameters and With the goal of smoothing the spatial spectrum, the spatial spectrum function of the noise subspace is constructed as follows:

[0054]

[0055] in, As an exponential factor, it takes a positive number greater than 0, typically 0.5 or 1; exist It has a local minimum value; let The noise projection vector is evenly distributed; the hyperparameters are determined experimentally. The optimal value; the two spatial spectral functions of the noise subspace are obtained as follows: and .

[0056] Furthermore, step 5 includes the following steps:

[0057] Based on the spatial spectrum function of the signal subspace in step 2 Step 4: Two spatial spectrum functions of the noise subspace and Given that when hour, It has a maximum value, and and Having a local minimum, we can construct the following two different forms of the final spatial spectrum function by comprehensively utilizing information from the signal subspace and the noise subspace:

[0058] ,

[0059] and

[0060] , .

[0061] Two spatial spectral functions and spatial spectrum function The largest The angle corresponding to each maximum value is the estimated source angle.

[0062] In a second aspect, the present invention provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0063] Memory, used to store computer programs;

[0064] When the processor executes the program stored in the memory, it implements the above-mentioned array direction finding method based on the summation and product of projection vector elements.

[0065] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the array orientation finding method based on the summation and product of projection vector elements.

[0066] The advantages of this invention compared to the prior art are:

[0067] (1) As can be seen from the technical solution provided by the present invention above, the sample covariance matrix of the array received data is eigenvalued to obtain the estimated signal subspace and noise subspace; the numerical characteristics of the sample covariance matrix are analyzed in depth, and the subspace spanned by the signal direction vector is equivalent to the signal subspace, and the signal direction vector and the noise subspace are orthogonal. Based on the summation and product of the elements of the signal projection vector and the noise projection vector, two different forms of spatial spectrum functions are constructed. While improving the estimation accuracy, it has ultra-high direction finding resolution, especially in the case of low signal-to-noise ratio, small snapshot, and nearby signal source.

[0068] (2) This invention overcomes the problem that most existing subspace-based direction finding methods suffer from a significant performance degradation due to subspace leakage when the signal-to-noise ratio is low and the number of snapshots is small. It provides an array-based direction finding method based on the summation and product of projected vector elements, achieving high estimation accuracy and high-resolution direction finding, especially advantageous in scenarios with low signal-to-noise ratios (≤5dB), small number of snapshots (≤100), and proximity to signal sources. Specifically, according to... Figure 3 For angle intervals of The first form of spatial spectrum function is proposed for the neighboring information source. At a signal-to-noise ratio of 5dB and a snapshot count of 50, the root mean square error is within... The proposed second form of spatial spectrum function achieves an estimation success rate of around 30%. At a signal-to-noise ratio of 5dB and a snapshot count of 50, the root mean square error is within... It achieves an estimation success rate of 90%, while the traditional multi-signal classification method (MUSIC) has a root mean square error and estimation success rate of 5dB signal-to-noise ratio and 50 snapshots, respectively. The values ​​above and 0% indicate that the MUSIC method fails to estimate under these conditions and cannot distinguish between the two information sources. Attached Figure Description

[0069] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0070] Figure 1 This is a flowchart of an array direction finding method based on the summation and product of projection vector elements provided in an embodiment of the present invention;

[0071] Figure 2 A schematic diagram of an array signal receiving model provided in an embodiment of the present invention;

[0072] Figure 3This paper presents a comparison of the two direction-finding methods (Proposed1 and Proposed2) and three representative algorithms proposed in this invention under 500 Monte Carlo experiments provided in this embodiment. The comparison algorithms are: Multi-Signal Classification (MUSIC), Signal Subspace Scaling Multi-Signal Classification (SSMUSIC), and Shrinkage-based Multi-Signal Classification (Shrinkage). A represents the comparison result of root mean square error as a function of signal-to-noise ratio (SNR), and B represents the comparison result of estimation success rate as a function of SNR. The experimental conditions are: a 10-element uniform linear array, an element spacing of half a wavelength, a snapshot number of 50, and an incident angle of two uncorrelated signal sources. and The angle scanning range is The scanning interval is The absolute error of the first estimation at each angle is within Internally, it is considered successful; the signal-to-noise ratio varies from -10dB to 20dB; exponential factor. and hyperparameters . Detailed Implementation

[0073] This invention performs eigenvalue decomposition on the sample covariance matrix of the array received data to obtain estimated signal and noise subspaces. By deeply analyzing the numerical characteristics of the sample covariance matrix, and utilizing the equivalence of the subspace spanned by the signal direction vector and the orthogonality of the signal and noise subspaces, a new direction-finding spatial spectrum function is constructed based on the summation and product of the elements of the signal and noise projection vectors. This approach improves estimation accuracy while achieving ultra-high direction-finding resolution, particularly advantageous in low signal-to-noise ratio, small snapshot, and near-source scenarios.

[0074] like Figure 1 As shown, the present invention mainly includes the following steps:

[0075] Step 1: When the number of data samples received by the array is limited, perform eigenvalue decomposition on the sample covariance matrix to obtain the estimated signal subspace and noise subspace, and determine the relationship between the estimated signal subspace and noise subspace and the real signal subspace and noise subspace.

[0076] Step 2: Project the scanning direction vector onto the estimated signal subspace to obtain the signal projection vector. Combine the results of the estimated signal subspace in Step 1 to determine the range of the magnitude values ​​of each element of the signal projection vector. Based on the summation and product of the elements of the signal projection vector, obtain the spatial spectrum function of the signal subspace.

[0077] Step 3: Project the scanning direction vector onto the estimated noise subspace to obtain the noise projection vector. Combine the results of the noise subspace estimated in Step 1 to determine the range of the magnitude of each element of the noise projection vector and obtain the result of the error of each element of the noise projection vector.

[0078] Step 4: Based on the results of the noise projection vector in Step 3, perform pseudo-peak removal processing based on the summation and product of the noise projection vector elements to obtain two spatial spectrum functions for the noise subspace. The first spatial spectrum function is constructed based on the estimation error of each element of the equalized noise projection vector; the second spatial spectrum function is constructed based on the smoothed spatial spectrum.

[0079] Step 5: By combining the spatial spectrum functions of the signal subspace and noise subspace obtained in Steps 2 and 4, two different forms of the final spatial spectrum function are obtained, further improving the angle resolution and estimation accuracy. The final spatial spectrum function with the largest... The angle corresponding to each maximum value is the estimated source angle.

[0080] The above-described scheme of this invention, compared with existing subspace-based super-resolution direction finding methods, performs eigenvalue decomposition on the sample covariance matrix of the array received data to obtain estimated signal and noise subspaces. By deeply analyzing the numerical characteristics of the sample covariance matrix, and utilizing the equivalence and orthogonality between the subspace spanned by the signal direction vector and the signal subspace, a new direction finding spatial spectrum function is constructed based on the summation and product of the elements of the signal and noise projection vectors. This approach improves estimation accuracy while achieving ultra-high direction finding resolution, especially advantageous in low signal-to-noise ratio, small snapshot, and near-source scenarios.

[0081] To facilitate understanding, we will first introduce the Multiple Signal Classification (MUSIC) method, and then provide a detailed explanation of the five steps mentioned above.

[0082] This invention is applicable to any type of array, including linear arrays, circular arrays, conformal arrays, etc., and the applicable directions of arrival include one-dimensional azimuth, one-dimensional elevation, and two-dimensional azimuth and elevation. For ease of calculation, this invention only applies to... Figure 2 The given linear array will be discussed, and the specific array signal model is as follows:

[0083] The linear array receives images from different incident angles in the space. of A far-field narrowband signal, with the first array element on the right designated as the reference element, and the spacings of the other array elements from right to left relative to the reference element as follows: Because the incident angles of each signal are different, the plane wavefronts of each signal are different, resulting in different time delays for each array element relative to its arrival at the reference array element, and consequently, different signal direction vectors. Therefore, the array's observation time... The received data (referred to as the array reception data) Each snapshot data point is represented as:

[0084]

[0085] in, and Representing signal and noise respectively. , It is the first The waveforms of each signal, each signal All have zero mean and are uncorrelated. It is the first The direction vector of each signal , It is additive, independent, identically distributed, zero-mean white noise, and each signal... It is independent of the noise of each array element.

[0086] The array receives the signal vector. Covariance matrix for:

[0087]

[0088] Based on the assumptions, and The rank of all ,therefore Is the rank Hermitian positive semidefinite matrix, its The non-zero positive eigenvalues ​​are arranged in order of magnitude as follows: . It is a Hermitian positive definite matrix, and its The following non-zero positive eigenvalues, arranged in order of magnitude, satisfy:

[0089]

[0090] The corresponding feature vectors are respectively ,but:

[0091]

[0092] For all From the properties of eigenvalue decomposition, we can obtain:

[0093]

[0094] therefore,

[0095]

[0096] This means:

[0097] .

[0098] The above formula shows that the eigenvector corresponding to the minimum eigenvalue is orthogonal to the signal direction vector. The eigenvectors corresponding to the large eigenvalues Zhang forms a subspace, which is composed of the remaining... The eigenvectors corresponding to a set of equal small eigenvalues Zhang Cheng has another subspace. Since these two subspaces are orthogonal, the former is related to the signal and is called the signal subspace, denoted as . The latter is the complement space of the signal subspace, called the noise subspace, denoted as . .

[0099] Create the following function:

[0100]

[0101] When on During the scan, its Each peak corresponds to the angle of the signal incident direction.

[0102] In practical engineering, the ideal array covariance matrix Difficult to obtain, can only be obtained using the array sample covariance matrix to replace The array receives data 3D sample covariance matrix for:

[0103]

[0104] in, The number of snapshots for the array to receive sample data.

[0105] The objective of this invention is to perform eigenvalue decomposition on the sample covariance matrix of the array received data to obtain estimated signal and noise subspaces. Through in-depth analysis of the numerical characteristics of the sample covariance matrix, and utilizing the equivalence of the subspace spanned by the signal direction vector and the orthogonality of the signal and noise subspaces, a new direction-finding spatial spectrum function is constructed based on the summation and product of the elements of the signal and noise projection vectors. This achieves significantly improved estimation accuracy while maintaining extremely high direction-finding resolution, particularly advantageous in low signal-to-noise ratio, small snapshot, and near-source scenarios. The invention is implemented in the following five steps.

[0106] Step 1:

[0107] An unrelated far-field narrowband signal from Incident to A uniform linear array Less than The covariance matrix of the array received data Eigenvalue decomposition, and eigenvalues ​​arranged in non-increasing order, i.e. ,forward eigenvalues The corresponding feature vectors constitute the real signal subspace The remaining eigenvalues The corresponding feature vectors constitute the real noise subspace In practical applications, the number of snapshots is limited, and what is obtained is the sample covariance matrix of the received data. For the sample covariance matrix Perform eigenvalue decomposition to obtain the estimated signal subspace. and estimated noise subspace The estimated signal subspace and noise subspace satisfy the following relationship with the true signal subspace and noise subspace:

[0108] ,

[0109] ,

[0110] in, and These are the error matrices for the signal subspace and the noise subspace, respectively. and It is the error vector, and , .

[0111] Step 2:

[0112] Step 21, according to A uniform linear array can be used to obtain arbitrary directional angles. Corresponding scanning direction vector And normalize the scanning direction vector, that is:

[0113]

[0114] Step 22: Set the scanning direction vector Projecting the signal onto the estimated signal subspace yields the signal projection vector. :

[0115] ,

[0116] in, and These represent the conjugate transpose and transpose operations of a matrix or vector, respectively. Based on the definition of the complex vector inner product, the range of the magnitudes of each element of the signal projection vector is as follows:

[0117] ,

[0118] In the formula:

[0119]

[0120] in, and They are vectors and vector The Hermitian angle and pseudo-angle between them, and respectively satisfying and , This indicates the operation of taking the modulus value of a single variable or the modulus value of each element of a vector. Indicates calculation Norm operations;

[0121] Step 23: Based on the signal direction vector, i.e. , The spanned subspace is equivalent to the signal subspace, and the signal direction vector is orthogonal to the noise subspace, thus obtaining the true signal projection vector. satisfy:

[0122]

[0123] In the formula:

[0124]

[0125]

[0126] According to the above formula, when the number of snapshots is small (not exceeding 100), the signal projection vector... of norm The vector that approaches 1 and is obtained by taking the modulus of each element of the signal projection vector. The largest element tends to 1; when the scanning angle is not in the source direction, i.e. hour, The value of decreases, and the vector The smallest element becomes significantly smaller;

[0127] Step 24: Based on the results of the signal projection vectors in steps 22 and 23, increase the source direction, i.e. and non-source directions, i.e. The objective is the difference between the corresponding objective functions. The spatial spectrum function of the signal subspace is constructed as follows:

[0128]

[0129] in, As an exponential factor, it takes a positive number greater than 0, typically 2, and exist It has a maximum value at that time.

[0130] Step 3:

[0131] Step 31: Set the scanning direction vector Projecting onto the estimated noise subspace yields the noise projection vector. :

[0132] ,

[0133] Based on the definition of the inner product of complex vectors, the range of the magnitudes of each element of the noise projection vector is obtained as follows:

[0134]

[0135] Step 32: Arrange the elements of the noise projection vector in non-increasing order of their magnitudes, i.e. Based on the error between the estimated noise subspace and the true noise subspace, and according to the signal direction vector, , Orthogonal to the noise subspace, the noise projection vector located in the source direction satisfies:

[0136]

[0137]

[0138] In the formula:

[0139]

[0140]

[0141] Among them, the error modulus of each element Also arranged in non-increasing order.

[0142] Step 4:

[0143] Step 41: Design the first spatial spectrum function based on the noise projection vector. With the goal of balancing the errors of each element of the noise projection vector, construct the spatial spectrum function of the noise subspace as follows:

[0144]

[0145] in, As an exponential factor, it takes a positive number greater than 0, typically 0.5 or 1. , Indicates rounding down; exist It has a minimum value;

[0146] Step 42: Design a second spatial spectrum function based on the noise projection vector, dividing the noise projection vector into two parts, namely... and ,in For hyperparameters and With the goal of smoothing the spatial spectrum, the spatial spectrum function of the noise subspace is constructed as follows:

[0147]

[0148] in, As an exponential factor, it takes a positive number greater than 0, typically 0.5 or 1; exist It has a local minimum value; let The noise projection vector is evenly distributed; however, to obtain the best estimation performance, the hyperparameters can also be determined experimentally. The optimal value is obtained; thus, the two spatial spectral functions of the noise subspace are obtained as follows: and .

[0149] Step 5:

[0150] Based on the spatial spectrum function of the signal subspace in step 2 Step 4: Two spatial spectrum functions of the noise subspace and Given that when hour, It has a maximum value, and and Having a local minimum, we can construct the following two different forms of the final spatial spectrum function by comprehensively utilizing information from the signal subspace and the noise subspace:

[0151] ,

[0152] and

[0153] , .

[0154] Two spatial spectral functions and spatial spectrum function The largest The angle corresponding to each maximum value is the estimated source angle.

[0155] like Figure 2 As shown, for the sake of simplicity, Figure 2 Only given A schematic diagram of a linear array receiving a narrowband far-field signal in space, where the angle between the incident direction of the signal and the array normal is... It is assumed that the signal is incident on each array element in the form of a plane wave, with the first array element on the right designated as the reference array element. This represents the spacing between other array elements and the reference array element.

[0156] Figure 3 The present invention provides comparative results of two direction-finding methods (Proposed1 and Proposed2) and three representative algorithms proposed in this invention under 500 Monte Carlo experiments in embodiments of the invention. The compared algorithms are: Multi-Signal Classification (MUSIC), Signal Subspace Scaling Multi-Signal Classification (SSMUSIC), and Shrinkage-Based Multi-Signal Classification (Shrinkage). Figure 3 In the figure, A represents the root mean square error comparison result as a function of signal-to-noise ratio. Figure 3 In the diagram, B represents the comparison of estimation success rate as the signal-to-noise ratio changes. The experimental conditions were: a 10-element uniform linear array, element spacing of half a wavelength, 50 snapshots, and incident angles of the two uncorrelated sources. and The angle scanning range is The scanning interval is The absolute error of the first estimation at each angle is within Internally, it is considered successful; the signal-to-noise ratio varies from -10dB to 20dB; exponential factor. and hyperparameters .

[0157] Figure 3 This indicates that under conditions of low signal-to-noise ratio, small snapshots, and adjacent signals, the estimation success rate of the proposed method is significantly higher than that of the MUSIC method, SSMUSIC method, and Shrinkage method. The root mean square error of the estimation method proposed in this invention is significantly lower than that of the MUSIC method, SSMUSIC method, and Shrinkage method, while improving estimation accuracy and resolution.

[0158] Through the above description of the embodiments, those skilled in the art can clearly understand that the above embodiments can be implemented by software, or by using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions of the above embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, mobile hard drive, etc.), including several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0159] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An array direction finding method based on the summation and product of projected vector elements, characterized in that, Includes the following steps: Step 1: When the number of data samples received by the array is limited, perform eigenvalue decomposition on the sample covariance matrix to obtain the estimated signal subspace and noise subspace, and determine the relationship between the estimated signal subspace and noise subspace and the real signal subspace and noise subspace. Step 2: Project the scanning direction vector onto the estimated signal subspace to obtain the signal projection vector. Combine the results of the estimated signal subspace in Step 1 to determine the range of the magnitude values ​​of each element of the signal projection vector. Based on the summation and product of the elements of the signal projection vector, obtain the spatial spectrum function of the signal subspace. Step 3: Project the scanning direction vector onto the estimated noise subspace to obtain the noise projection vector. Combine the results of the noise subspace estimated in Step 1 to determine the range of the magnitude of each element of the noise projection vector and obtain the result of the error of each element of the noise projection vector. Step 4: Based on the results of the noise projection vector in Step 3, perform pseudo-peak removal processing based on the summation and product of the noise projection vector elements to obtain two spatial spectrum functions for the noise subspace. The first spatial spectrum function is constructed based on the estimation error of each element of the equalized noise projection vector; the second spatial spectrum function is constructed based on the smoothed spatial spectrum. Step 5: By combining the spatial spectrum functions of the signal subspace and noise subspace obtained in Steps 2 and 4, two different forms of the final spatial spectrum function are obtained, further improving the angle resolution and estimation accuracy. The final spatial spectrum function with the largest... The angle corresponding to each maximum value is the estimated source angle.

2. The array direction finding method based on the summation and product of projection vector elements according to claim 1, characterized in that: In step 1, An unrelated far-field narrowband signal from Incident to A uniform linear array Less than The covariance matrix of the array received data Eigenvalue decomposition, and eigenvalues ​​arranged in non-increasing order, i.e. ,forward eigenvalues The corresponding feature vectors constitute the real signal subspace The remaining eigenvalues The corresponding feature vectors constitute the real noise subspace In practical applications, the number of snapshots is limited, and what is obtained is the sample covariance matrix of the received data. For the sample covariance matrix Perform eigenvalue decomposition to obtain the estimated signal subspace. and estimated noise subspace The estimated signal subspace and noise subspace satisfy the following relationship with the true signal subspace and noise subspace: ， ， in, and These are the error matrices for the signal subspace and the noise subspace, respectively. and It is the error vector, and , .

3. The array direction finding method based on the summation and product of projection vector elements according to claim 2, characterized in that: Step 2 includes the following steps: Step 21, according to A uniform linear array can be used to obtain arbitrary directional angles. Corresponding scanning direction vector And normalize the scanning direction vector, that is: Step 22: Set the scanning direction vector Projecting the signal onto the estimated signal subspace yields the signal projection vector. : ， in, and Let represent the conjugate transpose and transpose operations of a matrix or vector, respectively. According to the definition of the complex vector inner product, the range of the magnitudes of each element of the signal projection vector is as follows: ， In the formula: in, and They are vectors and vector The Hermitian angle and pseudo-angle between them, and respectively satisfying and , This indicates the operation of taking the modulus value of a single variable or the modulus value of each element of a vector. Indicates calculation Norm operations; Step 23: Based on the signal direction vector, i.e. , The spanned subspace is equivalent to the signal subspace, and the signal direction vector is orthogonal to the noise subspace, thus obtaining the true signal projection vector. satisfy: In the formula: According to the above formula, when the number of snapshots is small, the signal projection vector... of norm The vector that approaches 1 and is obtained by taking the modulus of each element of the signal projection vector. The largest element tends to 1; when the scanning angle is not in the source direction, i.e. hour, The value of decreases, and the vector The smallest element becomes significantly smaller; Step 24: Based on the results of the signal projection vectors in steps 22 and 23, increase the source direction, i.e. and non-source directions, i.e. The objective is the difference between the corresponding objective functions. The spatial spectrum function of the signal subspace is constructed as follows: in, As an exponential factor, it takes a positive number greater than 0, and exist It has a maximum value at that time.

4. The array direction finding method based on the summation and product of projection vector elements according to claim 3, characterized in that: Step 3 includes the following steps: Step 31: Set the scanning direction vector Projecting onto the estimated noise subspace yields the noise projection vector. : ， Based on the definition of the inner product of complex vectors, the range of the magnitudes of each element of the noise projection vector is obtained as follows: Step 32: Arrange the elements of the noise projection vector in non-increasing order of their magnitudes, i.e. Based on the error between the estimated noise subspace and the true noise subspace, and according to the signal direction vector, , Orthogonal to the noise subspace, the noise projection vector located in the source direction satisfies: In the formula: Among them, the error modulus of each element .

5. The array direction finding method based on the summation and product of projection vector elements according to claim 4, characterized in that: Step 4 includes the following steps: Step 41: Design the first spatial spectrum function based on the noise projection vector. With the goal of balancing the errors of each element of the noise projection vector, construct the spatial spectrum function of the noise subspace as follows: in, As an exponential factor, take a positive number greater than 0. , Indicates rounding down; exist It has a minimum value; Step 42: Design a second spatial spectrum function based on the noise projection vector, dividing the noise projection vector into two parts, namely... and ,in For hyperparameters and With the goal of smoothing the spatial spectrum, the spatial spectrum function of the noise subspace is constructed as follows: in, As an exponential factor, it takes a positive number greater than 0, typically 0.5 or 1; exist It has a local minimum value; let By equally dividing the noise projection vector, two spatial spectral functions of the noise subspace are obtained, respectively. and .

6. The array direction finding method based on the summation and product of projected vector elements according to claim 5, characterized in that: Step 5 includes the following steps: Based on the spatial spectrum function of the signal subspace in step 2 Step 4: Two spatial spectrum functions of the noise subspace and It is known that when hour, It has a maximum value, and and Having a local minimum, we can construct the following two different forms of the final spatial spectrum function by comprehensively utilizing information from the signal subspace and the noise subspace: ， and ， Two spatial spectral functions and spatial spectrum function The largest The angle corresponding to each maximum value is the estimated source angle.

7. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the method of any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-6.

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