Improved spatial smoothing source angle estimation method and device based on coprime linear arrays

Abstract

This invention relates to an improved spatially smoothed source angle estimation method and apparatus based on a coprime linear array. The method includes: acquiring a signal from a source under test using an augmented coprime array to obtain a received signal; vectorizing the covariance matrix of the received signal, sorting the resulting vectors according to the element positions of the uniform linear array, and processing them according to a data processing strategy to obtain a virtual signal received by a virtual array; uniformly dividing the virtual array into overlapping virtual subarrays based on a pre-constructed spatial smoothing rule, and calculating the spatial smoothing covariance matrix of the received signals from the virtual subarrays; performing eigenvalue decomposition on the spatial smoothing covariance matrix using a predefined spatial spectrum estimation method to obtain a spatial spectrum function; and performing spectral peak search on the spatial spectrum function to determine the source angle of the source under test. The method provided by this invention improves the array degrees of freedom and the accuracy of source angle estimation by constructing a larger number of virtual array elements.

Description

Technical Field

[0001] This invention relates to the field of spatial spectrum estimation, and more particularly to an improved method and apparatus for estimating the angle of spatially smoothed information sources based on coprime linear arrays. Background Technology

[0002] Direction of Arrival (DOA) estimation is a branch of array signal processing that has been rapidly developed and widely applied in fields such as radar early warning, mobile communication, sonar alarm, earthquake monitoring, and radio navigation.

[0003] A signal source has many possible propagation paths and angles of arrival. With the development of technology, in many application scenarios, multiple transmitters work at the same time, which often leads to the estimated number of signal sources being greater than the actual number of physical array elements.

[0004] In existing technologies, the number of sources that can be estimated using traditional uniform linear arrays is limited by the number of physical array elements: a uniform linear array with M physical array elements can only estimate a maximum of M-1 sources. Therefore, increasing the number of physical array elements for source estimation leads to increased estimation complexity. In practical applications, this results in drawbacks such as low degrees of freedom, low estimation efficiency, low accuracy, large bias, and high cost. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides an improved method and apparatus for estimating the spatial smoothing source angle based on coprime linear arrays, which solves the technical problems of low degree of freedom, low estimation efficiency, low accuracy, large bias and high cost in the existing DOA estimation.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, in a first aspect, embodiments of the present invention provide an improved method for estimating the angle of a spatially smooth source based on a coprime linear array, comprising the following steps:

[0009] S1. Based on a pre-constructed augmented coprime array, the signal from the source under test is acquired to obtain the received signal; the covariance matrix of the received signal is vectorized, and the resulting vector is sorted according to the element positions of the uniform linear array and processed according to a predefined data processing strategy to obtain the virtual array received signal.

[0010] S2. Based on the pre-constructed spatial smoothing rules, the received signal of the virtual array is uniformly divided into mutually overlapping received signals of the virtual sub-array, and the spatial smoothing covariance matrix of the received signal of the virtual sub-array is calculated.

[0011] S3. Using a predefined spatial spectrum estimation method, perform eigenvalue decomposition on the spatial smooth covariance matrix to obtain the spatial spectrum function;

[0012] S4. Perform spectral peak search on the spatial spectral function to determine the source angle of the source to be tested.

[0013] Optionally, the obtained vectors are sorted according to the element positions of a uniform linear array and processed according to a predefined data processing strategy, including:

[0014] The obtained vectors are sorted according to the positions of the elements of the uniform linear array. The average value of the repeated virtual element signals in the virtual elements of the vectors is calculated. The average value is used to replace the repeated virtual element signals to obtain the virtual array received signal.

[0015] Optionally, the obtained vectors are sorted according to the element positions of a uniform linear array and processed according to a predefined data processing strategy, including:

[0016] The obtained vectors are sorted according to the positions of the array elements of a uniform linear array, and the missing array elements in the vectors are interpolated using the array interpolation method to obtain the virtual array received signal.

[0017] Optionally, in S1,

[0018] The augmented coprime array includes a first subarray and a second subarray;

[0019] The first subarray comprises 2M array elements with an element spacing of Nd, and the second subarray comprises N array elements with an element spacing of Md, wherein M and N are coprime.

[0020] The first subarray and the second subarray are overlapped with their first array elements overlapping to obtain an overlapping coprime array; the overlapping coprime array includes 2M+N-1 array elements.

[0021] The received signal X(t) is obtained by acquiring the signal from the source under test based on the overlapping coprime array;

[0022] Calculate the covariance matrix R of the received signal X(t). x ;

[0023] For the covariance matrix R x The vectorization process involves sorting the obtained vectors according to the positions of the array elements of a uniform linear array and processing them according to a predefined data processing strategy to obtain vector z, which represents the received signal of the virtual array.

[0024] Optionally, the signal of the source under test is a far-field narrowband signal emitted by the source under test.

[0025] Optionally, the step of interpolating the vector using array interpolation to obtain continuous virtual array elements specifically includes:

[0026] Calculate the average value of the received signals of the virtual array elements before and after the missing array element, and insert it into the vector as the value of the missing array element to obtain continuous virtual array elements and obtain the received signals of the virtual array.

[0027] The virtual array receives the following signal:

[0028]

[0029] L ex z[ represents the set of all array element positions within the range [-N(2M-1)d, N(2M-1)d] g ] and z(h) represent the received signals of the virtual array elements before and after the missing array element.

[0030] Optionally, the received signal X(t) is:

[0031] X(t) = A(θ)s(t) + n(t);

[0032] Where θ = [θ1, ..., θ2] K ] T ; The direction matrix of the overlapping coprime array; It is the waveform vector of the signal to be measured;

[0033] n(t) is a function with mean 0 and variance σ. 2 Additive white Gaussian noise;

[0034] K is the number of incoherent far-field narrowband signals;

[0035] λ is the wavelength of the signal to be measured, and the element spacing is d. l i d(i=2,3,…,2M+N-1) represents the position of the element of the overlapping coprime matrix.

[0036] Optionally, the covariance matrix R x for:

[0037] R X =E[X(t)X H [(t)]=AR s A H +σ 2 I;

[0038] in, Let be the average power of the kth incident signal to be measured;

[0039] The virtual array receives the signal z as follows:

[0040] z = vec(R) X )=Bp+σ 2 I n ;

[0041] B is the direction matrix for the received signals of the virtual array;

[0042]

[0043] The I n =vec(I), vec(·) matrix vectorization operation, (.) ＊ This indicates the conjugate operation.

[0044] Optionally, S2 includes:

[0045] S201. The received signal of the virtual array is evenly divided into N(2M-1)+1 overlapping subarrays, and each overlapping subarray includes N(2M-1)+1 virtual array elements;

[0046] S202. Calculate the covariance matrix of each virtual subarray.

[0047]

[0048] In the formula z exi This indicates the signal received by the i-th virtual subarray;

[0049] S203. Using the averaging method, sum the covariance matrices of the received signals of the N(2M-1)+1 virtual subarrays, take the average value, and obtain the spatial smoothing covariance matrix.

[0050] The spatial smoothing covariance matrix is:

[0051]

[0052] Secondly, the present invention also provides an improved spatial smoothing source angle estimation device for coprime linear arrays, comprising:

[0053] The processing unit is used to acquire the signal of the source under test based on a pre-constructed augmented coprime array to obtain the received signal; to perform vectorization processing on the covariance matrix of the received signal, to sort the obtained vector according to the array element positions of the uniform linear array and to process it according to a predefined data processing strategy to obtain the virtual array received signal.

[0054] The computing unit is used to uniformly divide the received signal of the virtual array into mutually overlapping received signals of the virtual sub-array based on a pre-built spatial smoothing rule, and to calculate the spatial smoothing covariance matrix of the received signals of the virtual sub-array.

[0055] The function determination unit is used to perform eigenvalue decomposition on the spatial smooth covariance matrix using a predefined spatial spectrum estimation method to obtain the spatial spectrum function.

[0056] An angle determination unit is used to perform spectral peak search on the spatial spectral function to determine the source angle of the source to be tested.

[0057] (III) Beneficial Effects

[0058] This invention provides an improved spatial smoothing source angle estimation method and apparatus based on a coprime linear array. By constructing an augmented coprime linear array, virtual array elements far exceeding physical array elements are added. Furthermore, data processing strategies are used to maximize the preservation of received signals, maintaining data integrity. Then, the source angle to be measured is determined through spatial smoothing rules, spatial spectral functions, and spectral peak search, improving the accuracy of source angle determination and reducing the estimation error. This method effectively estimates the source angle, offering high identification efficiency and low cost. Attached Figure Description

[0059] Figure 1 A flowchart illustrating an improved spatial smoothing source angle estimation method based on a coprime linear array, provided as an embodiment of the present invention;

[0060] Figure 2 (a) and (b) are schematic diagrams of an augmented coprime linear array subarray and an overlapping coprime array, respectively, provided in an embodiment of the present invention.

[0061] Figure 3 This is a schematic diagram of virtual array received signal smoothing provided in an embodiment of the present invention;

[0062] Figure 4 This is a schematic diagram of virtual array received signal smoothing provided in another embodiment of the present invention;

[0063] Figure 5 For the present invention Figure 3 and Figure 4 Spatial spectrum comparison diagram in the embodiment;

[0064] Figure 5 (a)(b)(c) are Figure 3 Spatial spectrum of the Chinese embodiment;

[0065] Figure 5 (e)(d)(f) are Figure 4 Spatial spectrum of the Chinese embodiment;

[0066] Figure 6 This is a source angle error curve provided in an embodiment of the present invention;

[0067] Figure 7 A source angle error curve diagram provided for another embodiment of the present invention;

[0068] Figure 8 The performance curve is provided for one embodiment of the present invention. Detailed Implementation

[0069] To better explain and facilitate understanding of the present invention, it will be described in detail below with reference to the accompanying drawings and specific embodiments. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a clearer and more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0070] Direction of Arrival (DOA) estimation is a crucial aspect of array signal processing, experiencing rapid development and widespread application in fields such as radar early warning, mobile communications, sonar alarms, earthquake monitoring, and radio navigation. In the national economy, accurate source angle information can be used for aviation and maritime navigation, beacon positioning, emergency search and rescue radio monitoring, locating illegal radio stations, and locating personnel and vehicles. In the military field, using DOA estimation technology for accurate positioning, tracking, and reconnaissance of tactical targets (aircraft, missiles, ships, radar stations, etc.) can significantly improve the combat effectiveness of combat units, further enhance the performance of various advanced weapons, and lay the foundation for jamming enemy communications and precision strikes. In daily life, it is also closely related to our daily activities and production. For example, when applied to microphone array voice acquisition systems, it requires interference noise suppression and desired signal direction identification and enhancement to achieve real-time translation applications such as voice collection and input. However, due to its widespread application, existing technologies suffer from drawbacks such as increased estimation complexity, low degrees of freedom, low estimation efficiency, low accuracy, large biases, and high costs. Therefore, this invention provides an improved spatially smooth source angle estimation method based on coprime linear arrays, which can be applied to estimate the source angle direction of electromagnetic wave signals in the above-mentioned scenarios, such as... Figure 1 As shown, the following steps may be included:

[0071] S1. Based on a pre-constructed augmented coprime array, the signal from the source under test is acquired to obtain the received signal; the covariance matrix of the received signal is vectorized, and the resulting vectors are sorted according to the element positions of the uniform linear array, and processed according to a predefined data processing strategy to obtain the virtual array received signal. The signal from the source under test is an electromagnetic wave signal, such as a far-field narrowband signal emitted by the source under test.

[0072] Specifically, the augmented coprime array may include a first subarray and a second subarray;

[0073] The first subarray and the second subarray are overlapped with their first array elements overlapping to obtain an overlapping coprime array.

[0074] S2. Based on the pre-constructed spatial smoothing rules, the received signal of the virtual array is uniformly divided into mutually overlapping received signals of the virtual sub-array, and the spatial smoothing covariance matrix of the received signal of the virtual sub-array is calculated.

[0075] S3. Using the predefined spatial spectrum estimation method (Multiple Signal Classification, MUSIC), perform eigenvalue decomposition on the spatial smooth covariance matrix to obtain the spatial spectrum function.

[0076] S4. Perform spectral peak search on the spatial spectral function to determine the source angle of the source to be tested.

[0077] This invention provides an improved spatial smoothing source angle estimation method based on coprime linear arrays. By reconstructing the virtual array, a number of virtual array elements far exceeding the number of physical array elements is generated, breaking through the limitation of the number of physical array elements on the degree of freedom. The high degree of freedom improves the performance of source angle estimation.

[0078] In one embodiment, such as Figure 2 As shown in (a), the augmented coprime array may include two uniform linear arrays, a first subarray and a second subarray; the first subarray includes 2M array elements with an element spacing of Nd, and the second subarray includes N array elements with an element spacing of Md, wherein M and N are coprime and satisfy M < N.

[0079] like Figure 2 As shown in (b), the first subarray and the second subarray are overlapped and combined into a non-uniform linear overlapping coprime array with the first array element overlapping. The overlapping coprime array includes 2M+N-1 array elements. The received signal X(t) is obtained by acquiring the signal of the source under test based on the overlapping coprime array.

[0080] The position of the array element can be denoted as L={nNd|0≤n≤2M-1}∪{mMd|0≤m≤N-1}.

[0081] In one embodiment, K incoherent narrowband far-field signals are... From the direction of arrival respectively If the incident augmented coprime array is such that the data received by the array is:

[0082] X(t) = A(θ)s(t) + n(t);

[0083] Where θ = [θ1, ..., θ2] K ] T , The direction matrix of the coprime arrays after overlap. It is the waveform vector of the signal, and n(t) is a vector with a mean of 0 and a variance of σ. 2 Additive white Gaussian noise.

[0084] The wavelength of the incident signal is λ, and the spacing between array elements is d (d≤λ / 2).

[0085]

[0086] in l i d(i=2,3,…,2M+N-1) represents the actual physical position of the array element of the overlapping coprime array.

[0087] Furthermore, based on the signal acquired from the source under test by the overlapping coprime array, the received signal X(t) is obtained, and the autocorrelation covariance matrix R of the received signal X(t) is calculated. x .

[0088] The covariance matrix R x for:

[0089] R X =E[X(t)X H [(t)]=AR s A H +σ 2 I;

[0090] in, Let be the average power of the k-th incident signal to be measured.

[0091] In practical applications, since it is difficult to obtain the autocorrelation covariance matrix of the ideal received data, the sample covariance matrix of the received signal at T sampling snapshots can be used as an approximation.

[0092] The sample covariance matrix is:

[0093]

[0094] Furthermore, the physical array element received signal X(t) is mapped into the virtual domain, and the covariance matrix R is then... x The vectorization process involves sorting the obtained vectors according to the positions of the array elements of a uniform linear array and processing them according to a predefined data processing strategy to obtain vector z, which represents the received signal of the virtual array.

[0095] It can be represented as:

[0096] z = vec(R) X )=Bp+σ 2 I n ;

[0097] in, This represents the direction matrix of the received signal of the virtual array. I n =vec(I), where vec(.) represents the matrix vectorization operation, which "pulls" the matrix into a vector column-wise. This represents the Kronecker product operation. ＊ This represents the conjugate operation. p is a single-shot signal vector and p has a rank of 1.

[0098] The vector z contains (2M+N-1) elements. 2 Each element represents a signal received by a virtual array element. That is, the 2M+N-1 physical array elements are expanded into (2M+N-1) through virtual array reconstruction. 2 A virtual array element is generated in the range [-N(2M-1)d, N(2M-1)d].

[0099] In one embodiment, the process of sorting the obtained vectors according to the element positions of the uniform linear array and processing them according to a predefined data processing strategy can be implemented as follows: sorting the obtained vectors according to the element positions of the uniform linear array and deleting redundant rows, such as... Figure 3 As shown, Figure 3 This is a schematic diagram of virtual array received signal smoothing provided in one embodiment of the present invention. Figure 3 In this embodiment, the data processing strategy used is to sort the obtained vectors according to the element positions of a uniform linear array and delete redundant rows.

[0100] The vector z contains unordered and redundant elements, i.e., repeated virtual array element signals, and also exhibits some missing virtual array elements, resulting in discontinuity in the received signal of the virtual array. During step S1, the vector is reordered and deredundanted, and the largest continuous virtual array element in the received signal of the virtual array is selected for spatial smoothing calculation.

[0101] In this embodiment, firstly, a difference set array is used to describe the position of the virtual array element. The difference set array is as follows:

[0102] L diff ={±(Mn-Nm)d, 0≤m≤2M-1, 0≤n≤N-1}.

[0103] As can be seen from the difference set array, the virtual array element contains a virtual uniform linear subarray consisting of positions from -MNd to MNd. The elements from positions -MNd to MNd in the received signal of the virtual array are extracted and denoted as... That is, the spatial smoothing calculation is performed on the received signal z1 of the virtual array with array element positions located at {-MNd, ..., -d, 0, d, ..., MNd}. This is equivalent to using a virtual uniform linear subarray with array element positions located at {{-MNd, ..., -d, 0, d, ..., MNd} to acquire the signal.

[0104] Specifically, such as Figure 3 In the illustrated embodiment, the virtual array receiving signal z1 is divided into MN+1 overlapping uniform virtual subarrays. Each uniform virtual subarray includes MN+1 virtual array elements. The positions of the virtual array elements in the i-th virtual subarray are {(-i+1+q)d, q=0,1,2,…,MN}. The signal received by the i-th virtual subarray is taken from the (MN+2-i)-th row to the (2MN+2-i)-th row of z1, denoted as z 1i .

[0105] Calculate the covariance matrix of each virtual subarray:

[0106]

[0107] Furthermore, by summing the covariance matrices of the MN+1 virtual subarrays and taking the average, the spatial smoothing covariance matrix can be obtained, i.e.

[0108]

[0109] Furthermore, the spatial smoothing covariance matrix R is full rank, and the angle of the source to be measured is estimated using the classical spatial spectrum estimation method, namely the SS-MUSIC algorithm.

[0110] In other embodiments, besides missing array elements during acquisition, the virtual array obtained after vector reordering and redundancy removal is a non-continuous linear structure, containing "holes" of missing array elements. During spatial smoothing calculations, only the largest continuous virtual array element is extracted, leading to the loss of received signals from some virtual array elements. This, in turn, reduces the array aperture and degrees of freedom, and decreases the accuracy of source angle estimation. Therefore, in some embodiments, the obtained vectors are sorted according to the element positions of a uniform linear array and processed according to a predefined data processing strategy, which can also be implemented as follows:

[0111] The obtained vectors are sorted according to the positions of the array elements of the uniform linear array. The average value of the repeated virtual array element signals in the vectors is calculated. The average value is used to replace the repeated virtual array element signals to obtain the virtual array received signal.

[0112] And / or,

[0113] The obtained vectors are sorted according to the positions of the array elements of a uniform linear array. The vectors are then interpolated using an array interpolation method to obtain continuous virtual array elements, thus obtaining the virtual array received signal.

[0114] For example, such as Figure 4 As shown, Figure 4 This is a schematic diagram of virtual array receiving signal smoothing provided in another embodiment of the present invention.

[0115] In this embodiment, the vector is reordered while the received signals of the original virtual array elements remain unchanged. First, interpolation is performed on the "holes" of the missing array elements to calculate the average value of the virtual received signals before and after the missing array element, which is then inserted into the vector as the value of the missing array element. Further, the average value of the signals of the repeated virtual array elements in the original virtual array elements is taken to obtain continuous virtual array elements and thus obtain the virtual array received signal.

[0116] The virtual array receives the following signal:

[0117]

[0118] Where L ex Let z[g] represent the set of all array element positions within the range [-N(2M-1)d, N(2M-1)d], and z[g] and z(h] represent the virtual array element received signals before and after the missing array element.

[0119] Furthermore, for the virtual array received signal after array interpolation, step S2 can be specifically implemented as follows:

[0120] S201. The received signal of the virtual array is evenly divided into N(2M-1)+1 overlapping subarrays, and each overlapping subarray includes N(2M-1)+1 virtual array elements.

[0121] S202. Calculate the covariance matrix of each virtual subarray:

[0122]

[0123] In the formula z cxi This indicates the signal received by the i-th virtual subarray;

[0124] S203. Using the averaging method, sum the covariance matrices of the received signals of the N(2M-1)+1 virtual subarrays, take the average value, and obtain the spatial smoothing covariance matrix.

[0125] The spatial smoothing covariance matrix is:

[0126]

[0127] The present invention provides an improved spatial smoothing method for estimating the source angle of a coprime linear array. This method increases the number of virtual array elements in the coprime array by adding elements much larger than the actual physical array elements. The positions of the virtual elements are related to the position differences of the physical elements, increasing the degrees of freedom and improving the accuracy of the calculated source angle. An array interpolation approach is used to construct a linear uniform array containing all virtual elements, and the signals of repeated virtual elements are averaged to maximize the preservation of the received signal integrity. Spatial smoothing is used to construct a full-rank virtual array covariance matrix from a single-rank matrix. The source angle is then calculated using the spatial spectrum estimation method (MUSIC). This effectively preserves all vector z (i.e., the received signal from the virtual array), increasing data completeness and improving the source identification rate.

[0128] The improved spatial smoothing source angle estimation method for coprime linear arrays provided in the above embodiments of the present invention can effectively suppress surrounding interference and noise for signal reception and processing. For example, a microphone array voice acquisition system applying this method can effectively suppress surrounding interference and noise, and can also complete voice collection and recording in a specified direction for real-time translation applications.

[0129] To better explain the above technical solutions, several computer simulation embodiments will be presented here as illustrations.

[0130] In the following embodiments, a first spatial spectrum function and a second spatial spectrum function are used respectively. The first spatial spectrum function is a function obtained based on the spatial smoothing covariance matrix R, that is, the spatial spectrum function obtained after vector reordering and redundancy removal. The second spatial spectrum function is based on the spatial smoothing covariance matrix R. ex The obtained function is the spatial spectrum function obtained after array interpolation and averaging the received signals from the virtual array elements.

[0131] The spatial smoothing covariance matrix R is:

[0132]

[0133] The spatial smoothing covariance matrix Rex is:

[0134]

[0135] In the preferred augmented coprime array, M=3 and N=4. The two subarrays are recombined into a non-uniform linear array with the first array element overlapping, containing 2M+N-1=9 physical array elements. The positions of the physical array elements are located at {0, 3d, 4d, 6d, 8d, 9d, 12d, 16d, 20d}.

[0136] Given that the power of the incident signals is equal, the root mean square error (RMSE) of the algorithm is defined as follows:

[0137]

[0138] in Let J represent the estimated angle of the k-th source target in the j-th experiment, and let J represent the number of Monte Carlo experiments, with the value of J set to 100.

[0139] Example 1

[0140] The signal-to-noise ratio (SNR) of the incident signal is 0 dB, the number of snapshots T is set to 500, and the angle between the source and the array is between -90° and 90°. Simulations are performed with the number of sources K = 7, K = 11, and K = 13.

[0141] Simulation results are as follows Figure 5 As shown, Figure 5 (a), (b), and (c) show the peak response results of the first spatial spectral function when the number of information sources is K=7, K=11, and K=13, respectively. Figure 5 (d), (e), and (f) represent the peak response results of the second spatial spectral function when the number of information sources is K=7, K=11, and K=13, respectively. The vertical lines in the figure represent the incident angle of the information source.

[0142] Compare Figure 5 (a) and Figure 5 (d) The peak response results are all quite obvious, that is, when the number of information sources is 7, the information sources can be effectively distinguished.

[0143] Compare Figure 5 (d) and Figure 5 (e), Figure 5 (e) shows a very clear peak response, effectively distinguishing 11 signal sources. Figure 5(d) indicates that some peak response results are low, there is estimation bias, and the sharpness of the peak response is low.

[0144] Compare Figure 5 (c) and Figure 5 (f), Figure 5 (c) shows no peak response results, meaning that when the number of sources is 13, the first spatial spectral function can no longer distinguish the sources. Figure 5 (f) shows a clear peak response result, which can clearly and effectively distinguish 13 information sources.

[0145] The response results in Example 1 reflect that the virtual array generated after array interpolation and average repetition of the virtual array element received signals, which includes all virtual array elements, has a high degree of freedom and effectively improves the accuracy of source resolution.

[0146] Example 2

[0147] This embodiment shows the root mean square error variation curve of source angle estimation using the first and second spatial spectrum functions when the signal-to-noise ratio changes.

[0148] The angle of the source under test is set to K=7, and the angle range of the source relative to the array is between -90° and 90°. The number of snapshots T is still set to 500, and the signal-to-noise ratio of the signal received by the array element changes from -8dB to 12dB. The curves of the RMSE of the estimated angle as a function of the signal-to-noise ratio are obtained by the first spatial spectrum function and the second spatial spectrum function.

[0149] Simulation results are as follows Figure 6 As shown, the triangle represents the curve of the RMSE of the second spatial spectral function estimation angle as a function of the signal-to-noise ratio, and the circle represents the curve of the RMSE of the first spatial spectral function estimation angle as a function of the signal-to-noise ratio.

[0150] like Figure 6 As shown, when the signal-to-noise ratio is -8dB to 0dB, the source angle estimation error of the second spatial spectrum function is significantly smaller than that of the first spatial spectrum function. When the signal-to-noise ratio is 0dB to 12dB, the source angle estimation error of the second spatial spectrum function is basically consistent with that of the first spatial spectrum function.

[0151] The simulation results of Example 2 show that after array interpolation and average repetitive virtual array elements, the generated spatial spectrum function can better estimate the source angle when the signal-to-noise ratio is low.

[0152] Example 3

[0153] This embodiment shows the root mean square error variation curve of source angle estimation using the first and second spatial spectrum functions when the number of snapshots changes.

[0154] The angle of the source under test is set to K-7, and the angle of the source relative to the array is between -90° and 90°. The signal-to-noise ratio (SNR) of the incident signal is set to 0 dB, and the number of snapshots T is changed from 100 to 800. The curves of the RMSE of the estimated angle with the number of snapshots are obtained by the first spatial spectrum function and the second spatial spectrum function.

[0155] Simulation results are as follows Figure 7 As shown, the triangle represents the curve of the RMSE of the estimated angle by the second spatial spectral function as a function of the number of snapshots, and the circle represents the curve of the RMSE of the estimated angle by the first spatial spectral function as a function of the number of snapshots. The larger the number of snapshots, the better the source angle estimation results of the first and second spatial spectral functions match. When the number of snapshots is small, the source angle estimation result of the second spatial spectral function has a smaller error than that of the first spatial spectral function.

[0156] Example 4

[0157] This embodiment shows the performance change curve of the second spatial spectral function as the number of sources changes.

[0158] The signal-to-noise ratio (SNR) of the incident signal varied from -8dB to 12dB, the number of snapshots T was set to 500, and the angle between the source and the array was between -90° and 90°. Simulations were performed with the number of sources K=7, K=11, and K=13.

[0159] Depend on Figure 8 It can be seen that as the number of information sources increases, the error in estimating the source angle by the second spatial spectrum function gradually increases, and the performance degrades.

[0160] As can be seen from the above embodiments, the improved spatial smoothing source angle estimation method based on coprime linear array provided by the present invention can effectively distinguish the number of sources and determine the source angle with small error when there are many sources, low signal-to-noise ratio and low number of snapshots. It is efficient, low cost and good performance.

[0161] In one embodiment of the present invention, an improved spatial smoothing source angle estimation device for coprime linear arrays is also provided, comprising:

[0162] The processing unit is used to acquire the signal of the source under test based on a pre-constructed augmented coprime array to obtain the received signal; to perform vectorization processing on the covariance matrix of the received signal, to sort the obtained vector according to the array element positions of the uniform linear array and to process it according to a predefined data processing strategy to obtain the virtual array received signal.

[0163] The computing unit is used to uniformly divide the received signal of the virtual array into mutually overlapping received signals of the virtual sub-array based on a pre-built spatial smoothing rule, and to calculate the spatial smoothing covariance matrix of the received signals of the virtual sub-array.

[0164] The function determination unit is used to perform eigenvalue decomposition on the spatial smoothing covariance matrix using the predefined spatial spectrum estimation method MUSIC to obtain the spatial spectrum function.

[0165] An angle determination unit is used to perform spectral peak search on the spatial spectral function to determine the source angle of the source to be tested.

[0166] Further, the processing unit sorts the obtained vectors according to the positions of the array elements of the uniform linear array, calculates the average value of the repeated virtual array element signals in the virtual array elements of the vectors, and replaces the repeated virtual array element signals with the average value to obtain the virtual array received signal.

[0167] Alternatively, the processing unit sorts the obtained vector according to the position of the array elements of a uniform linear array, uses array interpolation to interpolate the missing array elements in the vector, calculates the average value of the virtual array element received signal before and after the missing array element, inserts it into the vector as the value of the missing array element, obtains continuous virtual array elements, and obtains the virtual array received signal.

[0168] The virtual array receives the following signal:

[0169]

[0170] L ex Let z[g] represent the set of all array element positions within the range [-N(2M-1)d, N(2M-1)d], and z[g] and z(h] represent the virtual array element received signals before and after the missing array element.

[0171] The computing unit is used to uniformly divide the received signal of the virtual array into N(2M-1)+1 overlapping subarrays, each overlapping subarray comprising N(2M-1)+1 virtual array elements; and to calculate the covariance matrix of each virtual subarray.

[0172]

[0173] In the formula z cxi This indicates the signal received by the i-th virtual subarray;

[0174] The spatial smoothing covariance matrix is ​​obtained by summing the covariance matrices of the received signals of the N(2M-1)+1 virtual subarrays using the averaging method.

[0175] The spatial smoothing covariance matrix is:

[0176]

[0177] This invention provides an improved spatial smoothing method and apparatus for estimating source angles based on a coprime linear array. It constructs a linear uniform array containing all virtual array elements through array interpolation, and averages the signals of repeated virtual array elements. Then, using the concept of spatial smoothing, a single-rank matrix is ​​constructed into a full-rank virtual array covariance matrix. Finally, the source angle is determined using the classical spatial spectrum estimation method MUSIC. The constructed virtual uniform linear array includes a much larger number of virtual array elements than the actual number of physical array elements, while retaining all received signal information. This not only increases the array aperture and degrees of freedom but also improves the accuracy of source angle confirmation. Furthermore, it achieves high accuracy and small confirmation error even with a large number of sources, low signal-to-noise ratio, and sampling times of several hours, making it widely applicable.

[0178] The present invention provides an improved method and apparatus for estimating the spatial smoothing source angle based on a coprime linear array, which can effectively perform direction-of-arrival localization. It can maintain better performance in situations with multiple sources, large number of rapid sorting and low signal-to-noise ratio, improve the accuracy and efficiency of localization estimation, and reduce costs.

[0179] In the description of this invention, it should be understood that 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 indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0180] In the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. 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. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0181] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make modifications, alterations, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. An improved method for estimating the angle of a spatially smooth source based on a coprime linear array, characterized in that, Includes the following steps: S1. Based on a pre-constructed augmented coprime array, the signal from the source under test is acquired to obtain the received signal; The covariance matrix of the received signal is vectorized, and the resulting vector is sorted according to the element positions of the uniform linear array and processed according to a predefined data processing strategy to obtain the virtual array received signal. The augmented coprime array includes a first subarray and a second subarray; The first subarray comprises 2M array elements with an element spacing of Nd, and the second subarray comprises N array elements with an element spacing of Md, wherein M and N are coprime. The data processing strategy includes extracting the largest consecutive virtual array element from position -MNd to MNd in the received signal of the virtual array; The signal of the source under test is a far-field narrowband signal emitted by the source under test; The obtained vectors are sorted according to the element positions of a uniform linear array and processed according to a predefined data processing strategy, including: The obtained vectors are sorted according to the positions of the elements of the uniform linear array. The average value of the repeated virtual element signals in the virtual elements of the vectors is calculated. The average value is used to replace the repeated virtual element signals to obtain the virtual array received signal. And / or, The obtained vectors are sorted according to the positions of the array elements of a uniform linear array, and the missing array elements in the vectors are interpolated using the array interpolation method to obtain the virtual array received signal. S2. Based on the pre-constructed spatial smoothing rules, the received signal of the virtual array is uniformly divided into mutually overlapping received signals of the virtual sub-array, and the spatial smoothing covariance matrix of the received signal of the virtual sub-array is calculated. S3. Using a predefined spatial spectrum estimation method, perform eigenvalue decomposition on the spatial smooth covariance matrix to obtain the spatial spectrum function; S4. Perform spectral peak search on the spatial spectral function to determine the source angle of the source to be tested.

2. The estimation method as described in claim 1, characterized in that, In S1, The first subarray and the second subarray are overlapped in such a way that the first array element overlaps to obtain an overlapping coprime array; The overlapping coprime array includes Each array element; The received signal X(t) is obtained by acquiring the signal from the source under test based on the overlapping coprime array; Calculate the covariance matrix R of the received signal X(t). x ; For the covariance matrix R x The vectorization process involves sorting the obtained vectors according to the positions of the array elements of a uniform linear array and processing them according to a predefined data processing strategy to obtain vector z, which represents the received signal of the virtual array.

3. The estimation method as described in claim 1, characterized in that, The step of interpolating the vector using array interpolation to obtain continuous virtual array elements specifically includes: Calculate the average value of the received signals of the virtual array elements before and after the missing array element, and insert it into the vector as the value of the missing array element to obtain continuous virtual array elements and obtain the received signals of the virtual array. The virtual array receives the following signal: ； express The set of all array element positions within the range, and This indicates the received signals of the virtual array elements before and after the missing array element.

4. The estimation method as described in claim 2, characterized in that, The received signal X(t) is: ； in, ; The direction matrix of the overlapping coprime array; It is the waveform vector of the signal to be measured; It has a mean of 0 and a variance of Additive white Gaussian noise; K is the number of incoherent far-field narrowband signals; The Let be the wavelength of the signal to be measured, and let d be the spacing between the array elements. , represents the element positions of the overlapping coprime matrix.

5. The estimation method as described in claim 2, characterized in that, The covariance matrix R x for: ； in, , For the first The average power of each incident signal to be measured; The virtual array receives the signal z as follows: ； B is the direction matrix for the received signals of the virtual array; ; The , , Matrix vectorization operations This indicates the conjugate operation.

6. The estimation method as described in claim 3, characterized in that, S2 includes: S201, Divide the received signal of the virtual array evenly into... Each overlapping subarray includes a number of overlapping subarrays. One virtual array element; S202. Calculate the covariance matrix of each virtual subarray. ； In the formula Indicates the first Each virtual subarray receives signals; S203. Using the averaging method, the above... The spatial smoothing covariance matrix is ​​obtained by summing the covariance matrices of the signals received by each virtual subarray and taking the average value. The spatial smoothing covariance matrix is: 。 7. An improved spatially smoothed source angle estimation device for a coprime linear array, characterized in that, include: The processing unit is used to acquire the signal from the source under test based on a pre-constructed augmented coprime array to obtain the received signal; The covariance matrix of the received signal is vectorized, and the resulting vector is sorted according to the element positions of the uniform linear array and processed according to a predefined data processing strategy to obtain the virtual array received signal. The augmented coprime array includes a first subarray and a second subarray; The first subarray comprises 2M array elements with an element spacing of Nd, and the second subarray comprises N array elements with an element spacing of Md, wherein M and N are coprime. The data processing strategy includes extracting the largest consecutive virtual array element from position -MNd to MNd in the received signal of the virtual array; The signal of the source under test is a far-field narrowband signal emitted by the source under test; The obtained vectors are sorted according to the element positions of a uniform linear array and processed according to a predefined data processing strategy, including: The obtained vectors are sorted according to the positions of the elements of the uniform linear array. The average value of the repeated virtual element signals in the virtual elements of the vectors is calculated. The average value is used to replace the repeated virtual element signals to obtain the virtual array received signal. And / or, The obtained vectors are sorted according to the positions of the array elements of a uniform linear array, and the missing array elements in the vectors are interpolated using the array interpolation method to obtain the virtual array received signal. The computing unit is used to uniformly divide the received signal of the virtual array into mutually overlapping received signals of the virtual subarray based on a pre-built spatial smoothing rule, and to calculate the spatial smoothing covariance matrix of the received signals of the virtual subarray. The function determination unit is used to perform eigenvalue decomposition on the spatial smooth covariance matrix using a predefined spatial spectrum estimation method to obtain the spatial spectrum function. An angle determination unit is used to perform spectral peak search on the spatial spectral function to determine the source angle of the source to be tested.

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