A method, system, device and medium for estimating direction of arrival (DOA) of multi-frequency signals.

Abstract

This invention discloses a method, system, device, and medium for estimating the direction of arrival (DOA) of multi-frequency signals, relating to the field of radio direction finding. The method includes: receiving a target incident signal using a uniform linear array receiver model to obtain an array received signal; performing a Fast Fourier Transform (FFT) on the array received signal to obtain a discrete spectrum signal; extracting frequency domain data corresponding to spectral peaks from the discrete spectrum signal to obtain a frequency domain signal matrix; reconstructing the covariance matrix based on the frequency domain signal matrix to obtain the target covariance matrix; and using a multiple signal classification algorithm to determine the DOA of the target incident signal based on the target covariance matrix. This invention enables high-precision DOA estimation of multi-frequency signals under low signal-to-noise ratio (SNR) conditions.

Description

Technical Field

[0001] This invention relates to the field of radio direction finding, and in particular to a method, system, device, and medium for estimating the direction of arrival of multi-frequency signals. Background Technology

[0002] In the field of electromagnetic environment detection, Direction of Arrival (DOA) estimation is one of the most important technologies and a significant research direction in array signal processing. In recent decades, DOA estimation has been widely applied in numerous fields such as radar, sonar, wireless communication, and radio astronomy. With the deepening of theoretical research, DOA estimation methods have been continuously proposed and improved to obtain higher accuracy. Among these, subspace decomposition algorithms are the most typical super-resolution direction finding methods, such as the MUSIC method (multiple signal classification) and the ESPRIT method (rotation-invariant subspace). Compressed sensing theory has also been applied to DOA estimation. Due to the spatial sparsity of the DOA estimation signal model, it can be transformed into a sparse representation. Researchers use sparse reconstruction methods based on compressed sensing theory for DOA estimation. However, the methods described above can only achieve high-precision target direction finding under conditions of high signal-to-noise ratio and high snapshot count. Under lower signal-to-noise ratio conditions, the direction finding accuracy is poor. Furthermore, because multi-frequency target signals affect the selection of array element spacing, thus affecting the estimation accuracy of DOA, traditional algorithms rarely study multi-source, multi-frequency interference sources.

[0003] To overcome noise interference, researchers have proposed a higher-order cumulant method, which possesses Gaussian noise suppression capabilities not found in second-order statistics. Some scholars have introduced higher-order statistics to extend the virtual array antenna, improving DOA estimation accuracy to some extent under low signal-to-noise ratio (SNR) conditions. However, introducing higher-order statistics leads to algorithm redundancy, significantly increasing computational complexity. Another approach involves an enhanced spatial smoothing method. First, it utilizes the strong correlation of the signal and the weak correlation of noise in the spatiotemporal domain to construct a subarray spatiotemporal correlation matrix, eliminating the influence of noise. Then, it employs a squared spatial smoothing technique to reconstruct the spatiotemporally smoothed array covariance matrix. Finally, it combines this with a subspace-based method to obtain the DOA estimate. This proposed method improves noise suppression and DOA estimation performance under low SNR conditions, but none of these methods can achieve DOA estimation for multi-frequency signals. Summary of the Invention

[0004] The purpose of this invention is to provide a method, system, device and medium for estimating the direction of arrival (DOA) of multi-frequency signals, so as to achieve high-precision DOA estimation of multi-frequency signals under low signal-to-noise ratio conditions.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for estimating the direction of arrival (DOA) of a multi-frequency signal includes:

[0007] A uniform linear array receiving model is used to receive the target incident signal to obtain the array received signal; the uniform linear array receiving model consists of several linearly arranged antennas, and the spacing between adjacent antennas is half the wavelength corresponding to the highest frequency signal in the target incident signal; the target incident signal consists of several narrowband far-field signals with different directions and frequencies.

[0008] Perform a Fast Fourier Transform on the received signal from the array to obtain a discrete spectrum signal;

[0009] Frequency domain data corresponding to spectral peaks are extracted from the discrete spectral signal to obtain a frequency domain signal matrix;

[0010] The covariance matrix is ​​reconstructed based on the frequency domain signal matrix to obtain the target covariance matrix;

[0011] A multiple signal classification algorithm is used to determine the direction of arrival of the incident signal of the target based on the target covariance matrix.

[0012] Optionally, the array receives a signal as an N×M matrix; where M is the number of sampling points and N is the number of antennas; the expression for the array receives the signal is:

[0013] x(t) = As(t) + n(t);

[0014] x(t) = [x1(t), x2(t), ..., x N (t)] T ;

[0015] s(t)=[s1(t),s2(t),...,s Q (t)] T ;

[0016] n(t) = [n1(t), n2(t), ..., n N (t)] T ;

[0017] A=[a(θ1),...,a(θ Q )];

[0018]

[0019] Where x(t) is the array received signal matrix, x1(t), x2(t), ..., x N s(t) represents the received signals from N antennas; s(t) is the target incident signal matrix, s1(t), s2(t), ..., s Q(t) represents Q narrowband far-field signals; n(t) is a Gaussian white noise signal matrix, n1(t), n2(t), ..., n N (t) represents the Gaussian white noise signal of N antennas; A is the array antenna steering vector, a(θ1),...,a(θ) Q θ1, θ2, ..., θ3 are the steering vectors of Q narrowband far-field signals. Q denoted by , where d represents the direction of the Q narrowband far-field signals; d represents the spacing between adjacent antennas; λ represents the wavelength corresponding to the highest frequency signal in the incident signal from the target; t represents the time period, and the number of sampling points in each time period is M; Q represents the number of narrowband far-field signals; and q represents the sequence number of the narrowband far-field signals.

[0020] Optionally, the received signal from the array is subjected to a Fast Fourier Transform to obtain a discrete spectrum signal, as shown in the following formula:

[0021] X FFT =[X1,X2,...,X N ] T ;

[0022]

[0023]

[0024] Among them, X FFT For discrete spectrum signals; X1, X2, ..., X N These are the frequency domain data of the received signals from N antennas after undergoing Fast Fourier Transform; These are the frequency domain data of the received signal from the i-th antenna after undergoing a Fast Fourier Transform (FFT) at M sampling points; N is the number of antennas; M is the number of sampling points; i is the antenna number; and k and m are both sampling point numbers.

[0025] Optionally, frequency domain data corresponding to spectral peaks are extracted from the discrete spectral signal to obtain a frequency domain signal matrix, as shown in the following formula:

[0026]

[0027]

[0028] Among them, X F It is a frequency domain signal matrix; These are the frequency domain data corresponding to the Q spectral peaks in the discrete spectrum signal; The f-th digit of the received signal from N antennas after undergoing a Fast Fourier Transform is... q Frequency domain data of 1 sampling point; N is the number of antennas; M is the number of sampling points; Q is the number of narrowband far-field signals; q is the index of the narrowband far-field signal; f qThis is the sequence number of the sampling point.

[0029] Optionally, the covariance matrix is ​​reconstructed based on the frequency domain signal matrix to obtain the target covariance matrix, as shown in the following formula:

[0030]

[0031] Among them, R F X is the target covariance matrix; F X is a frequency domain signal matrix; F H is the conjugate transpose of the frequency domain signal matrix; Q is the number of narrowband far-field signals.

[0032] Optionally, a multiple signal classification algorithm is employed to determine the direction of arrival of the incident signal of the target based on the target covariance matrix, specifically including:

[0033] The target covariance matrix is ​​decomposed into eigenvalues ​​to obtain the eigenvector matrix and the corresponding diagonal matrix.

[0034] Based on the magnitude of the eigenvalues ​​in the diagonal matrix, the eigenvector matrix is ​​divided into a signal subspace and a noise subspace;

[0035] The spatial spectrum function is determined based on the steering vector of the signal subspace and the noise subspace;

[0036] The direction of arrival of the incident signal from the target is obtained by performing a spectral peak search on the spatial spectral function.

[0037] Optionally, the expression for the spatial spectral function is:

[0038]

[0039] Among them, P MUSIC U is the spatial spectrum estimate; N For the noise subspace; U H N Let be the conjugate transpose matrix of the noise subspace; a(θ) is the steering vector of the signal subspace; a H (θ) is the conjugate transpose of the guiding vector in the signal subspace.

[0040] A multi-frequency signal direction-of-arrival estimation system includes:

[0041] An array receiving signal acquisition module is used to receive a target incident signal using a uniform linear array receiving model to obtain an array received signal; the uniform linear array receiving model consists of several linearly arranged antennas, and the spacing between adjacent antennas is half the wavelength corresponding to the highest frequency signal in the target incident signal; the target incident signal consists of several narrowband far-field signals with different directions and frequencies.

[0042] The discrete spectrum signal determination module is used to perform a fast Fourier transform on the received signal of the array to obtain a discrete spectrum signal;

[0043] The frequency domain signal matrix determination module is used to extract the frequency domain data corresponding to the spectral peaks from the discrete spectral signal to obtain the frequency domain signal matrix.

[0044] The target covariance matrix determination module is used to reconstruct the covariance matrix based on the frequency domain signal matrix to obtain the target covariance matrix;

[0045] The direction of arrival determination module is used to determine the direction of arrival of the target incident signal based on the target covariance matrix using a multiple signal classification algorithm.

[0046] An electronic device includes a memory and a processor, the memory storing a computer program, and the processor running the computer program to enable the electronic device to perform the multi-frequency signal direction of arrival estimation method described above.

[0047] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described multi-frequency signal direction-of-arrival estimation method.

[0048] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0049] The multi-frequency signal direction-of-arrival estimation method provided by this invention uses a uniform linear array receiving model to receive the target incident signal. It performs a time-frequency domain conversion on the array received signal using a fast Fourier transform to obtain a discrete spectrum signal. Frequency domain data corresponding to the spectral peaks are extracted from the discrete spectrum signal to eliminate most noise signals, resulting in a frequency domain signal matrix. The covariance matrix is ​​then reconstructed using the frequency domain signal matrix, and a multiple signal classification algorithm is employed to determine the target incident signal's direction of arrival based on the obtained target covariance matrix. This method enables high-precision direction-of-arrival estimation of multi-frequency signals under low signal-to-noise ratio conditions. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. 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.

[0051] Figure 1 A flowchart of the multi-frequency signal direction of arrival estimation method provided by the present invention;

[0052] Figure 2A schematic diagram of the uniform linear array receiving model provided by the present invention;

[0053] Figure 3 The curve showing the change in DOA estimation accuracy with signal-to-noise ratio provided by this invention;

[0054] Figure 4 The graph showing the variation of the root mean square error of DOA estimation with the signal-to-noise ratio provided by this invention;

[0055] Figure 5 This is a block diagram of the multi-frequency signal direction of arrival estimation system provided by the present invention.

[0056] Symbol explanation:

[0057] Array received signal acquisition module-1, discrete spectrum signal determination module-2, frequency domain signal matrix determination module-3, target covariance matrix determination module-4, and direction of arrival determination module-5. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] The purpose of this invention is to provide a method, system, device and medium for estimating the direction of arrival (DOA) of multi-frequency signals, so as to achieve high-precision DOA estimation of multi-frequency signals under low signal-to-noise ratio conditions.

[0060] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] Example 1

[0062] This invention provides a method for estimating the direction of arrival (DOA) of a multi-frequency signal. For example... Figure 1 As shown, the method includes:

[0063] Step S1: The target incident signal is received using a uniform linear array receiving model to obtain the array received signal; the uniform linear array receiving model is a receiving antenna matrix, which consists of several linearly arranged antennas, and the spacing between adjacent antennas is half the wavelength corresponding to the highest frequency signal in the target incident signal; the target incident signal consists of several narrowband far-field signals with different directions and frequencies.

[0064] like Figure 2As shown, assume the receiving antenna matrix has N antennas, arranged linearly to form a uniform linear array, with the spacing between each antenna d = λ / 2 (λ is the wavelength corresponding to the highest frequency signal in the incident signal from the target). There are Q distinct antennas with directions θ1, θ2, ..., θ... Q The frequencies are f1, f2, ..., f Q Narrowband far-field signal s q (t) is incident on a uniform linear array, where the signal received by the i-th array antenna can be expressed as:

[0065]

[0066] Where, x i (t) represents the received signal from the i-th antenna in the receiving antenna matrix; n i (t) represents the Gaussian white noise signal; e represents the natural constant; j represents the imaginary number.

[0067] The received signal from the array antenna can be represented in matrix form as follows:

[0068] x(t) = As(t) + n(t).

[0069] Where x(t), s(t), and n(t) can be expressed as:

[0070] x(t) = [x1(t), x2(t), ..., x N (t)] T ;

[0071] s(t)=[s1(t),s2(t),...,s Q (t)] T ;

[0072] n(t) = [n1(t), n2(t), ..., n N (t)] T .

[0073] A can be represented as:

[0074] A=[a(θ1),...,a(θ Q )];

[0075]

[0076] Where x(t) is the array received signal matrix, x1(t), x2(t), ..., x N s(t) represents the received signals from N antennas; s(t) is the target incident signal matrix, s1(t), s2(t), ..., s Q(t) represents Q narrowband far-field signals; n(t) is a Gaussian white noise signal matrix, n1(t), n2(t), ..., n N (t) represents the Gaussian white noise signal of N antennas; A is the array antenna steering vector, a(θ1),...,a(θ) Q θ1, θ2, ..., θ3 are the steering vectors of Q narrowband far-field signals. Q denoted by , where d represents the direction of the Q narrowband far-field signals; d represents the spacing between adjacent antennas; λ represents the wavelength corresponding to the highest frequency signal in the incident signal from the target; t represents the time period, and the number of sampling points in each time period is M; Q represents the number of narrowband far-field signals, i.e., the number of incident signal sources; q represents the sequence number of the narrowband far-field signals; and the superscript T indicates transpose.

[0077] If the number of signal sampling points (also called the number of snapshots) is M, then the array receiving signal matrix is ​​an N×M matrix. Due to the presence of noise, the target signal will be submerged in noise under low signal-to-noise ratio conditions. When performing DOA estimation in the time domain, noise will affect the accuracy of DOA estimation.

[0078] Step S2: Perform a fast Fourier transform on the received signal of the array to obtain a discrete spectrum signal.

[0079] Specifically, a Fast Fourier Transform (FFT) is performed on each array received signal. For an array received signal x(t) that is an N×M matrix, each row corresponds to signals from N antennas with M snapshots. The FFT is then applied to the array received signal x(t) according to the FFT formula:

[0080]

[0081] Where M is the number of signal snapshots, i.e., the number of sampling points for each antenna receiving the signal, k = 1, 2, ..., M, i = 1, 2, ..., N. The frequency domain array signal receiving matrix, i.e., the discrete spectrum signal, is obtained through Fast Fourier Transform.

[0082] X FFT =[X1,X2,...,X N ] T ;

[0083]

[0084]

[0085] Among them, X FFT Represents discrete spectrum signals; X1, X2, ..., X N These are the frequency domain data of the received signals from N antennas after undergoing Fast Fourier Transform; These are the frequency domain data of the received signal from the i-th antenna after undergoing a Fast Fourier Transform (FFT) at M sampling points; N is the number of antennas; M is the number of sampling points; i is the antenna number; and k and m are both sampling point numbers.

[0086] Step S3: Extract the frequency domain data corresponding to the spectral peaks from the discrete spectral signal to obtain the frequency domain signal matrix.

[0087] Specifically, discrete spectral signal X FFT Composed of noise spectrum and signal spectrum, when there are Q incident signals of different frequencies, Q peaks and corresponding useful signal spectra can be found in the received signal after the fast Fourier transform of each antenna, while the other points are useless noise spectra.

[0088] Since the matrix steering vector is independent of time, the formula for the Fast Fourier Transform of each array antenna signal can be written as:

[0089]

[0090]

[0091] Among them, a n Let s(m) be the nth row of the array antenna steering vector A, and s(m) be the mth column of the target incident signal matrix s(t).

[0092] Therefore, the discrete spectrum signals of the data received by N antennas are completely identical, and the peak positions corresponding to the incident signals of each antenna are also the same. By selecting X... FFT The frequency domain signal matrix X is composed of the Q columns of signals corresponding to the Q spectral peaks in a discrete spectral signal. F :

[0093]

[0094]

[0095]

[0096] Among them, X F It is a frequency domain signal matrix; These are the frequency domain data corresponding to the Q spectral peaks in the discrete spectrum signal; The f-th digit of the received signal from N antennas after undergoing a Fast Fourier Transform is... q Frequency domain data of 1 sampling point; N is the number of antennas; M is the number of sampling points; Q is the number of narrowband far-field signals; q is the index of the narrowband far-field signal; f q The sampling point number is used; it can be seen that the X formed is... F It is an N×Q matrix.

[0097] Step S4: Reconstruct the covariance matrix based on the frequency domain signal matrix to obtain the target covariance matrix.

[0098] The covariance matrix R of the array received signal is a Hermitian square matrix, where R = R H The frequency domain signal matrix X extracted earlier F Reconstruct the covariance matrix R F :

[0099]

[0100] Among them, R F X is the target covariance matrix; F X is a frequency domain signal matrix; F H is the conjugate transpose of the frequency domain signal matrix; Q is the number of narrowband far-field signals.

[0101] Step S5: Using a multiple signal classification algorithm, determine the direction of arrival of the incident signal of the target based on the target covariance matrix.

[0102] This step specifically includes:

[0103] (1) Perform eigenvalue decomposition on the target covariance matrix to obtain the eigenvector matrix and the corresponding diagonal matrix.

[0104] Since the signal and noise are independent, the covariance matrix R F We obtain this through eigenvalue decomposition:

[0105] R F =UΣU H ;

[0106] Where, U = [e1, e2, ..., e N [Equation] represents the eigenvector matrix, e1, e2, ..., e N Let be the characteristic vectors of N antennas, and Σ be a diagonal matrix composed of eigenvalues, as detailed below:

[0107]

[0108] Where λ1,λ2,...,λ N These are the characteristic values ​​of N antennas.

[0109] (2) Based on the magnitude of the eigenvalues ​​in the diagonal matrix, the eigenvector matrix is ​​divided into a signal subspace and a noise subspace.

[0110] The above eigenvalues ​​satisfy the following relationship:

[0111] λ1≥λ2≥…≥λ Q >λ Q+1=…=λ N =σ 2 .

[0112] Where, σ 2 To determine the noise power, the Q largest eigenvalues ​​in the diagonal matrix Σ are used to form the first diagonal matrix Σ. s Its corresponding feature vector U s =[e1 e2…e Q The signal subspace is formed by the NQ smaller eigenvalues ​​in the diagonal matrix Σ, which together form the second diagonal matrix Σ. N Its corresponding feature vector U N =[e Q+1 e Q+2 …e N The noise subspace is formed. Then the signal covariance matrix R... F It can be broken down into:

[0113] R F =U s Σ s U s H +U N Σ N U H N .

[0114] The superscript H indicates the conjugate transpose.

[0115] (3) Determine the spatial spectrum function based on the steering vector of the signal subspace and the noise subspace.

[0116] Ideally, the signal subspace and the noise subspace are orthogonal to each other, meaning the steering vector of the signal subspace is also orthogonal to the noise subspace.

[0117] a H (θ)U N =0.

[0118] The presence of noise leads to imperfect orthogonality, so the traditional DOA estimation MUSIC algorithm is implemented using a minimum optimization search, i.e.:

[0119] θ MUSIC =arg θ mina H (θ)U N U H N a(θ).

[0120] Therefore, the spectral estimation formula of the MUSIC algorithm, i.e., the spatial spectral function, is:

[0121]

[0122] Among them, P MUSIC U is the spatial spectrum estimate; N For the noise subspace; U H N Let be the conjugate transpose matrix of the noise subspace; a(θ) is the steering vector of the signal subspace; a H (θ) is the conjugate transpose of the guiding vector in the signal subspace.

[0123] (4) Perform a spectral peak search on the spatial spectral function to obtain the direction of arrival of the target incident signal.

[0124] Specifically, the spatial spectrum corresponding to the θ value is searched within the range of -90° to 90°, and the θ value at the peak of the spatial spectrum is the direction of arrival of the incident signal of the target.

[0125] Furthermore, in order to verify the correctness and advancement of the method of the present invention, simulation experiments were conducted, and the effects are illustrated through the following examples.

[0126] The simulation environment was set as follows: number of array antennas N = 8, number of snapshots M = 256, incident signal Q = 2, incident signal angles θ1 = 20°, θ2 = 50°, and frequencies f1 = 1575.42MHz and f2 = 1268.52MHz, respectively. By performing a Fast Fourier Transform on the array received signal matrix, the data corresponding to the target signal was extracted, and the data covariance matrix was reconstructed. DOA estimation was performed using a signal subspace spectrum search method. The error was measured by calculating the root mean square error, defined as:

[0127]

[0128] in, Let represent the angle of the q-th incident signal in the k-th Monte Carlo experiment, with a total of K = 300 Monte Carlo experiments performed, and Q being the number of incident signal sources. Simulation results are compared with those of the traditional MUSIC algorithm, the ESPRIT algorithm, and the orthogonal matched pursuit DOA estimation algorithm based on compressed sensing.

[0129] Simulation 1:

[0130] The accuracy of DOA estimation is analyzed as a function of signal-to-noise ratio (SNR). The independent variable, SNR, gradually increases from -15 dB to 10 dB. Figure 3 It can be seen that among the four DOA estimation algorithms, the DOA estimation accuracy of the algorithm of this invention is consistently better than the other three algorithms when the signal-to-noise ratio is below 0dB. When the signal-to-noise ratio drops to below -10dB, the algorithm of this invention still maintains a high DOA estimation accuracy, while the other three algorithms lose the DOA estimation result and the spatial spectrum is severely distorted. The experiment shows that the algorithm of this invention has a significant advantage in DOA estimation of multi-frequency signals under low signal-to-noise ratio conditions.

[0131] Simulation 2:

[0132] Analyzing the performance change of RMSE in DOA estimation with signal-to-noise ratio (SNR), since the DOA accuracy of the other two algorithms drops significantly when the SNR is below 0 dB, the independent variable SNR is gradually increased from 0 dB to 10 dB. Figure 4 It can be seen that among the four DOA estimation algorithms, the DOA estimation performance of the algorithm of this invention is always better than the other three algorithms. Compared with the traditional MUSIC algorithm, ESPRIT algorithm and orthogonal matching pursuit DOA estimation algorithm based on compressed sensing, the RMSE of the algorithm of this invention is smaller, and its DOA estimation performance is greatly improved. It can be seen from the trend of the RMSE curve of the algorithm of this invention that the RMSE value will remain at a low level when the signal-to-noise ratio is below 0dB.

[0133] Therefore, this invention, based on Fast Fourier Transform (FFT), performs time-frequency domain conversion on the array received signal, then extracts the signal corresponding to the target signal frequency to reconstruct the array received signal data covariance matrix, and finally uses the reconstructed covariance matrix to perform spatial spectrum search for DOA estimation. Simulation results show that the method of this invention significantly improves the accuracy of DOA estimation for multi-frequency signals under low signal-to-noise ratio (SNR) conditions. The SNR required for the same RMSE by this invention differs from existing techniques by up to 10 dB, and it maintains high DOA estimation performance even at SNRs below 0 dB, outperforming existing algorithms.

[0134] Example 2

[0135] To implement the method corresponding to Embodiment 1 above and achieve the corresponding functions and technical effects, a multi-frequency signal direction-of-arrival estimation system is provided below. For example... Figure 5 As shown, the system includes:

[0136] The array receiving signal acquisition module 1 is used to receive the target incident signal using a uniform linear array receiving model to obtain the array receiving signal; the uniform linear array receiving model consists of several linearly arranged antennas, and the spacing between adjacent antennas is half the wavelength corresponding to the highest frequency signal in the target incident signal; the target incident signal consists of several narrowband far-field signals with different directions and frequencies.

[0137] Discrete spectrum signal determination module 2 is used to perform a fast Fourier transform on the received signal of the array to obtain a discrete spectrum signal.

[0138] The frequency domain signal matrix determination module 3 is used to extract the frequency domain data corresponding to the spectral peaks from the discrete spectral signal to obtain the frequency domain signal matrix.

[0139] The target covariance matrix determination module 4 is used to reconstruct the covariance matrix based on the frequency domain signal matrix to obtain the target covariance matrix.

[0140] The direction of arrival determination module 5 is used to determine the direction of arrival of the target incident signal based on the target covariance matrix using a multiple signal classification algorithm.

[0141] Example 3

[0142] This invention also provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor runs the computer program to enable the electronic device to perform the multi-frequency signal direction-of-arrival estimation method of Embodiment 1. The electronic device may be a server.

[0143] In addition, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the multi-frequency signal direction-of-arrival estimation method in Embodiment 1.

[0144] In summary, the multi-frequency signal direction-of-arrival (DOA) estimation method disclosed in this invention, while maintaining the same physical array element spacing, performs time-frequency domain conversion on the received signal using the Fast Fourier Transform (FFT). By extracting the frequency domain data of the target frequency point and reconstructing the covariance matrix of the array received signal data, it can effectively eliminate noise components in the array received signal data, thereby better suppressing the impact of noise signals on the DOA estimation of the target signal. Compared with traditional DOA estimation methods, this invention has two significant advantages: First, under low signal-to-noise ratio (SNR) conditions, this invention can achieve accurate DOA estimation, exhibiting good DOA estimation performance even at SNR below 0 dB, with high estimation accuracy. At an SNR of -10 dB, the DOA estimation error remains essentially within ±2°. Second, this invention can simultaneously perform DOA estimation for target signals at multiple frequencies, a capability not found in traditional algorithms. These two points demonstrate the high engineering application value of this invention.

[0145] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0146] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for estimating the direction of arrival (DOA) of a multi-frequency signal, characterized in that, include: A uniform linear array receiving model is used to receive the incident signal from the target, and the array received signal is obtained. The uniform linear array receiving model consists of several linearly arranged antennas, and the spacing between adjacent antennas is half the wavelength corresponding to the highest frequency signal in the target incident signal; the target incident signal consists of several narrowband far-field signals with different directions and frequencies. Perform a Fast Fourier Transform on the received signal from the array to obtain a discrete spectrum signal; Frequency domain data corresponding to spectral peaks are extracted from the discrete spectral signal to obtain a frequency domain signal matrix; The target covariance matrix is ​​obtained by reconstructing the covariance matrix based on the frequency domain signal matrix; the specific formula for reconstructing the covariance matrix based on the frequency domain signal matrix is ​​as follows: ;in, Let the target covariance matrix be denoted as 'covariance'. It is a frequency domain signal matrix; is the conjugate transpose of the frequency domain signal matrix; Q is the number of narrowband far-field signals; A multiple signal classification algorithm is used to determine the direction of arrival (ROA) of the target incident signal based on the target covariance matrix. Specifically, this includes: performing eigenvalue decomposition on the target covariance matrix to obtain an eigenvector matrix and a corresponding diagonal matrix; dividing the eigenvector matrix into a signal subspace and a noise subspace based on the magnitude of the eigenvalues ​​in the diagonal matrix; determining a spatial spectrum function based on the steering vector of the signal subspace and the noise subspace; and performing a spectral peak search on the spatial spectrum function to obtain the ROA of the target incident signal. The expression for the spatial spectrum function is: ;in, This is a spatial spectrum estimate; For noise subspace; Let be the conjugate transpose of the noise subspace; The guiding vector of the signal subspace; Let be the conjugate transpose of the guiding vector in the signal subspace.

2. The method for estimating the direction of arrival (DOA) of a multi-frequency signal according to claim 1, characterized in that, The array receives the signal as follows: The matrix; where M is the number of sampling points and N is the number of antennas; the expression for the signal received by the array is: ； ； ； ； ； ， ； in, For array receiving signal matrix, These are the received signals from N antennas; For the target incident signal matrix, These are Q narrowband far-field signals; The signal matrix is ​​Gaussian white noise. These are Gaussian white noise signals for N antennas respectively; This is the steering vector for the array antenna. These are the steering vectors for the Q narrowband far-field signals, These represent the directions of the Q narrowband far-field signals; The spacing between adjacent antennas; t is the wavelength corresponding to the highest frequency signal in the incident signal; t is the time period, and the number of sampling points in each time period is M; Q is the number of narrowband far-field signals; q is the sequence number of the narrowband far-field signals.

3. The method for estimating the direction of arrival (DOA) of a multi-frequency signal according to claim 1, characterized in that, Performing a Fast Fourier Transform on the received signal from the array yields a discrete spectrum signal, as shown in the following formula: ； ， ； ， ； in, It is a discrete spectrum signal; These are the frequency domain data of the received signals from N antennas after undergoing Fast Fourier Transform; These are the frequency domain data of the received signal from the i-th antenna after undergoing a Fast Fourier Transform (FFT) at M sampling points; N is the number of antennas; M is the number of sampling points; i is the antenna index; k and m are both sampling point indices. Let t represent the received signals from N antennas, and t be the time period.

4. The method for estimating the direction of arrival (DOA) of a multi-frequency signal according to claim 1, characterized in that, The frequency domain data corresponding to the spectral peaks are extracted from the discrete spectral signal to obtain the frequency domain signal matrix, as shown in the following formula: ； ， ， ； in, It is a frequency domain signal matrix; These are the frequency domain data corresponding to the Q spectral peaks in the discrete spectrum signal; The received signals from N antennas are respectively processed by the Fast Fourier Transform (FFT) to obtain the i-th... Frequency domain data of 1 sampling point; N is the number of antennas; M is the number of sampling points; Q is the number of narrowband far-field signals; q is the sequence number of the narrowband far-field signal; This is the sequence number of the sampling point.

5. A multi-frequency signal direction-of-arrival estimation system, characterized in that, include: The array receiving signal acquisition module is used to receive the target incident signal using a uniform linear array receiving model to obtain the array receiving signal. The uniform linear array receiving model consists of several linearly arranged antennas, and the spacing between adjacent antennas is half the wavelength corresponding to the highest frequency signal in the target incident signal; the target incident signal consists of several narrowband far-field signals with different directions and frequencies. The discrete spectrum signal determination module is used to perform a fast Fourier transform on the received signal of the array to obtain a discrete spectrum signal; The frequency domain signal matrix determination module is used to extract the frequency domain data corresponding to the spectral peaks from the discrete spectral signal to obtain the frequency domain signal matrix. The target covariance matrix determination module is used to reconstruct the covariance matrix based on the frequency domain signal matrix to obtain the target covariance matrix; the specific formula for reconstructing the covariance matrix based on the frequency domain signal matrix to obtain the target covariance matrix is ​​as follows: ;in, Let the target covariance matrix be denoted as 'covariance'. It is a frequency domain signal matrix; is the conjugate transpose of the frequency domain signal matrix; Q is the number of narrowband far-field signals; The direction-of-arrival (DOA) determination module is used to determine the DOA of the target incident signal based on the target covariance matrix using a multiple signal classification algorithm. Specifically, this includes: performing eigenvalue decomposition on the target covariance matrix to obtain an eigenvector matrix and a corresponding diagonal matrix; dividing the eigenvector matrix into a signal subspace and a noise subspace based on the magnitude of the eigenvalues ​​in the diagonal matrix; determining a spatial spectrum function based on the steering vector of the signal subspace and the noise subspace; and performing a spectral peak search on the spatial spectrum function to obtain the DOA of the target incident signal. The expression for the spatial spectrum function is: ;in, This is a spatial spectrum estimate; For noise subspace; Let be the conjugate transpose of the noise subspace; The guiding vector of the signal subspace; Let be the conjugate transpose of the guiding vector in the signal subspace.

6. An electronic device, characterized in that, The device includes a memory and a processor, the memory being used to store a computer program, and the processor running the computer program to cause the electronic device to perform the multi-frequency signal direction-of-arrival estimation method as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the multi-frequency signal direction-of-arrival estimation method as described in any one of claims 1 to 4.

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