A frequency-difference-based spatial anti-aliasing direction-of-arrival estimation method and system

Abstract

The application discloses a kind of spatial anti-aliasing azimuth estimation method and system based on frequency difference, receive K unrelated wideband signals;The array received signal in time domain is converted into frequency domain representation;Design time domain reference signal, by converting into frequency domain representation;Array received signal and reference signal are frequency-differentiated, and equivalent covariance matrix is calculated;Eigenvalue decomposition is carried out to equivalent covariance matrix, and noise subspace is extracted, and the target azimuth estimation result on single frequency point is calculated;The target azimuth estimation result of each frequency point is accumulated, and the target estimation result under corresponding angle is obtained;Reference signal is scanned according to grid accuracy, and the peak value obtained is the final target azimuth estimation result.The application realizes the spatial anti-aliasing effect under multiple array conditions, avoids the problem that target azimuth estimation fails due to cross term, and improves the accuracy of target azimuth estimation result.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a spatial anti-aliasing azimuth estimation method and system based on frequency difference. Background Technology

[0002] In sonar systems, direction-of-arrival (DOA) estimation is an important research area. To obtain larger array apertures, sparse, large-aperture uniform linear arrays are typically constructed, with element spacing much larger than the incident signal wavelength. This leads to phase ambiguity and numerous grating lobes in the azimuth spectrum, affecting the accuracy of target azimuth estimation. According to the spatial Nyquist sampling theorem, the element spacing of a sonar array should be half the wavelength of the incident signal. However, for narrowband signals, as the signal frequency increases, the wavelength decreases accordingly, resulting in periodic azimuth ambiguity in the azimuth spectrum, a phenomenon known as spatial aliasing. Similarly, for broadband signals, when the element spacing is greater than half the wavelength, spatial aliasing occurs at every frequency point, thus negatively impacting the azimuth estimation performance of broadband signals.

[0003] In practice, especially in the case of sparse large arrays, the element spacing will be difficult to meet the half-wavelength requirement, so it is necessary to conduct research on grating lobe deblurring technology.

[0004] In recent years, scholars have proposed a series of methods for solving spatial aliasing based on frequency difference techniques. Frequency difference processing involves multiplying the array observations of one frequency point with the conjugate form of the array observations of another frequency point, while the frequency difference between the two frequency points must satisfy the spatial Nyquist theorem. Frequency difference techniques are essentially an operation that can completely solve the spatial aliasing problem through frequency reduction. However, when solving multi-target spatial aliasing problems, the presence of cross terms in traditional frequency difference techniques can affect the target orientation estimation results, making it impossible to accurately estimate the true target orientation.

[0005] In summary, for the case of grating lobes in target azimuth estimation of large-size arrays in practical applications, it is essential to propose a high-resolution azimuth estimation method that can achieve spatial anti-aliasing for multiple targets to solve the grating lobe ambiguity problem. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a spatial anti-aliasing azimuth estimation method and system based on frequency difference, which addresses the shortcomings of the prior art and solves the technical problem of grating lobe ambiguity in target azimuth estimation.

[0007] The present invention adopts the following technical solution:

[0008] A spatial anti-aliasing azimuth estimation method based on frequency difference includes the following steps:

[0009] S1. The sensor array receives K uncorrelated broadband signals and converts the data received by the sensor array into a frequency domain representation. Each frequency signal is a narrowband array received signal.

[0010] S2, Set the noise-free parameters and the incident azimuth as follows: The time-domain reference signal is obtained and converted into a frequency-domain representation, with each frequency point signal being a narrowband reference signal;

[0011] S3. Perform frequency difference processing on the narrowband array received signal obtained in step S1 and the narrowband reference signal with a frequency difference of Δf from the narrowband array received signal in step S2 to obtain the equivalent array output, and calculate the covariance matrix of the equivalent array output.

[0012] S4. The target orientation estimation method based on subspace is to perform eigenvector decomposition on the covariance matrix of the equivalent array output obtained in step S3, extract the noise subspace, multiply the conjugate transpose of the noise subspace with the steering vector after frequency difference, sum up each frequency point and take the reciprocal to obtain the target orientation estimation result of the single frequency narrowband signal.

[0013] S5. Let i = i + 1, and repeat steps S2, S3, and S4 to calculate the scanning grid for each reference signal incident angle. Azimuth spectrum estimation information The results are stored in vector P, which is the spatial orientation spectrum. A peak search operation is performed on P, and the obtained peak is used as the final target orientation estimation result.

[0014] Specifically, step S1 is as follows:

[0015] S101. A horizontal uniform linear array consisting of M sensors is used to receive K broadband signals.

[0016] S102. Divide the time T of the K wideband signals received in step S101 into L data segments, each segment having a length of T / L. Then, perform a Q-point FFT operation on each data segment to divide the wideband signal into Q narrowband array received signals. Write the narrowband array received signals into matrix form x. l (f q ), where f q For frequency.

[0017] Furthermore, in step S102, the frequency f q The narrowband array receiving signal matrix x l (f q )for:

[0018] x l (f q )=[x 1,l (f q ),L,x M,l (f q )] T

[0019] in,(·) T It is the transpose symbol, x m,l (f q ) is the frequency domain array output of the m-th array element in the l-th data segment.

[0020] Specifically, step S2 is as follows:

[0021] S201. The angle value Θ of the time-domain reference signal is [0°, 180°]. The angle value Θ is divided into equally spaced intervals and used as the scanning angle grid of the reference signal. A Gaussian random sequence is used as the time-domain reference signal s. r (t), t∈[0,T], where T is the signal time length, and the time-domain reference signal s r The incident angle of (t) is The incident angle of the reference signal The incident direction as a time-domain reference signal;

[0022] S202, the time-domain reference signal s of length T. r (t) is divided into L data segments, each with a length of T. / L, perform a Q-point FFT on each data segment to divide the reference signal into Q narrowband signals, where the frequency f in the l-th data segment is... q The frequency domain representation of the upper reference signal is as follows

[0023] Furthermore, in step S202, the array output of the reference signal frequency domain in the l-th data segment for:

[0024]

[0025] in, It is the steering vector of the reference signal, x m,l (f q ) is the frequency domain array output of the m-th array element in the l-th data segment.

[0026] Specifically, step S3 is as follows:

[0027] Calculate the equivalent array output of the received signal and the reference signal with a frequency difference of Δf from the received signal in step S2; output the equivalent array output of the l-th data segment of the m-th element. Writing in vector form Obtain the equivalent covariance matrix for:

[0028]

[0029] Where E{·} denotes the mathematical expectation operator, f is the matrix formed by the equivalent array outputs on each array element. q is the center frequency of the reference signal in the q-th frequency band, and Δf is the frequency difference, (·) H It is the conjugate transpose symbol.

[0030] Specifically, step S4 is as follows:

[0031] S401. The covariance matrix obtained in step S3 Feature decomposition is performed to obtain the noise subspace;

[0032] S402. Using the noise subspace obtained in step S401, calculate the target azimuth spectrum estimation information on a single angle grid, and then calculate the different frequencies f. q Narrowband signal azimuth spectrum information The results are accumulated and the reciprocal is recorded to obtain the target azimuth estimation result at the single reference signal scanning angle. And store it in vector P.

[0033] Furthermore, in step S402, the target azimuth estimation result at the single reference signal scanning angle... for:

[0034]

[0035] in, This is the lower limit frequency for broadband signals. This represents the upper frequency limit for broadband signals. The result of the conjugate transpose of the noise subspace With frequency Δf and angle θ steering vector of the reference signal The product of.

[0036] Specifically, in step S5, when i>dim(Θ), the loop scan ends, dim(Θ) represents the dimension of the set Θ, and a peak search operation is performed on P, and the obtained peak is used as the final target orientation estimation result.

[0037] Secondly, embodiments of the present invention provide a spatial anti-aliasing azimuth estimation system based on frequency difference, comprising:

[0038] The receiving module receives K uncorrelated broadband signals from the sensor array and converts the data received by the sensor array into a frequency domain representation. Each frequency signal is a narrowband array received signal.

[0039] Reference signal module, set to have no noise term and incident azimuth as... The time-domain reference signal is obtained and converted into a frequency-domain representation, with each frequency point signal being a narrowband reference signal;

[0040] The differential module performs frequency differential processing on the narrowband array received signal obtained from the receiving signal module and the narrowband reference signal in the reference signal module whose frequency difference with the narrowband array received signal is Δf, to obtain the equivalent array output, and calculates the covariance matrix of the equivalent array output.

[0041] The extraction module, based on the subspace target orientation estimation method, performs eigenvector decomposition on the covariance matrix of the equivalent array output obtained by the difference module to extract the noise subspace. The conjugate transpose of the noise subspace is multiplied with the steering vector after frequency difference, and the summation and reciprocal of each frequency point are calculated to obtain the target orientation estimation result of the single-frequency narrowband signal.

[0042] The estimation module, setting i = i + 1, repeatedly executes the reference signal module, the difference module, and the extraction module to calculate the azimuth spectrum estimation information on the scanning grid for each incident angle of the reference signal. The results are stored in vector P, which is the spatial orientation spectrum. A peak search operation is performed on P, and the obtained peak is used as the final target orientation estimation result.

[0043] Compared with the prior art, the present invention has at least the following beneficial effects:

[0044] A spatial anti-aliasing azimuth estimation method based on frequency difference is proposed. The received signal of each broadband array is represented in the frequency domain and divided into narrowband signals. A reference signal is pre-designed and represented in the frequency domain. Frequency difference processing is performed between the reference signal and the received signal at each frequency point to calculate the equivalent covariance matrix after frequency difference, achieving frequency reduction to ensure the array element spacing is equivalent to half a wavelength. The target azimuth estimation result is obtained by calculating the reciprocal of the sum of the products of the conjugate transpose of the noise subspace and the steering vector at the frequency difference of the reference signal at each frequency point. Based on the concept of frequency difference technology and combined with the subspace method, high-resolution azimuth estimation is achieved by calculating the equivalent covariance matrix after frequency difference between the reference signal and the incident signal, realizing high-resolution azimuth estimation capability for spatial anti-aliasing. Furthermore, by improving the subspace method, the computational load is reduced and the computational speed is improved, achieving spatial anti-aliasing target azimuth estimation.

[0045] Furthermore, the time T of the received broadband signal is divided into L data segments, and then a Q-point FFT operation is performed on each data segment to divide the broadband signal into Q narrowband array received signals for processing, so as to facilitate subsequent matrix operations.

[0046] Furthermore, after dividing the broadband received signal into narrowband array received signals, the output of the narrowband array received signal array after performing FFT operations on each data segment is written in matrix form, that is, the frequency f q The array output of the narrowband array receiving signal is represented as x. l (f q This facilitates subsequent calculations of the equivalent array output.

[0047] Furthermore, the time T of the broadband reference signal is divided into L data segments, and then a Q-point FFT operation is performed on each data segment. The broadband signal is divided into Q narrowband signals according to the frequency for processing, which facilitates subsequent matrix operations.

[0048] Furthermore, the received signal x is calculated. l (f q ) and a reference signal with a frequency difference of Δf from the received signal. The equivalent array output, and the equivalent array output of the m-th array element and the l-th data segment. Writing it in vector form facilitates the subsequent calculation of the equivalent covariance matrix.

[0049] Furthermore, the equivalent covariance matrix is ​​calculated. This facilitates the subsequent acquisition of the noise subspace.

[0050] Furthermore, the equivalent covariance matrix Eigenvalue decomposition is performed to obtain the noise subspace. The conjugate transpose of the noise subspace is then calculated. With frequency Δf and angle θ steering vector of the reference signal The product of these terms yields different frequencies f. q Narrowband signal azimuth spectrum information This facilitates subsequent calculations of the target azimuth estimation results at the single reference signal scanning angle.

[0051] Furthermore, by using different frequencies f q Narrowband signal azimuth spectrum information By accumulating the data, all signal information can be included to obtain the target azimuth estimation result at the single reference signal scanning angle. This facilitates subsequent calculations of the target's actual location.

[0052] Furthermore, the target azimuth spectrum estimation information is calculated on each spatial angle scan grid. The loop ends when i > dim(Θ), and the azimuth spectrum information of each element in the loop is recorded. Store the vector P to obtain target azimuth estimation information from all angles, and further obtain the target azimuth estimation result with anti-aliasing.

[0053] It is understandable that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0054] In summary, this invention achieves spatial anti-aliasing under various array conditions, improving the accuracy of target azimuth estimation results; it utilizes frequency differential technology to avoid the impact of grating lobe ambiguity on target azimuth estimation; and it uses reference signals to assist in calculating the equivalent covariance matrix, avoiding the target azimuth estimation failure problem caused by the cross terms of the received signal itself.

[0055] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the process of the present invention;

[0057] Figure 2 This is a schematic diagram of the system of the present invention;

[0058] Figure 3 This is a schematic diagram of the target azimuth estimation results in the case of a single target.

[0059] Figure 4 This is a schematic diagram of the target azimuth estimation results after FD processing;

[0060] Figure 5 This is a schematic diagram of the target azimuth estimation results at different frequency points in the case of a single target according to the present invention. Among them, (a) is the azimuth map with a reference signal angle of 20°, and (b) is the azimuth map with a reference signal angle of 60°.

[0061] Figure 6 This is a schematic diagram of the target orientation estimation results in the case of a single target according to the present invention;

[0062] Figure 7 This is a schematic diagram showing the target orientation estimation results using the method of the present invention in a dual-target scenario. Detailed Implementation

[0063] 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, not all, of the embodiments of the present invention. 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.

[0064] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0065] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0066] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this document generally indicates that the preceding and following objects have an "or" relationship.

[0067] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0068] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0069] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0070] This invention provides a spatial anti-aliasing azimuth estimation method based on frequency difference. It combines the theoretical concept of frequency difference technology with subspace azimuth estimation methods to achieve spatial anti-aliasing target azimuth estimation, involving fields such as array signal processing, spatial anti-aliasing, and target azimuth estimation. By pre-designing a reference signal, the reference signal and the received signal at each frequency point are subjected to frequency difference processing to calculate the equivalent covariance matrix after frequency difference, thereby achieving frequency reduction. The target azimuth estimation result is obtained by calculating the reciprocal of the sum of the products of the conjugate transpose of the noise subspace at each frequency point and the steering vector at the frequency difference of the reference signal.

[0071] Please see Figure 1 The present invention provides a spatial anti-aliasing azimuth estimation method based on frequency difference, comprising the following steps:

[0072] S1. Consider a horizontal uniform linear array consisting of M sensors, which receives K uncorrelated broadband signals. Represent the data received by the sensor array in the frequency domain. The signal at each frequency point is the signal received by the narrowband array.

[0073] S101. Obtain the array received time-domain signal;

[0074] Consider a horizontal uniform linear array consisting of M sensors, receiving K broadband signals.

[0075] The m-th array element outputs x. m (t) is:

[0076]

[0077] Where 1≤m≤M, 0≤t≤T, s k (t) is the waveform of the k-th wideband random signal, n m (t) is the noise waveform, τ mk It is the propagation delay of the k-th signal on the m-th array element, and T is the signal reception time.

[0078] Propagation delay τ mk for:

[0079] τ mk = (m-1)dcosθ k / c

[0080] Where c is the speed of sound in water, d is the element spacing, and θ is the distance between the array elements. k It is the incident azimuth angle of the k-th signal.

[0081] S102. Represent the received signal in the frequency domain.

[0082] The time T of the received K wideband signals is divided into L data segments, each with a length of T / L. Then, a Q-point FFT operation is performed on each data segment to divide the wideband signal into Q narrowband array received signals, with the frequency f... q The signal received by the upper narrowband array is represented in matrix form x l (f q The frequency domain array output of the m-th element in the l-th data segment is denoted as x. m,l (f q ), f q It is the frequency of the signal at the q-th frequency point.

[0083] Frequency f q The narrowband array received signal is represented as follows:

[0084] x l (f q )=[x 1,l (f q ),L,x M,l (f q )] T

[0085] in,(·) T It is the transpose symbol.

[0086] S2. Design an azimuth grid Θ, with a value range of [0°, 180°]. Divide the angle values ​​Θ into equal intervals with an angle interval of Δ. Design a noise-free time-domain reference signal RS. r The incident angle of (t) is The incident angle of the reference signal The incident direction is used as the time-domain reference signal, and the initial value is set to i = 1, which is...

[0087] S201, Design time-domain reference signal;

[0088] The reference signal is denoted as s r (t), t∈[0,T], is a Gaussian random sequence, where T is the signal duration and the incident angle of the reference signal is given.

[0089] S202. Convert the time-domain reference signal to the frequency domain.

[0090] The time-domain reference signal s of length T r (t) is divided into L data segments, each with a length of T / L. A Q-point FFT is performed on each data segment, dividing the reference signal into Q narrowband signals. The frequency f in the l-th data segment... q The frequency domain representation of the upper reference signal is as follows

[0091] In the l-th data segment, the frequency f q The array output in the frequency domain of the upper reference signal is represented as:

[0092]

[0093] in, It is the steering vector of the reference signal.

[0094] The component of the steering vector of the reference signal on the m-th element is:

[0095]

[0096] Among them, f q It is the frequency of the reference signal at the q-th frequency point. It is the incident angle of the reference signal.

[0097] S3. Perform frequency difference processing on the narrowband array received signal obtained in step S1 and the narrowband reference signal with a frequency difference of Δf from the narrowband array received signal in step S2 to obtain the equivalent array output, and calculate the equivalent covariance matrix.

[0098] S301. Calculate the equivalent array output of the narrowband array received signal obtained in step S1 and the narrowband reference signal with a frequency difference of Δf from the narrowband received signal in step S2.

[0099] The main idea of ​​frequency differential technology is to perform differential processing on different frequencies of the signal. The frequency difference Δf satisfies the spatial Nyquist sampling theorem, that is, the element spacing d = c / (2Δf).

[0100] x m,l (f q )and Multiplying by the conjugate transpose of the given values ​​yields the equivalent array output of the l-th data segment of the m-th element at the frequency difference Δf, which is:

[0101]

[0102] in, It is the frequency of the signal. This is the lower limit frequency for broadband signals. For the upper limit frequency of broadband signals, (·) * It is a conjugate symbol.

[0103] S302. Calculate the covariance matrix of the equivalent array output.

[0104] Output the equivalent array of the m-th element and the l-th data segment. In vector form, denoted as:

[0105]

[0106] Its covariance matrix is ​​calculated as follows:

[0107]

[0108] Where E{·} denotes the mathematical expectation operator, (·) H It is the conjugate transpose symbol.

[0109] S4. The target orientation estimation method based on subspace is to perform eigenvector decomposition on the covariance matrix of the equivalent array output obtained in step S3, extract the noise subspace, multiply the conjugate transpose of the noise subspace with the steering vector after frequency difference, sum up each frequency point, and take its reciprocal to obtain the target orientation estimation result of the single frequency narrowband signal.

[0110] S401. The covariance matrix obtained in step S3 Feature decomposition is performed to obtain the noise subspace;

[0111] For equivalent covariance matrix Perform feature decomposition, i.e. Where Λ is a diagonal matrix composed of eigenvalues ​​arranged in descending order, and E can be written as E = [E s E n ], where E s and E n These are the signal subspace and the noise subspace, respectively, composed of the eigenvectors corresponding to the K larger eigenvalues ​​and the MK smaller eigenvalues.

[0112] S402. Using the noise subspace obtained in step S401, calculate the target azimuth spectrum estimation information on a single angle grid, and then calculate the different frequencies f. q Narrowband signal azimuth spectrum information The results are accumulated and the reciprocal is recorded to obtain the target azimuth estimation result at the single reference signal scanning angle.

[0113] The result of the conjugate transpose of the noise subspace With frequency Δf and angle θ steering vector of the reference signal The product of, denoted as Specifically:

[0114]

[0115] in(·) H It is the conjugate transpose symbol. It has a frequency of Δf and an angle of . The reference signal steering vector is as follows:

[0116]

[0117] Where j is the imaginary number sign, d is the element spacing, c is the speed of sound propagation in water, M is the number of elements, and (·) T It is the transpose symbol.

[0118] f q Various frequency points when taking different values Perform accumulation and record the reciprocal of the result, denoted as . as follows:

[0119]

[0120] S5. Divide the azimuth grid into multiple grid points with grid precision Δ, and perform cyclic scanning of the reference signal according to the grid precision to obtain the peak value as the final target azimuth estimation result.

[0121] Let i = i + 1, and repeat steps S3, S4, and S5 to calculate the scanning grid for each reference signal incident angle. The azimuth spectrum estimation information is denoted as The loop continues until i > dim(Θ), where dim(Θ) represents the dimension of the set Θ. The target azimuth estimation result at each single reference signal scan angle in the loop is then processed. Store the data in vector P, perform a peak search operation on the data set P, and obtain the final target orientation estimation result.

[0122] In another embodiment of the present invention, please refer to Figure 2 This paper provides a spatial anti-aliasing azimuth estimation system based on frequency difference. This system can be used to implement the above-mentioned spatial anti-aliasing azimuth estimation method based on frequency difference. Specifically, the spatial anti-aliasing azimuth estimation system based on frequency difference includes a receiving signal module, a reference signal module, a differential module, an extraction module, and an estimation module.

[0123] Among them, the receiving signal module receives K uncorrelated broadband signals from the sensor array and converts the data received by the sensor array into a frequency domain representation. Each frequency signal is a narrowband array received signal.

[0124] Reference signal module, set to have no noise term and incident azimuth as... The time-domain reference signal is obtained and converted into a frequency-domain representation, with each frequency point signal being a narrowband reference signal;

[0125] The differential module performs frequency differential processing on the narrowband array received signal obtained from the receiving signal module and the narrowband reference signal in the reference signal module whose frequency difference with the narrowband array received signal is Δf, to obtain the equivalent array output, and calculates the covariance matrix of the equivalent array output.

[0126] The extraction module, based on the subspace target orientation estimation method, performs eigenvector decomposition on the covariance matrix of the equivalent array output obtained by the difference module to extract the noise subspace. The conjugate transpose of the noise subspace is multiplied with the steering vector after frequency difference, and the summation and reciprocal of each frequency point are calculated to obtain the target orientation estimation result of the single-frequency narrowband signal.

[0127] The estimation module, setting i = i + 1, repeatedly executes the reference signal module, the difference module, and the extraction module to calculate the azimuth spectrum estimation information on the scanning grid for each incident angle of the reference signal. The results are stored in vector P, which is the spatial orientation spectrum. A peak search operation is performed on P, and the obtained peak is used as the final target orientation estimation result.

[0128] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0129] Example 1

[0130] A uniform linear array is used as the signal receiving array. Consider a 10-element uniform linear array, selecting a wideband signal frequency band of 2–2.4 kHz and a sampling rate of 5 kHz. The speed of sound is set to 1500 m / s, the element spacing is 3.75 m (corresponding to half the wavelength of 200 Hz), the number of snapshots is 150, and each snapshot contains 500 sampling points. In the simulation, it is assumed that there is only one signal, the incident signal power is set to 5 dB, the signal-to-noise ratio (SNR) is 0 dB, and the selected Δf is 200 Hz.

[0131] Please see Figure 3 Let there be only one broadband incident signal with a bandwidth of 2 to 2.4 kHz and an incident angle of 60°; Figure 3This is the azimuth spectrum of the conventional algorithm. Because the element spacing is more than five times the signal wavelength for frequencies of 2–2.4 kHz, severe spatial aliasing occurs. Since the direction of the grating lobes changes with frequency, accumulating the spatial spectrum along the frequency domain can suppress spatial aliasing to some extent, reducing the number of grating lobes.

[0132] Please see Figure 4 This represents the DOA estimation result under the traditional FD method; from Figure 4 The main lobe appears significantly wider, resulting in a decrease in resolution. This is because frequency differential processing downsamples each frequency component of the signal to Δf, or 200Hz. However, after the FD operation, the grating lobe is suppressed, leading to a more accurate DOA estimation result.

[0133] By using the spatial anti-aliasing estimation method based on frequency difference proposed in this invention, and processing under the same conditions as the above methods, a target azimuth estimation result with higher resolution and better estimation accuracy is obtained.

[0134] Please see Figure 5 When the azimuth of the reference signal is selected as 20°, combined with conventional methods, the azimuth maps of each frequency point are as follows: Figure 5 As shown in (a), the exact incident azimuth of the received signal cannot be estimated. Because the reference signal azimuth and the incident azimuth are different, it can be seen that there are almost no overlapping peaks at the 60° position. Figure 5 (b) shows the case where the incident azimuth of the reference signal is selected at 60°, i.e., the azimuth of the incident signal is the same. In this case, the peak values ​​of almost all frequency points coincide at the 60° azimuth. Therefore, when performing angle scanning, if the incident azimuth of the reference signal is not the same as the incident signal azimuth, a high peak value will not be generated, while if the incident azimuth of the reference signal is the same as the incident signal azimuth, a high peak value will be generated.

[0135] By using the method proposed in this application to generate numerical output, the estimated true incident azimuth of the target under this method can be obtained, such as... Figure 6 As shown.

[0136] Example 2

[0137] Using a uniform linear array as the signal receiving array, consider a 10-element uniform linear array, select a wideband signal frequency band of 2-2.4kHz, a sampling rate of 5kHz, a sound velocity of 1500m / s, set the element spacing to half wavelength (frequency of 200Hz), the number of snapshots to 150, and the number of sampling points in each snapshot to 500.

[0138] In the simulation, to demonstrate the effectiveness of the algorithm, the number of incident signals was adjusted. It was assumed that there were two broadband incident signals, each with a bandwidth of 2–2.4 kHz, and incident angles of 60° and 75° respectively. A Δf of 200 Hz was selected. Without changing the energy of the incident signals, the power of both signals was set to 5 dB, and the signal-to-noise ratio (SNR) was 0 dB. Please refer to [link / reference]. Figure 7 The spatial anti-aliasing estimation method based on frequency difference proposed in this invention can accurately estimate the true location of the target without spatial aliasing. Figure 7 As can be seen, there are two relatively high peaks only at the actual incident target position, and the burrs at other positions can be ignored. Therefore, it can be determined that the method of the present invention has good spatial anti-aliasing capability.

[0139] In summary, this invention provides a spatial anti-aliasing azimuth estimation method and system based on frequency difference, which achieves spatial anti-aliasing under various array conditions and improves the accuracy of target azimuth estimation results. By utilizing frequency difference technology, the influence of grating lobe ambiguity on target azimuth estimation is avoided. By using reference signals to assist in the calculation of the equivalent covariance matrix, the problem of target azimuth estimation failure caused by the cross terms of the received signal itself is avoided.

[0140] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0141] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0142] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0143] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0144] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A spatial anti-aliasing azimuth estimation method based on frequency difference, characterized in that, Includes the following steps: S1. The sensor array receives K uncorrelated broadband signals and converts the data received by the sensor array into a frequency domain representation. Each frequency signal is a narrowband array received signal. S2, Set the noise-free parameters and the incident azimuth as follows: The time-domain reference signal is obtained and converted into a frequency-domain representation, with each frequency point signal being a narrowband reference signal, specifically: S201, Angle value of time-domain reference signal for , take angle value The scanning angle grid is divided into equally spaced sections and used as a reference signal, with a Gaussian random sequence used as the time-domain reference signal. , For signal duration, the time-domain reference signal The angle of incidence is , The incident angle of the reference signal The incident direction as a time-domain reference signal; S202, length Time-domain reference signal Divided into There are data segments, each with a length of . Perform on each data segment Point FFT divides the reference signal into The first narrowband signal, the... Frequency in each data segment The frequency domain representation of the upper reference signal is as follows , No. The array output of the reference signal frequency domain in each data segment for: in, It is the steering vector of the reference signal. For the first In the data segment, the first The frequency domain array output of each array element; S3. The frequency difference between the narrowband array received signal obtained in step S1 and the frequency difference between the narrowband array received signal and the signal obtained in step S2 is... The narrowband reference signal is subjected to frequency differential processing to obtain the equivalent array output, and the covariance matrix of the equivalent array output is calculated. S4. The target orientation estimation method based on subspace is to perform eigenvector decomposition on the covariance matrix of the equivalent array output obtained in step S3, extract the noise subspace, multiply the conjugate transpose of the noise subspace with the steering vector of the reference signal, sum up the frequency points and take the reciprocal to obtain the target orientation estimation result of the single-frequency narrowband signal. S5, Order Repeat steps S2, S3, and S4 to calculate the incident angle of each reference signal. Azimuth spectrum estimation information on the scanning grid and store in a vector In, vector For the spatial orientation spectrum, Perform a peak search operation and use the obtained peak as the final target orientation estimate.

2. The spatial anti-aliasing azimuth estimation method based on frequency difference according to claim 1, characterized in that, Step S1 is as follows: S101, adopting a single... A horizontal uniform linear array of sensors receives... One broadband signal; S102, Received in step S101 The time of a broadband signal Divided into There are data segments, each with a length of . Then perform processing on each data segment. Point FFT operation divides the broadband signal into A narrowband array receives the signal, and the narrowband array received signal is written in matrix form. ,in, For frequency.

3. The spatial anti-aliasing azimuth estimation method based on frequency difference according to claim 2, characterized in that, In step S102, frequency Narrowband array receiving signal matrix for: in, It is the transpose symbol. For the first In the data segment, the first The frequency domain array output of each array element.

4. The spatial anti-aliasing azimuth estimation method based on frequency difference according to claim 1, characterized in that, Step S3 is as follows: Calculate the frequency difference between the received signal and the received signal in step S2. The equivalent array output of the reference signal; the first Each formation element Equivalent array output of each data segment Writing in vector form The equivalent covariance matrix is ​​obtained. for: in, Represents the mathematical expectation operator. The matrix formed by the equivalent array outputs on each array element. The reference signal is at the 1st The center frequency of each frequency band This is the frequency difference. It is the conjugate transpose symbol.

5. The spatial anti-aliasing azimuth estimation method based on frequency difference according to claim 1, characterized in that, Step S4 is as follows: S401. The covariance matrix obtained in step S3 Feature decomposition is performed to obtain the noise subspace; S402. Using the noise subspace obtained in step S401, calculate the target azimuth spectrum estimation information on a single angle grid, and divide different frequencies. Narrowband signal azimuth spectrum information The results are accumulated and the reciprocal is recorded to obtain the target azimuth estimation result at the single reference signal scanning angle. And store in a vector middle.

6. The spatial anti-aliasing azimuth estimation method based on frequency difference according to claim 5, characterized in that, In step S402, the target azimuth estimation result at the single reference signal scanning angle for: in, This is the lower limit frequency for broadband signals. This represents the upper frequency limit for broadband signals. The result of the conjugate transpose of the noise subspace With frequency , angle is steering vector of the reference signal The product of.

7. The spatial anti-aliasing azimuth estimation method based on frequency difference according to claim 1, characterized in that, In step S5, when >dim( When ), the loop scan ends, dim( ) represents a set The dimension, for Perform a peak search operation and use the obtained peak as the final target orientation estimate.

8. A spatial anti-aliasing azimuth estimation system based on frequency difference, characterized in that, include: The receiving module receives K uncorrelated broadband signals from the sensor array and converts the data received by the sensor array into a frequency domain representation. Each frequency signal is a narrowband array received signal. Reference signal module, set to have no noise term and incident azimuth as... The time-domain reference signal is obtained and converted into a frequency-domain representation, with each frequency point signal being a narrowband reference signal, specifically: Angle values ​​of the time-domain reference signal for , take angle value The scanning angle grid is divided into equally spaced sections and used as a reference signal, with a Gaussian random sequence used as the time-domain reference signal. , For signal duration, the time-domain reference signal The angle of incidence is , The incident angle of the reference signal The incident direction as a time-domain reference signal; length Time-domain reference signal Divided into There are data segments, each with a length of . Perform on each data segment Point FFT divides the reference signal into The first narrowband signal, the... Frequency in each data segment The frequency domain representation of the upper reference signal is as follows , No. The array output of the reference signal frequency domain in each data segment for: in, It is the steering vector of the reference signal. For the first In the data segment, the first The frequency domain array output of each array element; The differential module converts the frequency difference between the narrowband array received signal obtained from the receiving signal module and the frequency difference between the narrowband array received signal and the frequency difference between the reference signal module and the narrowband array received signal. The narrowband reference signal is subjected to frequency differential processing to obtain the equivalent array output, and the covariance matrix of the equivalent array output is calculated. The extraction module, based on the subspace target orientation estimation method, performs eigenvector decomposition on the covariance matrix of the equivalent array output obtained by the difference module, extracts the noise subspace, multiplies the conjugate transpose of the noise subspace with the steering vector of the reference signal, sums up the frequency points and takes the reciprocal, and obtains the target orientation estimation result of the single-frequency narrowband signal. The estimation module, let Repeatedly execute the reference signal module, differential module, and extraction module to calculate the incident angle of each reference signal. Azimuth spectrum estimation information on the scanning grid and store in a vector In, vector For the spatial orientation spectrum, Perform a peak search operation and use the obtained peak as the final target orientation estimate.

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