A Spatial Spectrum Estimation Method and System for Multi-Frequency Deambiguation in Sparsely Arrayed Radar

Abstract

This invention discloses a spatial spectrum estimation method and system for multi-frequency deambiguation of sparse array radar, relating to the field of array signal processing technology. This method can obtain high-precision two-dimensional angle estimation, is applicable to sparse arrays of arbitrary configurations, and can perform deambiguation without the aid of a physical short baseline. It offers flexible array configuration and strong universality of the angle measurement method. The specific scheme is as follows: design the sparse array configuration and operating frequency of the array angle measurement system; acquire the array received signal at each operating frequency; select the signal operating frequency for spatial spectrum estimation, and calculate the positions of all spectral peaks in the spatial spectrum; calculate the ambiguity number estimation error corresponding to each spectral peak based on signals at other frequencies; the spectral peak with the smallest ambiguity number estimation error is the target position.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, specifically to a spatial spectrum estimation method and system for multi-frequency deambiguation of sparse array radar. Background Technology

[0002] With the rapid development of spatial spectrum estimation technology, array angle measurement technology has been widely applied in radar, sonar, and communication fields. Among them, subspace algorithms, based on the orthogonality of signal and noise subspaces, have achieved high-precision measurement of target angles. In 1986, Schmidt, in his paper "Multiple Emitter Location and Signal Parameter Estimation" published in the journal *IEEE Transactions on Antennas and Propagation*, first introduced the subspace decomposition method into spatial spectrum estimation and proposed the Multiple Signal Classification (MUSIC) algorithm, sparking a research boom in spatial spectrum estimation. Since a larger array aperture-to-wavelength ratio results in higher angle measurement accuracy, the traditional approach to expanding the array aperture in dense arrays is to increase the number of physical array elements while ensuring that the element spacing is no greater than half a wavelength. Compared to dense arrays, sparse arrays (element spacing greater than half a wavelength) can achieve a large array aperture and high angle measurement accuracy with fewer elements, and at a lower development cost. However, due to not meeting the requirements of the spatial sampling theorem, sparse array angle measurement suffers from phase ambiguity.

[0003] To address the issue of phase ambiguity in angle measurement, Zhang Liang et al., in their 2012 paper "A Broadband Direction Finding Method for Passive Seekers Based on Circular Interferometers" published in Volume 34, Issue 3 of *Systems Engineering and Electronics*, derived a broadband angle measurement method based on a 5-element circular interferometer, which can obtain unambiguous angle estimation results. In their 2021 paper "A Multiple Joint MUSIC Deambiguity Method Based on Rotational Ambiguity Cancellation Criterion" published in Volume 37, Issue 4 of *Signal Processing*, Cui Ao et al. derived the nonlinear relationship between the ambiguity angle and the rotation angle of a sparse uniform linear array, proposed an angle rotational ambiguity cancellation criterion, constructed a sparse X-shaped array based on this criterion, and used the multiple joint MUSIC method for deambiguity and angle measurement.

[0004] Zhang Liang et al.'s method is only applicable to 5-element uniform circular arrays and requires the use of unambiguous short baselines for auxiliary deambiguation; Cui Ao et al.'s method is applicable to the constructed X-shaped arrays, but the array configuration is limited and only one-dimensional angle estimates can be obtained.

[0005] It can be seen that the existing solutions are only applicable to specific array configurations. How to defuzzify sparse arrays with arbitrary array configurations has become an urgent problem to be studied. Summary of the Invention

[0006] In view of this, the present invention provides a spatial spectrum estimation method and system for multi-frequency deambiguation of sparse array radar, which can obtain high-precision two-dimensional angle estimation, is applicable to sparse arrays of arbitrary array configurations, can perform deambiguation without the assistance of physical short baselines, has flexible array configuration, and the angle measurement method has strong universality.

[0007] To achieve the above objectives, one embodiment of the present invention provides a technical solution for a spatial spectrum estimation method for multi-frequency defuzzification of sparse arrays, specifically including the following steps:

[0008] Design the sparse array configuration and operating frequency of the array angle measurement system;

[0009] Acquire the array received signal at each operating frequency;

[0010] Select the signal operating frequency to perform spatial spectrum estimation, and calculate the positions of all spectral peaks in the spatial spectrum;

[0011] Based on signals from other frequencies, calculate the ambiguity number estimation error corresponding to each spectral peak;

[0012] The spectral peak with the smallest fuzzy number estimation error is the target location.

[0013] Furthermore, the design of the sparse array configuration and operating frequency of the array angle measurement system specifically includes the following steps: for arbitrary configurations... The array is sparsely arranged, and the two-dimensional incident angle of the signal is... , The pitch angle, The azimuth angle is and the array operating frequency is . , M For array common M Operating frequency, corresponding wavelength is In the formula The speed of light; Elementary rare-array arrays at each operating wavelength in the design All elements satisfy the sparse distribution characteristic, meaning the spacing between adjacent elements is greater than half a wavelength. , N Greater than or equal to 3.

[0014] Furthermore, the array received signal at each operating frequency is obtained, specifically as follows:

[0015] The radar sequentially transmits signals at different frequencies, and at each operating frequency, the array receives the signals. for: (1)

[0016] in, for The array receives signal vectors in dimensional form. For echo signal, for A 3D noise signal vector. For frequency The guide vector below.

[0017] Furthermore, spatial spectrum estimation is performed at the selected signal operating frequency, and the positions of all spectral peaks in the spatial spectrum are calculated, specifically as follows:

[0018] Select signal operating frequency Perform spatial spectrum estimation to obtain the spatial spectrum function;

[0019] Find and number all spectral peaks of the spatial spectral function, including both the target true spectral peaks and pseudo-peaks caused by array sparseness; assume a total of Each spectral peak has a corresponding two-dimensional incident angle. .

[0020] Furthermore, select the signal operating frequency. Spatial spectrum estimation is performed to obtain the spatial spectrum function. The specific method for spatial spectrum estimation is as follows:

[0021] First, based on the received signal at that frequency Calculate the covariance matrix :

[0022] (2)

[0023] in, This represents the operation of calculating the mathematical expectation;

[0024] Perform eigenvalue decomposition on the covariance matrix:

[0025] (3)

[0026] in, A diagonal matrix composed of principal eigenvalues. It is a diagonal matrix composed of small eigenvalues. The signal subspace is represented by the eigenvectors corresponding to the principal eigenvalues. The largest eigenvalue in the subspace is the principal eigenvalue, and the rest are the smaller eigenvalues. Representing the noise subspace, by The eigenvectors are composed of the eigenvalues ​​corresponding to the small eigenvalues, and their relationship with the signal frequency is... The target guidance vector is orthogonal, that is:

[0027] (4)

[0028] Based on equation (4), construct the following problem to solve for the signal frequency. Estimated target angle:

[0029] (5)

[0030] They are respectively The estimated value; its corresponding spatial spectral function is:

[0031] (6).

[0032] Furthermore, based on signals at other frequencies, the ambiguity number estimation error corresponding to each spectral peak is calculated, specifically as follows:

[0033] from Selecting any two array elements from the array elements yields... Combinations; in frequency Next, based on the received signal The phase difference between each pair of array elements is calculated, and the phase difference between any two array elements is then calculated as follows:

[0034] ;

[0035] in, ; ; They represent the first The corresponding numbers of the double array elements, ;

[0036] According to the Each spectral peak corresponding angle Calculate the frequency Next Calculated phase difference between two array elements :

[0037] (7)

[0038] in, Indicates the first The vector connecting the positions of the bi-array elements. It is a 3×1 dimensional real matrix. Indicates the first The unit direction vector corresponding to the angle of each spectral peak. The wavelength of the signal;

[0039] For the actual angle of the target, the phase difference calculated according to equation (7) is used. Phase difference measurement The difference is If the number is an integer multiple of , then the th The fuzzy number estimation error under each spectral peak Defined as:

[0040] (8)

[0041] Since the actual target angle corresponds to the difference between the calculated and measured phase difference between the dual array elements at each frequency, the calculated value is also equal to the measured value. Integer multiples, i.e., fuzzy number estimation error The value approaches 0; however, the angle corresponding to the spurious peak does not satisfy this relationship, i.e., the fuzzy number estimation error... Greater than 0.

[0042] Another embodiment of the present invention provides a sparse array multi-frequency deambiguation spatial spectrum estimation system, including an array design module, an array signal receiving module, a spatial spectrum estimation module, an ambiguity number estimation error module, and a target position estimation module;

[0043] The array design module is used to design the sparse array configuration and operating frequency of the array angle measurement system.

[0044] The array signal receiving module is used to acquire the array received signal at each operating frequency;

[0045] The spatial spectrum estimation module is used to perform spatial spectrum estimation on a selected signal operating frequency and calculate the positions of all spectral peaks in the spatial spectrum.

[0046] The fuzzy number estimation error module is used to calculate the fuzzy number estimation error corresponding to each spectral peak based on signals from other frequencies.

[0047] The target location estimation module is used to determine the target location by identifying the spectral peak with the smallest fuzzy number estimation error.

[0048] Furthermore, the formation design module is specifically designed as follows:

[0049] For arbitrary configurations The array is sparsely arranged, and the two-dimensional incident angle of the signal is... , The pitch angle, The azimuth angle is and the array operating frequency is . , M For array common M Operating frequency, corresponding wavelength is In the formula The speed of light; Elementary rare-array arrays at each operating wavelength in the design All elements satisfy the sparse distribution characteristic, meaning the spacing between adjacent elements is greater than half a wavelength. , N Greater than or equal to 3.

[0050] Furthermore, the array signal receiving module specifically uses the following method to perform spatial spectrum estimation and calculate the positions of all spectral peaks in the spatial spectrum:

[0051] Select signal operating frequency Spatial spectrum estimation is performed to obtain the spatial spectrum function; firstly, based on the received signal at that frequency... Calculate the covariance matrix :

[0052] (2)

[0053] in, This represents the operation of calculating the mathematical expectation;

[0054] Perform eigenvalue decomposition on the covariance matrix:

[0055] (3)

[0056] in, A diagonal matrix composed of principal eigenvalues. It is a diagonal matrix composed of small eigenvalues. The signal subspace is represented by the eigenvectors corresponding to the principal eigenvalues. The largest eigenvalue in the subspace is the principal eigenvalue, and the rest are the smaller eigenvalues. Representing the noise subspace, by The eigenvectors are composed of the eigenvalues ​​corresponding to the small eigenvalues, and their relationship with the signal frequency is... The target guidance vector is orthogonal, that is:

[0057] (4)

[0058] Based on equation (4), construct the following problem to solve for the signal frequency. Estimated target angle:

[0059] (5)

[0060] They are respectively The estimated value; its corresponding spatial spectral function is:

[0061] (6)

[0062] Find and number all spectral peaks of the spatial spectral function, including both the target true spectral peaks and pseudo-peaks caused by array sparseness; assume a total of Each spectral peak has a corresponding two-dimensional incident angle. .

[0063] Furthermore, the fuzzy number estimation error module calculates the fuzzy number estimation error corresponding to each spectral peak in the following manner:

[0064] from Selecting any two array elements from the array elements yields... Combinations; in frequency Next, based on the received signal Once the phase difference between any two array elements is determined, the phase difference between any two array elements is then calculated.

[0065] ;

[0066] in, ; ; They represent the first The corresponding numbers of the double array elements, ;

[0067] According to the Each spectral peak corresponding angle Calculate the frequency Next Calculated phase difference between two array elements :

[0068] (7)

[0069] in, Indicates the first The vector connecting the positions of the bi-array elements. It is a 3×1 dimensional real matrix. Indicates the first The unit direction vector corresponding to the angle of each spectral peak. The wavelength of the signal;

[0070] For the actual angle of the target, the phase difference calculated according to equation (7) is used. Phase difference measurement The difference is If the number is an integer multiple of , then the th The fuzzy number estimation error under each spectral peak Defined as:

[0071] (8)

[0072] Since the actual target angle corresponds to the difference between the calculated and measured phase difference between the dual array elements at each frequency, the calculated value is also equal to the measured value. Integer multiples, i.e., fuzzy number estimation error The value approaches 0; however, the angle corresponding to the spurious peak does not satisfy this relationship, i.e., the fuzzy number estimation error... Greater than 0.

[0073] Beneficial effects:

[0074] This invention proposes a spatial spectrum estimation method and system for sparse array multi-frequency deambiguation. The sparse array radar utilizes this method, receiving signals at different frequencies and deambiguing based on the ambiguity number estimation error of the spatial spectrum estimation results. This invention achieves high-precision two-dimensional angle estimation, is applicable to sparse arrays of arbitrary configurations, and can perform deambiguation without the aid of a physical short baseline. It offers flexible array configuration and strong universality of the angle measurement method. This invention enables two-dimensional angle estimation, deambiguation based on multiple operating frequency signals, flexible array configuration, and high angle measurement accuracy. Attached Figure Description

[0075] Figure 1 This is a flowchart of the present invention;

[0076] Figure 2 A schematic diagram of the array structure selected for this embodiment;

[0077] Figure 3 This is a schematic diagram of the single-step deblurring effect;

[0078] Figure 4 A diagram illustrating the success rate of defuzzification;

[0079] Figure 5 This is a schematic diagram of the root mean square error of angle measurement. Detailed Implementation

[0080] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0081] Example 1:

[0082] This invention proposes a spatial spectrum estimation method for sparse arrays with multi-frequency deambiguity, to solve the problems of deambiguity and two-dimensional high-precision angle measurement in spatial spectrum estimation of sparse arrays. This invention is applicable to sparse arrays of arbitrary configurations, and the specific steps are as follows:

[0083] Step 1: Design the sparse array configuration and operating frequency of the array angle measurement system.

[0084] Considering arbitrary configurations The array is arranged in a sparse manner, considering the two-dimensional incident angle of the signal as follows: , This refers to the pitch angle, which ranges from 0 to 90 degrees. The azimuth angle is 0-360 degrees, and the array operating frequency is... M represents the total number of operating frequencies of the array, corresponding to wavelengths of M. In the formula It is the speed of light. Elementary rare-array arrays at each operating wavelength in the design All elements satisfy the sparse distribution characteristic, meaning the spacing between adjacent elements is greater than half a wavelength. N is greater than or equal to 3.

[0085] Step 2: Acquire the array received signal at each operating frequency

[0086] The radar sequentially transmits signals at different frequencies, and at each operating frequency, the array receives the signals. It can be represented as

[0087] (1)

[0088] In the formula, for The array receives signal vectors in dimensional form. For echo signal, for A 3D noise signal vector. For frequency The guide vector below.

[0089] Step 3: Select the signal operating frequency and perform spatial spectrum estimation.

[0090] Select signal operating frequency Spatial spectrum estimation is performed. First, based on the received signal at that frequency... Calculate the covariance matrix :

[0091] (2)

[0092] In the formula, This indicates the operation of calculating the expected value of a mathematical expression.

[0093] Eigendecomposition of the covariance matrix yields:

[0094] (3)

[0095] In the formula, A diagonal matrix composed of principal eigenvalues. It is a diagonal matrix composed of small eigenvalues. The signal subspace is represented by the eigenvectors corresponding to the principal eigenvalues. The largest eigenvalue in the subspace is the principal eigenvalue, and the rest are the smaller eigenvalues. Representing the noise subspace, by The eigenvectors are composed of the eigenvalues ​​corresponding to the small eigenvalues, and their relationship with the signal frequency is... The target guidance vector is orthogonal, that is:

[0096] (4)

[0097] According to equation (4), the following problem can be constructed to solve for the signal frequency. The estimated angle of the target is below.

[0098] (5)

[0099] They are respectively The estimated value; its corresponding spatial spectral function is

[0100] (6).

[0101] To find and number all spectral peaks of the spatial spectral function, an ergonomic method can be used in this embodiment of the invention. This includes both the target true spectral peaks and pseudo-peaks caused by the sparse distribution of the array. Assume there are a total of... Each spectral peak has a corresponding two-dimensional incident angle. .

[0102] Step 4: Deblur based on signals from other frequencies

[0103] from By selecting any two array elements from the array elements, we can obtain Combinations. In frequency Next, based on the received signal Once the phase difference between any two array elements is determined, the phase difference between any two array elements is then calculated.

[0104] ;

[0105] in, ; ; They represent the first The corresponding numbers of the double array elements, ;

[0106] According to the Each spectral peak ( The corresponding angle The frequency can be obtained. Next Calculated phase difference between two array elements :

[0107] (7)

[0108] In the formula, Indicates the first The vector connecting the positions of the bi-array elements. It is a 3x1 real matrix. Indicates the first The unit direction vector corresponding to the angle of each spectral peak. The wavelength is the signal wavelength.

[0109] For the actual angle of the target, the phase difference calculated according to equation (7) is used. Phase difference measurement The difference is If it is an integer multiple of , then the th The fuzzy number estimation error under each spectral peak Defined as

[0110] (8)

[0111] Since the actual target angle corresponds to the difference between the calculated and measured phase difference between the dual array elements at each frequency, the calculated value is also equal to the measured value. The expression is an integer multiple, meaning it approaches 0; however, the angle corresponding to the pseudo-peak does not satisfy this relationship, meaning the expression is greater than 0.

[0112] fuzzy number estimation error ( Arrange them in ascending order, and the angle value of the spectral peak with the smallest error is the estimated value of the actual angle of the target.

[0113] This invention proposes a spatial spectrum estimation method for multi-frequency resolution of angular ambiguity in sparse arrays, such as... Figure 1 As shown, this method is based on multi-frequency deambiguity and realizes two-dimensional incident angle measurement through spatial spectrum estimation, which has the advantages of flexible array configuration and high angle measurement accuracy.

[0114] In this embodiment, a 9-element uniform rectangular array is set, with the element spacing along the x-axis and y-axis... ,like Figure 2 As shown.

[0115] Three operating frequencies are designed, and they are selected as follows: The corresponding wavelengths are respectively The arrays described above are sparsely distributed relative to the three operating wavelengths. The radar target angle is set to... .

[0116] When the signal-to-noise ratio is 0dB and the number of snapshots is 100, the single simulation results are as follows: Figure 3 As shown, the proposed method can be seen to identify the true location of the target from multiple spectral peaks, and the deblurring result is correct.

[0117] With a fixed number of snapshots of 50, and traversing the signal-to-noise ratio (SNR), 500 Monte Carlo simulation experiments were conducted at each SNR. The curves showing the changes in the unblurring success rate and the root mean square error (RMSE) of angle measurement as a function of the SNR were obtained, as shown below. Figure 4 and Figure 5 As shown in the figure. The simulation results show that the proposed method can achieve high-precision two-dimensional angle estimation without ambiguity. The higher the signal-to-noise ratio, the higher the success rate of ambiguity resolution and the smaller the root mean square error of angle measurement.

[0118] Example 2:

[0119] Another embodiment of the present invention provides a sparse array multi-frequency defuzzification spatial spectrum estimation system, characterized in that it includes an array design module, an array signal receiving module, a spatial spectrum estimation module, a fuzzy number estimation error module, and a target position estimation module.

[0120] The array design module is used to design the sparse array configuration and operating frequency of the array angle measurement system.

[0121] The array signal receiving module is used to acquire the array received signal at each operating frequency.

[0122] The spatial spectrum estimation module is used to perform spatial spectrum estimation at the selected signal operating frequency and calculate the positions of all spectral peaks in the spatial spectrum.

[0123] The fuzzy number estimation error module is used to calculate the fuzzy number estimation error corresponding to each spectral peak based on signals from other frequencies.

[0124] The target location estimation module is used to determine the target location by identifying the spectral peak with the smallest fuzzy number estimation error.

[0125] The formation design module is designed as follows:

[0126] For arbitrary configurations The array is sparsely arranged, and the two-dimensional incident angle of the signal is... , The pitch angle, The azimuth angle is and the array operating frequency is . , M For array common M Operating frequency, corresponding wavelength is In the formula The speed of light; Elementary rare-array arrays at each operating wavelength in the design All elements satisfy the sparse distribution characteristic, meaning the spacing between adjacent elements is greater than half a wavelength. , N Greater than or equal to 3.

[0127] The array signal receiving module specifically uses the following method to perform spatial spectrum estimation and calculate the positions of all spectral peaks in the spatial spectrum:

[0128] Select signal operating frequency Spatial spectrum estimation is performed to obtain the spatial spectrum function; firstly, based on the received signal at that frequency... Calculate the covariance matrix :

[0129] (2)

[0130] in, This indicates the operation of calculating the expected value of a mathematical expression.

[0131] Perform eigenvalue decomposition on the covariance matrix:

[0132] (3)

[0133] in, A diagonal matrix composed of principal eigenvalues. It is a diagonal matrix composed of small eigenvalues. The signal subspace is represented by the eigenvectors corresponding to the principal eigenvalues. The largest eigenvalue in the subspace is the principal eigenvalue, and the rest are the smaller eigenvalues. Representing the noise subspace, by The eigenvectors are composed of the eigenvalues ​​corresponding to the small eigenvalues, and their relationship with the signal frequency is... The target guidance vector is orthogonal, that is:

[0134] (4)

[0135] Based on equation (4), construct the following problem to solve for the signal frequency. Estimated target angle:

[0136] (5)

[0137] They are respectively The estimated value; its corresponding spatial spectral function is:

[0138] (6)

[0139] Find and number all spectral peaks of the spatial spectral function, including both the target true spectral peaks and pseudo-peaks caused by array sparseness; assume a total of Each spectral peak has a corresponding two-dimensional incident angle. .

[0140] The fuzzy number estimation error module calculates the fuzzy number estimation error for each spectral peak in the following manner:

[0141] from Selecting any two array elements from the array elements yields... Combinations; in frequency Next, based on the received signal Once the phase difference between any two array elements is determined, the phase difference between any two array elements is then calculated.

[0142] ;

[0143] in, ; ; They represent the first The corresponding numbers of the double array elements, .

[0144] According to the Each spectral peak corresponding angle Calculate the frequency Next Calculated phase difference between two array elements :

[0145] (7)

[0146] in, Indicates the first The vector connecting the positions of the bi-array elements. It is a 3×1 dimensional real matrix. Indicates the first The unit direction vector corresponding to the angle of each spectral peak. The wavelength is the signal wavelength.

[0147] For the actual angle of the target, the phase difference calculated according to equation (7) is used. Phase difference measurement The difference is If the number is an integer multiple of , then the th The fuzzy number estimation error under each spectral peak Defined as:

[0148] (8)

[0149] Since the actual target angle corresponds to the difference between the calculated and measured phase difference between the dual array elements at each frequency, the calculated value is also equal to the measured value. Integer multiples, i.e., fuzzy number estimation error The value approaches 0; however, the angle corresponding to the spurious peak does not satisfy this relationship, i.e., the fuzzy number estimation error... Greater than 0.

[0150] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A spatial spectrum estimation method for sparse array multi-frequency defuzzification, characterized in that, Includes the following steps: Design the sparse array configuration and operating frequency of the array angle measurement system; specifically including the following steps: For arbitrary configurations The array is sparsely arranged, and the two-dimensional incident angle of the signal is... , The pitch angle, The azimuth angle is and the array operating frequency is . , , M For array common M Operating frequency, corresponding wavelength is In the formula The speed of light; Elementary rare-array arrays at each operating wavelength in the design All elements satisfy the sparse distribution characteristic, meaning the spacing between adjacent elements is greater than half a wavelength. , N Greater than or equal to 3; The array received signal at each operating frequency is obtained as follows: The radar sequentially transmits signals at different frequencies, and at each operating frequency, the array receives the signals. for: (1) in, for The array receives signal vectors in dimensional form. For echo signal, for A 3D noise signal vector. For frequency The guide vector below; Spatial spectrum estimation is performed at the selected signal operating frequency, and the positions of all spectral peaks in the spatial spectrum are calculated, specifically as follows: Select signal operating frequency Perform spatial spectrum estimation to obtain the spatial spectrum function; Find and number all spectral peaks of the spatial spectral function, including the target true spectral peaks and pseudo-peaks caused by array sparseness; assume a total of Each spectral peak has a corresponding two-dimensional incident angle. ; The spatial spectrum estimation is performed using the following method: First, based on the received signal at that frequency Calculate the covariance matrix : (2) in, This represents the operation of calculating the mathematical expectation; Perform eigenvalue decomposition on the covariance matrix: (3) in, A diagonal matrix composed of principal eigenvalues. It is a diagonal matrix composed of small eigenvalues. The signal subspace is represented by the eigenvectors corresponding to the principal eigenvalues. The largest eigenvalue in the subspace is the principal eigenvalue, and the rest are the smaller eigenvalues. Representing the noise subspace, by The eigenvectors are composed of the eigenvalues ​​corresponding to the small eigenvalues, and their relationship with the signal frequency is... The target guidance vector is orthogonal, that is: (4) Based on equation (4), construct the following problem to solve for the signal frequency. Estimated target angle: （5） They are respectively The estimated value; its corresponding spatial spectral function is: （6）； Based on signals from other frequencies, calculate the ambiguity number estimation error corresponding to each spectral peak; The spectral peak with the smallest fuzzy number estimation error is the target location.

2. The spatial spectrum estimation method for sparse array multi-frequency defuzzification as described in claim 1, characterized in that, The calculation of the ambiguity number estimation error corresponding to each spectral peak based on signals of other frequencies is specifically as follows: from Selecting any two array elements from the array elements yields... Combinations; in frequency Next, based on the received signal Once the phase difference between any two array elements is determined, the phase difference between any two array elements is then calculated. ； in, ; ; They represent the first The corresponding numbers of the double array elements, ; According to the Each spectral peak Corresponding angle Calculate the frequency Next Calculated phase difference between two array elements : （7） in, Indicates the first The vector connecting the positions of the two matrix elements. It is a 3×1 dimensional real matrix. Indicates the first The unit direction vector corresponding to the angle of each spectral peak. The wavelength of the signal; For the actual angle of the target, the phase difference calculated according to equation (7) is used. Phase difference measurement The difference is If the number is an integer multiple of , then the th The fuzzy number estimation error under each spectral peak Defined as: （8） Since the actual target angle corresponds to the difference between the calculated and measured phase difference between the dual array elements at each frequency, the calculated value is also equal to the measured value. Integer multiples, i.e., fuzzy number estimation error The value approaches 0; however, the angle corresponding to the spurious peak does not satisfy this relationship, i.e., the fuzzy number estimation error... Greater than 0.

3. A sparse array multi-frequency unfuzzy spatial spectrum estimation system, characterized in that, It includes an array design module, an array signal receiving module, a spatial spectrum estimation module, an ambiguity number estimation error module, and a target position estimation module; The array design module is used to design the sparse array configuration and operating frequency of the array angle measurement system; The array signal receiving module is used to acquire the array received signal at each operating frequency; The spatial spectrum estimation module is used to select the signal operating frequency to perform spatial spectrum estimation and calculate the positions of all spectral peaks in the spatial spectrum; The fuzzy number estimation error module is used to calculate the fuzzy number estimation error corresponding to each spectral peak based on signals of other frequencies. The target location estimation module is used to determine the target location by the spectral peak with the smallest fuzzy number estimation error. The formation design module is specifically designed as follows: For arbitrary configurations The array is sparsely arranged, and the two-dimensional incident angle of the signal is... , The pitch angle, The azimuth angle is and the array operating frequency is . , M For array common M Operating frequency, corresponding wavelength is In the formula The speed of light; Elementary rare-array arrays at each operating wavelength in the design All elements satisfy the sparse distribution characteristic, meaning the spacing between adjacent elements is greater than half a wavelength. , N Greater than or equal to 3; The array signal receiving module specifically uses the following method to perform spatial spectrum estimation and calculate the positions of all spectral peaks in the spatial spectrum: Select signal operating frequency Perform spatial spectrum estimation to obtain the spatial spectrum function; First, based on the received signal at that frequency Calculate the covariance matrix : (2) in, This represents the operation of calculating the mathematical expectation; Perform eigenvalue decomposition on the covariance matrix: (3) in, A diagonal matrix composed of principal eigenvalues. It is a diagonal matrix composed of small eigenvalues. The signal subspace is represented by the eigenvectors corresponding to the principal eigenvalues. The largest eigenvalue in the subspace is the principal eigenvalue, and the rest are the smaller eigenvalues. Representing the noise subspace, by The eigenvectors are composed of the eigenvalues ​​corresponding to the small eigenvalues, and their relationship with the signal frequency is... The target guidance vector is orthogonal, that is: (4) Based on equation (4), construct the following problem to solve for the signal frequency. Estimated target angle: （5） They are respectively The estimated value; its corresponding spatial spectral function is: （6） Find and number all spectral peaks of the spatial spectral function, including the target true spectral peaks and pseudo-peaks caused by array sparseness; assume a total of Each spectral peak has a corresponding two-dimensional incident angle. .

4. The sparse array multi-frequency unfuzzy spatial spectrum estimation system as described in claim 3, characterized in that, The fuzzy number estimation error module calculates the fuzzy number estimation error corresponding to each spectral peak in the following manner: from Selecting any two array elements from the array elements yields... Combinations; in frequency Next, based on the received signal Once the phase difference between any two array elements is determined, the phase difference between any two array elements is then calculated. ； in, ; ; They represent the first The corresponding numbers of the double array elements, ; According to the Each spectral peak Corresponding angle Calculate the frequency Next Calculated phase difference between two array elements : （7） in, Indicates the first The vector connecting the positions of the two matrix elements. It is a 3×1 dimensional real matrix. Indicates the first The unit direction vector corresponding to the angle of each spectral peak. The wavelength of the signal; For the actual angle of the target, the phase difference calculated according to equation (7) is used. Phase difference measurement The difference is If the number is an integer multiple of , then the th The fuzzy number estimation error under each spectral peak Defined as: （8） Since the actual target angle corresponds to the difference between the calculated and measured phase difference between the dual array elements at each frequency, the calculated value is also equal to the measured value. Integer multiples, i.e., fuzzy number estimation error The value approaches 0; however, the angle corresponding to the spurious peak does not satisfy this relationship, i.e., the fuzzy number estimation error... Greater than 0.

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