A distributed array direction-of-arrival estimation method with arbitrary sub-array configuration

Abstract

The present invention provides a distributed array direction-of-arrival (DOA) estimation method for arbitrary subarray configurations, comprising the steps of constructing a distributed array with arbitrary subarray configurations, digitally channelizing incoming signal data received by the distributed array, separating the incoming signal data, estimating the phase difference of each received signal due to the inter-subarray baseline length and the covariance matrix of the received signal data, calculating all ambiguous phase differences for each signal based on the inter-subarray baseline lengths and obtaining corresponding DOA estimates, and substituting all ambiguous DOA estimates for each signal into a multiple signal classification spatial spectrum deambiguation method to obtain high-precision, unambiguous DOA estimates for all incoming signals. This method allows for arbitrary arrangement of array elements within the subarray, addressing the limitations of baseline arrangement imposed by deambiguation methods such as long-short baselines and staggered baselines. The method offers flexible array configuration and ease of engineering implementation, making it suitable for small platforms such as micro- and nano-satellites and drones, and possessing broad market application prospects.

Description

Technical Field

[0001] The invention relates to a distributed array direction of arrival estimation method with arbitrary sub-array configurations, belonging to the technical field of signal processing. Background Art

[0002] Direction-of-arrival (DOA) estimation is a key research area in array signal processing, widely applied and studied in fields such as radar, wireless communications, sonar, electronic reconnaissance, and microwave warning. The physical aperture of an array is a key parameter closely related to its DOA estimation performance. The larger the physical aperture, the higher the angular resolution and DOA estimation accuracy. Distributed arrays, consisting of multiple distributed subarrays, can increase the physical aperture and improve DOA estimation performance without increasing the number of array elements. In particular, combining methods such as phase interferometry or spatial spectrum estimation with distributed arrays can achieve high-precision and high-angular-resolution DOA estimation, thus garnering widespread attention. However, because the baseline length between subarrays in a distributed array is much longer than half a wavelength, the direction-of-arrival (DOA) results require deambiguation. Deambiguation methods such as long-short baselines and staggered baselines impose specific requirements on the array baseline arrangement, which impacts practical engineering applications on small platforms such as micro- and nanosatellites and drones. Summary of the Invention

[0003] The technical problem solved by the present invention is to overcome the shortcomings of the existing technology, provide a distributed array direction of arrival estimation method with arbitrary sub-array configuration, and solve the problem of the limitation of baseline arrangement on long and short baseline, staggered baseline and other deambiguation methods.

[0004] The technical solution of the present invention is: a distributed array direction of arrival estimation method with arbitrary sub-array configuration, comprising:

[0005] 1) Construct a distributed array with arbitrary sub-array configurations;

[0006] 2) Perform digital channelization processing on the incident signal received by the distributed array to obtain N incident signal receiving data x N (t);

[0007] 3) Based on the received data of the nth incident signal, estimate the phase difference caused by the baseline length between the two sub-arrays Simultaneously estimate the covariance matrix of the received data of the nth incident signal

[0008] 4) According to the phase difference and the covariance matrix Calculate the set of angle estimates with periodic ambiguity and the noise subspace

[0009] 5) The angle estimation value set with periodic blur Substitute into the multiple signal classification spatial spectrum defuzzification to obtain the unambiguous angle estimate of the nth signal

[0010] 6) Steps 3) to 5) are performed on the received data of the N incident signals simultaneously to obtain unambiguous angle estimation results of the N incident signals.

[0011] The method of constructing a distributed array of arbitrary sub-array configurations includes:

[0012] The distributed array is composed of two sub-arrays, each sub-array has M array elements, the array elements are non-uniformly distributed and have the same configuration; the position of the distributed array elements is d = [d1, d2, ..., d M ,d M+1 ,d M+2 ,...,d 2M ] T , select the first element of sub-array 1 as the reference element d1=0, then d m is the position of the mth array element, m=1,2,...,2M, D is the baseline distance between sub-arrays; assuming that N incoherent and different frequency far-field narrowband signals are incident on the distributed array, θ n is the nth incident signal azimuth, n=1,2,...,N; then the array satisfies d M -d1=d 2M -d M+1 >(M-1)λ n , D>>λ n ,λ n is the wavelength of the nth incident signal.

[0013] The flow matrix A(θ) of the distributed array is obtained as:

[0014] A(θ)=[a(θ1),a(θ2),...a(θ n )...,a(θ N )];

[0015] Where, represents the steering vector of the nth incident signal, j is an imaginary unit;

[0016] Then the signal data x(t) received by the distributed array at time t is:

[0017] x(t)=As(t)+n(t),t=1,2,...,L

[0018] Where, s(t)=[s1(t),s2(t),...,s N (t)] Tis the complex envelope vector of the signal at time t, n(t)=[n1(t),n2(t),…,n 2M (t,l)] T is the noise vector at time t, and L is the number of accumulated snapshots.

[0019] N incident signals receive data x N (t), the 1st to Nth incident signal receiving data x1(t)~x N (t) Specifically:

[0020]

[0021] The phase difference caused by the baseline length between the two sub-arrays is estimated by receiving data based on the nth incident signal. Simultaneously estimate the covariance matrix of the received data of the nth incident signal include:

[0022] The phase difference caused by the baseline length between the two sub-arrays in, is the phase difference between the mth array element and the m+Mth array element of the distributed array when receiving the nth incident signal at time t.

[0023] The covariance matrix of the received data in,[·] H represents the conjugate transpose.

[0024] The phase difference and the covariance matrix Calculate the set of angle estimates with periodic ambiguity and the noise subspace include:

[0025] According to the baseline length D between sub-arrays and the wavelength λ of the nth incident signal n Calculate the set of all fuzzy phase values Then calculate the angle estimation value set with periodic ambiguity

[0026] The covariance matrix of the received data for the nth incident signal Perform eigenvalue decomposition to obtain the noise subspace

[0027] The base line length D between the sub-arrays and the wavelength λ of the nth incident signal n Calculate the set of all fuzzy phase values Then calculate the angle estimation value set with periodic ambiguity include:

[0028] Since the baseline length between sub-arrays D>>λn , then the phase difference It has periodic ambiguity, according to the baseline length D between sub-arrays and the wavelength λ of the nth incident signal n , calculate all the fuzzy phases in Round up and round down respectively, and then calculate the angle estimation value set with periodic ambiguity

[0029] The covariance matrix of the received data for the nth incident signal Perform eigenvalue decomposition to obtain the noise subspace include:

[0030] The covariance matrix of the received data for the nth incident signal Perform eigenvalue decomposition to obtain the eigenvalue matrix and the eigenvector matrix From the eigenvector matrix Extract the eigenvalue matrix The eigenvectors corresponding to the 2M-1 small eigenvalues ​​in the noise subspace are formed by these 2M-1 eigenvectors.

[0031] The set of angle estimates that will have periodic ambiguity Substitute into the multiple signal classification spatial spectrum defuzzification to obtain the unambiguous angle estimate of the nth signal, that is, the direction of arrival estimate include:

[0032] The angle estimate set with periodic blur Towards the noise subspace Projection, deblurring to obtain unambiguous angle estimation, i.e. direction of arrival estimation

[0033]

[0034] in, Represents searching for the element “*” that minimizes the sequence “·”.

[0035] The advantages of the present invention compared with the prior art are:

[0036] (1) This invention utilizes the low system complexity and large aperture characteristics of distributed arrays and combines phase interferometry with spatial spectrum estimation methods. Compared with traditional direction-of-arrival estimation methods, the array arrangement is more flexible and easier to implement in engineering. It can be applied to small platforms such as micro-nano satellites and drones, and has broad market application prospects.

[0037] (2) The present invention substitutes the ambiguity angle value of each incident signal obtained by using the large baseline between subarrays into the multiple signal classification spatial spectrum deambiguation to obtain a high-precision and unambiguous direction of arrival estimate for each incident signal. This method allows for arbitrary arrangement of array elements within the subarray, thus solving the problem of baseline arrangement limitations imposed by deambiguation methods such as long and short baselines and staggered baselines. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flowchart for the implementation of the present invention;

[0039] Figure 2 Schematic diagram of a distributed array using any sub-array configuration of the present invention;

[0040] Figure 3 This is a graph showing the variation of the direction of arrival estimation accuracy with the signal-to-noise ratio for three incident signals of different frequencies and directions of arrival according to the present invention;

[0041] Figure 4 This is a graph showing the variation of the success rate of direction of arrival estimation and deambiguation with the signal-to-noise ratio for three incident signals with different frequencies and directions of arrival according to the present invention;

[0042] Figure 5 This is a graph showing the variation of the direction of arrival estimation accuracy with the signal-to-noise ratio under the condition of random distribution of sub-array elements of the distributed array of the present invention;

[0043] Figure 6 This is a graph showing how the success rate of direction of arrival estimation and deambiguation changes with the signal-to-noise ratio under the condition of random distribution of elements in the distributed array sub-array of the present invention. DETAILED DESCRIPTION

[0044] like Figure 1 As shown, the incident signal data received by the distributed array is digitally channelized, the incident signal data is separated, the phase difference of each received signal due to the baseline length between sub-arrays and the covariance matrix of the received signal data are estimated, all fuzzy phase differences of each signal are calculated according to the baseline length between sub-arrays, and the corresponding direction of arrival estimates are obtained. All fuzzy direction of arrival estimates of each signal are substituted into the multiple signal classification spatial spectrum deambiguation, and high-precision and unambiguous direction of arrival estimates of all incident signals are obtained.

[0045] The content and effects of the present invention will be described in detail below with reference to the accompanying drawings.

[0046] Reference Figure 1 , the present invention comprises the following steps:

[0047] Step 1: Construct a distributed array of arbitrary sub-array configurations:

[0048] 1a) Press Figure 2As shown in the figure, a distributed array is formed by two sub-arrays with M elements, non-uniformly distributed elements and the same configuration. The position of the elements in the distributed array is d = [d1, d2, ..., d M ,d M+1 ,d M+2 ,...,d 2M ] T , select the first element of sub-array 1 as the reference element d1=0, then d m (m=1,2,...,2M) is the position of the mth array element, and D is the baseline distance between sub-arrays. Assume that N incoherent and different frequency far-field narrowband signals are incident on the distributed array, θ n (n=1,2,…,N) is the nth incident signal azimuth, then the array satisfies d M -d1=d 2M -d M+1 >(M-1)λ n , D>>λ n ,λ n is the wavelength of the nth incident signal.

[0049] 1b) Get the manifold matrix A(θ) of the array:

[0050] A(θ)=[a(θ1),a(θ2),...a(θ n )...,a(θ N )];

[0051] Where, is the steering vector of the nth incident signal, and j is an imaginary unit. Then the signal data x(t) received by the distributed array at time t is:

[0052] x(t)=As(t)+n(t),t=1,2,...,L

[0053] Where, s(t)=[s1(t),s2(t),...,s N (t)] T is the complex envelope vector of the signal at time t, n(t)=[n1(t),n2(t),...,n 2M (t,l)] T is the noise vector at time t, and L is the number of accumulated snapshots.

[0054] Step 2: Perform digital channelization processing on the incident signal received by the distributed array constructed in step 1) to separate the 1st to Nth incident signal receiving data x1(t)~x N (t):

[0055]

[0056] Step 3: Estimate the phase difference caused by the baseline length between the two sub-arrays based on the nth incident signal data Simultaneously estimate the covariance matrix of the nth incident signal data

[0057] The phase difference caused by the baseline length between the two sub-arrays in, is the phase difference between the mth array element and the m+Mth array element of the distributed array when receiving the nth incident signal at time t; the covariance matrix of the received data in,[·] H represents the conjugate transpose.

[0058] Step 4: According to the phase difference and the covariance matrix Obtain a set of angle estimates with high accuracy but periodic ambiguity and the noise subspace

[0059] 4a) Since D>>λ n , then the phase difference It has periodic ambiguity, according to the baseline length D between sub-arrays and the wavelength λ of the nth incident signal n Calculate all fuzzy phases Round up and down respectively, and then calculate the angle estimation value set with high precision but periodic ambiguity

[0060] 4b) The covariance matrix of the received data for the nth incident signal Perform eigenvalue decomposition to obtain the eigenvalue matrix and the eigenvector matrix From the eigenvector matrix Extract the eigenvalue matrix The eigenvectors corresponding to the 2M-1 small eigenvalues ​​in the noise subspace are formed by these 2M-1 eigenvectors.

[0061] Step 5: Substitute the multiple signal classification spatial spectrum defuzzification to obtain the high-precision and unambiguous angle estimation of the nth signal

[0062] The blurred angle estimates are aggregated Towards the noise subspace Projection and deambiguation to obtain a high-precision and unambiguous estimate of the direction of arrival of the incident signal It is done by the following formula:

[0063]

[0064] in, Represents searching for the element “*” that minimizes the sequence “·”.

[0065] Step 6: Perform steps 3) to 5) on the received data of N incident signals at the same time to obtain high-precision and unambiguous angle estimation of the N incident signals, i.e., the direction of arrival estimation result.

[0066] The effect of the present invention is further illustrated by the following computational simulation:

[0067] Simulation Experiment 1: A Monte Carlo simulation experiment is performed on three incident signals with different frequencies and different directions of arrival to determine how the accuracy of direction of arrival estimation varies with the signal-to-noise ratio using the present invention.

[0068] In this simulation, the present invention uses two one-dimensional linear array sub-arrays with the same array configuration and non-uniformly distributed array elements to form a distributed array, where: the number of sub-array elements M = 6, the array element positions are {0, 0.353, 0.765, 0.87, 1.095, 1.5, 6.375, 6.728, 7.14, 7.245, 7.47, 7.875} (unit: meter), and the baseline length between sub-arrays is 6.375 meters.

[0069] The target parameters selected for the simulation are: number of incident signals N = 3, signal frequencies f1 = 1.92 GHz, f2 = 2 GHz, f3 = 2.03 GHz, directions of arrival θ1 = 27.3°, θ2 = 21.5°, θ3 = 15.1°, number of Monte Carlo experiments 200 times, number of snapshots L = 50, and the simulation results are as follows: Figure 3 、 Figure 4 The horizontal axis represents the signal-to-noise ratio (SNR) from -10dB to 20dB, and the vertical axis represents the root mean square error (RMSE) of the direction of arrival (DOA) estimation.

[0070]

[0071] in They represent the estimated direction of arrival value of the n-th source in the k-th Monte Carlo experiment, and K represents the number of Monte Carlo experiments.

[0072] Simulation experiment 2: A Monte Carlo simulation experiment is performed to determine the variation of the direction of arrival estimation accuracy with the signal-to-noise ratio under the condition of random distribution of the elements of the distributed array sub-array of the present invention.

[0073] In this simulation, the present invention uses two one-dimensional linear array sub-arrays with the same array configuration and randomly distributed array elements to form a distributed array, where: the number of sub-array elements M = 5, the sub-array aperture is 1 meter, the sub-array elements are randomly distributed within the aperture of 1 meter (the array element positions are randomly redistributed in each Monte Carlo experiment), and the baseline length between sub-arrays is 10 meters.

[0074] The target parameters selected for the simulation are: number of incident signals N = 1, signal frequency f = 3 GHz, direction of arrival θ = 31.4°, number of Monte Carlo experiments 200 times, number of snapshots L = 50, and the simulation results are as follows: Figure 5 、 Figure 6 The horizontal axis represents the signal-to-noise ratio (SNR) from -10dB to 20dB, and the vertical axis represents the root mean square error (RMS) of the direction of arrival (DOA) estimation.

[0075] Depend on Figure 3 、 Figure 4 It can be seen that the present invention can successfully deambiguate the three incident signals under the condition of a signal-to-noise ratio greater than or equal to -4dB to obtain a high-precision and unambiguous direction of arrival estimate. Simulation experiments prove that the present invention can use a distributed array to achieve high-precision direction of arrival estimation of multiple incident signals with different frequencies at the same time. Figure 5 、 Figure 6 It can be seen that under the condition of a signal-to-noise ratio of greater than or equal to -4dB, the present invention can successfully deambiguate and obtain a high-precision, unambiguous direction of arrival estimate for any subarray element distribution. Simulation experiments prove that the deambiguation performance of the present invention is not limited by the element distribution within the subarray, that is, the baseline arrangement.

[0076] Although the present invention has been disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solutions of the present invention using the technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the scope of protection of the technical solutions of the present invention.

Claims

1. A distributed array direction of arrival estimation method with arbitrary sub-array configuration, characterized in that: include: 1) Construct a distributed array with arbitrary sub-array configurations; 2) Perform digital channelization processing on the incident signal received by the distributed array to obtain N incident signal receiving data x N (t); 3) Based on the received data of the nth incident signal, estimate the phase difference caused by the baseline length between the two sub-arrays Simultaneously estimate the covariance matrix of the received data of the nth incident signal 4) According to the phase difference and the covariance matrix Calculate the set of angle estimates with periodic ambiguity and the noise subspace 5) The angle estimation value set with periodic blur Substitute into the multiple signal classification spatial spectrum defuzzification to obtain the unambiguous angle estimate of the nth signal 6) Steps 3) to 5) are performed on the received data of the N incident signals simultaneously to obtain unambiguous angle estimation results of the N incident signals.

2. The method for estimating the direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 1, characterized in that: The method of constructing a distributed array of arbitrary sub-array configurations includes: The distributed array is composed of two sub-arrays, each sub-array has M array elements, the array elements are non-uniformly distributed and have the same configuration; the position of the distributed array elements is d = [d1, d2, ..., d M ,d M+1 ,d M+2 ,...,d 2M ] T , select the first element of sub-array 1 as the reference element d1=0, then d m is the position of the mth array element, m=1,2,...,2M, D is the baseline distance between sub-arrays; assuming that N incoherent and different frequency far-field narrowband signals are incident on the distributed array, θ n is the nth incident signal azimuth, n=1,2,...,N; then the array satisfies d M -d1=d 2M -d M+1 >(M-1)λ n , D>>λ n ,λ n is the wavelength of the nth incident signal.

3. The method for estimating the direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 2, characterized in that: The flow matrix A(θ) of the distributed array is obtained as: A(θ)=[a(θ1),a(θ2),...a(θ n )...,a(θ N )]; Where, represents the steering vector of the nth incident signal, j is an imaginary unit; Then the signal data x(t) received by the distributed array at time t is: x(t)=As(t)+n(t),t=1,2,...,L Where, s(t)=[s1(t),s2(t),...,s N (t)] T is the complex envelope vector of the signal at time t, n(t)=[n1(t),n2(t),...,n 2M (t,l)] T is the noise vector at time t, and L is the number of accumulated snapshots.

4. The method for estimating the direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 3, characterized in that: N incident signals receive data x N (t), the 1st to Nth incident signal receiving data x1(t)~x N (t) Specifically:

5. The method for estimating the direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 4, characterized in that: The phase difference caused by the baseline length between the two sub-arrays is estimated by receiving data based on the nth incident signal. Simultaneously estimate the covariance matrix of the received data of the nth incident signal include: The phase difference caused by the baseline length between the two sub-arrays in, is the phase difference between the mth array element and the m+Mth array element of the distributed array when receiving the nth incident signal at time t.

6. The method for estimating the direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 5, characterized in that: The covariance matrix of the received data in,[·] H represents the conjugate transpose.

7. The method for estimating the direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 1, characterized in that: The phase difference and the covariance matrix Calculate the set of angle estimates with periodic ambiguity and the noise subspace include: According to the baseline length D between sub-arrays and the wavelength λ of the nth incident signal n Calculate the set of all fuzzy phase values Then calculate the angle estimation value set with periodic ambiguity The covariance matrix of the received data for the nth incident signal Perform eigenvalue decomposition to obtain the noise subspace 8. The method for estimating the direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 7, characterized in that: The base line length D between the sub-arrays and the wavelength λ of the nth incident signal n Calculate the set of all fuzzy phase values Then calculate the angle estimation value set with periodic ambiguity include: Since the baseline length between sub-arrays D>>λ n , then the phase difference It has periodic ambiguity, according to the baseline length D between sub-arrays and the wavelength λ of the nth incident signal n , calculate all the fuzzy phases in Round up and round down respectively, and then calculate the angle estimation value set with periodic ambiguity 9. The method for estimating the direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 8, characterized in that: The covariance matrix of the received data for the nth incident signal Perform eigenvalue decomposition to obtain the noise subspace include: The covariance matrix of the received data for the nth incident signal Perform eigenvalue decomposition to obtain the eigenvalue matrix and the eigenvector matrix From the eigenvector matrix Extract the eigenvalue matrix The eigenvectors corresponding to the 2M-1 small eigenvalues ​​in the noise subspace are formed by these 2M-1 eigenvectors.

10. The method for estimating direction of arrival of a distributed array with arbitrary sub-array configuration according to claim 9, characterized in that: The set of angle estimates that will have periodic ambiguity Substitute into the multiple signal classification spatial spectrum defuzzification to obtain the unambiguous angle estimate of the nth signal, that is, the direction of arrival estimate include: The angle estimate set with periodic blur Towards the noise subspace Projection, deblurring to obtain unambiguous angle estimation, i.e. direction of arrival estimation in, Represents searching for the element "*" that minimizes the sequence "·".

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