Distributed array DOA (direction of arrival) estimation method for sub-array with arbitrary configuration

Abstract

The invention discloses a method for estimating the direction of arrival of a distributed array with any sub-array configuration, and the method comprises the steps: constructing the distributed array with any sub-array configuration, carrying out the digital channelization processing of incident signal data received by the distributed array, separating the incident signal data, and obtaining the direction of arrival of the distributed array with any sub-array configuration. Estimating the phase difference generated by the baseline length between the subarrays of each received signal and the covariance matrix of the received signal data, calculating all fuzzy phase differences of each signal according to the baseline length between the subarrays, and obtaining a corresponding direction of arrival estimation value; and respectively substituting all fuzzy direction-of-arrival estimation values of each signal into the multiple signal classification spatial spectrum for ambiguity resolution to obtain high-precision and unambiguous direction-of-arrival estimation values of all incident signals. According to the method, the array elements in the subarrays can be randomly arranged, the problem that the arrangement of baselines is limited by ambiguity resolution methods of long and short baselines, staggered baselines and the like is solved, the array arrangement mode is flexible, engineering implementation is easy, and the method can be suitable for micro-nano satellites, unmanned aerial vehicles and other small platforms and has wide 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 estimation is an important research field in array signal processing. It has been widely used and studied in the fields of radar, wireless communication, sonar, electronic reconnaissance and microwave warning. The physical aperture of the array is an important parameter closely related to the performance of the array direction of arrival estimation. The larger the physical aperture of the array, the higher the angular resolution and direction of arrival estimation accuracy of the array. Distributed arrays composed of multiple distributed sub-arrays can improve the array physical aperture and the array direction of arrival estimation performance without increasing the number of array elements. In particular, the combination of phase interferometer or spatial spectrum estimation with distributed arrays can obtain high-precision and high-angular resolution direction of arrival estimation results, which has attracted widespread attention. However, since the baseline length between distributed array sub-arrays is much longer than half a wavelength, the direction finding results need to be deambiguated, and deambiguation methods such as long and short baselines and staggered baselines have specific requirements for the array baseline arrangement, which will affect the actual engineering application on small platforms such as micro-nano satellites and drones. Summary of the invention

[0003] The technical problem solved by the present invention is to overcome the deficiencies of the prior art, provide a distributed array direction of arrival estimation method with arbitrary subarray configuration, and solve the limitation problem 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 configuration;

[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) According to the nth incident signal receiving data, 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 estimate with periodic blur is set Substitute into the multiple signal classification spatial spectrum defuzzification to obtain the unambiguous angle estimate of the nth signal

[0010] 6) Perform steps 3) to 5) on the received data of N incident signals at the same time 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 of which has M array elements, and 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 subarray 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 subarrays; assuming that N incoherent far-field narrowband signals with different frequencies 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] In the formula, 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 receiving data according to the nth incident signal estimates 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 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 the set of angle estimates with periodic ambiguity is calculated

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

[0027] The method is based on the inter-subarray baseline length D and the wavelength λ of the nth incident signal. n Calculate the set of all fuzzy phase values Then the set of angle estimates with periodic ambiguity is calculated 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 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 is Perform eigenvalue decomposition to obtain the eigenvalue matrix With 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 deambiguation 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 To 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) The present invention utilizes the characteristics of low system complexity and large aperture of distributed arrays, and combines phase interferometer with spatial spectrum estimation method. Compared with the traditional direction of arrival estimation method, 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 fuzzy angle value of each incident signal obtained by using the large baseline between sub-arrays into the multiple signal classification spatial spectrum defuzzification to obtain a high-precision and unambiguous wave direction of arrival estimation value of each incident signal. The array elements in the sub-array can be arranged arbitrarily in this method, which solves the problem of the limitation of baseline arrangement on defuzzification methods such as long and short baselines and staggered baselines; BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart for realizing the present invention;

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

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

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

[0043] Figure 6 This is a graph showing how the success rate of deambiguation for direction of arrival estimation varies 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 are separated, the phase difference of each received signal caused by the baseline length between sub-arrays and the covariance matrix of the received signal data are estimated, all the fuzzy phase differences of each signal are calculated according to the baseline length between sub-arrays, and the corresponding arrival direction estimation value is obtained, all the fuzzy arrival direction estimation values ​​of each signal are substituted into the multiple signal classification spatial spectrum defuzzification, and the high-precision and unambiguous arrival direction estimation values ​​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 with arbitrary subarray configuration:

[0048] 1a) Press Figure 2As shown in the figure, a distributed array is composed of two sub-arrays with M array elements, non-uniform array elements and the same configuration. The array element position of the distributed array is d = [d1, d2, ..., d M ,d M+1 ,d M+2 ,...,d 2M ] T , select the first element of subarray 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 subarrays. 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 azimuth angle of the nth incident signal, 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 flow matrix A(θ) of the array:

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

[0051] In the formula, 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 receiving the nth incident signal at time t; the covariance matrix of the received data in,[·] H represents the conjugate transpose.

[0058] Step 4: Based on 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 the fuzzy phases Round up and down respectively, and then calculate a set of angle estimates with high accuracy 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 With 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 combined To the noise subspace Projection and deambiguation to obtain a high-precision, 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 arrival directions to determine whether the arrival direction estimation accuracy varies with the signal-to-noise ratio.

[0068] In this simulation, the present invention adopts two one-dimensional linear array sub-arrays with the same array configuration and non-uniformly distributed array elements to form a distributed array, wherein: the number of sub-array elements M=6, the array element positions {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, wave direction 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 As shown in the figure, the horizontal axis represents the change of the signal-to-noise ratio from -10dB to 20dB, and the vertical axis represents the root mean square error (RMSE) of the direction of arrival estimation.

[0070]

[0071] in They represent the estimated value of the direction of arrival of the nth source in the kth Monte Carlo experiment respectively, and K represents the number of Monte Carlo experiments.

[0072] Simulation experiment 2: A Monte Carlo simulation experiment is performed on the variation of the DOA 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, wherein: 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, wave direction of arrival θ = 31.4°, number of Monte Carlo experiments 200 times, number of snapshots L = 50. The simulation results are as follows Figure 5 , Figure 6 As shown in the figure, the horizontal axis represents the change of signal-to-noise ratio from -10dB to 20dB, and the vertical axis represents the root mean square error of the direction of arrival 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 DOA estimation value. The simulation experiment proves that the present invention can use a distributed array to achieve high-precision DOA 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 greater than or equal to -4dB, any sub-array element distribution can successfully deambiguate to obtain a high-precision, unambiguous direction of arrival estimate. Simulation experiments prove that the deambiguation performance of the present invention is not limited by the element distribution within the sub-array, i.e., the baseline arrangement.

[0076] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention by 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 solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A distributed array direction of arrival estimation method with arbitrary subarray configuration, characterized in that: include: 1) Construct a distributed array with arbitrary sub-array configuration; 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) According to the nth incident signal receiving data, 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 estimate with periodic blur is set Substitute into the multiple signal classification spatial spectrum defuzzification to obtain the unambiguous angle estimate of the nth signal 6) Perform steps 3) to 5) on the received data of N incident signals at the same time 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 subarray 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 of which has M array elements, and 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 subarray 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 subarrays; assuming that N incoherent far-field narrowband signals with different frequencies 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 subarray 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 )]; In the formula, 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 subarray 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 subarray configuration according to claim 4, characterized in that: The receiving data according to the nth incident signal estimates 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 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 subarray 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 subarray 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 the set of angle estimates with periodic ambiguity is calculated The covariance matrix of the received data for the nth incident signal is Perform eigenvalue decomposition to obtain the noise subspace 8. The method for estimating the direction of arrival of a distributed array with arbitrary subarray configuration according to claim 7, characterized in that: The method is based on the inter-subarray baseline length D and the wavelength λ of the nth incident signal. n Calculate the set of all fuzzy phase values Then the set of angle estimates with periodic ambiguity is calculated 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 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 subarray 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 is Perform eigenvalue decomposition to obtain the eigenvalue matrix With 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 the 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 deambiguation 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 To 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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