阅读说明：本技术 一种基于多级扩展嵌套阵列的波达方向估计方法 (Direction-of-arrival estimation method based on multi-stage extended nested array ) 是由 周延 刘冠豪 李艳艳 汪霖 姜博 陈晓璇 孟娜 刘成 张万绪 于 2019-09-09 设计创作，主要内容包括：本发明属于信号处理技术领域,具体涉及一种基于多级扩展嵌套阵列的波达方向估计方法,包括：获取初始信号；根据所述初始信号得到移动后信号；根据所述移动后信号得到接收信号模型；根据所述接收信号模型得到信号的协方差矩阵。本发明将扩展嵌套阵列推广到多级扩展嵌套阵列,在阵元数相同的情况下多级扩展嵌套阵列的均匀自由度大于扩展嵌套阵列的均匀自由度,进而使得多级扩展嵌套阵列在波达方向估计中能够检测到更多的信号源,估计性能更准确。(The invention belongs to the technical field of signal processing, and particularly relates to a wave arrival direction estimation method based on a multilevel extended nested array, which comprises the following steps: acquiring an initial signal; obtaining a moved signal according to the initial signal; obtaining a received signal model according to the moved signal; and obtaining a covariance matrix of the signal according to the received signal model. The method and the device have the advantages that the expanded nested array is popularized to the multi-stage expanded nested array, the uniform degree of freedom of the multi-stage expanded nested array is greater than that of the expanded nested array under the condition that the array elements are the same, further, the multi-stage expanded nested array can detect more signal sources in the estimation of the direction of arrival, and the estimation performance is more accurate.)

1. A method for estimating a direction of arrival based on a multi-stage extended nested array is characterized by comprising the following steps:

acquiring an initial signal;

obtaining a moved signal according to the initial signal;

obtaining a received signal model according to the moved signal;

and obtaining a covariance matrix of the signal according to the received signal model.

2. The method for estimating the direction of arrival based on the multilevel extended nested array according to claim 1, wherein the obtaining of the initial signal comprises:

1a, establishing a multi-stage expansion nested array formed by two stages of nested arrays;

the position of N array elements in the nested array can be expressed as:

wherein N is₁Is the number of elements of a first-level nested array, N₂The number of elements of the second-level nested array is; d_NAIs the distance between the first array elements of the array, d_NAAlpha is an integer, alpha is more than or equal to 1 and less than or equal to 2K +1, K is the array expansion frequency of the multilevel expansion nested array, d is the half wavelength of the signal carrier, and d is lambda/2; n is₁And n₂Numbering different array elements in the two-stage nested array;

1b, obtaining Q unrelated initial signals according to the multilevel expansion nested array; the Q uncorrelated initial signals obtained by expanding the nested array at t time can be expressed as:

wherein s (t) ═ s₁(t)exp(-j2πvtsin(θ₁)/λ)，…，s_Q(t)exp(-j2πvtsin(θ_Q)/λ)]^T，s_q(t) is a signal source, Q is more than or equal to 1 and less than or equal to Q, and epsilon (t) is a complex Gaussian white noise vector; a is array fashion matrix, A ═ a₁(θ₁)，…，a₁(θ_Q)](ii) a a (θ q) is a signal guide vector a (θ q) ═ 1, exp (-j2 π d2sin (θ q)/λ), …, exp (-j2 π dNSin (θ q)/λ)]^TJ is a virtual unit, d_NIs the position of the Nth array element in the array, N ═ N₁+N₂；θ_qObtaining a direction of arrival angle for the qth signal; v is the multi-stage extended nested array moving speed, and the moving speed v is constant.

3. The method for estimating the direction of arrival based on the multilevel extended nested array according to claim 2, wherein obtaining a shifted signal according to the initial signal comprises:

assuming d ═ v τ, the initial post-shift signal received on the sparse array at time t + k τ when the array is shifted can be expressed as:

when the received signal in the received signal model is a narrow-band signal, the formula is simplified by s_q(t+kτ)＝s_q(t) exp (j2 π fk τ), we can get:

wherein, B_kArray prevalence matrix for signals after the kth shift of the array, B_k＝[b_k(θ₁)，…，b_k(θ_Q)]，b_k(θ_q)＝exp(-j2πkdsin(θ_q)/λ)a(θ_q) F is the carrier frequency of the initial signal; τ is the time interval over which the signal is received.

4. The method for estimating the direction of arrival based on the multilevel extended nested array according to claim 3, wherein obtaining a received signal model according to the shifted signal comprises:

3a, carrying out phase correction on the moved signal to obtain a corrected moved signal;

3b, representing the corrected and moved signals in a proper form to obtain a received signal model;

signals received at different times are represented in the form of appropriate quantities, denoted y (t), namely:

where C is the set of popular arrays of the array at each time,

5. the method according to claim 4, wherein the covariance matrix is expressed as:

R_y＝E[y(t)y^H(t)]＝CR_sC^H+σ²i, wherein the dimension of I is (K +1) N, sigma²Is the power of the noise.

Technical Field

The invention belongs to the technical field of signal processing, and particularly relates to a direction of arrival estimation method based on a multi-stage extended nested array.

Background

Direction of arrival (DOA) estimation has been considered an important issue for array signal processing in the fields of radar, sonar, and the like. Conventional DOA estimation methods such as MUSIC (Multiple Signal Classification, spatial spectrum estimation algorithm) and ESPRIT (two-dimensional rotation invariant subspace algorithm) can solve the Signal arrival angle estimation of at most N-1 incoherent sources by a uniform linear array including N arrays. For DOA estimation, a high degree of freedom is always satisfactory, since it can detect a large number of signal sources and achieve excellent estimation performance under such conditions. However, a high degree of freedom is often not achievable for various reasons, such as space limitations and hardware costs.

In recent years, methods for solving estimation of directions of arrival of signal sources more than the number of array elements by using sparse arrays have attracted extensive attention of relevant researchers and practitioners, and models of various sparse arrays such as Minimum Redundant Array (MRA), co-prime array (CA), Nested Array (NA), and the like have been proposed. The minimum redundant array is a linear sparse array designed for obtaining the maximum possible virtual uniform linear array aperture, however, the position of the array element in the minimum redundant array can only be implicitly expressed, so that the determination is difficult; the co-prime array is composed of two uniform linear arrays with a co-prime relationship, can analyze more sources than a single array, and is easy to design, however, the differential optimization array of the co-prime array is not continuous; for nested arrays, the degree of freedom improvement is low.

Disclosure of Invention

In order to solve the above problems in the prior art, the present invention provides a direction of arrival estimation method based on a multi-stage extended nested array. The technical problem to be solved by the invention is realized by the following technical scheme:

a method for estimating a direction of arrival based on a multi-stage extended nested array comprises the following steps:

acquiring an initial signal;

obtaining a moved signal according to the initial signal;

obtaining a received signal model according to the moved signal;

and obtaining a covariance matrix of the signal according to the received signal model.

In one embodiment of the present invention, acquiring an initial signal comprises:

1a, establishing a multi-stage expansion nested array formed by two stages of nested arrays;

the position of N array elements in the nested array can be expressed as:

wherein N is₁Is the number of elements of a first-level nested array, N₂The number of elements of the second-level nested array is; d_NAIs the distance between the first array elements of the array, d_NAAlpha is an integer, alpha is more than or equal to 1 and less than or equal to 2K +1, K is the array expansion frequency of the multilevel expansion nested array, d is the half wavelength of the signal carrier, and d is lambda/2; n is₁And n₂Numbering different array elements in the two-stage nested array;

1b, obtaining Q unrelated initial signals according to the multilevel expansion nested array; the Q uncorrelated initial signals obtained by expanding the nested array at t time can be expressed as:

wherein s (t) ═ s₁(t)exp(-j2πvtsin(θ₁)/λ)，…，s_Q(t)exp(-j2πvtsin(θ_Q)/λ)]^T，s_q(t) is a signal source, Q is more than or equal to 1 and less than or equal to Q, and epsilon (t) is complex Gaussian white noiseAn acoustic vector; a is array fashion matrix, A ═ a₁(θ₁)，…，a₁(θ_Q)](ii) a a (θ q) is a signal guide vector a (θ q) ═ 1, exp (-j2 π d2sin (θ q)/λ), …, exp (-j2 π dNSin (θ q)/λ)]^TJ is a virtual unit, d_NIs the position of the Nth array element in the array, N ═ N₁+N₂；θ_qObtaining a direction of arrival angle for the qth signal; v is the multi-stage extended nested array moving speed, and the moving speed v is constant.

In one embodiment of the present invention, obtaining a post-movement signal according to the initial signal includes:

assuming d ═ v τ, the initial post-shift signal received on the sparse array at time t + k τ when the array is shifted can be expressed as:

when the received signal in the received signal model is a narrow-band signal, simplifying the formula s_q(t+kτ)＝s_q(t) exp (j2 π fk τ), we can get:

wherein, B_kArray prevalence matrix for signals after the kth shift of the array, B_k＝[b_k(θ₁)，…，b_k(θ_Q)]，b_k(θ_q)＝exp(-j2πkdsin(θ_q)/λ)a(θ_q) F is the carrier frequency of the initial signal; τ is the time interval over which the signal is received.

In an embodiment of the present invention, obtaining a received signal model according to the post-movement signal includes:

3a, carrying out phase correction on the moved signal to obtain a corrected moved signal;

3b, representing the corrected and moved signals in a proper form to obtain a received signal model;

signals received at different times are represented in the form of appropriate quantities, denoted y (t), namely:

where C is the set of popular arrays of the array at each time,

in one embodiment of the invention, the covariance matrix is represented as:

R_y＝E[y(t)y^H(t)]＝CR_sC^H+σ²i, wherein the dimension of I is (K +1) N, sigma²Is the power of the noise.

The invention has the beneficial effects that:

the method and the device have the advantages that the expanded nested array is popularized to the multi-stage expanded nested array, the uniform degree of freedom of the multi-stage expanded nested array is greater than that of the expanded nested array under the condition that the array elements are the same, further, the multi-stage expanded nested array can detect more signal sources in the estimation of the direction of arrival, and the estimation performance is more accurate.

The present invention will be described in further detail with reference to the accompanying drawings and examples.

Drawings

Fig. 1 is a flowchart of a direction of arrival estimation method based on a multi-stage extended nested array according to an embodiment of the present invention;

fig. 2 is a schematic diagram of a multi-stage extended nested array model of a direction of arrival estimation method based on a multi-stage extended nested array according to an embodiment of the present invention;

fig. 3 is a schematic diagram of a non-negative part differential optimization array of a two-stage extended nested array based on a direction of arrival estimation method of the multi-stage extended nested array according to an embodiment of the present invention;

fig. 4 is a schematic diagram of a secondary extended nested array weight function under different values of a in a direction of arrival estimation method based on a multi-stage extended nested array according to an embodiment of the present invention;

fig. 5 is a root mean square error of DOA estimation under different signal-to-noise ratios of an extended nested array and a second-stage extended nested array according to a direction-of-arrival estimation method based on a multi-stage extended nested array provided in an embodiment of the present invention;

fig. 6 is a MUSIC spectrum of an extended nested array and a two-stage extended nested array in a direction of arrival estimation method based on a multi-stage extended nested array according to an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.

Referring to fig. 1, fig. 1 is a flowchart of a method for estimating a direction of arrival based on a multi-stage extended nested array according to an embodiment of the present invention, including:

acquiring an initial signal;

obtaining a moved signal according to the initial signal;

obtaining a received signal model according to the moved signal;

and obtaining a covariance matrix of the signal according to the received signal model.

The method and the device have the advantages that the expanded nested array is popularized to the multi-stage expanded nested array, the uniform degree of freedom of the multi-stage expanded nested array is greater than that of the expanded nested array under the condition that the array elements are the same, further, the multi-stage expanded nested array can detect more signal sources in the estimation of the direction of arrival, and the estimation performance is more accurate.

In an embodiment of the present invention, please refer to fig. 2, fig. 2 is a schematic diagram of a multi-stage extended nested array model of a direction of arrival estimation method based on a multi-stage extended nested array according to an embodiment of the present invention, and acquiring an initial signal includes:

1a, establishing a multi-stage expansion nested array formed by two stages of nested arrays;

the position of N array elements in the nested array can be expressed as:

wherein N is₁Is the number of elements of a first-level nested array, N₂The number of elements of the second-level nested array is; d_NAIs the distance between the first array elements of the array, d_NAAlpha is an integer, alpha is more than or equal to 1 and less than or equal to 2K +1, K is the array expansion frequency of the multilevel expansion nested array, d is the half wavelength of the signal carrier, and d is lambda/2; n is₁And n₂Numbering different array elements in the two-stage nested array;

1b, obtaining Q unrelated initial signals according to the multilevel expansion nested array; the Q uncorrelated initial signals obtained by expanding the nested array at t time can be expressed as:

wherein s (t) ═ s₁(t)exp(-j2πvtsin(θ₁)/λ)，…，s_Q(t)exp(-j2πvtsin(θ_Q)/λ)]^T，s_q(t) is a signal source, Q is more than or equal to 1 and less than or equal to Q, and epsilon (t) is a complex Gaussian white noise vector; a is array fashion matrix, A ═ a₁(θ₁)，…，a₁(θ_Q)](ii) a a (θ q) is a signal guide vector a (θ q) ═ 1, exp (-j2 π d2sin (θ q)/λ), …, exp (-j2 π dNSin (θ q)/λ)]^TJ is a virtual unit, d_NIs the position of the Nth array element in the array, N ═ N₁+N₂；θ_qObtaining a direction of arrival angle for the qth signal; v is the multi-stage extended nested array moving speed, and the moving speed v is constant.

In one embodiment of the present invention, obtaining a post-movement signal according to the initial signal includes:

assuming d ═ v τ, the initial post-shift signal received on the sparse array at time t + k τ when the array is shifted can be expressed as:

when the received signal in the received signal model is a narrow-band signal, simplifying the formula s_q(t+kτ)＝s_q(t) exp (j2 π fk τ), we can get:

wherein, B_kArray prevalence matrix for signals after the kth shift of the array, B_k＝[b_k(θ₁)，…，b_k(θ_Q)]，b_k(θ_q)＝exp(-j2πkdsin(θ_q)/λ)a(θ_q) F is the carrier frequency of the initial signal; τ is the time interval over which the signal is received.

In an embodiment of the present invention, obtaining a received signal model according to the post-movement signal includes:

3a, carrying out phase correction on the moved signal to obtain a corrected moved signal;

3b, representing the corrected and moved signals in a proper form to obtain a received signal model;

signals received at different times are represented in the form of appropriate quantities, denoted y (t), namely:

where C is the set of popular arrays of the array at each time,

in one embodiment of the invention, the covariance matrix is represented as:

R_y＝E[y(t)y^H(t)]＝CR_sC^H+σ²i, wherein the dimension of I is (K+1)N，σ²Is the power of the noise.

Further, the estimation value of the Sample Clutter Matrix (SCM) is obtained

Wherein L is the number of fast beats. Received signal model R_yIncluding the initial signal x (t) and the shifted signal

The self-correlation information and the cross-correlation information of (2), and the information contains the position information of the antenna elements at different time instants.

Further, when the array element of the nested array is moved by the distance kd, the antenna element position is changed to the following position:

wherein P is_I～P_KThe composed composite extended nested array P can be represented as:

P_Iand P_KArray element positions of the nested array and the shifted nested array are respectively; thus, P_IAnd P_KMust satisfy the following set of elements in the autocorrelation array:

wherein D_sIs symmetrical, only D is considered in this embodiment_sNon-negative part of (2) to

And (4) showing.

Furthermore, P_IAnd P_KMay be represented as:

wherein the step function

Further, different P_kThe cross-correlation array elements between are represented as:

wherein k is₁And k₂Are all taken from the set {1, 2, …, K } and K₁≠k₂。

In the formation of P_IAnd P_kAfter the cross-correlation array elements between, the differential free array of the multi-level extended nested array can be represented as:

P_Iand P_KIs not a negative element set in the autocorrelation array

P_IAnd P_KSet of elements in the cross-correlation array of

And different P_kSet of cross-correlation array elements between

Through simplification, the following can be obtained:

where β, β' and β "are numbers of different array elements in the virtual seismic source array, since d_NADifferential self of multi-stage extended nested arrayFrom an array

Reordering can be performed to obtain:

differential free array based on reordered multilevel extended nested arraysHas the following properties:

1.

middle largest element M_maxIs [ alpha (N)₁N₂+N₂-1)+K]d, and M_maxThe maximum number of signals which can be estimated by the differential optimization array;

2. when alpha is not less than 1 and not more than 2K +1

Is uninterrupted, and when alpha > 2K +1

An interruption exists;

differential free array of reordered multi-level extended nested array

It can be seen that 2K consecutive numbers are inserted between α β and α (β -1). To realize

The gap between α β and α (β -1) must be smaller than 2K, i.e., α β - α (β -1) -1 ═ α -1 ≦ 2K. On the other hand, alpha is a positive integer, so alpha is not less than 1.

3. When alpha is 2K +1

Minimal redundancy;

the range of alpha is limited to 1 to 2K + 1. However, when K is a large value, the range of a is still large. Meanwhile, selecting different values of alpha affects the performance of the differential optimization array in the DOA estimation. From Property 1, it was found that as alpha value increases, M_maxIt will also increase, which is advantageous for DOA estimation. Because the corresponding differential optimization arrays are continuous only when a is less than or equal to 2K + 1; when a is 2K +1, a (β -1) + K is not overlapped with a β -K, and then the corresponding subset { a (β -1) + K, a β -K, …, a β -1, a β, a β +1, …, a β + K, a (β +1) -K } is obtained to be continuous, and there is no redundant element in the corresponding subset, so that the differential optimization matrix at this time can obtain the most number of estimable signals, and further the minimum redundancy is realized.

Further, the differential free array D of the multi-stage extended nested array is combined according to the property 1 and the property 2_MThe symmetry is realized, and the uniform degree of freedom of the multi-stage expanded nested array is obtained when a is more than or equal to 1 and less than or equal to 2K + 1:

2M_max+1＝2a(N₁N₂+N₂-1)+2K+1，

assuming that a nested array is constructed by totally adopting N array elements, the maximum uniform freedom degree of the multilevel expanded nested array can be obtained:

wherein

Uniform degrees of freedom for nested arrays; according to the maximum uniform degree of freedom formula of the multi-stage extended nested array, the fact that the maximum uniform degree of freedom of the multi-stage extended nested array is in direct proportion to the value of alpha and is related to the value of K is found, and therefore when alpha is larger than or equal to 1 and smaller than or equal to 2K +1, the performance of DOA estimation of the multi-stage extended nested array is greatly improved. In addition, when K is 1, the multilevel extended nested array becomes an extended nested array. Referring to FIG. 3, FIG. 3 shows an embodiment of the present inventionAccording to the wave arrival direction estimation method based on the multi-stage extended nested array, the schematic diagram of the non-negative part differential optimization array of the two-stage extended nested array is provided, when the value range of alpha is 1 & lt alpha & gt & lt 5 & lt alpha & gt, the non-negative part of the differential optimization array generated by the two-stage extended nested array is provided, wherein N is the non-negative part of the differential optimization array generated by the two-stage extended nested array, and₁and N₂The values of (1) are all 4, and the figure shows that the uniform degree of freedom of the secondary expansion nested array is always higher than that of the expansion nested array.

In one embodiment of the invention, the number of array elements in each level of the two-level nested array is 4, so the source positions of the two-level nested array are constructed as follows:

fig. 4 is a schematic diagram of a secondary extended nested array weight function under different values a in a direction of arrival estimation method based on a multi-stage extended nested array according to an embodiment of the present invention, where weight functions when α ═ 1, α ═ 2, α ═ 3, α ═ 4, α ═ 5, and α ═ 6 sequentially correspond to weight functions w (m) in fig. 4(a), fig. 4(b), fig. 4(c), fig. 4(d), fig. 4(e), and fig. 4(f) in fig. 4, and when values of a are different, the weight functions w (m) are obtained, that is, the number of occurrences of elements in the optimized array, and w (m) represents the uniform degree of freedom and redundancy of the secondary extended nested array, and thus it can be seen that as the value of α increases, the uniform degree of freedom of the secondary extended nested array increases and the redundancy is also reduced. As shown in fig. 3(f), when a value of α is 6, α > 2K +1, and K ═ 2, the differential optimization array of the secondary extended nested array is no longer continuous; therefore, in the secondary extended nested array, as shown in fig. 4(e), when a value of α is 5, the maximum uniform degree of freedom and the minimum redundancy can be obtained; meanwhile, when alpha is 5, the redundancy of the differential optimization array of the secondary extension nested array is higher than that of the nested array with the same array element number.

Referring to fig. 5, fig. 5 is a diagram illustrating a root mean square error of DOA estimation under different signal-to-noise ratios of an extended nested array and a second-level extended nested array according to a direction-of-arrival estimation method based on a multi-level extended nested array provided in an embodiment of the present invention, where the root mean square error is defined as:

wherein N is_MCIs the total number of Monte Carlo experiments, Q is the total number of signals,

is the p theta in the n-th Monte Carlo experiment_qN is the number of monte carlo trials. Fig. 5(a) shows the root mean square error of the DOA estimation of the extended nested array in the signal-to-noise ratio variation range of-20 dB to 20dB, and fig. 5(b) shows the root mean square error of the DOA of the secondary extended nested array in the signal-to-noise ratio variation range of-20 dB to 20dB, it is obvious that the RMSE value of the secondary extended nested array is minimum when a is 5; further, when alpha is less than or equal to 1 and less than or equal to 3, the DOA estimation effect estimation difference between the expanded nested array and the second-level expanded nested array is very small; when alpha is more than or equal to 4 and less than or equal to 5, the estimation performance of the secondary extended nested array is better, and therefore, the DOA estimation performance of the secondary extended nested array is improved along with the increase of the a value.

Fig. 6 is a MUSIC spectrum of an extended nested array and a two-stage extended nested array in a method for estimating an arrival direction based on a multi-stage extended nested array according to an embodiment of the present invention, where fig. 6(a) is the MUSIC spectrum of the extended nested array when a is 3, fig. 6(b) and fig. 6(c) are the MUSIC spectra of the two-stage extended nested array when a is 4 and a is 5, respectively, where a signal source is an incoherent signal source in which arrival angles of 50 signals are uniformly distributed between-50 ° and 50 °, a signal-to-noise ratio of the system is 10dB, and each signal has 1000 snapshots; as can be contrasted from fig. 6, when α ═ 4 or α ═ 5, the secondary extended nested array can detect the signal arrival angles of all 50 signal sources.

The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.