Coherent and incoherent signal mixed DOA estimation method based on vector space projection

Abstract

A coherent and incoherent signal mixed DOA estimation method based on vector space projection comprises the following steps: step S1, constructing a first pseudo-array manifold model Ac (theta) of a coherent signal and an incoherent signal of a target through a signal vector of an antenna signal; s2, solving a unitary matrix T for constructing a second pseudo-array manifold model A'c (theta) according to the signal subspace value Us and the total signal value X of all antenna signals; s3, according to the unitary matrix T, establishing a second pseudo array flow pattern model A'c (theta), # imgabs0 # A'c (theta) = [ac1,..., acp,..., acP]; acp represents a steering vector for linearly representing coupling of the pth group of the second pseudo-array manifold model through a correlation coefficient; s4, according to a beam space construction spectrum function, separating the coherent signal from the incoherent signal to realize incoherent signal DOA estimation; s5, a sparse reconstruction method is adopted, and the projection value omega pgt is obtained; and performing recovery of correlation coefficients according to the acp corresponding to the correlation coefficient 0, thereby realizing DOA estimation of the coherent signal. The method has the advantage that the DOA estimation is realized by distinguishing the incoherent signal sources under the condition that the coherent signals and the incoherent signals are mixed.

Description

Technical Field

[0001] The invention belongs to the field of array signal processing, and in particular relates to a mixed DOA estimation method of coherent and incoherent signals based on vector space projection. Background Art

[0002] Array signal processing is an important branch of modern signal processing. Array signal processing uses a group of antenna arrays arranged in a specific way in space to sample spatial propagation signals in both the time domain and the spatial domain to obtain corresponding sampling data, and then processes the sampling data of the antenna array to extract and restore useful information of the spatial signal.

[0003] Compared with a single sensor, array signal processing has the advantages of good anti-interference ability, high signal gain, and high spatial resolution. DOA (Direction of arrival) estimation is an important research topic in the field of array signal processing and is widely used in radar, sonar, navigation and other fields.

[0004] Most of the existing DOA estimation algorithms are limited to the study of incoherent and coherent signals separately. As the signal environment becomes increasingly complex, in the actual direction finding environment in the future, the incoming signal model in the actual estimation process is often not a simple narrow-band far-field signal. In order to better fit the actual situation, research is conducted on the parameter estimation of the mixed model of coherent and incoherent signals and the mixed model of near-field and far-field signals.

[0005] The MUSIC algorithm (Multiple Signal Classification) is an algorithm based on subspace decomposition. Once proposed in the 1970s, it has established its enduring status and achieved super-resolution estimation. The MUSIC algorithm performs angle estimation based on the orthogonality of the signal subspace and the noise subspace, and obtains the angle to be estimated by searching the spectral peak position.

[0006] The Capon beamforming algorithm (Capon is the name of a scientist, and the algorithm he proposed is named after Capon) adaptively selects weighting vectors to minimize the output power of the array under the condition of no distortion of the useful signal. When the array steering vector of the useful signal is accurately obtained, the Capon beamforming algorithm has good resolution and beam pointing performance. In the spatial spectrum estimation technology, when the incoming wave information contains coherent signals, the signal subspace and the noise subspace of the signal data covariance matrix have overlapping parts instead of being orthogonal, and do not have the characteristics of the Toeplitz matrix (i.e., T-shaped matrix), which will cause pseudo peaks in the spatial spectrum and DOA estimation failure. Existing coherent signal estimation algorithms such as spatial smoothing technology can solve the problem of coherent signal DOA estimation, but the array aperture will be sacrificed to decorrelate the signal during the algorithm estimation process; although the Toeplitz matrix reconstruction method has no aperture loss, the signal prior is incomplete during the signal averaging process, and the estimation accuracy is not high.

[0007] The direction finding problem under the coexistence of incoherent and coherent signals is one of the current important research directions in the field of array signal processing. Traditional direction finding algorithms face challenges when facing high signal density and complex coherent signals, which limits the improvement of antenna array utilization and direction finding accuracy. Summary of the invention

[0008] The purpose of the present invention is to provide a method for estimating the mixed DOA of coherent and incoherent signals based on vector space projection, which has the advantage of being able to distinguish incoherent sources and realize DOA estimation when coherent signals and incoherent signals are mixed.

[0009] To achieve the above object, the present invention provides a method for estimating mixed DOA of coherent and incoherent signals based on vector space projection, the method comprising: step S1, constructing a first pseudo array flow model A of the coherent signal and the incoherent signal of the target through the signal vector of the antenna signal c (θ); Step S2, according to the signal subspace value U s The total signal value X of all antenna signals is used to construct the second pseudo array flow model A' c (θ) unitary matrix T; Step S3, establish a second pseudo array flow model A' according to the unitary matrix T c (θ), A' c (θ)=[a c1 ,...,a cp ,...,a cP ]; a cp The p-th group of the second pseudo array flow pattern model is linearly represented by the correlation coefficient to express the coupled steering vector; Step S4, constructing the spectrum function for a according to the beam space cpProjection is performed to separate the coherent signal and the incoherent signal to achieve DOA estimation of the incoherent signal; step S5, using the sparse reconstruction method, the projection value ω p >0 corresponding to a cp , recover the correlation coefficient and realize the coherent signal DOA estimation.

[0010] Preferably, the antenna array includes M array elements, m=1, 2...M; the antenna array receives K antenna signals of the target, k=1, 2...K; the K antenna signals are divided into P groups, each group is represented by L p , p=1, 2…P.

[0011] Preferably, the step S1 comprises: step S11, the antenna array receives a total of K antenna signals from the target, and divides the K antenna signals into P groups L p , the i-th antenna signal of the p-th group is represented by s p,i ; Step S12, pre-processing all antenna signals; Step S13, pre-processing each group L one by one p Select an initial signal s to which the group belongs p,origin Step S14, for groups L1 to L p The antenna signal of the group to which it belongs is based on the initial signal s p,origin The expression of s p,i =α p,i s p,origin ,i=1,…,α p,i is the antenna signal s p,i Compared to the initial signal s p,origin The correlation coefficient of all antenna signals in the pth group is obtained one by one using the initial signal s p,origin The set S represented by p ={s p,1 =α p, 1s p,origin , ......}; Step S15, construct the total signal value X equation of all antenna signals under the signal vector, and obtain the reference signal s of different groups P (K), and then obtain the first pseudo array flow model A c (θ).

[0012] Preferably, the step S12 comprises: performing down-conversion on a total of K antenna signals one by one to obtain a down-conversion representation of the corresponding kth signal Among them, ρ k is the complex amplitude of the kth antenna signal, represents the composite function of the kth signal, and (τ) represents the down-conversion function.

[0013] Preferably, the step S15 comprises: step S151, constructing the total signal value X=A(θ)s(K) of all antenna signals under the signal vector, and the total signal value of all antenna signals under the signal quantity Solving the equation, we get s(K). Wherein, A(θ) represents the actual array flow model of all antenna signals, and A(θ) is obtained through actual measurement, s(K) represents the signal vector set of all antenna signals; s p (k) represents the initial signal vector of the kth signal in the total antenna signal, and p represents the group; α p is the correlation coefficient vector of the p-th group; a(θ p,i )α p,i s p,origin is the signal quantity of a single signal; Step S152, obtain the reference signal s of all antenna signals according to s(K) P re(K),s(K)=Βs P re(K); where, B=blkdiag(α1,α2,...α p ......,α P ), Β represents a block diagonal matrix, s P re(K) is the reference signal of all antenna signals, s P re(K)=[s 1(re) ,....s p(re) .....,s P(re) ] T ,s p(re) represents the reference signal of the pth group; step S153, according to s P re(K) obtains the first pseudo array flow model A c (θ):X=A c (θ)s P re(K); Solve to obtain the first pseudo array flow model A c (θ).

[0014] Preferably, the step S2 includes: step S21, synchronously sampling all antenna signals to construct a sampling covariance matrix R; synchronously sampling all antenna signals for a total of L times, that is, the number of snapshots is L, l=1, 2...L, the total signal value of all antenna signals is X, and the sampling covariance matrix is ​​expressed as Step S22, obtaining the signal subspace U s ; Step S23, perform eigenvalue decomposition on the sampling covariance matrix R, and according to the signal subspace U s Find the unitary matrix T.

[0015] Preferably, the step S23 comprises: step S231, performing eigenvalue decomposition on the sampling covariance matrix R Among them, λ m is the eigenvalue of the mth array element, u m is the characteristic vector of the mth array element; S The diagonal matrix representing the signal characteristics of the signal subspace, U N represents the noise subspace, Λ N The diagonal matrix representing the signal characteristics of the noise subspace; Step S232, the signal subspace U s Divide into two different (M-1)×P matrices, the two matrices are the first M-1 row matrix and the last M-1 row matrix; Step S233, respectively obtain the signal value U of the first M-1 row matrix B And the signal value U of the M-1 row matrix E ; U B =U s [1:(M-1),:],U E =U s [2:M,:], where,,: represents the total value function; Step S234, according to the signal value U of the first M-1 rows of the matrix B And the signal value U of the M-1 row matrix E Obtain the rotation transformation matrix Φ of the first M-1 rows and the last M-1 rows; U B =(A B (θ)Β)T,U E =(A E (θ)Β)T,A B (θ)Φ=A E (θ) where A B (θ) is all the elements of the first M-1 rows of the matrix, A E (θ) are all the elements of the matrix of the next M-1 rows;

[0016] Step S235, establish an equation and obtain the unitary matrix T according to Φ;

[0017]

[0018] Wherein, Λ is the diagonal matrix of signal characteristics of all antenna signals.

[0019] Preferably, the step S3 comprises: a. cp It is expressed as:

[0020]

[0021] Among them, a'(θ p,i ) represents the steering vector of the i-th antenna signal in the p-th group coupled linearly through the correlation coefficient.

[0022] Preferably, the step S4 comprises: step S41, constructing a spectral function by a beamforming algorithm according to the orthogonality of the signal subspace and the noise subspace, cp in (I M -a cp (a H cp a cp ) -1 a H cp ) is projected to separate the coherent signal from the incoherent signal, where I M represents the identity matrix; the projection value ω p =min|U s H (:,p)(I M -a cp (a H cp a cp ) -1 a H cp ) s H (:, p)|; (:, p) means using the total value function for the internal elements of the pth group; Step S42, if a cp The corresponding signal is an incoherent signal. Because of the presence of noise, the signal subspace vector U s (:,p) in (I M -a cp (a H cp a cp ) -1 a H cp ) will be zero, then ω p →0, at this time a cp All are incoherent signals; if a cp is the corresponding coherent signal, the signal subspace vector U s (:,p) in (I M -a cp (a H cp a cp ) -1 a H cp ) will not be zero, so ω p >0; will U s (:,p) is replaced by a p (θ), where a p (θ) represents the guiding vector constant of the pth group, constructing the new projection value ω p function ωp →0 guiding vector a ci Substitute the above function to achieve the capture of incoherent signals; step S43, perform DOA estimation on all incoherent signals.

[0023] Preferably, the step S5 comprises: step S51, one by one p >0 corresponding to a cp Construct the corresponding sparse model y p ;y p =A p (θ)α p +n',A p (θ) represents the array flow model composed of all the steering vectors of the pth group, α p represents the correlation coefficient vector of the pth group, and n' is the error factor; Step S52, group a is converted one by one cp The corresponding α p Defined as unknown sparse signals to be recovered, group a is cp The space is divided into N equal parts, n = 1, 2 ... N; wherein each group is divided into N equal parts; step S53, the steering vector and correlation coefficient sparse model of the p-th group are obtained one by one, and the coherent sub-coefficient of the p-th group is obtained one by one Step S531, construct the model equation y of the pth group one by one p ; Among them, a p (θ n ) is the steering vector of the nth equally divided space of the pth group, represents the coherent sub-coefficient of the p-th group, represents the error factor under the model corresponding to the p-th group; Step S532, solve the equations corresponding to the p-th group one by one to obtain the coherent sub-coefficients of the p-th group Step S54, using orthogonal matching pursuit algorithm Reconstruction is performed to achieve DOA estimation of coherent signals.

[0024] In summary, compared with the prior art, the present invention provides a method for estimating mixed DOA of coherent and incoherent signals based on vector space projection, which has the following beneficial effects:

[0025] First, the present invention uses a subspace projection method to achieve DOA estimation, focusing on optimizing the utilization efficiency of the array and being able to distinguish between incoherent signals and coherent signal groups.

[0026] Second, the present invention utilizes the sparsity between the array response and the coherence coefficient of the coherent signal, does not lose the array aperture in the presence of the coherent signal, effectively improves the array utilization, improves the estimation accuracy, and realizes the DOA estimation of the coherent source and the incoherent signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The scatter plot is for 50 Monte Carlo tests at 5dB signal-to-noise ratio.

[0028] Figure 2 The scatter plot is for 50 Monte Carlo tests at 10dB signal-to-noise ratio.

[0029] Figure 3 The scatter plot is for 50 Monte Carlo tests at 15dB signal-to-noise ratio.

[0030] Figure 4 This is the spectrum peak diagram of the mixed source signal separation at a 5dB signal-to-noise ratio.

[0031] Figure 5 This is the spectrum peak diagram of the mixed source signal separation under a 10dB signal-to-noise ratio.

[0032] Figure 6 This is the spectrum peak diagram of the mixed source signal separation at a signal-to-noise ratio of 15dB.

[0033] Figure 7 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0034] The following will be combined with the attached embodiment of the present invention Figure 1 ~Attached Figure 7 , the technical solutions, structural features, objectives achieved and effects in the embodiments of the present invention are described in detail.

[0035] It should be noted that the drawings are in a very simplified form and use non-precise proportions. They are only used to conveniently and clearly assist in explaining the embodiments of the present invention, and are not used to limit the conditions for the implementation of the present invention. Therefore, they have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size, without affecting the effects and purposes that can be achieved by the present invention, should still fall within the scope of the technical content disclosed by the present invention.

[0036] It should be noted that, in the present invention, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only the elements explicitly listed, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0037] The present invention provides a method for estimating the mixed DOA (Direction of arrival) of coherent and incoherent signals based on vector space projection, which realizes the DOA estimation of coherent signals and incoherent signals by an antenna array. Wherein, DOA estimation refers to obtaining the distance information and azimuth information of the target according to the antenna signal received from the target by the antenna array; wherein the antenna signal includes a plurality of coherent signals and a plurality of incoherent signals.

[0038] The coherent signal refers to the antenna signal whose two antenna signals both meet the coherence conditions; the coherence conditions are as follows: in the encounter area, the two antenna signals (1) have the same vibration direction; (2) have the same vibration frequency; and (3) have the same phase or the phase difference remains constant; the incoherent signal refers to the antenna signal other than the coherent signal, which can be understood as an interference signal.

[0039] The purpose of the present invention is to achieve DOA estimation of coherent signals and incoherent signals, to solve the challenges of antenna arrays when facing high signal density and complex signals, and to limit the array utilization and the difficulty in improving direction finding accuracy.

[0040] like Figure 7 As shown, the method includes:

[0041] Step S1, constructing a first pseudo array flow model A of the target's coherent signal and incoherent signal through the signal vector of the antenna signal c (θ);

[0042] Specifically, the antenna array includes M array elements, m=1, 2...M, the array element refers to the receiver or sensor that constitutes the antenna array, the array element can be an antenna, a microphone, an acoustic sensor, etc., for receiving signals from the target, and the array element is the starting unit for DOA estimation; the antenna array receives K antenna signals of the target, k=1, 2...K; when the antenna signal is analyzed, the K antenna signals can be divided into P groups, each group is represented by L p, p = 1, 2, ... P, where each group includes i signals, where i only represents the counting unit, because each group L p The number of signals is different, i will change, where s p,i represents the ith antenna signal in the pth group. However, no matter how the groups are classified, the antenna signal always satisfies After the antenna array receives the target signal (including coherent signals and incoherent signals), it is not difficult to understand that the coherent signals and incoherent signals among the K signals are mixed together.

[0043] Step S2: according to the signal subspace value U s The total signal value X of all antenna signals is used to construct the second pseudo array flow model A' c The unitary matrix T of (θ);

[0044] Among them, the first pseudo array flow model A c (θ) is constructed by means of signal vector, the second pseudo array flow model A' c (θ) is constructed by sampling values. The calculation and processing of the two pseudo-array flow models will be described in detail later.

[0045] Step S3: Establish a second pseudo array flow model A' according to the unitary matrix T c (θ), A' c (θ)=[a c1 ,...,a cp ,...,a cP ],in, represents the pseudo-inverse matrix of the matrix, which will not be described in detail later; a cp The p-th group of the second pseudo-array flow model is represented by a steering vector coupled linearly through a correlation coefficient.

[0046] Step S4, constructing a spectrum function according to the beam space cp Projection is performed to separate the coherent signal from the incoherent signal, and the DOA estimation of the incoherent signal is realized.

[0047] Step S5, using sparse reconstruction method, the projection value ω p >0 corresponding to a cp , recover the correlation coefficient and realize the coherent signal DOA estimation.

[0048] No matter how the antenna signals are transformed, they are all corresponding to each other. For example, antenna signals belonging to the same group will not stop belonging to the same group after transformation.

[0049] The step S1 comprises:

[0050] Step S11: The antenna array receives K antenna signals from the target, k = 1, 2, ..., K, and divides the K antenna signals into P groups L p , p = 1, 2, ... P, the i-th antenna signal of the p-th group is represented by s p,i ;

[0051] This step is to first classify the total K antenna signals and classify similar signals into the same group. This is the existing technology and will not be described in detail. If the group contains only one signal, the signal can be directly identified as an incoherent signal. It can be marked in advance to facilitate subsequent judgment and save computing resources, but it does not affect the subsequent judgment process.

[0052] Step S12, preprocessing the antenna signal;

[0053] The step S12 may specifically be performed by down-converting the K antenna signals one by one. Among them, ρ k is the complex amplitude of the kth antenna signal, represents the composite function of the kth signal, and (τ) represents the down-conversion function; the purpose of this step is to reduce the sampling frequency and obtain valuable data at the same time, which is equivalent to performing a form transformation.

[0054] Step S13, for each group L one by one p Select an initial signal s to which the group belongs p,origin ;

[0055] Because in the antenna signal, the antenna signals in the same group can be linearly represented by any other antenna signals belonging to the same group, so group L is selected p An antenna signal in the group is used as the initial signal, and the other antenna signals in the same group are subsequently sent to the same group with the initial signal s p,origin As the benchmark, linear representation is performed to achieve consistency of operation. For the initial signal s p,origin There is no restriction on the selection of , as long as it belongs to the group to which the antenna signal belongs.

[0056] Step S14: for groups L1 to L p The antenna signal of the group to which it belongs is based on the initial signal s p,origin The expression of s p,i =α p,i s p,origin ,i=1,…,where α p,i is the antenna signal s p,i Compared to the initial signal s p,origin The correlation coefficient of all antenna signals in the pth group is obtained one by one using the initial signal s p,originThe set S represented by p ={s p,1 =α p,1 s p,origin ,......};

[0057] Among them, if s p,i Equal to s p,origin , at this time α p,i =1, in order to maintain the consistency of representation, although the two are the same, the initial signal s is still needed p,origin For p,i Since the number of antenna signals in each group is unknown, the maximum value of i corresponding to each group is uncertain and is only used as an algebraic representation to form S p ={s p,1 =α p, 1s p,origin ,......} this way of expression.

[0058] Step S15, construct the total signal value X equation of all antenna signals under the signal vector, and obtain the reference signal s of different groups P (K), and then obtain the first pseudo array flow model A c (θ);

[0059] Specifically, the step S15 includes:

[0060] Step S151, construct the total signal value X=A(θ)s(K) of all antenna signals under the signal vector, and construct the total signal value of all antenna signals under the signal quantity Solving the equation, we get s(K).

[0061] Wherein, A(θ) represents the actual array flow model of all antenna signals, and A(θ) is obtained through actual measurement, s(K) represents the signal vector set of all antenna signals; s p (k) represents the initial signal vector of the kth signal in the total antenna signal, and p represents the group; α p is the correlation coefficient vector of the p-th group; a(θ p,i )α p,i s p,origin is the signal quantity of a single signal (set representation), where p and i are used to indicate the location of the signal, α p,i s p,origin As mentioned above, it plays a role in unified expression.

[0062] Step S152: Obtain reference signals s of all antenna signals according to s(K) P re(K),s(K)=Βs Pre(K);

[0063] Among them, B=blkdiag(α1,α2,...α p ......,α P ), Β represents a block diagonal matrix, s P re(K) is the reference signal of different groups, which can be obtained by solving, s P re(K)=[s 1(re) ,....s p(re) .....,s P(re) ] T ,s p(re) represents the reference signal of the p-th group.

[0064] Step S153, according to s P re(K) obtains the first pseudo array flow model A c (θ):

[0065] X=A c (θ)s P re(K);

[0066] At this time, the first pseudo array flow model A is obtained by solving c (θ).

[0067] The step S2 comprises:

[0068] Step S21, synchronously sampling all antenna signals to construct a sampling covariance matrix R;

[0069] Specifically, all antenna signals are synchronously sampled L times, that is, the number of snapshots (sampling points) is L, l=1, 2...L, and the total signal value of all antenna signals is obtained as X, where X is the same as X in step S1, but a different method is used to obtain the total signal value of all antenna signals; the sampling covariance matrix is ​​expressed as H represents transposed conjugate, and will not be described in detail below.

[0070] Step S22, obtaining the signal subspace U s ;

[0071] The signal subspace is composed of the sampling covariance matrix and the eigenvector corresponding to the antenna signal. It is obtained by real-time measurement. The signal subspace U s The expression form is consistent with the arrangement of antenna signals, for example, there are K signals in total, P groups, etc. This step belongs to the prior art and will not be described in detail here.

[0072] Step S23, perform eigenvalue decomposition on the sampling covariance matrix R, and calculate the signal subspace U s Obtain the unitary matrix T;

[0073] The step S23 comprises:

[0074] Step S231, perform eigenvalue decomposition on the sampling covariance matrix R

[0075] Among them, because there are a total of M array elements, each array element is used as a standard, and the eigenvalue R is decomposed one by one through the eigenvector, λ m is the eigenvalue of the mth array element, u m is the characteristic vector of the mth array element; S The diagonal matrix representing the signal characteristics of the signal subspace, U N represents the noise subspace, Λ N A diagonal matrix representing the signal characteristics of the noise subspace.

[0076] Step S232: transform the signal subspace U s Divide into two different (M-1)×P matrices, the two matrices are the first M-1 row matrix and the second M-1 row matrix;

[0077] Since there are M array elements and P groups, the signal subspace U s is expressed as an M×P matrix; this step can be understood as equivalent to a matrix without the first row and a matrix without the last row, so it is M-1 rows.

[0078] Step S233, respectively obtain the signal values ​​U of the first M-1 rows of the matrix B And the signal value U of the M-1 row matrix E ; U B =U s [1:(M-1),:],U E =U s [2:M,:], where,: represents the total value function;

[0079] For example, [1:(M-1),:] represents the signal values ​​of all elements from the 1st row to the M-1th row.

[0080] Step S234: based on the signal value U of the first M-1 rows of the matrix B And the signal value U of the M-1 row matrix E Obtain the rotation transformation matrix Φ of the last M-1 rows of the first M-1 rows;

[0081] U B =(A B (θ)Β)T,U E =(A E (θ)Β)T,A B (θ)Φ=A E (θ) where AB (θ) is the first M-1

[0082] All elements of the row matrix, A E (θ) are all elements of the next M-1 row matrices.

[0083] Step S235, establish an equation and obtain the unitary matrix T according to Φ;

[0084]

[0085] Wherein, Λ is the diagonal matrix of signal characteristics of all antenna signals.

[0086] The step S3 comprises: a. cp It is expressed as:

[0087]

[0088] Among them, a'(θ p,i ) represents the steering vector of the i-th antenna signal in the p-th group linearly represented by the correlation coefficient, where p and i represent the position of the antenna signal.

[0089] Then establish the second pseudo array flow model A' c (θ), A' c (θ)=[a c1 ,...,a cp ,...,a cP ]; a cp The p-th group of the second pseudo-array flow model is represented by a steering vector coupled linearly through a correlation coefficient.

[0090] Specifically, step S4 includes:

[0091] Step S41, according to the orthogonality of the signal subspace and the noise subspace, a spectral function is constructed by a beamforming algorithm, and a cp in (I M -a cp (a H cp a cp ) -1 a H cp ) is projected to separate the coherent signal from the incoherent signal, where I M Represents the identity matrix, which is an M×M matrix whose elements are all 1;

[0092] That is, the projection value ω p =min|U s H (:,p)(I M -acp (a H cp a cp ) -1 a H cp ) s H (:,p)|; (:,p) means using the total value function for the internal elements of the pth group. This step is used to obtain the signal subspace vector corresponding to the signal subspace;

[0093] Step S42, if a cp The corresponding signal is an incoherent signal. Because of the presence of noise, the signal subspace vector U s (:,p) in (I M -a cp (a H cp a cp ) -1 a H cp ) will be zero, then ω p →0, at this time a cp All are incoherent signals;

[0094] If a cp is the corresponding coherent signal, the signal subspace vector U s (:,p) in (I M -a cp (a H cp a cp ) -1 a H cp ) will not be zero, so ω p >0; will U s (:,p) is replaced by a p (θ), where a p (θ) represents the guiding vector constant of the pth group, constructing the new projection value ω p function ω p →0 guiding vector a ci Substitute into the above function to achieve the capture of incoherent signals.

[0095] Step S43: performing DOA estimation on all incoherent signals.

[0096] The step S5 comprises:

[0097] Step S51, one by one p >0 corresponding to a cp Construct the corresponding sparse model y p ;

[0098] y p =A p (θ)α p +n',A p (θ) represents the array flow model composed of all the steering vectors of the pth group, α p represents the correlation coefficient vector of the pth group, and n' is the error factor. In addition, since some groups are incoherent signals, they are not in the order of y1 to y P If they are arranged one by one in the order of , if there is an incoherent signal in the middle, there will inevitably be a jump in the p value.

[0099] Step S52: group a cp The corresponding α p Defined as unknown sparse signals to be recovered, group a is cp The space is divided into N equal parts, n = 1, 2, ... N; each ethnic group is divided into N equal parts;

[0100] Step S53, obtaining the guidance vector and correlation coefficient sparse model y of the pth group one by one p , and obtain the coherent sub-coefficients of the p-th group one by one

[0101] Step S531, construct the model equation y of the pth group one by one p ;

[0102]

[0103] Among them, a p (θ n ) is the steering vector of the nth equally divided space of the pth group, represents the coherent coefficient of the pth group (unknown), represents the error factor under the model corresponding to the p-th population;

[0104] Step S532, solve the equations corresponding to the p-th group one by one to obtain the coherent sub-coefficients of the p-th group

[0105] Step S54, using orthogonal matching pursuit algorithm Reconstruction is performed to achieve DOA estimation of coherent signals.

[0106] The following is the simulation data under the specific embodiment.

[0107] Simulation 1: In order to verify the effectiveness of the coherent and incoherent signal algorithms, the signal arrival angle estimation scatter plot is simulated. The array uses uniform array elements, the number of array elements is 12, and the number of incoming wave sources is set to 8, which are incident on the receiving array element, including 2 coherent signals. The noise is white noise, the signal-to-noise ratio is 5dB, 10dB, and 15dB, the number of synchronous sampling is set to 500 times, and 50 Monte Carlo tests are performed.

[0108] Results from simulation 1 Figure 1 , Figure 2 , Figure 3 It can be seen that the estimation algorithm for mixing coherent signals and incoherent signals of the present invention has high accuracy.

[0109] Simulation 2: This section simulates and verifies the effectiveness of the proposed method for separating incoherent signals from coherent signals. The array is set to a uniform linear array. The array configuration is the same as in Simulation 1, the incoming wave angle is set consistently, the signal-to-noise ratio is set to 5dB, 10dB, and 15dB, and the number of synchronous sampling is set to 500 times.

[0110] Results from simulation 2 Figure 4 , Figure 5 , Figure 6 It can be seen that the method for separating coherent signals from incoherent signals proposed in the present invention has sharp spectrum peaks and high estimation accuracy.

[0111] Although the content of the present invention has been described in detail through the above preferred embodiments, it should be appreciated that the above description should not be considered as a limitation of the present invention. After reading the above content, it will be apparent to those skilled in the art that various modifications and substitutions of the present invention will occur. Therefore, the protection scope of the present invention should be limited by the appended claims.

Claims

1. A method for estimating mixed DOA of coherent and incoherent signals based on vector space projection, characterized in that: The method comprises: Step S1, constructing a first pseudo array flow model A of the target's coherent signal and incoherent signal through the signal vector of the antenna signal c (θ); Step S2: according to the signal subspace value U s The total signal value X of all antenna signals is used to construct the second pseudo array flow model A' c The unitary matrix T of (θ); Step S3: Establish a second pseudo array flow model A' according to the unitary matrix T c (θ), A' c (θ)=[a c1 ,...,a cp ,...,a cP ]; a cp The p-th group of the second pseudo-array flow pattern model is represented by a steering vector coupled by a linear representation of a correlation coefficient; Step S4, constructing a spectrum function according to the beam space cp Perform projection to separate coherent signals from incoherent signals and realize DOA estimation of incoherent signals; Step S5, using sparse reconstruction method, the projection value ω p >0 corresponding to a cp , recover the correlation coefficient and realize the coherent signal DOA estimation.

2. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 1, characterized in that: The antenna array includes M array elements, m=1, 2...M; the antenna array receives K antenna signals of the target, k=1, 2...K; the K antenna signals are divided into P groups, each group is represented by L p , p=1, 2…P.

3. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 2, characterized in that: The step S1 comprises: Step S11: The antenna array receives K antenna signals from the target and divides the K antenna signals into P groups L p , the i-th antenna signal of the p-th group is represented by s p,i ; Step S12, preprocessing all antenna signals; Step S13, for each group L one by one p Select an initial signal s belonging to the group p,origin ; Step S14: for groups L1 to L p The antenna signal of the group to which it belongs is based on the initial signal s p,origin The expression of s p,i =α p,i s p,origin ,i=1,…,α p,i is the antenna signal s p,i Compared to the initial signal s p,origin The correlation coefficient of all antenna signals in the pth group is obtained one by one using the initial signal s p,origin The set S represented by p ={s p,1 =α p, 1s p,origin ,......}; Step S15, construct the total signal value X equation of all antenna signals under the signal vector, and obtain the reference signal s of different groups P (K), and then obtain the first pseudo array flow model A c (θ).

4. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 3, characterized in that: The step S12 includes: performing down-conversion on the K antenna signals one by one to obtain the down-conversion representation of the corresponding kth signal Among them, ρ k is the complex amplitude of the kth antenna signal, represents the composite function of the kth signal, and (τ) represents the down-conversion function.

5. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 4, characterized in that: The step S15 comprises: Step S151, construct the total signal value X=A(θ)s(K) of all antenna signals under the signal vector, and the total signal value of all antenna signals under the signal quantity Solving the equation, we get s(K). Wherein, A(θ) represents the actual array flow model of all antenna signals, and A(θ) is obtained through actual measurement, s(K) represents the signal vector set of all antenna signals; s p (k) represents the initial signal vector of the kth signal in the total antenna signal, and p represents the group; α p is the correlation coefficient vector of the p-th group; a(θ p,i )α p,i s p,origin A semaphore for a single signal; Step S152, obtain the reference signal s of all antenna signals according to s(K) P re(K),s(K)=Βs P re(K); Among them, B=blkdiag(α1,α2,...α p ......,α P ), Β represents a block diagonal matrix, s P re(K) is the reference signal of all antenna signals, s P re(K)=[s 1(re) ,....s p(re) .....,s P(re) ] T ,s p(re) represents the reference signal of the p-th group; Step S153, according to s P re(K) obtains the first pseudo array flow model A c (θ): X=A c (θ)s P re(K); Solve to obtain the first pseudo array flow model A c (θ).

6. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 5, characterized in that: The step S2 comprises: Step S21, synchronously sampling all antenna signals to construct a sampling covariance matrix R; All antenna signals are sampled synchronously for a total of L times, that is, the number of snapshots is L, l = 1, 2...L, the total signal value of all antenna signals is X, and the sampling covariance matrix is ​​expressed as Step S22, obtaining the signal subspace U s ; Step S23, perform eigenvalue decomposition on the sampling covariance matrix R, and calculate the signal subspace U s Find the unitary matrix T.

7. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 6, characterized in that: The step S23 comprises: Step S231, perform eigenvalue decomposition on the sampling covariance matrix R Among them, λ m is the eigenvalue of the mth array element, u m is the characteristic vector of the mth array element; Λ S The diagonal matrix representing the signal characteristics of the signal subspace, U N represents the noise subspace, Λ N A diagonal matrix representing the signal characteristics of the noise subspace; Step S232: transform the signal subspace U s Divide into two different (M-1)×P matrices, the two matrices are the first M-1 row matrix and the second M-1 row matrix; Step S233, respectively obtain the signal values ​​U of the first M-1 rows of the matrix B And the signal value U of the M-1 row matrix E ; U B =U s [1:(M-1),:],U E =U s [2:M,:], where,: represents the total value function; Step S234: based on the signal value U of the first M-1 rows of the matrix B And the signal value U of the M-1 row matrix E Obtain the rotation transformation matrix Φ of the first M-1 rows and the last M-1 rows; U B =(A B (θ)Β)T,U E =(A E (θ)Β)T,A B (θ)Φ=A E (θ) where A B (θ) is all the elements of the first M-1 rows of the matrix, A E (θ) are all the elements of the matrix of the next M-1 rows; Step S235, establish an equation and obtain the unitary matrix T according to Φ; Wherein, Λ is the diagonal matrix of signal characteristics of all antenna signals.

8. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 7, characterized in that: The step S3 comprises: a. cp It is expressed as: Among them, a'(θ p,i ) represents the steering vector of the i-th antenna signal in the p-th group coupled linearly through the correlation coefficient.

9. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 8, characterized in that: The step S4 comprises: Step S41, according to the orthogonality of the signal subspace and the noise subspace, a spectral function is constructed by a beamforming algorithm, and a cp in (I M -a cp (a H cp a cp ) -1 a H cp ) is projected to separate the coherent signal from the incoherent signal, where I M represents the identity matrix; the projection value ω p =min|U s H (:,p)(I M -a cp (a H cp a cp ) -1 a H cp ) s H (:,p)|; (:,p) means using the total value function for the internal elements of the pth group; Step S42, if a cp The corresponding signal is an incoherent signal. Because of the presence of noise, the signal subspace vector U s (:,p) in (I M -a cp (a H cp a cp ) -1 a H cp ) will be zero, then ω p →0, at this time a cp All are incoherent signals; if a cp is the corresponding coherent signal, the signal subspace vector U s (:,p) in (I M -a cp (a H cp a cp ) -1 a H cp ) will not be zero, so ω p >0; will U s (:,p) is replaced by a p (θ), where a p (θ) represents the guiding vector constant of the pth group, constructing the new projection value ω p function ω p →0 guiding vector a ci Substitute the above function to achieve the capture of incoherent signals; Step S43: performing DOA estimation on all incoherent signals.

10. The method for estimating mixed DOA of coherent and incoherent signals based on vector space projection according to claim 9, characterized in that: The step S5 comprises: Step S51, one by one p >0 corresponding to a cp Construct the corresponding sparse model y p ; y p =A p (θ)α p +n',A p (θ) represents the array flow model composed of all the steering vectors of the pth group, α p represents the correlation coefficient vector of the pth group, n' is the error factor; Step S52: group a cp The corresponding α p Defined as unknown sparse signals to be recovered, group a is cp The space is divided into N equal parts, n = 1, 2, ... N; each ethnic group is divided into N equal parts; Step S53, obtaining the steering vector and correlation coefficient sparse model of the p-th group one by one, and obtaining the coherent sub-coefficient of the p-th group one by one Step S531, construct the model equation y of the pth group one by one p ; Among them, a p (θ n ) is the steering vector of the nth equally divided space of the pth group, represents the coherent sub-coefficient of the p-th group, represents the error factor under the model corresponding to the p-th group; Step S532, solve the equations corresponding to the p-th group one by one to obtain the coherent sub-coefficients of the p-th group Step S54, using orthogonal matching pursuit algorithm Reconstruction is performed to achieve DOA estimation of coherent signals.

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