Navigation interference source positioning method and system based on sparse array optimization

Abstract

The invention provides a navigation interference source positioning method and system based on sparse array optimization, and relates to the technical field of array signal processing, a sparse array antenna is arranged, and then a noise component in an array covariance matrix of the sparse array antenna is removed by using a first optimization model, so that the positioning accuracy of a navigation interference source is improved. The method is more suitable for a complex noise environment, and compared with a traditional mode that signals and noise are divided through eigenvalue decomposition, the requirement for the environment noise is low. The array element number of the virtual array is further increased by vectorizing the pure covariance matrix, acquiring the virtual array, increasing the array element number and the array aperture, carrying out overlap removal and hole interpolation on the virtual array and carrying out hole interpolation reduction by using the second optimization model, so that the array is linear and uniform; and the degree of freedom and precision of navigation interference source positioning estimation are improved. According to the method, the noise subspace is calculated by using the quasi-orthogonal projection algorithm, the number of to-be-positioned navigation interference source targets does not need to be known, the positioning process is more direct and efficient, the number of interference sources does not need to be determined by spending extra time and resources, and the method can be applied to more fields and scenes to meet the requirements of different users.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and more specifically, to a navigation interference source positioning method and system based on sparse array optimization. Background Art

[0002] The BeiDou satellite navigation system is an important national space-time infrastructure, widely used in civil and military fields such as driving navigation, Internet of Things, and life services, and has a significant impact on social production. However, since the navigation signals of the BeiDou satellite navigation system are public and broadcast, they are susceptible to interference when used. In order to avoid significant losses caused by interference, it is necessary to locate the source of navigation interference as soon as possible when interference occurs.

[0003] Direction of Arrival (DOA) estimation is a method to estimate the direction of arrival of a signal through array signal processing technology. DOA estimation uses the phase difference of the signal received by the antenna array in space to calculate the direction of arrival of the signal. In the field of navigation, DOA estimation can be used to detect and locate interference sources and determine the angle between the azimuth of the interference source and the antenna array, i.e., θ. The accuracy and real-time performance of DOA estimation are of great significance to ensure the normal operation of the navigation system.

[0004] Currently, among DOA estimation methods, spatial spectrum estimation technology has developed rapidly. The most mature one is the Multiple Signal Classification (MUSIC) algorithm proposed by Schmidt RO et al. This algorithm decomposes the covariance matrix of the array received data into a signal subspace and a noise subspace perpendicular to it through the matrix spectrum decomposition theory. Using the orthogonal characteristics of these two subspaces, a spatial spectrum function is constructed. By traversing and searching the spatial spectrum function, a spatial spectrum curve is obtained, and the search value corresponding to the peak position of the curve is used as the DOA estimation value. This innovation not only significantly improves the resolution of DOA estimation, but also breaks through the physical aperture limitation in traditional spatial spectrum estimation algorithms, namely the Rayleigh limit, and plays an important role in promoting the research and development of subspace algorithms. However, this type of algorithm has the following disadvantages: (1) It assumes that the noise power of each array element is consistent, and has high requirements for environmental noise. When the noise power of each array element is different, the accuracy of the algorithm decreases. (2) After eigenvalue decomposition, the premise of using this algorithm is that the number of interference sources is known or has been correctly estimated. However, in actual scenarios, interference sources are generally hidden, and the number of interference sources is difficult to know and varies. (3) This algorithm requires that the number of antenna array elements is greater than the number of interference sources. The maximum number of interference sources that can be estimated is small. When estimating the location of navigation interference sources, the number of physical array elements limits the estimation freedom, resulting in a low estimation freedom. Summary of the invention

[0005] In order to solve the problems that the current DOA estimation method used for locating navigation interference sources has low positioning accuracy and estimation freedom, and requires a known number of interference sources, the present invention proposes a navigation interference source positioning method and system based on sparse array optimization, which adopts sparse array and virtual technology to increase the number of array elements and array aperture, break through the limitation of the number of physical array elements on the estimation freedom, improve the estimation freedom and accuracy of navigation interference source positioning, and the number of navigation interference source targets to be located does not need to be known, so the positioning process is more direct and efficient, and there is no need to spend extra time and resources to determine the number of interference sources. It can be applied to more fields and scenarios to meet the needs of different users.

[0006] In order to achieve the above technical effects, the technical solution of the present invention is as follows:

[0007] In a first aspect, the present application proposes a navigation interference source positioning method based on sparse array optimization, comprising: S1: obtaining an array output vector of a sparse array antenna and an array covariance matrix of the array output vector;

[0008] S2: constructing and solving a first optimization model based on the array variance matrix to remove the noise component in the array covariance matrix and obtain a pure covariance matrix;

[0009] S3: vectorizing the clean covariance matrix to obtain a virtual array, and de-overlapping the virtual array to obtain a de-overlapped virtual array;

[0010] S4: interpolating the hole positions of the virtual array after de-overlapping to obtain an interpolated virtual array, constructing and solving a second optimization model to restore the interpolated array elements of the interpolated virtual array;

[0011] S5: using the quasi-orthogonal projection method, the noise subspace of the interpolated virtual array is calculated, and the spatial spectrum function of the interpolated virtual array is constructed based on the noise subspace;

[0012] S6: construct a spatial spectrum curve corresponding to the spatial spectrum function, search the spatial spectrum curve within a set angle range, determine the angle value of the direction of arrival, and locate the navigation interference source.

[0013] Preferably, mutually prime numbers M and N are set, the coordinate of the first element of the sparse array antenna is set to 0, d is taken as the unit distance of the element spacing, one element is placed every Nd interval, and one element is placed every Md interval, and the sparse array antenna has M+N-1 elements; the element coordinate set is:

[0014] Preferably, suppose there are K navigation interference sources in total, and the signal emitted by the interference source is recorded as {s 1 (t), s 2 (t), ..., s K(t)}, the direction of arrival is denoted as {θ 1 ,θ 2 , ..., θ K}, the power is recorded as The frequency of the interference signal is denoted as f c , the signal wavelength is recorded as λ; the array element output of the i-th array element of the sparse array antenna includes the signal and noise components emitted by all navigation interference sources, expressed as:

[0015]

[0016] in, Then the array output of the sparse array antenna is expressed as: x(t) = As(t) + n(t), where, represents the array output vector, represents the steering matrix, represents the steering vector, represents the additive white Gaussian noise vector;

[0017] The calculation expression of the array covariance matrix of the array output vector is:

[0018]

[0019] in, represents the noise power diagonal matrix, represents the signal power diagonal matrix, (·) H represents the conjugate transpose of a matrix;

[0020] Collect the output data of the T snapshot sparse array antenna, and the array covariance matrix of the approximate array output vector is:

[0021] Preferably, let the noise component be R e , R e is a diagonal matrix, the clean covariance matrix is ​​R, then: The first optimization model is established, and the expression is:

[0022] min rank(R)

[0023]

[0024] R e =diag(r 1 , r 2 , ..., r M+N-1 )

[0025] Among them, rank() represents the rank operation, which iteratively optimizes and solves the first optimization model to obtain R e ,Depend on Get the clean covariance matrix R.

[0026] According to the above technical solution, considering that the noise component is a diagonal matrix, the existence of the noise component will increase the rank of the covariance matrix. The noise component is extracted with the minimum rank of the covariance matrix, which is more suitable for complex noise environments and has low requirements on environmental noise.

[0027] Preferably, the elements in the clean covariance matrix R are expressed as: Vectorize the clean covariance matrix R to get a virtual array. The output vector of the virtual array is in, Represents a single snapshot signal of a virtual source, represents the virtual steering matrix, and the elements in the virtual steering matrix B are expressed as: represents the Kronecker product, ⊙ represents the Hadamard product; where m, n ≤ M+N-1 and l = i(M+N-1)+j, therefore, the lth element of the output vector y of the virtual array is the coordinate UU m -u n The virtual array receives the wave arrival direction {θ 1 , ..., θ K}, the element position set of the virtual array is expressed as Represents a physical array element position set, the number of elements is less than (M+N-1) 2 There is overlap of virtual array element positions;

[0028] The average value of the virtual array element outputs of the overlapping virtual arrays is taken to achieve de-overlapping of the virtual arrays and obtain the de-overlapped virtual array. The output vector of the de-overlapped virtual array is The calculation expression of the element is:

[0029] Among them, v l represents the position of the lth virtual array element, C l Indicates the number of overlaps.

[0030] According to the above technical solution, after the pure covariance matrix is ​​vectorized, a virtual array is obtained, and the virtual array is de-overlapped, thereby increasing the number of array elements and the array aperture.

[0031] Preferably, the hole positions of the virtual array after de-overlapping are interpolated with 0 values ​​to obtain an output vector z of the interpolated virtual array. The interpolation array element output is first set to 0, and the position set of the interpolation virtual array is: The vector z element is calculated as follows:

[0032]

[0033] Among them, w l =(l-(N-1)M-1)d represents the coordinates of the lth element of the interpolated virtual array, and the interpolated element label vector is z 0.1 ∈{0, 1} 2(N-1)M+1 , the expression is:

[0034] Define the vector Toeplitz matrix function T(·), which constructs the Toeplitz matrix with the (N-1)M+1 elements after the vector as the first column elements and the reverse order of the (N-1)M+1 elements before the vector as the first row elements, and obtains the interpolation array covariance matrix: And the interpolation element label matrix P = T (z 0，1 );

[0035] Construct the second optimization model, the expression is:

[0036]

[0037] P⊙R z =P⊙R 0

[0038] Among them, R z represents the reconstructed interpolation virtual array covariance matrix, in, represents the steering matrix of the interpolated virtual array, R b is the reconstruction error; relax the second optimization model, transform the constraints into penalty terms and solve them, and get R z , in R z When the rank of is minimum, the interpolation elements of the interpolation virtual array are correctly restored.

[0039] According to the above technical means, as the virtual array elements and array aperture increase, some holes appear on the virtual array. Through interpolation and interpolation data restoration, the number of elements is further increased and a large-aperture linear uniform array is constructed. Using M+N-1 physical elements, up to 2(N-1)M interference sources can be estimated, which greatly improves the DOA estimation freedom and estimation accuracy.

[0040] Preferably, the process of calculating the noise subspace of the interpolated virtual array using the quasi-orthogonal projection method is as follows:

[0041]

[0042] Among them, U n represents the noise subspace.

[0043] Preferably, the spatial spectrum function expression of the interpolation virtual array constructed based on the noise subspace is:

[0044]

[0045] in, θ∈(0,180].

[0046] According to the above technical means, the noise subspace is calculated using a quasi-orthogonal projection method, which does not require the number of navigation interference sources as a known parameter, thereby improving the scope of application.

[0047] Preferably, the value of the wave arrival direction angle range θ is used as the horizontal coordinate, and the spatial spectrum The amplitude value is taken as the ordinate, and the spatial spectrum curve is drawn. The spatial spectrum curve is searched within the angle range of θ∈(0,180], and the abscissa θ of the peak position is taken as the angle value of the wave arrival direction to locate the navigation interference source.

[0048] In a second aspect, the present application proposes a navigation interference source positioning system based on sparse array optimization, the system is used to implement the navigation interference source positioning method, including:

[0049] A sparse array antenna data acquisition unit, used to acquire an array output vector of the sparse array antenna and an array covariance matrix of the array output vector;

[0050] A denoising unit constructs and solves a first optimization model based on the array variance matrix to remove noise components in the array covariance matrix to obtain a pure covariance matrix;

[0051] A virtual array de-overlapping unit is used to vectorize the pure covariance matrix to obtain a virtual array, and de-overlap the virtual array to obtain a de-overlapped virtual array;

[0052] An interpolation element restoration unit is used to interpolate the hole positions of the virtual array after de-overlapping to obtain an interpolated virtual array, construct a second optimization model and solve it to restore the interpolation elements of the interpolated virtual array;

[0053] A noise subspace calculation unit is used to calculate the noise subspace of the interpolated virtual array by using a quasi-orthogonal projection method, and to construct a spatial spectrum function of the interpolated virtual array based on the noise subspace;

[0054] The spectrum search unit is used to construct a spatial spectrum curve corresponding to the spatial spectrum function, search the spatial spectrum curve within a set angle range, determine the angle value of the wave arrival direction, and locate the navigation interference source.

[0055] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0056] The present invention proposes a navigation interference source positioning method and system based on sparse array optimization. By arranging sparse array antennas, and then using a first optimization model to remove the noise component in the array covariance matrix of the sparse array antenna, the present invention is more suitable for complex noise environments. Compared with the traditional method of using eigenvalue decomposition to divide signals and noise, the environmental noise requirement is low. By vectorizing the pure covariance matrix, a virtual array is obtained, the number of array elements and the array aperture are increased, and the virtual array is de-overlapped, the holes are interpolated, and the second optimization model is used to perform hole interpolation restoration, and the number of virtual array elements is further increased, so that the array is linearly uniform, and the freedom and accuracy of navigation interference source positioning estimation are improved. The present invention uses a quasi-orthogonal projection algorithm to calculate the noise subspace. The number of navigation interference source targets to be located does not need to be known, and the positioning process is more direct and efficient. There is no need to spend extra time and resources to determine the number of interference sources. It can be applied to more fields and scenarios to meet the needs of different users. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A schematic diagram showing a flow chart of a navigation interference source positioning method based on sparse array optimization proposed in an embodiment of the present invention;

[0058] Figure 2 A schematic diagram showing a geometric layout of a sparse array element arrangement proposed in an embodiment of the present invention;

[0059] Figure 3 A schematic diagram showing that interference signals transmitted by a navigation interference source according to an embodiment of the present invention are received by a sparse array antenna;

[0060] Figure 4 A schematic diagram showing the geometric layout of sparse array physical elements, virtual array elements and holes proposed in an embodiment of the present invention;

[0061] Figure 5 A schematic diagram showing the structure of a navigation interference source positioning system based on sparse array optimization proposed in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0063] In order to better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the actual size;

[0064] It is understandable to those skilled in the art that descriptions of certain well-known contents in the drawings may be omitted.

[0065] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0066] The positional relationships described in the drawings are only for illustrative purposes and should not be construed as limiting the present patent;

[0067] Example 1

[0068] This embodiment proposes a navigation interference source positioning method based on sparse array optimization. The flowchart of this method is shown in Figure 1 , including the following steps:

[0069] S1: Obtain the array output vector of the sparse array antenna and the array covariance matrix of the array output vector;

[0070] S2: constructing and solving a first optimization model based on the array variance matrix to remove the noise component in the array covariance matrix and obtain a pure covariance matrix;

[0071] S3: vectorizing the clean covariance matrix to obtain a virtual array, and de-overlapping the virtual array to obtain a de-overlapped virtual array;

[0072] S4: interpolating the hole positions of the virtual array after de-overlapping to obtain an interpolated virtual array, constructing and solving a second optimization model to restore the interpolated array elements of the interpolated virtual array;

[0073] S5: using the quasi-orthogonal projection method, the noise subspace of the interpolated virtual array is calculated, and the spatial spectrum function of the interpolated virtual array is constructed based on the noise subspace;

[0074] S6: construct a spatial spectrum curve corresponding to the spatial spectrum function, search the spatial spectrum curve within a set angle range, determine the angle value of the direction of arrival, and locate the navigation interference source.

[0075] The navigation interference source positioning method based on sparse array optimization proposed in this embodiment arranges sparse array antennas, and then uses the first optimization model to remove the noise components in the array covariance matrix of the sparse array antennas, so that the present invention is more suitable for complex noise environments. Compared with the traditional method of dividing signals and noise by eigenvalue decomposition, it has low requirements for environmental noise. By vectorizing the pure covariance matrix, a virtual array is obtained, the number of array elements and the array aperture are increased, and the virtual array is de-overlapped, the holes are interpolated, and the second optimization model is used to perform hole interpolation restoration, and the number of virtual array elements is further increased, so that the array is linearly uniform, and the freedom and accuracy of navigation interference source positioning estimation are improved. The present invention uses a quasi-orthogonal projection algorithm to calculate the noise subspace. The number of navigation interference source targets to be located does not need to be known, and the positioning process is more direct and efficient. There is no need to spend extra time and resources to determine the number of interference sources. It can be applied to more fields and scenarios to meet the needs of different users. It has the following advantages:

[0076] (1) Applicable to more complex noise environments. This embodiment uses the first optimization model to extract the noise components distributed on the diagonal in the covariance matrix of the sparse array output. During the de-optimization process, the noise components will gradually approach the true value, making the method proposed in this embodiment applicable to more complex noise environments.

[0077] (2) The implementation process of this embodiment uses a quasi-orthogonal projection algorithm to calculate the noise subspace. The introduction of this algorithm makes it unnecessary to use the number of navigation interference sources as a parameter during the implementation of the solution, so the number of interference sources does not need to be known.

[0078] (3) It has higher estimation accuracy and estimation freedom. This embodiment uses sparse array and virtual technology to increase the number of array elements and array aperture, and through data interpolation and interpolation data restoration, the number of array elements is further increased and a large-aperture linear uniform array is constructed.

[0079] Example 2

[0080] like Figure 2 As shown, in this embodiment, the coprime numbers M and N are set, the coordinate of the first element of the sparse array antenna is set to 0, and d is the unit distance of the element spacing (generally, it can be directly set to half a wavelength, i.e. ), one array element is placed every Nd interval, and one array element is also placed every Md interval. The sparse array antenna has M+N-1 array elements; the array element coordinate set is:

[0081] In actual implementation, the terminal equipment of the Beidou satellite navigation system uses an array antenna to receive satellite navigation signals. When the array antenna is interfered with, take two interference sources as an example. Figure 3 As shown, the number of interference sources in the actual scenario is unknown. Several long-distance navigation interference sources transmit interference signals. The interference signals propagate through the air to the array antenna. The angle between the position of the navigation interference source and the array is DOA, recorded as θ. The interference signal transmits a narrowband signal. The center frequency of the interference signal is the same as the frequency band of the Beidou satellite navigation system used by the terminal device. For example, when the terminal device uses the Beidou-3 B1 frequency band, the center frequency of the interference source is 1575.420MHz. The frequency band-center frequency comparison table of the Beidou satellite navigation system is as follows:

[0082]

[0083] Assume that there are K navigation interference sources in total, and the signal emitted by the interference source is recorded as {s 1 (t),s 2 (t),…,s K (t)}, the direction of arrival is denoted as {θ 1 ,θ 2 ,…,θK}, the power is recorded as The frequency of the interference signal is denoted as f c , the signal wavelength is denoted as λ.

[0084] The array element output of the i-th array element of the sparse array antenna includes the signal and noise components emitted by all navigation interference sources, which can be expressed as: in, Then the array output of the sparse array antenna is expressed as: a(t) = As(t) + n(t), where, represents the array output vector, represents the steering matrix, represents the steering vector, represents the additive white Gaussian noise vector; the calculation expression of the array covariance matrix of the array output vector is:

[0085]

[0086] in, represents the noise power diagonal matrix, represents the signal power diagonal matrix, (·) H Represents the conjugate transpose of a matrix.

[0087] Since the mathematical expectation cannot be accurately calculated in actual use, a multi-snap average value can be used for approximate representation. In this embodiment, the output data of T-snap sparse array antennas are collected, and the array covariance matrix of the approximate array output vector is:

[0088] As mentioned in the above process, the array element output of the sparse array antenna includes the signal and noise components emitted by all navigation interference sources, and the covariance matrix of the array output is The existence of noise components in will affect the estimation accuracy. Let the noise component be R e , R e is a diagonal matrix, the clean covariance matrix is ​​R, then: The presence of noise components will increase the rank of the clean covariance matrix. If the rank of the clean covariance matrix is ​​smaller, the noise component is removed more thoroughly. Therefore, the following first optimization model is established, and the expression is:

[0089] min rank(R)

[0090]

[0091] R e =diah(r 1 ,r 2 ,…,r M+N-1 )

[0092] Among them, rank() represents the rank operation, which iteratively optimizes and solves the first optimization model to obtain R e ,Depend on Get the clean covariance matrix R.

[0093] In this embodiment, considering that the first optimization model is non-convex optimization, in order to facilitate the solution, the original first optimization model is relaxed to obtain the following optimization model:

[0094] min∥R∥ *

[0095]

[0096] R e =diag(r 1 ,r 2 ,…,r M+N-1 )

[0097] The above optimization model is solved by the following iterative optimization steps:

[0098] (1) Initialize weight parameters Γ, μ, ρ, ε; (2) Calculate intermediate parameters (3) Calculate singular value decomposition (4) Update singular values (5) Calculation (6) Calculate intermediate variables (7) Solve the optimization objective (8) Update auxiliary variables μ←μ×ρ; (9) Calculate the optimization error If the error is greater than the threshold ∈>ε and the number of iterations has not reached the preset upper limit, return to (2) and repeat a new round of iterative updates; otherwise, continue to execute backward.

[0099] The elements in the clean covariance matrix R are expressed as: Vectorize the clean covariance matrix R to get a virtual array. The output vector of the virtual array is in, Represents a single snapshot signal of a virtual source, represents the virtual steering matrix, and the elements in the virtual steering matrix B are expressed as: represents the Kronecker product, ⊙ represents the Hadamard product; where m, n ≤ M + N - 1 and l = i (M + N - 1) + j, therefore, the lth element of the output vector y of the virtual array is the coordinate u m -u n The virtual array receives the wave arrival direction {θ 1, ..., θ K}, the element position set of the virtual array is expressed as Represents a physical array element position set, the number of elements is less than (M+N-1) 2 There is overlap of virtual array element positions;

[0100] The average value of the virtual array element outputs of the overlapping virtual arrays is taken to achieve de-overlapping of the virtual arrays and obtain the de-overlapped virtual array. The output vector of the de-overlapped virtual array is The calculation expression of the element is:

[0101] Among them, v l represents the position of the lth virtual array element, C l Indicates the number of overlaps.

[0102] Assuming that M = 3 and N = 5, the physical array element position set and virtual array element position set Elements such as Figure 4 As shown by Figure 4 It can be seen that the virtual array has a much larger number of array elements and a larger array aperture than the physical array, but there are also some vacant positions on the virtual array, called holes. The existence of holes reduces the degree of freedom of the virtual array on the one hand, and destroys the linear uniformity of the virtual array on the other hand.

[0103] In order to further improve the performance, in this embodiment, the hole positions of the virtual array after de-overlapping are interpolated with 0 values ​​to obtain the output vector z of the interpolated virtual array. The interpolation array element output is first set to 0, and the position set of the interpolation virtual array is: The vector z element is calculated as follows:

[0104]

[0105] Among them, w l =(l-(N-1)M-1)d represents the coordinates of the lth element of the interpolated virtual array, and the interpolated element label vector is z 0，1 ∈{0, 1} 2(N-1)M+1 , the expression is:

[0106] In order to restore the data of the interpolation array element, the vector Toeplitz matrix function T(·) is defined. This function constructs the Toeplitz matrix with the (N-1)M+1 elements after the vector as the first column elements and the reverse order of the (N-1)M+1 elements before the vector as the first row elements, and obtains the interpolation array covariance matrix: And the interpolation element label matrix P = T (z 0，1 );

[0107] When the interpolated array elements are correctly restored, the reconstructed covariance matrix R z It has a lower rank, so it can be determined that the optimization goal is to reconstruct the covariance matrix R while keeping the existing data unchanged. z The rank of is minimized and the following second optimization model is constructed, which is expressed as:

[0108]

[0109] P⊙R z =P⊙R 0

[0110] Among them, R z represents the reconstructed interpolation virtual array covariance matrix, in, represents the steering matrix of the interpolated virtual array, R b is the reconstruction error; relax the second optimization model, transform the constraints into penalty terms and solve them, and get R z , in R z When the rank of is minimum, the interpolation elements of the interpolation virtual array are correctly restored.

[0111] For the second optimization model above, the solution process is as follows:

[0112] (1) Initialize the target matrix R z ←0, initialize auxiliary variable o l , μ, ρ, ε; (2) Calculate the intermediate matrix Z = R z +μP⊙(R 0 -R z );(3) Singular value decomposition (4) Update the singular value ∑ z ←(∑ z -λμI) + ; (5) Calculate the target (6) Calculate the error variable c=|oo l |; (7) Update auxiliary variable o l ←o, μ←μ×ρ; (8) If the error is greater than the set threshold c>ε and the number of iterations has not reached the preset upper limit, return to (2) and repeat a new round of iterative update; otherwise, continue to execute backward.

[0113] When solving to the target R z Then, using the quasi-orthogonal projection method, the process of calculating the noise subspace of the interpolated virtual array is:

[0114]

[0115] Among them, U n Represents the noise subspace. Compared with the traditional orthogonal projection matrix, the quasi-orthogonal projection matrix used in the present invention adds a perturbation value τI. In the ideal case, R b = 0, the perturbation value τI ensures that the inverse matrix is ​​full rank and hardly affects the orthogonal operation result; in actual use, R b ≠0 and rank(R z )>K, then the perturbation value τI ensures that the orthogonal projection result will not be compressed to the null space.

[0116] In this embodiment, the spatial spectrum function expression of the interpolation virtual array constructed based on the noise subspace is:

[0117]

[0118] in, θ∈(0,180].

[0119] Finally, the value of the wave arrival direction angle range θ is taken as the horizontal coordinate, and the spatial spectrum The amplitude value is taken as the ordinate, and the spatial spectrum curve is drawn. The spatial spectrum curve is searched within the angle range of θ∈(0, 180], and the abscissa θ of the peak position is taken as the angle value of the wave arrival direction to locate the navigation interference source.

[0120] Example 3

[0121] like Figure 5As shown, this embodiment proposes a navigation interference source positioning system based on sparse array optimization, which is used to implement a navigation interference source positioning method, including: a sparse array antenna data acquisition unit, a denoising unit, a virtual array de-overlapping unit, an interpolation array element restoration unit, a noise subspace calculation unit and a spectrum search unit. Among them, the sparse array antenna data acquisition unit is used to obtain the array output vector of the sparse array antenna and the array covariance matrix of the array output vector; the denoising unit constructs a first optimization model based on the array variance matrix and solves it to remove the noise component in the array covariance matrix to obtain a pure covariance matrix. The virtual array de-overlapping unit is used to vectorize the pure covariance matrix to obtain a virtual array, and de-overlap the virtual array to obtain a virtual array after de-overlapping. The interpolation array element restoration unit is used to interpolate the hole positions of the virtual array after de-overlapping to obtain an interpolated virtual array, and construct a second optimization model and solve it to restore the interpolation array elements of the interpolated virtual array. The noise subspace calculation unit is used to calculate the noise subspace of the interpolated virtual array using a quasi-orthogonal projection method, and to construct the spatial spectrum function of the interpolated virtual array based on the noise subspace. The spectrum search unit is used to construct a spatial spectrum curve corresponding to the spatial spectrum function, search for the spatial spectrum curve within a set angle range, determine the angle value of the direction of arrival, and locate the navigation interference source.

[0122] The array element output of the i-th array element of the sparse array antenna of this embodiment includes the signal and noise components transmitted by all navigation interference sources, which is expressed as: in, Then the array output of the sparse array antenna is expressed as: x(t) = As(t) + n(t), where, represents the array output vector, represents the steering matrix, represents the steering vector, represents the additive white Gaussian noise vector; the calculation expression of the array covariance matrix of the array output vector is:

[0123]

[0124] in, represents the noise power diagonal matrix, represents the signal power diagonal matrix, (·) H Represents the conjugate transpose of a matrix.

[0125] Since the mathematical expectation cannot be accurately calculated in actual use, a multi-snap average value can be used for approximate representation. In this embodiment, the output data of T-snap sparse array antennas are collected, and the array covariance matrix of the approximate array output vector is:

[0126] Consider the covariance matrix of the array output The existence of noise components in will affect the estimation accuracy. Let the noise component be R e , R e is a diagonal matrix, the clean covariance matrix is ​​R, then: The presence of noise components will increase the rank of the clean covariance matrix. If the rank of the clean covariance matrix is ​​smaller, the noise component is removed more thoroughly. Therefore, the following first optimization model is established, and the expression is:

[0127] min rank(R)

[0128]

[0129] R e =diag(r 1 , r 2 , ..., r M+N-1 )

[0130] Among them, rank() represents the rank operation, which iteratively optimizes and solves the first optimization model to obtain R e ,Depend on Get the clean covariance matrix R.

[0131] In this embodiment, considering that the first optimization model is non-convex optimization, in order to facilitate the solution, the original first optimization model is relaxed to obtain the following optimization model:

[0132] min||R|| *

[0133]

[0134] R e =diag(r 1 , r 2 , ..., r M+N-1 )

[0135] The above optimization model is solved by the following iterative optimization steps:

[0136] (1) Initialize weight parameters Γ, μ, ρ, ε; (2) Calculate intermediate parameters (3) Calculate singular value decomposition (4) Update singular values (5) Calculation (6) Calculate intermediate variables (7) Solve the optimization objective (8) Update auxiliary variables μ←μ×ρ; (9) Calculate the optimization error If the error is greater than the threshold ∈>ε and the number of iterations has not reached the preset upper limit, return to (2) and repeat a new round of iterative updates; otherwise, continue to execute backward.

[0137] The elements in the clean covariance matrix R are expressed as: Vectorize the clean covariance matrix R to get a virtual array. The output vector of the virtual array is in, Represents a single snapshot signal of a virtual source, represents the virtual steering matrix, and the elements in the virtual steering matrix B are expressed as: represents the Kronecker product, ⊙ represents the Hadamard product; where m, n ≤ M + N - 1 and l = i (M + N - 1) + j, therefore, the lth element of the output vector y of the virtual array is the coordinate u m -u n The virtual array receives the wave arrival direction {θ 1 , ..., θ K}, the element position set of the virtual array is expressed as Represents a physical array element position set, the number of elements is less than (M+N-1) 2 There is overlap of virtual array element positions;

[0138] The average value of the virtual array element outputs of the overlapping virtual arrays is taken to achieve de-overlapping of the virtual arrays and obtain the de-overlapped virtual array. The output vector of the de-overlapped virtual array is The calculation expression of the element is:

[0139] Among them, v l represents the position of the lth virtual array element, C l Indicates the number of overlaps.

[0140] In order to further improve the performance, in this embodiment, the hole positions of the virtual array after de-overlapping are interpolated with 0 values ​​to obtain the output vector z of the interpolated virtual array. The interpolation array element output is first set to 0, and the position set of the interpolation virtual array is: The vector z element is calculated as follows:

[0141]

[0142] Among them, w l =(l-(N-1)M-1)d represents the coordinates of the lth element of the interpolated virtual array, and the interpolated element label vector is z 0，1 ∈{0, 1}2(N-1)M+1 , the expression is:

[0143] In order to restore the data of the interpolation array element, the vector Toeplitz matrix function T(·) is defined. This function constructs the Toeplitz matrix with the (N-1)M+1 elements after the vector as the first column elements and the reverse order of the (N-1)M+1 elements before the vector as the first row elements, and obtains the interpolation array covariance matrix: And the interpolation element label matrix P = T (z 0，1 );

[0144] When the interpolated array elements are correctly restored, the reconstructed covariance matrix R z It has a lower rank, so it can be determined that the optimization goal is to reconstruct the covariance matrix R while keeping the existing data unchanged. z The rank of is minimized and the following second optimization model is constructed, which is expressed as:

[0145]

[0146] P⊙R z =P⊙R 0

[0147] Among them, R z represents the reconstructed interpolation virtual array covariance matrix, in, represents the steering matrix of the interpolated virtual array, R b is the reconstruction error; relax the second optimization model, transform the constraints into penalty terms and solve them, and get R z , in R z When the rank of is minimum, the interpolation elements of the interpolation virtual array are correctly restored.

[0148] For the second optimization model above, the solution process is as follows:

[0149] (1) Initialize the target matrix R z ←0, initialize auxiliary variable o l , μ, ρ, ε; (2) Calculate the intermediate matrix Z = R z +μP⊙(R 0 -R z );(3) Singular value decomposition (4) Update the singular value ∑ z ←(∑ z -λμI) + ; (5) Calculate the target (6) Calculate the error variable c=|oo l |; (7) Update auxiliary variable ol ←o, μ←μ×ρ; (8) If the error is greater than the set threshold c>ε and the number of iterations has not reached the preset upper limit, return to (2) and repeat a new round of iterative update; otherwise, continue to execute backward.

[0150] When solving to the target R z Then, using the quasi-orthogonal projection method, the process of calculating the noise subspace of the interpolated virtual array is:

[0151]

[0152] Among them, U n Represents the noise subspace. Compared with the traditional orthogonal projection matrix, the quasi-orthogonal projection matrix used in the present invention adds a perturbation value τI. In the ideal case, R b = 0, the perturbation value τI ensures that the inverse matrix is ​​full rank and hardly affects the orthogonal operation result; in actual use, R b ≠0 and rank(R z )>K, then the perturbation value τI ensures that the orthogonal projection result will not be compressed to the null space.

[0153] In this embodiment, the spatial spectrum function expression of the interpolation virtual array constructed based on the noise subspace is:

[0154]

[0155] in,

[0156] θ∈(0,180].

[0157] Finally, the value of the wave arrival direction angle range θ is taken as the horizontal coordinate, and the spatial spectrum The amplitude value is taken as the ordinate, and the spatial spectrum curve is drawn. The spatial spectrum curve is searched within the angle range of θ∈(0, 180], and the abscissa θ of the peak position is taken as the angle value of the wave arrival direction to locate the navigation interference source.

[0158] The embodiments are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A navigation interference source positioning method based on sparse array optimization, characterized in that: include: S1: Obtain the array output vector of the sparse array antenna and the array covariance matrix of the array output vector; S2: constructing and solving a first optimization model based on the array variance matrix to remove the noise component in the array covariance matrix and obtain a pure covariance matrix; S3: vectorizing the clean covariance matrix to obtain a virtual array, and de-overlapping the virtual array to obtain a de-overlapped virtual array; S4: interpolating the hole positions of the virtual array after de-overlapping to obtain an interpolated virtual array, constructing and solving a second optimization model to restore the interpolated array elements of the interpolated virtual array; S5: using the quasi-orthogonal projection method, the noise subspace of the interpolated virtual array is calculated, and the spatial spectrum function of the interpolated virtual array is constructed based on the noise subspace; S6: construct a spatial spectrum curve corresponding to the spatial spectrum function, search the spatial spectrum curve within a set angle range, determine the angle value of the direction of arrival, and locate the navigation interference source.

2. The navigation interference source positioning method based on sparse array optimization according to claim 1 is characterized in that: Set the coprime numbers M and N, set the coordinate of the first element of the sparse array antenna to 0, take d as the unit distance of the element spacing, place an element every Nd intervals, and place an element every Md intervals. The sparse array antenna has M+N-1 elements; the element coordinate set is:

3. The navigation interference source positioning method based on sparse array optimization according to claim 2 is characterized in that: Assume that there are K navigation interference sources in total, and the signals emitted by the interference sources are recorded as {s1(t),s2(t),…,s K (t)}, and the arrival direction is recorded as {θ1,θ2,…,θ K }, the power is recorded as The frequency of the interference signal is denoted as f c , the signal wavelength is recorded as λ; the array element output of the i-th array element of the sparse array antenna includes the signal and noise components emitted by all navigation interference sources, expressed as: in, Then the array output of the sparse array antenna is expressed as: x(t) = As(t) + n(t), where, represents the array output vector, represents the steering matrix, represents the steering vector, represents the additive white Gaussian noise vector; the calculation expression of the array covariance matrix of the array output vector is: in, represents the noise power diagonal matrix, represents the signal power diagonal matrix, (·) H represents the conjugate transpose of a matrix; Collect the output data of the T snapshot sparse array antenna, and the array covariance matrix of the approximate array output vector is:

4. The navigation interference source positioning method based on sparse array optimization according to claim 3 is characterized in that: Assume the noise component is R e , R e is a diagonal matrix, the clean covariance matrix is ​​R, then: The first optimization model is established, and the expression is: minrank(R) R e =diag(r1,r2,…,r M+N-1 ) Among them, rank() represents the rank operation, which iteratively optimizes and solves the first optimization model to obtain R e ,Depend on Get the clean covariance matrix R.

5. The navigation interference source positioning method based on sparse array optimization according to claim 4 is characterized in that: The elements in the clean covariance matrix R are expressed as: Vectorize the clean covariance matrix R to get a virtual array. The output vector of the virtual array is in, Represents a single snapshot signal of a virtual source, represents the virtual steering matrix, and the elements in the virtual steering matrix B are expressed as: represents the Kronecker product, ⊙ represents the Hadamard product; where m,n≤M+N-1 and l=i(M+N-1)+j, therefore, the lth element of the output vector y of the virtual array is the vector with coordinates u m -u n The virtual array receives the waves from the wave arrival directions {θ1,…,θ K }, the element position set of the virtual array is expressed as Represents a physical array element position set, the number of elements is less than (M+N-1) 2 There is overlap of virtual array element positions; The average value of the virtual array element outputs of the overlapping virtual arrays is taken to achieve de-overlapping of the virtual arrays and obtain the de-overlapped virtual array. The output vector of the de-overlapped virtual array is The calculation expression of the element is: Among them, v l represents the position of the lth virtual array element, C l Indicates the number of overlaps.

6. The method for locating a navigation interference source based on sparse array optimization according to claim 5, characterized in that: The hole positions of the virtual array after de-overlapping are interpolated with 0 values ​​to obtain the output vector z of the interpolated virtual array. The interpolation array element output is first set to 0, and the position set of the interpolation virtual array is: The vector z element is calculated as follows: Among them, w l =(l-(N-1)M-1)d represents the coordinates of the lth element of the interpolated virtual array, and the interpolated element label vector is z 0,1 ∈{0,1} 2(N-1)M+1 , the expression is: Define the vector Toeplitz matrix function T(·), which constructs the Toeplitz matrix with the (N-1)M+1 elements after the vector as the first column elements and the reverse order of the (N-1)M+1 elements before the vector as the first row elements, and obtains the interpolation array covariance matrix: And the interpolation element label matrix P = T (z 0,1 ); Construct the second optimization model, the expression is: s.t.P⊙R z =P⊙R0 Among them, R z represents the reconstructed interpolation virtual array covariance matrix, in, represents the steering matrix of the interpolated virtual array, R b is the reconstruction error; relax the second optimization model, transform the constraints into penalty terms and solve them, and get R z , in R z When the rank of is minimum, the interpolation elements of the interpolation virtual array are correctly restored.

7. The method for locating a navigation interference source based on sparse array optimization according to claim 6, characterized in that: Using the quasi-orthogonal projection method, the process of calculating the noise subspace of the interpolated virtual array is: Among them, U n represents the noise subspace.

8. The method for locating a navigation interference source based on sparse array optimization according to claim 7, characterized in that: The spatial spectrum function expression of the interpolation virtual array constructed based on the noise subspace is: in, θ∈(0,180].

9. The method for locating a navigation interference source based on sparse array optimization according to claim 8, characterized in that: The range of the wave arrival direction angle θ is the horizontal coordinate, and the spatial spectrum The amplitude value is taken as the ordinate, and the spatial spectrum curve is drawn. The spatial spectrum curve is searched within the angle range of θ∈(0,180], and the abscissa θ of the peak position is taken as the angle value of the wave arrival direction to locate the navigation interference source.

10. A navigation interference source positioning system based on sparse array optimization, characterized in that: The system is used to implement the navigation interference source positioning method according to claim 1, comprising: A sparse array antenna data acquisition unit, used to acquire an array output vector of the sparse array antenna and an array covariance matrix of the array output vector; A denoising unit constructs and solves a first optimization model based on the array variance matrix to remove noise components in the array covariance matrix to obtain a pure covariance matrix; A virtual array de-overlapping unit is used to vectorize the pure covariance matrix to obtain a virtual array, and de-overlap the virtual array to obtain a de-overlapped virtual array; An interpolation element restoration unit is used to interpolate the hole positions of the virtual array after de-overlapping to obtain an interpolated virtual array, construct a second optimization model and solve it to restore the interpolation elements of the interpolated virtual array; A noise subspace calculation unit is used to calculate the noise subspace of the interpolated virtual array by using a quasi-orthogonal projection method, and to construct a spatial spectrum function of the interpolated virtual array based on the noise subspace; The spectrum search unit is used to construct a spatial spectrum curve corresponding to the spatial spectrum function, search the spatial spectrum curve within a set angle range, determine the angle value of the direction of arrival, and locate the navigation interference source.

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