Passive radar multi-snapshot DOA estimation method and device based on sparse convex optimization

Abstract

The invention discloses a passive radar multi-snapshot DOA estimation method and device based on sparse convex optimization. The method comprises the steps that array receiving signals corresponding to multi-snapshot original input signals are acquired; based on a compressed sensing method, converting a direction of arrival estimation problem of an original input signal into an l2, th sparse recovery convex optimization problem; the l < 2, th > sparse recovery convex optimization problem is obtained by replacing a l < 0 > norm model in the l < 2, 0 > mixed norm sparse recovery optimization problem with a hyperbolic tangent function; in the l < 2, th > sparse recovery convex optimization problem, a l < 2, th > mixed norm model for minimizing an original input signal is taken as an optimization target, and the condition that the product of a dictionary matrix and the original input signal is equal to an array receiving signal is taken as a constraint condition; iteratively solving the 12, th sparse recovery convex optimization problem to obtain an original input signal; and according to the original input signal and the dictionary matrix, a direction of arrival estimation value corresponding to the original input signal is obtained, so that the estimation precision and the estimation efficiency of the direction of arrival are improved by effectively utilizing the multi-snapshot data.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and in particular relates to a passive radar multi-snapshot DOA (Direction of Arrival) estimation method and device based on sparse convex optimization. Background Art

[0002] Passive radar target positioning and tracking is a key technology in many environments, and there are many classifications of positioning methods, including direction finding positioning, frequency-azimuth joint positioning, direct positioning, etc. Many positioning methods require DOA information, among which there are many DOA estimation methods.

[0003] Bin Hu et al. proposed a method for off-grid DOA estimation in a multipath environment based on compressed sensing. The most important step of this method is to transform the signal reception model into an EIV (error-in-variables) model, and then use the total least squares method to estimate the sparse coefficients. The grid is updated using the estimated sparse coefficients, and the updated grid and the estimated sparse coefficients are used to estimate the DOA of the multipath. Linxi Liu et al. studied the DOA estimation problem of a one-dimensional uniform linear array system when the phase error between antennas is unknown. Based on the CS (Compressed Sensing) theory, the DOA estimation problem is transformed into a sparse reconstruction problem, and a DOA estimation method that iteratively updates sparse signals and phase errors is proposed by using the sparsity of the signal in the spatial domain. Berkan Kilic et al. proposed a hardware-efficient DOA estimation based on compressed sensing.

[0004] However, the above-mentioned sparse models for DOA estimation are all for single-snapshot signals, while multi-snapshot data often have better sparse recovery and can recover DOA with higher accuracy. In addition, the signals often used in reality are also multi-snapshot signals.

[0005] In summary, there is an urgent need for a DOA estimation method for multi-fast-beat signals with high estimation efficiency and high accuracy. Summary of the invention

[0006] In order to solve the above problems existing in the prior art, the present invention provides a passive radar multi-snapshot DOA estimation method and device based on sparse convex optimization.

[0007] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0008] In a first aspect, the present invention provides a passive radar multi-snap DOA estimation method based on sparse convex optimization, the passive radar multi-snap DOA estimation method comprising:

[0009] Obtain array received signals corresponding to multiple snapshots of original input signals;

[0010] Based on the compressed sensing method, the angle of arrival estimation problem of the original input signal is transformed into l 2,th Sparse recovery convex optimization problem; the l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem is obtained; the l 2,th The sparse recovery convex optimization problem is to minimize the l of the original input signal 2,th The mixed norm model is an optimization target, and the product of the dictionary matrix and the original input signal is equal to the array received signal as a constraint condition;

[0011] Iteratively solve the l 2,th A sparse recovery convex optimization problem is solved to obtain the original input signal; and an angle of arrival estimation value corresponding to the original input signal is obtained according to the original input signal and a dictionary matrix.

[0012] Optionally, based on a compressed sensing method, the angle of arrival estimation problem of the original input signal is converted into 2,th Sparse recovery convex optimization problem, including:

[0013] Based on the compressed sensing method, the array received signal and the dictionary matrix are used to convert the angle of arrival estimation problem corresponding to the original input signal into l 2,0 Mixed norm sparse recovery optimization problem;

[0014] The approximate model is obtained by using the hyperbolic tangent function to approximate the l0 norm model;

[0015] Using the approximate model to replace the l 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem obtains the l 2,th Sparse recovery convex optimization problem.

[0016] Optionally, the hyperbolic tangent function is used to approximate the l0 norm model to obtain an approximate model, including:

[0017]

[0018] Wherein, ‖x‖0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d represents the original input signal of the d-th snapshot; d = 1, 2, ..., D; D represents the total number of multiple snapshots; represents the approximate model; α represents the coefficient of variation of the independent variable, α>0.

[0019] Optionally, the l2,th The mixed norm model is:

[0020]

[0021] Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; x rowm represents the original input signal of multiple snapshots corresponding to the m-th array element, m=1, 2, ..., M, and M represents the total number of array elements.

[0022] Optionally, the l 2,th The sparse recovery convex optimization problem is:

[0023]

[0024] Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; A represents the dictionary matrix; X represents the original input signal; Y represents the array received signal; represents an r×n real number matrix; n represents the number of columns of the real number matrix; r represents the number of rows of the real number matrix.

[0025] In a second aspect, the present invention provides a passive radar multi-snap DOA estimation device based on sparse convex optimization, the passive radar multi-snap DOA estimation device comprising:

[0026] An array receiving signal acquisition module is used to acquire an array receiving signal corresponding to a multi-snap original input signal;

[0027] The problem conversion module is used to convert the angle of arrival estimation problem of the original input signal into an 2,th Sparse recovery convex optimization problem; the l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem is obtained; the l 2,th The sparse recovery convex optimization problem is to minimize the l of the original input signal 2,th The mixed norm model is an optimization target, and the product of the dictionary matrix and the original input signal is equal to the array received signal as a constraint condition;

[0028] Problem solving module, used to iteratively solve the l 2,th A sparse recovery convex optimization problem is solved to obtain the original input signal; and an angle of arrival estimation value corresponding to the original input signal is obtained according to the original input signal and a dictionary matrix.

[0029] Optionally, the problem conversion module is specifically used to:

[0030] Based on the compressed sensing method, the array received signal and the dictionary matrix are used to convert the angle of arrival estimation problem corresponding to the original input signal into l 2,0 Mixed norm sparse recovery optimization problem; using the hyperbolic tangent function to approximate the l0 norm model to obtain an approximate model; using the approximate model to replace the l 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem obtains the l 2,th Sparse recovery convex optimization problem.

[0031] Optionally, in the problem conversion module, the approximate model is obtained by using a hyperbolic tangent function to approximate the l0 norm model, including:

[0032]

[0033] Wherein, ||X||0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d represents the original input signal of the d-th snapshot; d = 1, 2, ..., D; D represents the total number of multiple snapshots; represents the approximate model; α represents the coefficient of variation of the independent variable, α>0.

[0034] Optionally, the l 2,th The mixed norm model is:

[0035]

[0036] Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; x rowm represents the original input signal of multiple snapshots corresponding to the m-th array element, m=1, 2, ..., M, and M represents the total number of array elements.

[0037] Optionally, the l 2,th The sparse recovery convex optimization problem is:

[0038]

[0039] Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; A represents the dictionary matrix; X represents the original input signal; Y represents the array received signal; represents an r×n real number matrix; n represents the number of columns of the real number matrix; r represents the number of rows of the real number matrix.

[0040] The invention provides a multi-snapshot DOA estimation method for passive radar based on sparse convex optimization. Based on the compressed sensing method, the DOA estimation problem of the sparse original input signal can be converted into a l 2,th Sparse recovery convex optimization problem, where l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the hybrid norm sparse recovery optimization problem is obtained, which solves the problem of l 2,0 The mixed norm sparse recovery optimization problem has poor interpretability and cannot be explicitly expressed in analytical expressions. 2,th In the sparse recovery convex optimization problem, the original input signal is minimized by l 2,th The mixed norm is taken as the optimization target, and the product of the dictionary matrix and the original input signal is equal to the array received signal as the constraint condition. The original input signal is obtained by iterative solution, and then the angle of arrival estimation value corresponding to the original input signal is obtained. This can effectively utilize multi-snapshot data and improve the accuracy and estimation efficiency of the angle of arrival estimation value corresponding to the original input signal.

[0041] The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flowchart of a passive radar multi-snapshot DOA estimation method based on sparse convex optimization provided by an embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of a passive radar scenario provided by an embodiment of the present invention;

[0044] Figure 3 is a schematic diagram of a hyperbolic tangent function provided by an embodiment of the present invention;

[0045] Figure 4 is the antenna pattern of a single array element;

[0046] Figure 5 This is an effect diagram of applying the passive radar multi-snapshot DOA estimation method provided by an embodiment of the present invention;

[0047] Figure 6 This is another effect diagram of applying the passive radar multi-snapshot DOA estimation method provided by an embodiment of the present invention;

[0048] Figure 7 1 is a comparison diagram of estimation errors between the passive radar multi-snapshot DOA estimation method provided by an embodiment of the present invention and the existing method;

[0049] Figure 8 It is a structural schematic diagram of a passive radar multi-quick shot DOA estimation device based on sparse convex optimization provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0051] In order to solve the problem that the existing DOA estimation method is often a DOA estimation method for a single snapshot signal, and the DOA estimation efficiency and accuracy are low, the embodiment of the present invention provides a passive radar multi-snapshot DOA estimation method based on sparse convex optimization, see Figure 1 , Figure 1 : is a flow chart of a passive radar multi-snapshot DOA estimation method based on sparse convex optimization provided by an embodiment of the present invention, which specifically includes the following steps:

[0052] Step S101, obtaining array received signals corresponding to multiple snapshot original input signals.

[0053] See also Figure 2 , Figure 2 Schematic diagram of passive radar scene provided by an embodiment of the present invention, first determine the signal receiving station, that is, the relevant parameters of the receiving array, the radiation source and the target. The path from the radiation source to the receiving array is a direct path.

[0054] Specifically, the relevant parameters of the signal receiving station may include the position, sampling frequency, and initial phase of the signal receiving station. The relevant parameters of the radiation source may include the position, transmission frequency, initial phase, and power of the radiation source. The relevant parameters of the target may include the radar irradiation area and position of the target. The target may be an aircraft, a ship, a vehicle, or a terrain.

[0055] Modeling of received signals based on electromagnetic environment and antenna characteristics:

[0056]

[0057] Among them, y m represents the signal received by the mth array element in the radar; k = 0, 1, ..., K-1, K represents the total number of targets; f0 represents the transmission frequency of the signal; τ m,k represents the delay of the kth target received by the mth array element; X k represents the direct wave signal of the kth target; z m (d) represents the noise of the mth array element in the dth snapshot; M represents the total number of array elements.

[0058] In actual array signal processing, it is basically a multi-snap situation, so the array receiving signal expression corresponding to the original input signal is:

[0059] Y = A(θ)X + Z;

[0060] The array receiving signal is Y = [y(t1), y(t2), ..., y(t D )] T , the received signal at the dth moment is y(t d ) represents; the incident signal matrix is ​​X = [x(t1), x(t2), ..., x(t D )] T , the incident signal at the dth moment is x(t d ) represents; the noise signal matrix is ​​Z = [z(t1), z(t2), …, z(t D )] T , the noise signal at the dth moment is z(t d ) represents; where d = 1, 2, ..., D; D represents the total number of multiple snapshots, that is, the total number of multiple samplings; the superscript T represents the transpose of the matrix. A(θ) is the array steering vector, which is also the dictionary matrix of the array receiving signal.

[0061] Step S102: Based on the compressed sensing method, the angle of arrival estimation problem of the original input signal is converted into 2,th Sparse recovery convex optimization problem; l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem is obtained; l 2,th In the sparse recovery convex optimization problem, the original input signal is minimized by l 2,th The mixed norm model is taken as the optimization objective, and the product of the dictionary matrix and the original input signal is equal to the array received signal as the constraint.

[0062] The problem of estimating the angle of arrival of the original input signal refers to estimating the angle of arrival of the original input signal using the array received signal. Compressed sensing method, also known as compressed sampling method or sparse sampling method, is a method that uses the sparsity of the signal to restore the signal through a small amount of unstructured measurements.

[0063] In the embodiment of the present invention, the array received signal expression is a compressed sensing theoretical formula, wherein the array received signal is sparse, that is, the number of non-zero elements in the array received signal is much smaller than the number of all elements, so the array received signal and the dictionary model A(θ) are models that satisfy sparse recovery, so the problem of wave angle estimation can be converted into l 2,th Sparse recovery convex optimization problem.

[0064] In the embodiment of the present invention, 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem is obtained. 2,0The mixed norm sparse recovery optimization problem has the NP-hard (Nondeterministic Polynomial time) property, so it cannot be solved by expression in actual use. In the embodiment of the present invention, the hyperbolic tangent function is used instead of l 2,0 The l0-norm model in the mixed-norm sparse recovery optimization problem solves this problem.

[0065] Based on this, the problem of estimating the angle of arrival of the original input signal is transformed into 2,th Sparse recovery convex optimization problem. Among them, l 2,th In the sparse recovery convex optimization problem, the original input signal is minimized by l 2,th The mixed norm model is taken as the optimization objective, and the product of the dictionary matrix and the original input signal is equal to the array received signal as the constraint.

[0066] Step S103, iteratively solve l 2,th The sparse recovery convex optimization problem is solved to obtain the original input signal; and the arrival angle estimation value corresponding to the original input signal is obtained according to the original input signal and the dictionary matrix.

[0067] In order to minimize the original input signal l 2,th The mixed norm model is used as the optimization target. The array receiving signal is continuously estimated through the original input signal and the dictionary matrix. That is, the product of the dictionary matrix and the original input signal is equal to the array receiving signal as the constraint condition. 2,th Sparse recovery convex optimization problem until the number of iterations is equal to the preset number or l 2,th When the sparse recovery convex optimization problem converges, the original input signal is obtained. On the basis of the original input signal, the arrival angle estimation value corresponding to the original input signal can be obtained by using the dictionary matrix.

[0068] In the embodiment of the present invention, based on the compressed sensing method, the problem of estimating the angle of arrival of the sparse original input signal can be transformed into 2,th Sparse recovery convex optimization problem, where l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the hybrid norm sparse recovery optimization problem is obtained, which solves the problem of l 2,0 The mixed norm sparse recovery optimization problem has poor interpretability and cannot be explicitly expressed in analytical expressions. 2,th In the sparse recovery convex optimization problem, the original input signal is minimized by l 2,thThe mixed norm model is used as the optimization target, and the product of the dictionary matrix and the original input signal is equal to the array received signal as the constraint condition. The original input signal is obtained by iterative solution, and then the angle of arrival estimation value corresponding to the original input signal is obtained. This can effectively utilize multi-snapshot data and improve the accuracy and estimation efficiency of the angle of arrival estimation value corresponding to the original input signal.

[0069] In one implementation, based on the compressed sensing method, the angle of arrival estimation problem of the original input signal is transformed into 2,th Sparse recovery convex optimization problem, including:

[0070] Based on the compressed sensing method, the angle of arrival estimation problem corresponding to the original input signal is transformed into l 2,0 Mixed norm sparse recovery optimization problem;

[0071] The approximate model is obtained by using the hyperbolic tangent function to approximate the l0 norm model;

[0072] Using an approximate model to replace l 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem is obtained. 2,th Sparse recovery convex optimization problem.

[0073] Firstly, based on the compressed sensing method, the angle of arrival estimation problem corresponding to the original input signal is transformed into l 2,0 The mixed norm sparse recovery optimization problem is illustrated.

[0074] In the embodiment of the present invention, the l2 norm model is defined as:

[0075]

[0076] Among them, ||X||2 represents the l2 norm of X, X represents the original input signal; x d Represents the original input signal of the d-th snapshot; d = 1, 2, ..., D; D represents the total number of multiple snapshots.

[0077] In the embodiment of the present invention, the matrix l of the original input signal 2,0 The mixed norm model is:

[0078] ||X|| 2，0 =‖[‖X row1 ||2;||X row2 ||2...;||X rowM ||2]||0;

[0079] Among them, ||X|| 2，0 l represents the original input signal X 2,0Mixed norm model; the original input signal of the m-th array element is represented by X rowm Indicates that m=1,2,...,M.

[0080] In one implementation, the hyperbolic tangent function is used to approximate the l0 norm model to obtain an approximate model, including:

[0081]

[0082] Among them, ||X||0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d represents the original input signal of the d-th snapshot; d = 1, 2, ..., D; D represents the total number of multiple snapshots; Represents the approximate model; α represents the coefficient of variation of the independent variable, α>0.

[0083] See also Figure 3 , Figure 3 is a schematic diagram of a hyperbolic tangent function provided in an embodiment of the present invention. Figure 3 The hyperbolic tangent function curves under different values ​​of α are given in , and the specific values ​​of α are α=1, α=2, α=10, α=20 and α=50. Figure 3 It can be seen that the larger the value of α is, the closer it is to the function of the l0 norm.

[0084] In the embodiment of the present invention, after obtaining the approximate model, the approximate model is used to replace l 2,0 The l0 norm model of the mixed norm model, we get l 2,th Mixed norm model, that is:

[0085]

[0086] Among them, ||X|| 2，0 l represents the original input signal X 2,0 Mixed norm model; ||X|| 2,th l represents the original input signal 2,th Mixed norm model; x rowm represents the original input signal of multiple snapshots corresponding to the m-th array element, m=1, 2, ..., M, and M represents the total number of array elements.

[0087] Therefore, in l 2,th In the sparse recovery convex optimization problem, l 2,th The mixed norm model is:

[0088]

[0089] In getting l 2,th Based on the mixed norm model, l 2,thThe sparse recovery convex optimization problem is:

[0090]

[0091] Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; A represents the dictionary matrix, i.e. A(θ); X represents the original input signal; Y represents the array received signal; represents an r×n real number matrix; n represents the number of columns of the real number matrix; r represents the number of rows of the real number matrix.

[0092] In an embodiment of the present invention, Among them, ||X|| g,h l represents the original input signal g,h Mixed norm model, g and h are any positive integers, ||X|| 2,th The 2 in the equation corresponds to g, and th indirectly corresponds to h. The number of rows in the matrix representing the element of the original input signal, The number of columns in the matrix representing the element of the original input signal, N represents the total number of rows in the matrix, and S represents the total number of columns in the matrix.

[0093] In the embodiment of the present invention, 2,th The input of the sparse recovery convex optimization algorithm is the array received signal Y, the dictionary matrix A and the sparsity U of the array received signal, and the output is the estimated value of the original input signal X. In the algorithm, X can be used * express.

[0094] In the iterative solution 2,th When solving sparse recovery convex optimization problems, initialize the number of iterations c = 1 and set V1 = I n , I n represents the n-order identity matrix. In the c-th iteration: Step 1, update the original input signal Step 2, use renew The main diagonal elements of ; Step 3, in the process of iterative solution, when the number of iterations c>U or convergence, the iteration is stopped, and finally the original input signal is obtained, and then the arrival angle estimation value corresponding to the original input signal is calculated based on the original input signal and the dictionary matrix.

[0095] The simulation experiment of applying the passive radar multi-snapshot DOA estimation method based on sparse convex optimization provided by the embodiment of the present invention is as follows. The radiation source used in the simulation experiment is the digital television signal DVB-T standard, whose carrier frequency is 522MHZ and signal bandwidth is 100kHZ. The parameters set in the simulation experiment are shown in Table 1:

[0096] Table 1

[0097]

[0098] The one-dimensional uniform linear array is used in this simulation experiment. Figure 4 , Figure 4 is the antenna pattern of a single array element, through Figure 4 It can be seen that the gains within the 60° angle space are similar.

[0099] An effect diagram of the passive radar multi-snapshot DOA estimation method provided by the embodiment of the present invention is shown in FIG. Figure 5 , wherein the horizontal axis represents angle (angle), and the vertical axis represents target (target). 2,th The angle of arrival estimation value corresponding to the original input signal solved by the sparse recovery convex optimization problem is highly consistent with the true DOA angle of arrival real value. Therefore, the passive radar multi-snapshot DOA estimation method provided by the embodiment of the present invention can achieve high-precision angle of arrival estimation.

[0100] See also Figure 6 , Figure 6 This is another effect diagram of the passive radar multi-snapshot DOA estimation method provided by the embodiment of the present invention, wherein the horizontal axis represents angle and the vertical axis represents target. Assuming that the DOA of the target is [10°, 20°, 30°], 1024 snapshots are used, and the signal-to-noise ratio is 10dB. It can be seen from the result diagram that the method provided by the present invention can correctly estimate the target DOA.

[0101] See also Figure 7 , Figure 7 : is a comparison diagram of the estimation errors of the passive radar multi-snapshot DOA estimation method provided by the embodiment of the present invention and the existing method, wherein the horizontal axis represents SNR (signal-to-noise ratio), in dB, and the vertical axis represents RMSE (root mean square error). Under the condition of signal-to-noise ratio [-30dB, 0dB], it can be seen that the angle measurement error of the method provided by the embodiment of the present invention is less than that of the method based on l 2,0 norm optimization method, and is better than the l which can also be convexly optimized 2,1 Norm optimization method.

[0102] Based on the same inventive concept, the embodiment of the present invention also provides a passive radar multi-snapshot DOA estimation device based on sparse convex optimization, see Figure 8 , Figure 8 1 is a schematic diagram of a passive radar multi-snap DOA estimation device based on sparse convex optimization provided by an embodiment of the present invention, wherein the passive radar multi-snap DOA estimation device comprises:

[0103] An array received signal acquisition module 801 is used to acquire an array received signal corresponding to a multi-snap original input signal;

[0104] The problem conversion module 802 is used to convert the angle of arrival estimation problem of the original input signal into the problem of estimating the angle of arrival of the original input signal based on the compressed sensing method. 2,th Sparse recovery convex optimization problem; l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem is obtained; l 2,th In the sparse recovery convex optimization problem, the original input signal l is minimized. 2,th The mixed norm model is the optimization objective, and the product of the dictionary matrix and the original input signal is equal to the array received signal as the constraint;

[0105] Problem solving module 803, used for iteratively solving l 2,th The sparse recovery convex optimization problem is solved to obtain the original input signal; and the arrival angle estimation value corresponding to the original input signal is obtained according to the original input signal and the dictionary matrix.

[0106] In the embodiment of the present invention, based on the compressed sensing method, the problem of estimating the angle of arrival of the sparse original input signal can be transformed into 2,th Sparse recovery convex optimization problem, where l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the hybrid norm sparse recovery optimization problem is obtained, which solves the problem of l 2,0 The mixed norm sparse recovery optimization problem has poor interpretability and cannot be explicitly expressed in analytical expressions. 2,th In the sparse recovery convex optimization problem, the original input signal l is minimized. 2,th The mixed norm model is used as the optimization target, and the product of the dictionary matrix and the original input signal is equal to the array received signal as the constraint condition. The original input signal is obtained by iterative solution, and then the angle of arrival estimation value corresponding to the original input signal is obtained. This can effectively utilize multi-snapshot data and improve the accuracy and estimation efficiency of the angle of arrival estimation value corresponding to the original input signal.

[0107] Optionally, the problem conversion module is specifically used to:

[0108] Based on the compressed sensing method, the sparse recovery estimation problem of the angle of arrival corresponding to the original input signal is converted into l 2,0 Mixed norm sparse recovery optimization problem; using the hyperbolic tangent function to approximate the l0 norm model to obtain an approximate model; using the approximate model to replace the l 2,0The l0 norm model in the mixed norm sparse recovery optimization problem obtains the l 2,th Sparse recovery convex optimization problem.

[0109] Optionally, in the problem conversion module, the approximate model is obtained by using a hyperbolic tangent function to approximate the l0 norm model, including:

[0110]

[0111] Wherein, ||X||0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d represents the original input signal of the d-th snapshot; d = 1, 2, ..., D; D represents the total number of multiple snapshots; represents the approximate model; α represents the coefficient of variation of the independent variable, α>0.

[0112] Optionally, the l 2,th The mixed norm model is:

[0113]

[0114] Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; x rowm represents the original input signal of multiple snapshots corresponding to the m-th array element, m=1, 2, ..., M, and M represents the total number of array elements.

[0115] Optionally, the l 2th The sparse recovery convex optimization problem is:

[0116]

[0117] Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; A represents the dictionary matrix; X represents the original input signal; Y represents the array received signal; represents an r×n real number matrix; n represents the number of columns of the real number matrix; r represents the number of rows of the real number matrix.

[0118] It should be noted that the terms "first", "second", etc. are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention.

[0119] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0120] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art can understand and implement other changes to the disclosed embodiments by viewing the drawings and the disclosed content. In the description of the present invention, the term "comprising" does not exclude other components or steps, "one" or "an" does not exclude multiple situations, and "multiple" means two or more, unless otherwise clearly and specifically limited. In addition, certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0121] As for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0122] It should be noted that the device of the embodiment of the present invention is a device that applies the above-mentioned passive radar multi-quick-shot DOA estimation method based on sparse convex optimization. All embodiments of the above-mentioned passive radar multi-quick-shot DOA estimation method based on sparse convex optimization are applicable to the device and can achieve the same or similar beneficial effects.

[0123] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A multi-snapshot DOA estimation method for passive radar based on sparse convex optimization, characterized in that: The passive radar multi-snap shot DOA estimation method comprises: Obtain array received signals corresponding to multiple snapshots of original input signals; Based on the compressed sensing method, the angle of arrival estimation problem of the original input signal is transformed into l 2,th Sparse recovery convex optimization problem; the l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem is obtained; the l 2,th The sparse recovery convex optimization problem is to minimize the l of the original input signal 2,th The mixed norm model is an optimization target, and the product of the dictionary matrix and the original input signal is equal to the array received signal as a constraint condition; Iteratively solve the l 2,th A sparse recovery convex optimization problem is solved to obtain the original input signal; and an angle of arrival estimation value corresponding to the original input signal is obtained according to the original input signal and a dictionary matrix.

2. The passive radar multi-snapshot DOA estimation method according to claim 1, characterized in that: Based on the compressed sensing method, the angle of arrival estimation problem of the original input signal is transformed into l 2,th Sparse recovery convex optimization problem, including: Based on the compressed sensing method, the array received signal and the dictionary matrix are used to convert the angle of arrival estimation problem corresponding to the original input signal into l 2,0 Mixed norm sparse recovery optimization problem; The approximate model is obtained by using the hyperbolic tangent function to approximate the l0 norm model; Using the approximate model to replace the l 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem obtains the l 2,th Sparse recovery convex optimization problem.

3. The passive radar multi-snapshot DOA estimation method according to claim 2, characterized in that: The hyperbolic tangent function is used to approximate the l0 norm model to obtain an approximate model, including: Wherein, ||X||0 represents the l0 norm model of the original input signal; tanhα represents the hyperbolic tangent function; x d represents the original input signal of the d-th snapshot; d = 1, 2, ..., D; D represents the total number of multiple snapshots; represents the approximate model; α represents the coefficient of variation of the independent variable, α>

0.

4. The passive radar multi-snapshot DOA estimation method according to claim 3, characterized in that: The l 2,th The mixed norm model is: Among them, ‖X‖ 2,th represents the original input signal l 2,th Mixed norm model; x rowm represents the original input signal of multiple snapshots corresponding to the m-th array element, m=1, 2, ..., M, and M represents the total number of array elements.

5. The passive radar multi-snapshot DOA estimation method according to claim 1, characterized in that: The l 2,th The sparse recovery convex optimization problem is: Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; A represents the dictionary matrix; X represents the original input signal; Y represents the array received signal; represents an r×n real number domain matrix; n represents the number of columns of the real number domain matrix; r represents the number of rows of the real number domain matrix.

6. A passive radar multi-snapshot DOA estimation device based on sparse convex optimization, characterized in that: The passive radar multi-fast shot DOA estimation device comprises: An array receiving signal acquisition module is used to acquire an array receiving signal corresponding to a multi-snap original input signal; The problem conversion module is used to convert the angle of arrival estimation problem of the original input signal into an 2,th Sparse recovery convex optimization problem; the l 2,th The sparse recovery convex optimization problem is solved by replacing l with the hyperbolic tangent function. 20 The l0 norm model in the mixed norm sparse recovery optimization problem is obtained; the l 2,th The sparse recovery convex optimization problem is to minimize the l of the original input signal 2,th The mixed norm model is an optimization target, and the product of the dictionary matrix and the original input signal is equal to the array received signal as a constraint condition; Problem solving module, used to iteratively solve the l 2,th A sparse recovery convex optimization problem is solved to obtain the original input signal; and an angle of arrival estimation value corresponding to the original input signal is obtained according to the original input signal and a dictionary matrix.

7. The passive radar multi-snapshot DOA estimation device according to claim 6, characterized in that: The problem conversion module is specifically used for: Based on the compressed sensing method, the array received signal and the dictionary matrix are used to convert the angle of arrival estimation problem corresponding to the original input signal into l 2,0 Mixed norm sparse recovery optimization problem; The hyperbolic tangent function is used to approximate the l0 norm model to obtain an approximate model; the approximate model is used to replace the l 2,0 The l0 norm model in the mixed norm sparse recovery optimization problem obtains the l 2,th Sparse recovery convex optimization problem.

8. The passive radar multi-snap DOA estimation device according to claim 7, characterized in that: In the problem conversion module, the hyperbolic tangent function is used to approximate the l0 norm model to obtain an approximate model, including: Wherein, ||X||0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d represents the original input signal of the d-th snapshot; d = 1, 2, ..., D; D represents the total number of multiple snapshots; represents the approximate model; α represents the coefficient of variation of the independent variable, α>

0.

9. The passive radar multi-snapshot DOA estimation device according to claim 6, characterized in that: The l 2th The mixed norm model is: Among them, ||X|| 2,th l represents the original input signal 2,th Mixed norm model; x rowm represents the original input signal of multiple snapshots corresponding to the m-th array element, m=1, 2, ..., M, and M represents the total number of array elements.

10. The passive radar multi-snapshot DOA estimation device according to claim 6, characterized in that: The l 2,th The sparse recovery convex optimization problem is: Among them, ||X|| 2,th represents the original input signal l 2,th Mixed norm model; A represents the dictionary matrix; X represents the original input signal; Y represents the array received signal; represents an r×n real number domain matrix; n represents the number of columns of the real number domain matrix; r represents the number of rows of the real number domain matrix.

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