Sparse convex optimization based passive radar multi-ping DOA estimation method and device
By transforming the DOA estimation problem into an l2,th sparse recovery convex optimization problem and using the hyperbolic tangent function to approximate the l0 norm model, the problem of low efficiency and accuracy in multi-shot signal estimation in the prior art is solved, and efficient and high-precision DOA estimation is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- XIDIAN UNIV
- Filing Date
- 2024-10-12
- Publication Date
- 2026-04-24
AI Technical Summary
Existing DOA estimation methods are mainly designed for single-shot signals, resulting in low estimation efficiency and accuracy, and making it difficult to effectively utilize the sparse recovery advantage of multi-shot signals.
The DOA estimation problem for multiple snapshots is transformed into an l2,th sparse recovery convex optimization problem. The l0 norm model is approximated using the hyperbolic tangent function, and the estimated DOA value is obtained by iteratively solving to minimize the l2,th mixed norm.
It improves the accuracy and efficiency of angle of arrival estimation for multi-snapshot signals, effectively utilizes multi-snapshot data, and solves the problems of poor interpretability and inability to express analytical expressions in the l2,0 mixed norm sparse recovery optimization problem in the prior art.
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Figure CN119179044B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radar technology, specifically relating to a passive radar multi-shot DOA (Direction of Arrival) estimation method and apparatus based on sparse convex optimization. Background Technology
[0002] Passive radar target localization and tracking is a crucial technology in many environments, and there are many classifications of localization methods, including direction-finding localization, frequency-azimuth joint localization, and direct localization. Many localization methods require DOA (Directory of Area) information, and there are numerous DOA estimation methods available.
[0003] Bin Hu et al. proposed an off-grid DOA estimation method for multipath environments based on compressed sensing. The most important step in this method is to transform the signal reception model into an EIV (error-in-variables) model, and then estimate the sparse coefficients using the total least squares method. The estimated sparse coefficients are used to update the grid, and the updated grid and the estimated sparse coefficients are used to estimate the DOA for multipath. Linxi Liu et al. studied the DOA estimation problem of a one-dimensional uniform linear array system under the condition of unknown inter-antenna phase error. Based on CS (Compressed Sensing) theory, the DOA estimation problem is transformed into a sparse reconstruction problem, and an iterative update method for DOA estimation of sparse signal and phase error is proposed by utilizing the sparsity of the signal in the spatial domain. Berkan Kilic et al. proposed a hardware-efficient DOA estimation method based on compressed sensing.
[0004] However, the sparse models for DOA estimation mentioned above are all for single-shot signals, while multi-shot data often has better sparsity recovery and can recover higher-precision DOA. In reality, the signals often used are also multi-shot signals.
[0005] In summary, there is an urgent need for a DOA estimation method that is efficient and accurate for multi-shot signals. Summary of the Invention
[0006] To address the aforementioned problems in the prior art, this invention provides a passive radar multi-shot DOA estimation method and apparatus based on sparse convex optimization.
[0007] The technical problem to be solved by this invention is achieved through the following technical solution:
[0008] In a first aspect, the present invention provides a passive radar multi-snapshot DOA estimation method based on sparse convex optimization, the passive radar multi-snapshot DOA estimation method comprising:
[0009] Acquire the array receive signal corresponding to the original input signal of multiple snapshots;
[0010] Based on compressed sensing, the angle of arrival estimation problem of the original input signal is transformed into l 2,th The 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 In the sparse recovery convex optimization problem, the goal is to minimize the l of the original input signal. 2,th The hybrid norm model is used as the optimization objective, with the constraint that the product of the dictionary matrix and the original input signal equals the array received signal.
[0011] Iteratively solve the l 2,th The sparse recovery convex optimization problem is used to obtain the original input signal; and the angle of arrival (OA) estimate corresponding to the original input signal is obtained based on the original input signal and the dictionary matrix.
[0012] Optionally, based on compressed sensing, the angle of arrival estimation problem of the original input signal is transformed into l 2,th Sparse recovery convex optimization problems include:
[0013] Based on compressed sensing, the angle-of-arrival (AOA) estimation problem corresponding to the original input signal is transformed into l using the array received signal and the dictionary matrix. 2,0 Mixture norm sparse recovery optimization problem;
[0014] An approximate model is obtained by approximating the l0 norm model using the hyperbolic tangent function;
[0015] Using the approximate model to replace l 2,0 The l0-norm model in the mixed-norm sparse recovery optimization problem yields the l... 2,th Sparse recovery convex optimization problem.
[0016] Optionally, an approximate model can be obtained by approximating the l0 norm model using the hyperbolic tangent function, including:
[0017]
[0018] Where ||x||0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d This represents the original input signal for the d-th snapshot; d = 1, 2, ..., D; D represents the total number of snapshots. The approximate model is represented by α; α represents the coefficient of change of the independent variable, and 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 Let m represent the original input signal of the multi-shot corresponding to the m-th array element, where 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 Hybrid norm model; A represents the dictionary matrix; X represents the original input signal; Y represents the array received signal; Let represent an r×n real-field matrix; n represents the number of columns in the real-field matrix; r represents the number of rows in the real-field matrix.
[0025] Secondly, the present invention provides a passive radar multi-snapshot DOA estimation device based on sparse convex optimization, the passive radar multi-snapshot DOA estimation device comprising:
[0026] The array receive signal acquisition module is used to acquire the array receive signal corresponding to the original input signal of multiple snapshots;
[0027] The problem transformation module is used to transform the angle-of-arrival estimation problem of the original input signal into a problem based on compressed sensing. 2,th The 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 In the sparse recovery convex optimization problem, the goal is to minimize the l of the original input signal. 2,th The hybrid norm model is used as the optimization objective, with the constraint that the product of the dictionary matrix and the original input signal equals the array received signal.
[0028] The problem-solving module is used to iteratively solve the problem of l. 2,th The sparse recovery convex optimization problem is used to obtain the original input signal; and the angle of arrival (OA) estimate corresponding to the original input signal is obtained based on the original input signal and the dictionary matrix.
[0029] Optionally, the problem transformation module is specifically used for:
[0030] Based on compressed sensing, the angle-of-arrival (AOA) estimation problem corresponding to the original input signal is transformed into l using the array received signal and the dictionary matrix. 2,0 The mixed norm sparse recovery optimization problem is solved; an approximate model is obtained by approximating the l0 norm model using the hyperbolic tangent function; this approximate model is then used to replace the l0 norm model. 2,0 The l0-norm model in the mixed-norm sparse recovery optimization problem yields the l... 2,th Sparse recovery convex optimization problem.
[0031] Optionally, in the problem transformation module, the approximate model is obtained by approximating the l0 norm model using the hyperbolic tangent function, including:
[0032]
[0033] Where ||X||0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d This represents the original input signal for the d-th snapshot; d = 1, 2, ..., D; D represents the total number of snapshots. The approximate model is represented by α; α represents the coefficient of change of the independent variable, and 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 Let m represent the original input signal of the multi-shot corresponding to the m-th array element, where 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 Hybrid norm model; A represents the dictionary matrix; X represents the original input signal; Y represents the array received signal; Let represent an r×n real-field matrix; n represents the number of columns in the real-field matrix; r represents the number of rows in the real-field matrix.
[0040] This invention provides a passive radar multi-shot DOA estimation method based on sparse convex optimization. Based on compressed sensing, it transforms the DOA estimation problem of sparse original input signals into a... 2,th The 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 mixed-norm sparse recovery optimization problem is obtained, which solves the problem in the existing technology. 2,0 The mixed-norm sparse recovery optimization problem suffers from poor interpretability and the inability to express it explicitly analytically. 2,th In the sparse recovery convex optimization problem, the goal is to minimize the l of the original input signal. 2,th Using the mixed norm as the optimization objective and the constraint that the product of the dictionary matrix and the original input signal equals the array received signal, the original input signal is obtained through iterative solution. Then, the angle of arrival (AHA) estimate corresponding to the original input signal is obtained. This method can effectively utilize multi-snapshot data and improve the accuracy and estimation efficiency of the AHA estimate corresponding to the original input signal.
[0041] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description
[0042] Figure 1 This is a flowchart illustrating the passive radar multi-shot DOA estimation method based on sparse convex optimization provided in an embodiment of the present invention.
[0043] Figure 2 This is a schematic diagram of a passive radar scenario provided in an embodiment of the present invention;
[0044] Figure 3 This is a schematic diagram of the hyperbolic tangent function provided in an embodiment of the present invention;
[0045] Figure 4 It is the antenna pattern of a single array element;
[0046] Figure 5 This is a rendering of the passive radar multi-shot DOA estimation method provided in the embodiments of the present invention;
[0047] Figure 6 This is another effect diagram of applying the passive radar multi-shot DOA estimation method provided in the embodiments of the present invention;
[0048] Figure 7 This is a comparison chart of the estimation errors between the passive radar multi-shot DOA estimation method provided in this embodiment of the invention and existing methods;
[0049] Figure 8 This is a schematic diagram of a passive radar multi-shot DOA estimation device based on sparse convex optimization provided in an embodiment of the present invention. Detailed Implementation
[0050] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.
[0051] To address the issues of low efficiency and low accuracy in existing DOA estimation methods, which are often designed for single-snapshot signals, this invention provides a passive radar multi-snapshot DOA estimation method based on sparse convex optimization. (See [link to relevant documentation]). Figure 1 , Figure 1 This is a flowchart illustrating the passive radar multi-shot DOA estimation method based on sparse convex optimization provided in this embodiment of the invention, which specifically includes the following steps:
[0052] Step S101: Obtain the array received signal corresponding to the original input signal of the multiple snapshots.
[0053] See Figure 2 , Figure 2 This is a schematic diagram of a passive radar scenario provided by an embodiment of the present invention. First, the relevant parameters of the signal receiving station, namely the receiving array, the radiation source, and the target, are determined. The path from the radiation source to the receiving array is a direct path.
[0054] Specifically, parameters related to the signal receiving station may include its location, sampling frequency, and initial phase. Parameters related to the radiation source may include its location, transmission frequency, initial phase, and power. Parameters related to the target may include its radar illumination area and location. The target can be an aircraft, ship, vehicle, or terrain, etc.
[0055] Modeling the received signal based on the electromagnetic environment and antenna characteristics:
[0056]
[0057] Among them, y m The signal received by the m-th element in the radar is represented by f0; k = 0, 1, ..., K-1, where K represents the total number of targets; f0 represents the signal transmission frequency; τ m,k X represents the time delay received by the m-th array element from the k-th target; k This represents the direct wave signal of the k-th target; z m (d) represents the noise of the m-th element in the d-th snapshot; M represents the total number of elements.
[0058] In practical array signal processing, it is basically a multi-shot scenario. Therefore, the expression for the array received signal corresponding to the original input signal is:
[0059] Y = A(θ)X + Z;
[0060] The array receives signals Y = [y(t1), y(t2), ..., y(t3)]. D )] T The received signal at time d is represented by y(t) d The incident signal matrix is X = [x(t1), x(t2), ..., x(t3)]. D )] T The incident signal at time d is represented by x(t) d The noise signal matrix is represented as Z = [z(t1), z(t2), ..., z(t)]. D )] T The noise signal at time d is represented by z(t) d ) represents the array steering vector, which is also the dictionary matrix of the array received signals.
[0061] Step S102: 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; 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,th In the sparse recovery convex optimization problem, the goal is to minimize the l of the original input signal. 2,th The mixed norm model is used as the optimization objective, with the constraint that the product of the dictionary matrix and the original input signal equals the array received signal.
[0062] The problem of angle-of-arrival (AOA) estimation of the original input signal refers to estimating the AOA of the original input signal using the received signal from the array. Compressed sensing, also known as compressed sampling or sparse sampling, is a method that utilizes the sparsity of the signal to recover the signal using a small number of unstructured measurements.
[0063] In this embodiment of the invention, the array received signal expression is a compressed sensing theoretical formula, where the array received signal is sparse, meaning the number of non-zero elements in the array received signal is much smaller than the total number of elements. Therefore, the array received signal and the dictionary model A(θ) satisfy the sparse recovery model, thus the angle of arrival estimation problem can be transformed into l 2,th Sparse recovery convex optimization problem.
[0064] In an embodiment of the present invention, 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 for the mixed-norm sparse recovery optimization problem is obtained. 2,0The mixed-norm sparse recovery optimization problem, due to its inherent NP-hard (Nondeterministic Polynomial time) nature, cannot be analytically solved in practice. In this embodiment of the 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 l 2,th The sparse recovery convex optimization problem. Where, l 2,th In the sparse recovery convex optimization problem, the goal is to minimize the l of the original input signal. 2,th The mixed norm model is used as the optimization objective, with the constraint that the product of the dictionary matrix and the original input signal equals the array received signal.
[0066] Step S103, iteratively solve l 2,th The sparse recovery convex optimization problem is used to obtain the original input signal; and the estimated angle of arrival (OA) of the original input signal is obtained based on 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 objective. It iteratively estimates the array received signal using the original input signal and the dictionary matrix. Specifically, it iteratively solves for l under the constraint that the product of the dictionary matrix and the original input signal equals the array received signal. 2,th The sparse recovery convex optimization problem continues until the number of iterations equals the preset number or l. 2,th When the sparse recovery convex optimization problem converges, the original input signal is obtained. Based on the original input signal, the estimated angle of arrival (OA) of the original input signal can be obtained by using the dictionary matrix.
[0068] In this embodiment of the invention, based on the compressed sensing method, the problem of estimating the angle of arrival of sparse original input signals can be transformed into l 2,th The 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 mixed-norm sparse recovery optimization problem is obtained, which solves the problem in the existing technology. 2,0 The mixed-norm sparse recovery optimization problem suffers from poor interpretability and the inability to express it explicitly analytically. 2,th In the sparse recovery convex optimization problem, the goal is to minimize the l of the original input signal. 2,thUsing the hybrid norm model as the optimization objective and the constraint that the product of the dictionary matrix and the original input signal equals the array received signal, the original input signal is obtained through iterative solution. Then, the angle of arrival (AHA) estimate corresponding to the original input signal is obtained. This method can effectively utilize multi-snapshot data and improve the accuracy and estimation efficiency of the AHA estimate corresponding to the original input signal.
[0069] In one implementation, based on compressed sensing, the angle of arrival estimation problem of the original input signal is transformed into l 2,th Sparse recovery convex optimization problems include:
[0070] Based on compressed sensing, the angle-of-arrival (AOA) estimation problem corresponding to the original input signal is transformed into l using the array received signal and dictionary matrix. 2,0 Mixture norm sparse recovery optimization problem;
[0071] An approximate model is obtained by approximating the l0 norm model using the hyperbolic tangent function;
[0072] Using an approximate model to replace l 2,0 The l0-norm model in the mixed-norm sparse recovery optimization problem yields l 2,th Sparse recovery convex optimization problem.
[0073] Firstly, based on compressed sensing, the problem of estimating the angle of arrival (AOA) of the original input signal is transformed into a problem using array-received signals and a dictionary matrix. 2,0 The problem of sparse recovery optimization with mixed norm is explained.
[0074] In this embodiment of the invention, the l2 norm model is defined as follows:
[0075]
[0076] Where ||X||2 represents the l2 norm of X, and X represents the original input signal; x d This represents the original input signal for the d-th snapshot; d = 1, 2, ..., D; D represents the total number of snapshots.
[0077] In this embodiment of the invention, the matrix of the original input signal is l 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 element in multiple snapshots is represented by X. rowm Let m = 1, 2, ..., M.
[0080] In one implementation, the l0-norm model is approximated using the hyperbolic tangent function, resulting in an approximate model including:
[0081]
[0082] Where ||X||0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d This represents the original input signal for the d-th snapshot; d = 1, 2, ..., D; D represents the total number of snapshots. This represents an approximate model; α represents the coefficient of variation of the independent variable, α>0.
[0083] See Figure 3 , Figure 3 This is a schematic diagram of the hyperbolic tangent function provided in an embodiment of the present invention. Figure 3 The curves of the hyperbolic tangent function for different values of α are given, specifically α = 1, α = 2, α = 10, α = 20, and α = 50. From... Figure 3 As can be seen from this, the larger the value of α, the closer it is to the function of the l0 norm.
[0084] In this embodiment of the 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 yields l 2,th Mixed norm model, i.e.:
[0085]
[0086] Among them, ||X|| 2，0 l represents the original input signal X 2,0 Mixture norm model; ||X|| 2,th l represents the original input signal 2,th Mixed norm model; x rowm Let m represent the original input signal of the multi-shot corresponding to the m-th array element, where 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] After obtaining 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 Hybrid norm model; A represents the dictionary matrix, i.e., A(θ); X represents the original input signal; Y represents the array received signal; Let represent an r×n real-field matrix; n represents the number of columns in the real-field matrix; r represents the number of rows in the real-field 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, where g and h are both arbitrary positive integers, ||X|| 2,th In this context, 2 corresponds to g, and th indirectly corresponds to h. The row number of an element in the matrix representing the original input signal. The column number of an element in the matrix representing 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 an embodiment of the present invention, l 2,th In the sparse recovery convex optimization problem algorithm, the inputs are the array received signal Y, the dictionary matrix A, and the sparsity U of the array received signal. The output is an estimate of the original input signal X, which can be expressed as X in the algorithm. * express.
[0094] In iterative solution l 2,th When solving the sparse recovery convex optimization problem, initialize the number of iterations c = 1 and let V1 = I. n I n Let represent an n-order identity matrix. In the c-th iteration: Step 1, update the original input signal. Step 2, use renew The main diagonal elements; Step 3, during the iterative solution process, when the number of iterations c>U or convergence occurs, the iteration stops, and the original input signal is finally obtained. Then, based on the original input signal and the dictionary matrix, the estimated angle of arrival corresponding to the original input signal is calculated.
[0095] The simulation experiment of the passive radar multi-shot DOA estimation method based on sparse convex optimization provided in the embodiments of the present invention is as follows. The radiation source used in the simulation experiment is the DVB-T digital television signal standard, with a carrier frequency of 522MHz and a signal bandwidth of 100kHz. The parameters set in the simulation experiment are shown in Table 1:
[0096] Table 1
[0097]
[0098] The simulation experiment uses a one-dimensional uniform linear array, see [link / reference]. Figure 4 , Figure 4 It is the antenna pattern of a single array element, through Figure 4 It can be seen that their gains are similar within a 60° angular space.
[0099] See the effect diagram of the passive radar multi-shot DOA estimation method provided in the embodiments of the present invention. Figure 5 Where the horizontal axis represents the angle and the vertical axis represents the target. Using the l-based [structure / mechanism] provided in this embodiment of the invention... 2,th The estimated angle of arrival (OA) of the original input signal used to solve the sparse recovery convex optimization problem highly overlaps with the true OA of the real DOA. Therefore, the passive radar multi-shot DOA estimation method provided in this embodiment of the invention can achieve high-precision OA estimation.
[0100] See Figure 6 , Figure 6 This is another effect diagram of the passive radar multi-snapshot DOA estimation method provided in the embodiments of the present invention, where the horizontal axis represents the angle and the vertical axis represents the target. Assuming the target's DOA is [10°, 20°, 30°], a signal with 1024 snapshots and a signal-to-noise ratio of 10dB is used. The result diagram shows that the method provided by the present invention can correctly estimate the target's DOA.
[0101] See Figure 7 , Figure 7 This is a comparison chart of the estimation errors between the passive radar multi-shot DOA estimation method provided in this embodiment of the invention and existing methods. The horizontal axis represents SNR (signal-to-noise ratio) in dB, and the vertical axis represents RMSE (root mean square error). Under SNR conditions of [-30dB, 0dB], it can be seen that the method provided in this embodiment of the invention has a smaller angle measurement error than the method based on l under low SNR conditions. 2,0 The norm optimization method is superior to the equally convex optimization method l. 2,1 Methods for norm optimization.
[0102] Based on the same inventive concept, embodiments of the present invention also provide a passive radar multi-shot DOA estimation device based on sparse convex optimization, see [link to relevant documentation]. Figure 8 , Figure 8 This is a schematic diagram of a passive radar multi-shot DOA estimation device based on sparse convex optimization provided in an embodiment of the present invention. The passive radar multi-shot DOA estimation device includes:
[0103] The array receiving signal acquisition module 801 is used to acquire the array receiving signal corresponding to the original input signal of multiple snapshots;
[0104] Problem transformation module 802 is used to transform the angle of arrival estimation problem of the original input signal into a problem based on compressed sensing. 2,th Sparse recovery convex optimization problem; 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,th In the sparse recovery convex optimization problem, the goal is to minimize the l of the original input signal. 2,th The hybrid norm model is used as the optimization objective, with the constraint that the product of the dictionary matrix and the original input signal equals the array received signal.
[0105] Problem-solving module 803 is used for iteratively solving l 2,th The sparse recovery convex optimization problem is used to obtain the original input signal; and the estimated angle of arrival (OA) of the original input signal is obtained based on the original input signal and the dictionary matrix.
[0106] In this embodiment of the invention, based on the compressed sensing method, the problem of estimating the angle of arrival of sparse original input signals can be transformed into l 2,th The 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 mixed-norm sparse recovery optimization problem is obtained, which solves the problem in the existing technology. 2,0 The mixed-norm sparse recovery optimization problem suffers from poor interpretability and the inability to express it explicitly analytically. 2,th In the sparse recovery convex optimization problem, the goal is to minimize the l of the original input signal. 2,th Using the hybrid norm model as the optimization objective and the constraint that the product of the dictionary matrix and the original input signal equals the array received signal, the original input signal is obtained through iterative solution. Then, the angle of arrival (AHA) estimate corresponding to the original input signal is obtained. This method can effectively utilize multi-snapshot data and improve the accuracy and estimation efficiency of the AHA estimate corresponding to the original input signal.
[0107] Optionally, the problem transformation module is specifically used for:
[0108] Based on compressed sensing, the sparse recovery estimation problem of the angle of arrival corresponding to the original input signal is transformed into l using the array received signal and the dictionary matrix. 2,0 The mixed norm sparse recovery optimization problem is solved; an approximate model is obtained by approximating the l0 norm model using the hyperbolic tangent function; this approximate model is then used to replace the l0 norm model. 2,0The l0-norm model in the mixed-norm sparse recovery optimization problem yields the l... 2,th Sparse recovery convex optimization problem.
[0109] Optionally, in the problem transformation module, the approximate model is obtained by approximating the l0 norm model using the hyperbolic tangent function, including:
[0110]
[0111] Where ||X||0 represents the l0 norm model of the original input signal; tanh represents the hyperbolic tangent function; x d This represents the original input signal for the d-th snapshot; d = 1, 2, ..., D; D represents the total number of snapshots. The approximate model is represented by α; α represents the coefficient of change of the independent variable, and 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 Let m represent the original input signal of the multi-shot corresponding to the m-th array element, where 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 Hybrid norm model; A represents the dictionary matrix; X represents the original input signal; Y represents the array received signal; Let represent an r×n real-field matrix; n represents the number of columns in the real-field matrix; r represents the number of rows in the real-field 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 such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders 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. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.
[0119] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.
[0120] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.
[0121] As the device embodiment is basically similar to the method embodiment, the description is relatively simple, and relevant parts can be found in the description of the method embodiment.
[0122] It should be noted that the device in this embodiment of the invention is a device that applies the above-mentioned passive radar multi-shot DOA estimation method based on sparse convex optimization. Therefore, all embodiments of the above-mentioned passive radar multi-shot DOA estimation method based on sparse convex optimization are applicable to this device and can achieve the same or similar beneficial effects.
[0123] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.
Claims
1. A passive radar multi-shot DOA estimation method based on sparse convex optimization, characterized in that, The passive radar multi-snapshot DOA estimation method includes: Acquire the array receive signal corresponding to the original input signal of multiple snapshots; Based on compressed sensing, the problem of estimating the angle of arrival of the original input signal is transformed into... The sparse recovery convex optimization problem; The sparse recovery convex optimization problem is replaced by using the hyperbolic tangent function. Mixture norm sparse recovery optimization problem The norm model is obtained; In the sparse recovery convex optimization problem, the goal is to minimize the original input signal. The hybrid norm model is used as the optimization objective, with the constraint that the product of the dictionary matrix and the original input signal equals the array received signal. Iterative solution of the above The sparse recovery convex optimization problem is used to obtain the original input signal; and the estimated angle of arrival (OA) of the original input signal is obtained based on the original input signal and the dictionary matrix. The The mixed norm model is: ； in, Represents the original input signal Mixed norm model; Indicates the first The original input signal corresponding to each array element and multiple snapshots. , Indicates the total number of array elements; Indicates the coefficient of change of the independent variable; The The sparse recovery convex optimization problem is: ； in, Represents the dictionary matrix; This represents the original input signal; This indicates that the array receives signals; express A real-field matrix; This represents the number of columns in the real number field matrix; This represents the row number of the real number field matrix; Iterative solution of the above The process of solving the sparse recovery convex optimization problem is as follows: Initialize the number of iterations ,make , express An identity matrix of order 1; In the In the next iteration: Step 1, update the current original input signal ; Step 2, use renew The main diagonal element; Step 3, when the number of iterations... Alternatively, the iteration can be stopped upon convergence to obtain the original input signal.
2. The passive radar multi-shot DOA estimation method according to claim 1, characterized in that, Based on compressed sensing, the problem of estimating the angle of arrival of the original input signal is transformed into... Sparse recovery convex optimization problems include: Based on compressed sensing, the angle-of-arrival estimation problem corresponding to the original input signal is transformed using the array received signal and the dictionary matrix. Mixture norm sparse recovery optimization problem; Approximation using the hyperbolic tangent function The norm model yields an approximate model; Using the approximate model to replace the Mixture norm sparse recovery optimization problem Norm model, to obtain the Sparse recovery convex optimization problem.
3. The passive radar multi-shot DOA estimation method according to claim 2, characterized in that, Approximation using the hyperbolic tangent function Norm models yield approximate models, including: ； in, Represents the original input signal Norm model; Represents the hyperbolic tangent function; Indicates the first The original input signal of a snapshot; ; This indicates the total number of shots. This represents the approximate model; Represents the coefficient of change of the independent variable. .
4. A passive radar multi-shot DOA estimation device based on sparse convex optimization, characterized in that, The passive radar multi-snapshot DOA estimation device includes: The array receive signal acquisition module is used to acquire the array receive signal corresponding to the original input signal of multiple snapshots; The problem transformation module is used to transform the angle of arrival estimation problem of the original input signal into a problem based on compressed sensing. The sparse recovery convex optimization problem; The sparse recovery convex optimization problem is replaced by using the hyperbolic tangent function. Mixture norm sparse recovery optimization problem The norm model is obtained; In the sparse recovery convex optimization problem, the goal is to minimize the original input signal. The hybrid norm model is used as the optimization objective, with the constraint that the product of the dictionary matrix and the original input signal equals the array received signal. The problem-solving module is used to iteratively solve the problem. The sparse recovery convex optimization problem is used to obtain the original input signal; and the estimated angle of arrival (OA) of the original input signal is obtained based on the original input signal and the dictionary matrix. The The mixed norm model is: ； in, Represents the original input signal Mixed norm model; Indicates the first The original input signal corresponding to each array element and multiple snapshots. , Indicates the total number of array elements; Indicates the coefficient of change of the independent variable; The The sparse recovery convex optimization problem is: ； in, Represents the dictionary matrix; This represents the original input signal; This indicates that the array receives signals; express A real-field matrix; This represents the number of columns in the real number field matrix; This represents the row number of the real number field matrix; Iterative solution of the above The process of solving the sparse recovery convex optimization problem is as follows: Initialize the number of iterations ,make , express An identity matrix of order 1; In the In the next iteration: Step 1, update the current original input signal ; Step 2, use renew The main diagonal element; Step 3, when the number of iterations... Alternatively, the iteration can be stopped upon convergence to obtain the original input signal.
5. The passive radar multi-shot DOA estimation device according to claim 4, characterized in that, The problem transformation module is specifically used for: Based on compressed sensing, the angle-of-arrival estimation problem corresponding to the original input signal is transformed using the array received signal and the dictionary matrix. Mixture norm sparse recovery optimization problem; Approximation using the hyperbolic tangent function The norm model yields an approximate model; the approximate model is then used to replace the original model. Mixture norm sparse recovery optimization problem Norm model, to obtain the Sparse recovery convex optimization problem.
6. The passive radar multi-shot DOA estimation device according to claim 5, characterized in that, In the problem transformation module, the hyperbolic tangent function is used for approximation. Norm models yield approximate models, including: ； in, Represents the original input signal Norm model; Represents the hyperbolic tangent function; Indicates the first The original input signal of a snapshot; ; This indicates the total number of shots. This represents the approximate model; Represents the coefficient of change of the independent variable. .