Radiation source signal parameter processing method in complex physical environment

Abstract

The embodiment of the invention discloses a radiation source signal parameter processing method in a complex physical environment, relates to the technical field of signal processing, and can complete DOA (Direction of Arrival) estimation of a multi-source frequency hopping signal under the condition of data missing. The method comprises the following steps: receiving a far-field multi-source frequency hopping signal through a uniform linear array; under the condition of observation missing, a sampling matrix of a received signal is obtained through continuous sampling of a linear array, a joint characteristic quantity is obtained through analysis, estimation false points caused by data missing are eliminated through an atomic norm soft threshold model, and the obtained angle characteristic frequencies are the angle characteristic frequencies of the signal at different sampling moments. Afterwards, the estimation of the frequency hopping moment can be realized by comparing whether the angle characteristic frequency at different sampling moments changes or not, and different frequencies of the mixed signal are obtained, so that the DOA estimation result of the signal is obtained by using the joint characteristic quantity.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a method for processing radiation source signal parameters in a complex physical environment. Background Art

[0002] Frequency hopping signals have been widely used in the military field due to their inherent low interception rate and anti-interference capabilities. In electronic reconnaissance, parameter estimation of frequency hopping signals is crucial. Multiple transmitters in a frequency hopping communication network often work simultaneously and at the same frequency, which makes it difficult to estimate and sort parameters of non-cooperative parties. In particular, there are a large number of non-line-of-sight transmissions and multipath interference in buildings and blocks in cities, resulting in the lack of information obtained by non-cooperative sensor networks. Therefore, the extraction of frequency hopping signal parameters in urban environments is more challenging. In addition, as densely populated areas, cities have a large number of electromagnetic spectrum activities, which bring strong electromagnetic interference to sensor equipment, further strengthening the degree of information loss of non-cooperative sensor networks.

[0003] Therefore, how to use the limited and discontinuous observation data obtained by the sensor network to achieve high-precision parameter estimation and sorting and identification of frequency hopping stations in urban environments is an important problem that needs to be solved in non-cooperative communication. Traditional parameter estimation methods mainly use techniques such as autocorrelation analysis, time-frequency analysis, and sparse reconstruction to identify and extract the parameters of frequency hopping signals. The autocorrelation method uses the periodic characteristics of the signal to estimate the frequency hopping rate and timing, but the effect is not ideal in a multi-signal environment; time-frequency analysis methods such as Wigner-Ville distribution and its improved version can provide higher time-frequency resolution, but are easily affected by cross-term interference; sparse reconstruction technology uses the sparsity of the signal for parameter estimation, which is suitable for low-speed frequency hopping signals, but performs poorly in high-speed frequency hopping scenarios; algorithms based on deep learning require a large amount of training data as input. In non-cooperative situations, a small amount of training data cannot meet the real-time requirements. At the same time, traditional methods are difficult to accurately extract signal parameters in an environment with missing data, and it is often difficult to estimate the signal parameters of the radiation source in a complex physical environment, especially the DOA (Direction of Arrival estimation) of multi-source frequency hopping signals cannot be completed in the absence of data. Summary of the invention

[0004] The embodiment of the present invention provides a method for processing radiation source signal parameters in a complex physical environment, which can complete DOA estimation of multi-source frequency hopping signals in the absence of data.

[0005] To achieve the above object, the embodiments of the present invention adopt the following technical solutions:

[0006] A method for processing radiation source signal parameters in complex physical environments, such as Fig.14 As shown, including:

[0007] S1. Obtaining an initial frequency hopping signal using an array signal receiving model;

[0008] S2, preprocessing the initial frequency hopping signal through an atomic norm soft threshold model;

[0009] S3, generating a joint feature quantity according to the preprocessed frequency hopping signal;

[0010] S4. Obtain the DOA estimation result of the signal using the joint feature quantity.

[0011] In complex environments, signals received by non-cooperative parties are often affected by electromagnetic interference and non-line-of-sight transmission, which usually results in partial missing observations of the receiving end signal. In this embodiment, in view of the characteristics of the missing signal, an array signal receiving model for complex electromagnetic environments is established in S1: x k (t) represents the kth frequency hopping signal, t represents the time parameter, K represents the number of frequency hopping signals, q represents the number of network stations, and f k,p represents the frequency of the pth frequency hopping point of the kth transmitter, p represents the frequency hopping point, A k To represent the signal amplitude of the transmitter, T k Indicates the frequency hopping period of the transmitter, represents the normalized boxcar function, when hour is 1, when hour is 0; j represents an imaginary number. An isotropic uniform linear array (i.e., linear array antenna) is used for signal reception, wherein the linear array has a total of M array elements, the array element spacing is d, and d<c / 2f max , c represents the speed of light, f max is the highest frequency.

[0012] Further, the initial frequency hopping signal is sampled to obtain an angular frequency characteristic quantity, wherein the angular frequency characteristic quantity of the kth transmitter at the nth moment is: θ k represents the incident angle of the kth frequency hopping signal and θ k ∈[-π / 2,π / 2], δ represents the sampling interval, f k,n is the instantaneous frequency of the kth transmitter at the nth moment;

[0013] f sis the sampling frequency of the array, spatial-sampling means spatial sampling, and time-sampling means time sampling;

[0014] Using angular frequency characteristics to establish a practical observation space-time matrix model Y(n) represents the signal received by the array antenna, A(n) represents the sampling matrix of the array antenna at the nth sampling, S(n) represents the matrix composed of the frequency hopping signal, represents the missing matrix, y N,M Indicates the signal information received by the Mth array element of the antenna at the Nth sampling time;

[0015] in, The mth array is subject to strong electromagnetic interference at time n. o and o' represent the independent variables of two Dirac functions respectively, n' represents a time different from n, and m' represents an array different from m.

[0016] The process of establishing the actual observation space-time matrix model using the angular frequency feature quantity includes:

[0017]

[0018] Among them, the array popularity matrix of the angular frequency feature is expressed as:

[0019] ω(n) represents Gaussian noise, L represents the length of the popular matrix, s K-1 (n) represents the signal transmitted by the Kth transmitter.

[0020] Specifically, in S2, it includes: establishing an atomic norm soft threshold model:

[0021] Among them, v is an intermediate variable, x represents the atomic set without missing observations and noise interference, u represents..., τ represents..., x Φ represents the sparse feature set of signal atoms under certain observations, represents the missing matrix, y Φ Indicates the actual received signal, y Φ =x Φ +w(n), w(n) represents Gaussian noise, w = 2e0, e0 is a vector and satisfies e0 = [1, 0, 0, ..., 0], T(u) represents a sparse feature matrix and represents a complex number set, M represents the array element length, and H represents the conjugate transpose of the matrix.

[0022] During the preprocessing process, the SDP problem of AST is converted into an asymmetric quadratic programming form: Represents μ φ The range of μ φ , μ represent the intermediate parameter 1 and intermediate parameter 2 in the calculation process respectively;

[0023] The atomic norm soft threshold model outputs the value of u and x Φ As a result of preprocessing.

[0024] In S3, the generated joint feature quantity is frequency-estimation means frequency estimation, and DOA-estimation means angle estimation.

[0025] In S4, it includes: performing MUSIC spatial spectrum estimation on the joint feature quantity at the estimation time, wherein the joint feature quantity at the estimation time is: Searching for the spatial spectrum peak and obtaining the DOA estimation result of the signal. The MUSIC spatial spectrum estimation includes: r(θ) represents an angle, and θ represents a direction vector about θ.

[0026] The method for processing radiation source signal parameters in a complex physical environment provided by an embodiment of the present invention receives a far-field multi-source frequency hopping signal through a uniform linear array. In the case of missing observations, the sampling matrix of the received signal obtained by continuous sampling of the linear array is analyzed to obtain a joint feature quantity, and the estimated pseudo-points caused by missing data are eliminated through the atomic norm soft threshold model, and the obtained angle characteristic frequency of the signal at different sampling times is obtained. Afterwards, by comparing whether the angle characteristic frequency changes at different sampling times, the frequency hopping time can be estimated, and different frequencies of the mixed signal can be obtained, so as to obtain the DOA estimation result of the signal using the joint feature quantity. The DOA estimation of multi-source frequency hopping signals is achieved in the case of missing data. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0028] Figure 1 A schematic diagram of the accuracy of frequency hopping time estimation without missing data provided by an embodiment of the present invention;

[0029] Figure 2A schematic diagram of the frequency hopping time estimation accuracy result under 20% data loss provided by an embodiment of the present invention;

[0030] Figure 3 A schematic diagram of the root mean square error of instantaneous frequency estimation without data loss provided by an embodiment of the present invention;

[0031] Figure 4 A schematic diagram of the root mean square error of instantaneous frequency estimation under 20% data loss provided by an embodiment of the present invention;

[0032] Figure 5 A schematic diagram of the root mean square error of DOA estimation without data loss provided by an embodiment of the present invention;

[0033] Figure 6 A schematic diagram of the root mean square error of DOA estimation under 20% data loss provided by an embodiment of the present invention;

[0034] Figure 7 A flow chart of JFV signal parameter estimation provided by an embodiment of the present invention;

[0035] Figure 8 A spectrum diagram of multiple radiation sources provided by an embodiment of the present invention;

[0036] Fig. 9 A schematic diagram of array input for estimating transition timing provided by an embodiment of the present invention;

[0037] Fig.10 A schematic diagram of JFV estimation results before and after the jump time provided by an embodiment of the present invention;

[0038] Fig.11 A schematic diagram of array input during instantaneous frequency estimation provided by an embodiment of the present invention;

[0039] Fig.12 A schematic diagram of instantaneous frequency estimation results provided by an embodiment of the present invention;

[0040] Fig.13 A schematic diagram of DOA estimation results provided by an embodiment of the present invention;

[0041] Fig.14 A schematic diagram of a method flow chart provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention will be described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention. It can be understood by those skilled in the art that, unless specifically stated, the singular forms "one", "one", "said" and "the" used herein may also include plural forms. It should be further understood that the term "including" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their groups. It should be understood that when we say that an element is "connected" or "coupled" to another element, it can be directly connected or coupled to other elements, or there may also be intermediate elements. In addition, the "connection" or "coupling" used here may include wireless connection or coupling. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as generally understood by those of ordinary skill in the art to which the present invention belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0043] An embodiment of the present invention provides a method for processing radiation source signal parameters in a complex physical environment, including:

[0044] 1. Construct an array signal receiving model for complex electromagnetic environments:

[0045] Specifically, due to the complex environment, the signals received by non-cooperative parties are often affected by electromagnetic interference and non-line-of-sight transmission, which usually leads to the loss of some observations of the receiving end signals. According to the characteristics of the missing signals, an array data observation model is proposed: Assuming that there are K frequency-hopping transmitter signals from q network stations, the kth signal can be x k (t) can be expressed as: Among them, f k,p The frequency of the pth frequency hopping point of the kth transmitter; A k is the signal amplitude of the transmitter; T k is the frequency hopping period of the transmitter; is the normalized boxcar function, is 1, is 0. Considering the actual deployment and computational complexity, we use an isotropic uniform linear array for signal reception. The linear array has M array elements, and the element spacing is d, satisfying d < c / 2f max , where c is the speed of light and f max is the highest frequency.

[0046] Assume that during the actual observation process, K signals received simultaneously satisfy K < M. Without considering the influence between antennas of the uniform linear array, we use θ k (θ k ∈[-π / 2,π / 2]) to represent the incident angle of the k-th frequency-hopping signal. On this basis, we define the basis containing signal characteristics in spatial or temporal sampling as the angular frequency characteristic quantity of the signal. If the sampling interval in the sampling process is represented as δ, then at the n-th moment, the angular frequency characteristic quantity of the k-th transmitter can be expressed as: where f k,n is the instantaneous frequency of the k-th transmitter at the n-th moment. f s is the sampling frequency of the array. Spatial sampling represents the sampling of signals by different array elements at the same moment; temporal sampling represents the sampling of signals by the same array element at different sampling moments. The array manifold matrix of the angular frequency characteristic quantity can be written as: Considering the additive white Gaussian noise ω(n) environment, the signal Y(n) received by the array antenna can be expressed as:

[0047]

[0048] s(n) = {x k.i}}, k ∈ (0, K), i ∈ (0, I)

[0049] In the formula, A(n) is the sampling matrix of the array at the n-th sampling. S(n) is the matrix composed of frequency-hopping signals. During the actual reception process, due to the influence of the complex environment, the observed data usually has missing values. Considering the particularity of the urban environment, non-line-of-sight transmission and multipath effects usually cause the sampling data of some antenna array elements to flicker, and strong electromagnetic interference will cause the data of several sampling moments to be missing. This embodiment designs a missing matrix φ for the above typical scenarios as shown in the following formula:

[0050]

[0051]

[0052] The row vectors in the missing matrix represent different sampling moments, and the column vectors represent different antenna array elements. The elements of the missing matrix in formula (7) can be represented by the Dirac function as shown, When the mth array is subjected to strong electromagnetic interference at time n, the collected data is lost or unavailable. Considering the above data loss, the actual observation space-time matrix is:

[0053] 2. Constructing an atomic norm soft threshold model under data loss:

[0054] Traditional methods cannot solve the parameter estimation problem in data-missing scenarios. The atomic norm has excellent processing capabilities for incomplete data and can meet the signal processing needs in data-missing scenarios. Therefore, the atomic norm soft threshold method is introduced for sparse data processing.

[0055] For the atomic norm problem under missing data, the following formula can be used:

[0056]

[0057] Among them, there are Where x represents the atomic set without missing observations and noise interference, x Φ Represents a sparse feature set of signal atoms that exist under certain observation conditions. Φ =x Φ +w(n) represents the actual received signal. v is an intermediate variable; w(n) represents Gaussian noise, w = 2e0, where e0 is a vector satisfying e0 = [1, 0, 0, ..., 0]; is a sparse feature matrix, is the first column in the T(u) matrix.

[0058] 3. To solve the SDP (Semi-Definite Programming) problem shown in the above formula, most traditional methods use the CVX toolkit to solve it. However, the CVX toolkit has problems such as large amount of calculation and long operation time, and cannot meet the computing requirements of high real-time and large data volumes. To address the above problems, the SDP problem of AST (Atomic Norm Soft Thresholding) under missing data is reformulated as an asymmetric quadratic programming, and the Lagrangian method is used to solve it, which reduces the computational complexity and realizes the rapid solution of the AST problem. The quadratic programming form of the above SDP problem is:

[0059] Construct the Lagrangian function and its dual problem, respectively:

[0060] Solving it, we can get u and the signal sparse feature x Φ .

[0061] 4. According to the results of the above solution process, construct the joint feature quantity:

[0062] According to the above solution results, the dual polynomial coefficients can be obtained: represents Fourier transform, where amp is the amplitude adjustment factor, defined as amp = grid_size / τ, where Grid_size is the grid size, which is generally a power of 2 to ensure sufficient resolution, τ is the regularization parameter, and F-1 is the result of the inverse Fourier transform. Based on this, the feature quantity of parameter estimation can be constructed to extract parameters such as the signal jump time, instantaneous frequency, and incoming wave direction. The peak part of the dual polynomial coefficient solved by AST is defined as the angular frequency feature quantity f afv , the solved T(u) matrix is ​​used as the T matrix feature quantity, and f afv And T(u) constitute the joint feature volume JFV, which is defined as:

[0063] When performing time-frequency estimation on a signal, JFV outputs the angular frequency feature, f afv The numerical value is the time or frequency characteristic of the observed signal. When DOA estimation is performed, the output contains the signal sparse feature T(u). And it can be used for DOA calculation. By constructing a joint feature, the time, frequency, and DOA estimation problems in signal parameter estimation are combined together, which improves the data processing capability of the method.

[0064] 5. Perform parameter estimation:

[0065] When using JFV to estimate the hopping time, its value range is closely related to the angle of the incoming wave direction and the frequency band of the frequency hopping signal. Considering that the value range of the angle of the incoming wave direction is (-π / 2, π / 2), JFV can be limited to: JFV = f afv

[0066] In order to achieve high-precision estimation of the frequency hopping time, the frequency hopping is determined by setting the angular frequency characteristic change threshold ξ. In multiple frequency hopping networks, the selection of ξ is closely related to the frequency hopping frequency interval of the network. If the frequency interval set included in the frequency hopping network is B: B = {θf|Δf = f k,h -f k',h' ;

[0067] k,k'∈[1,K],h,h'∈[1,H]}

[0068] Then the threshold ξ must satisfy: ξ<min(B)*dsin(θ) / c, B represents…, f k,h represents…, f k',h'represents..., Δf represents..., k, k' represent..., h, h' represent... respectively. If the angular frequency characteristics of the n-1th and nth sampling moments are fafv,n-1 and fafv,n respectively, then when |fafv,n-1-fafv,n|>ξ, the frequency hopping moment is the nth sampling moment. According to the hopping moment estimation, the signal can be divided into multiple steady-state segments. By calculating the angular frequency characteristics within the limited steady-state segment, the normalized instantaneous frequency of the steady-state segment can be obtained. By adding a frequency threshold limit, the characteristic quantity at the estimated moment can be obtained:

[0069] JFV=f afv

[0070]

[0071] fs represents the sampling frequency, and a signal segment y of length l can be obtained. n,1 ,y n,2 …y n+l-1,1 The instantaneous frequency f l As follows: l =f s *JFV, l indicates length.

[0072] In this embodiment, the joint feature value JFV is estimated using the MUSIC spatial spectrum, and the spatial spectrum is shown in the following formula: By searching for the spatial spectrum peak, the DOA estimation result of the signal can be obtained. This method can estimate the direction of the incoming wave at a specific frequency in a snapshot.

[0073] In this embodiment, by constructing a joint feature quantity, the parameter estimation problem of multi-source frequency hopping signals under 20% data missing is realized. Using the method proposed in this article, even in the case of 20% data missing, when the signal-to-noise ratio is higher than 10dB, the correct extraction of the frequency hopping signal parameters can be achieved. Even in an environment with 20% data missing, when the signal-to-noise ratio is higher than 10dB, the 32-array estimation accuracy of the frequency hopping time of the frequency hopping signal can reach more than 90%, the frequency estimation error is less than 1Mhz, and the angle error can be less than 0.5°. The corresponding experimental process and results are provided below:

[0074] The far-field multi-source frequency hopping signal is received by the uniform linear array. Considering the absence of observation, the sampling matrix of the received signal can be obtained by continuous sampling of the linear array. Considering different network stations composed of 6 transmitters, the time-frequency diagram is as follows Figure 8 As shown. The six places marked by the black solid lines are the cases where there are missing observations. We take each sampling moment as the dividing point and take the sampling signal vectors received by different array elements at the same sampling moment as the input, as follows Fig. 9As shown. The algorithm of the radiation source signal parameter processing method in a complex physical environment proposed in this embodiment of the article is used to obtain its joint characteristic quantity. And by adding a threshold limit, the estimated pseudo points caused by missing data are eliminated, and the angle characteristic frequency of the signal at different sampling times is obtained. By comparing whether the angle characteristic frequency changes at different sampling times, the frequency hopping time can be estimated.

[0075] from Fig.10 It can be seen that the solid line and the dotted line are the JFV estimation results at different times. If the peak values ​​are different, it is considered that a frequency jump has occurred at this time. By estimating the frequency hopping time, the data can be divided into multiple steady states, and the steady state signal fragments received by the same array element are used as input, such as Fig.11 , using the algorithm proposed in the article, the estimation of the joint feature quantity is realized. The instantaneous frequency of the signal can be obtained by calculating the product of the estimated value JFV and the sampling frequency fs, as shown in Fig.12 As shown. By calculation, different frequencies of the mixed signal can be obtained. The parameters of the specific frequency signal can be extracted by filtering, and the T(u) matrix after filtering can be calculated to accurately estimate the DOA, for example Fig.13 shown.

[0076] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, 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. The above is only a specific implementation method of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for processing radiation source signal parameters in a complex physical environment, characterized in that: include: S1. Obtaining an initial frequency hopping signal using an array signal receiving model; S2, preprocessing the initial frequency hopping signal through an atomic norm soft threshold model; S3, generating a joint feature quantity according to the preprocessed frequency hopping signal; S4. Obtain the DOA estimation result of the signal using the joint feature quantity.

2. The method according to claim 1, characterized in that In S1, it includes: Establish an array signal receiving model for complex electromagnetic environments: x k (t) represents the kth frequency hopping signal, t represents the time parameter, k represents the number of frequency hopping signals, q represents the number of network stations, K represents the number of signals, and f k,p represents the frequency of the pth frequency hopping point of the kth transmitter, p represents the frequency hopping point, A k To represent the signal amplitude of the transmitter, T k Indicates the frequency hopping period of the transmitter, represents the normalized boxcar function, when hour is 1, when hour is 0; j represents an imaginary number.

3. The method according to claim 1 or 2, characterized in that: An isotropic uniform linear array is used for signal reception, where the linear array has a total of M array elements, the array element spacing is d, and d<c / 2f max , c represents the speed of light, f max is the highest frequency.

4. The method according to claim 3, characterized in that Also includes: The initial frequency hopping signal is sampled to obtain an angular frequency characteristic quantity, wherein the angular frequency characteristic quantity of the kth transmitter at the nth moment is: θ k represents the incident angle of the kth frequency hopping signal and θ k ∈[-π / 2,π / 2], δ represents the sampling interval, f k,n is the instantaneous frequency of the kth transmitter at the nth moment, and afv is the abbreviation of the angular frequency characteristic; f s is the sampling frequency of the array, spatial-sampling means spatial sampling, and time-sampling means time sampling; Using angular frequency characteristics to establish a practical observation space-time matrix model Y(n) represents the signal received by the array antenna, A(n) represents the sampling matrix of the array antenna at the nth sampling, S(n) represents the matrix composed of the frequency hopping signal, φ represents the missing matrix, .× is the point multiplication operator, y N,M Indicates the signal information received by the Mth array element of the antenna at the Nth sampling time; in, The mth array is subject to strong electromagnetic interference at time n. o and o' represent the independent variables of two Dirac functions respectively, n' represents a time different from n, and m' represents an array different from m.

5. The method according to claim 4, characterized in that The process of establishing the actual observation space-time matrix model using the angular frequency feature quantity includes: Among them, the array popularity matrix of the angular frequency feature is expressed as: ω(n) represents Gaussian noise, L represents the length of the popular matrix, s K-1 (n) represents the signal transmitted by the Kth transmitter.

6. The method according to claim 4, characterized in that In S2, it includes: Build an atomic norm soft threshold model: Among them, v is an intermediate variable, x represents the atomic set without missing observations and noise interference, u represents..., τ represents..., x Φ represents the sparse feature set of signal atoms under certain observations, represents the missing matrix, y Φ Indicates the actual received signal, y Φ =x Φ +w(n), w(n) represents Gaussian noise, w = 2e0, e0 is a vector and satisfies e0 = [1, 0, 0, ..., 0], T(u) represents a sparse feature matrix and represents a complex number set, M represents the number of array elements, and H represents the conjugate transpose of the matrix. During the preprocessing process, the SDP problem of AST is converted into an asymmetric quadratic programming form: Represents μ φ The range of μ φ , μ represent the intermediate parameter 1 and intermediate parameter 2 in the calculation process respectively; The atomic norm soft threshold model outputs the value of u and x Φ As a result of preprocessing.

7. The method according to claim 6, characterized in that In S3, the generated joint feature quantity is frequency-estimation means frequency estimation, and DOA-estimation means angle estimation.

8. The method according to claim 7, characterized in that In S4, it includes: The MUSIC spatial spectrum is estimated for the joint feature at the estimation time, where the joint feature at the estimation time is: Search for the spatial spectrum peak and obtain the DOA estimation result of the signal.

9. The method according to claim 8, characterized in that The MUSIC spatial spectrum estimation includes: r(θ) represents a direction vector with respect to θ, and θ represents an angle.

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