Incoherent distribution broadband source angle-frequency joint distribution estimation method based on space-time sparse sampling

Abstract

The invention belongs to the technical field of signal processing, and relates to an incoherently distributed broadband source angle-frequency joint distribution estimation method based on space-time sparse sampling, which comprises the following steps: firstly, constructing a space-time sparse sampling structure, and collecting incoherently distributed broadband source signals through the space-time sparse sampling structure; secondly, estimating a covariance of an array output signal, constructing a rank minimization problem according to the low rank characteristic of an angle-frequency joint distribution matrix contained in a covariance matrix, and solving the rank minimization problem by using nuclear norm minimization to obtain an estimator of angle-frequency joint distribution; according to the method, the problem that angle-frequency joint distribution estimation is fuzzy in space one-dimensional sampling is effectively solved through a space-time sparse sampling structure, two-dimensional space array sampling is not needed, meanwhile, the sampling rate requirements of hardware on space and time are reduced, and the hardware cost is reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to a method for estimating the angle-frequency joint distribution of an incoherently distributed broadband source based on space-time sparse sampling. Background Art

[0002] In the field of passive detection such as radar, sonar, and electronic warfare, signal direction of arrival (DOA) and frequency estimation are important research topics. However, in recent years, with the widespread application of high-frequency broadband signals, in order to collect target signals, spatial and temporal sampling must meet the Nyquist theorem, which places higher requirements on hardware. For spatial sampling, array sensors are required to be densely installed, which not only makes hardware installation difficult, but also easily leads to mutual coupling of signals between adjacent sensors. For temporal sampling, the sampling rate should be greater than or equal to twice the highest frequency of the broadband signal, which places very high requirements on the sampling rate of the A / D converter and also increases the cost of the hardware.

[0003] In recent years, sparse sampling theory has been widely used in signal detection because it reduces sampling requirements and can effectively increase the system's degree of freedom and improve the performance of parameter estimation. In order to estimate the frequency and DOA of high-frequency broadband sources, many space-time sparse sampling methods have been proposed, but they are mainly for point source signals. However, in many complex signal transmission environments, signal diffusion or multipath propagation may cause the signal to diffuse in space. At this time, it may be more appropriate to adopt a distributed broadband source signal model. According to the correlation of signals from different spatial positions, the source signal can be divided into coherent and incoherent distributed sources. Similar distributed broadband sources can also be divided into coherent and incoherent distributed broadband sources. The present invention focuses on the angle and frequency distribution estimation of incoherent distributed broadband sources.

[0004] For the parameter estimation of incoherent distributed broadband sources, several methods have been proposed, such as the maximum likelihood method, the covariance matching method, the parameter polynomial method, the novel method combining the fractional Fourier transform algorithm with the distributed source parameter estimator, and the sparse Bayesian learning (SBL) method (ref. CF, Gerstoft P, Yao H. Bayesian sparse wideband source reconstruction of Japanese 2011 earthquake [A]. In: 2011 4th IEEE International Workshop on Computational Advances in MultiSensor Adaptive Processing (CAMSAP) [C], 2011: 273–276.). However, these methods all assume that the signal frequency distribution of the distributed broadband source is known and has the same frequency range. In practical applications, different broadband signals may have different frequency ranges. In addition, these methods mainly estimate the key parameters of the distribution based on a parameterized angular distribution model, while the exact angular distribution model is often unknown in practical applications. Some scholars have also proposed a low-rank matrix recovery method, which does not require the known distribution of angles and frequencies. The angle-frequency joint distribution can be estimated by using a two-dimensional space array to receive signals, and the key parameters of the distribution can be estimated as needed; for example: a method for estimating the angle and frequency parameters of an incoherently distributed broadband source with a patent application number of CN202110552754.8, which discloses obtaining far-field incoherently distributed broadband source signals through a receiving array, estimating the covariance of the incoherently distributed broadband source signal and vectorizing it; establishing a vectorized incoherently distributed broadband source signal covariance model, and reducing the dimensionality of the directional derivative matrix and the incoherently distributed broadband source signal covariance according to the row repeatability and singularity of the directional derivative matrix in the covariance model; formulating the incoherently distributed broadband source signal covariance model as a rank minimization problem, solving the rank minimization problem, obtaining an estimate of the angle-frequency joint distribution matrix, and combining a discrete grid estimator to estimate the key parameters of the angle and frequency distribution of the incoherently distributed broadband source. This prior art can reduce the complexity of calculation, but this method will cause the problem of fuzzy joint estimation of angle and frequency when using a one-dimensional linear array.

[0005] In summary, the existing methods have the following problems: (1) Conventional methods based on one-dimensional spatial sampling assume that the frequency is known and only estimate the angle distribution. (2) Low-rank matrix recovery methods use one-dimensional linear arrays for spatial sampling, which leads to the problem of fuzzy joint estimation of angle and frequency. It is necessary to use a two-dimensional spatial array to sample and estimate the joint distribution of angle and frequency, but this method will increase the hardware cost. (3) In addition, the above methods all have the problem of difficult spatial and temporal sampling for high-frequency broadband signals. Summary of the invention

[0006] In view of the existing incoherently distributed broadband source angle and frequency estimation methods, there are problems such as difficulty in sampling high-frequency broadband signals in space and time, fuzzy joint estimation of angle and frequency in one-dimensional linear arrays, and high hardware cost of two-dimensional spatial arrays. The present invention proposes an incoherently distributed broadband source angle-frequency joint distribution estimation method based on space-time sparse sampling, which includes:

[0007] S1. Constructing a space-time sparse sampling structure; collecting incoherently distributed broadband source signals through the space-time sparse sampling structure;

[0008] S2, estimating the covariance of the array output signal obtained based on space-time sparse sampling, and vectorizing the covariance;

[0009] S3, constructing a space-time directional derivative matrix based on the vectorized covariance;

[0010] S4, constructing the rank minimization problem of angle-frequency joint distribution estimation based on the covariance of array output signals and space-time directional derivative matrix;

[0011] S5. The rank minimization problem of the angle-frequency joint distribution estimation is transformed into a nuclear norm minimization problem, and the nuclear norm minimization problem is solved to obtain an estimate of the angle-frequency joint distribution matrix.

[0012] Beneficial effects of the present invention:

[0013] The present invention combines sparse sampling of space and time to reduce the system's requirements for the sampling rate of the source signal in space and time, thereby further reducing the hardware requirements for the detection system and reducing hardware costs. In addition, the present invention combines space-time sparse sampling with low-rank matrix recovery to overcome the problem of fuzzy angle-frequency joint distribution estimation when simply using spatial one-dimensional array sampling; at the same time, the accuracy of angle-frequency joint distribution estimation is further improved due to the increased degree of freedom of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a framework diagram of the space-time sparse sampling of the present invention;

[0015] Figure 2 is a flow chart of the angle-frequency joint distribution estimation method of the present invention;

[0016] Figure 3 It is a diagram of the angle-frequency joint distribution matrix of the actual simulation of the present invention;

[0017] Figure 4 An angle-frequency joint distribution matrix diagram estimated by simulation of the present invention;

[0018] Figure 5This is a graph showing how the NMSE of the angle-frequency joint distribution estimate varies with the signal-to-noise ratio. DETAILED DESCRIPTION

[0019] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] A method for estimating the joint angle-frequency distribution of incoherently distributed broadband sources based on space-time sparse sampling, such as Figure 2 As shown, the method includes:

[0021] S1. Constructing a space-time sparse sampling structure; collecting incoherently distributed broadband source signals through the space-time sparse sampling structure;

[0022] S2, estimating the covariance of the array output signal obtained based on space-time sparse sampling, and vectorizing the covariance;

[0023] S3, constructing a space-time directional derivative matrix based on the vectorized covariance;

[0024] S4, constructing the rank minimization problem of angle-frequency joint distribution estimation based on the covariance of array output signals and space-time directional derivative matrix;

[0025] S5. The rank minimization problem of the angle-frequency joint distribution estimation is transformed into a nuclear norm minimization problem, and the nuclear norm minimization problem is solved to obtain an estimate of the angle-frequency joint distribution matrix.

[0026] In this embodiment, if Figure 1 As shown, the space-time sparse sampling structure is a two-dimensional space-time sparse sampling structure, which includes a spatial sparse linear array containing N sensors, and each sensor obtains M sparse time samples.

[0027] Specifically, the minimum spacing between adjacent sensors in the airspace is set equal to the minimum half wavelength d of the broadband signal. s The sensor location can be represented by a set in and is an ascending integer sequence. Similarly, in the time domain, the minimum sampling interval is set equal to the Nyquist sampling interval d t =1 / (2f max ), where f max The maximum frequency sampling time representing a broadband signal can be given by an ordered set as in

[0028] Assume that there are K far-field incoherently distributed broadband source signals incident on a sparse linear array. According to the space-time sparse sampling framework, the signal received by the lth sensor at the mth sampling time can be expressed as:

[0029]

[0030] Where f and Γ are the frequency and frequency range of the source signal, respectively; θ and Θ are the azimuth and angular range of the source signal propagating in space, respectively; dS k (f) is a measure of the frequency spectrum of the kth source signal; γ k (θ,t) is the complex gain of the kth source signal propagating in the angular direction; j is the imaginary unit. τ l (θ) represents the time delay of the signal from the direction of arrival (DOA) θ to the lth sensor relative to the time delay of the signal to the reference sensor (usually set as the first sensor). τ l (θ)+h m d t It constitutes the time delay of space-time sampling. k,θ It represents the complex gain of the signal from the kth source when it propagates in the θ direction. dS k (f) represents a measure of the spectrum of the kth incoherently distributed broadband source signal. lm represents additive Gaussian white noise in space-time domain. m is an element of a sparse sequence, d t is the minimum sampling interval in the time domain.

[0031] According to the two-dimensional space-time sparse sampling structure, the array output signal can be expressed as a matrix:

[0032]

[0033] in(·) T For transposition, and N∈C N×M are the output matrix and noise matrix based on space-time sparse sampling respectively; N is the noise matrix. At the same time:

[0034]

[0035] Among them, a s (θ,f) and a t (f) represent the spatial direction vector and the temporal direction vector respectively. The traditional estimation method is mainly based on spatial array sampling, and the direction vector is only the spatial direction vector a s (θ,f).

[0036] For the convenience of subsequent calculations, the output matrix X is rearranged into a vector form, and formula (2) can be transformed into:

[0037]

[0038] Among them, a st (θ,f) is the space-time direction vector. n is the vectorization of the noise matrix N.

[0039] Repeat the space-time sparse sampling to obtain B space-time snapshots. At this time, the output x(t) of the t-th snapshot (t=1,2,...,B) can be written as:

[0040]

[0041] Among them, γ k,θ (t) and n(t) represent the complex gain γ of the t-th snapshot respectively. k,θ and the noise vector n.

[0042] In this embodiment, based on space-time sparse sampling, the covariance of the incoherently distributed broadband source signal is estimated. and vectorized to According to the output signal formula (6) x(t), the covariance of the array output signal under space-time sparse sampling is obtained as:

[0043]

[0044] Among them, E(·) represents expectation; (·) H represents conjugate transpose; R s and are the covariances of the source signal and Gaussian white noise respectively; the estimator of R is is the Gaussian white noise variance, I is the unit vector, Perform eigenvalue decomposition and The estimator is set to The minimum eigenvalue of ; The covariance estimator of the incoherently distributed broadband source signal is obtained from formula (7):

[0045]

[0046] Vectorized for:

[0047]

[0048] In the formula, vec(·) means stacking the matrix column by column into a column vector. here is a plural set.

[0049] In this embodiment, based on the space-time sparse sampling signal model, the signal covariance model is derived and vectorized to construct the space-time directional derivative matrix According to formula (6) of x(t), the covariance R of the source signal can be further derived: s for:

[0050]

[0051] Where K is the number of sources, k′ is used to represent the k′th source, k represents the kth source, θ′ is the angle of arrival of the source signal, and q kk′ (θ,θ′,f,f′) is the cross-correlation kernel, where (·) * represents the complex conjugate. It is assumed that the signals from different sources are uncorrelated. At the same time, for the same source, it is assumed that the complex gain γ in different wave arrival directions k,θ (t) are uncorrelated signals of different frequencies dS k (f) is also uncorrelated. At this time, the cross-correlation kernel q kk′ (θ,θ′,f,f′) can be re-expressed as:

[0052] q kk′ (θ,θ′,f,f′)=p k (θ)p k (f)δ(θ-θ′)δ(ff′)δ kk′ dfdf′ (12)

[0053] in, represents the power distribution of the kth incoherently distributed broadband source in the spatial domain, p k (f) is the power distribution in the frequency domain. Therefore, R s Formula (10) can be simplified as:

[0054]

[0055] In the formula, equal is the angle-frequency joint distribution.

[0056] In order to simplify the subsequent integral discretization expression, formula (13) is vectorized, so formula (7) can be vectorized as follows:

[0057]

[0058] in, at the same time

[0059]

[0060] in, is the matrix A st Vectorization of (θ,f), When it is empty, the direction vector a st The conjugate of (θ,f).

[0061] To simplify the integral in the formula, the angle-frequency joint distribution Discretize the observation range Θ and Γ into uniform grids θ = {θ 1 ,θ 2 ,…,θ G} and f={f 1 ,f 2 ,…,f H}, where G and H are the corresponding discrete points. represents the discretization of p(θ,f), then:

[0062]

[0063] Where P gh represents the element of the gth row and hth column of the angle-frequency joint distribution matrix P. Here, P is the angle-frequency joint distribution to be estimated by the present invention, and the next step is to estimate P using the obtained R.

[0064] Therefore, by replacing the integral in formula (14) with the summation, r can be approximated as:

[0065]

[0066] In the formula The vectorization of matrix P is:

[0067]

[0068] Finally, according to the vectorized R model formula (14), the space-time directional derivative matrix of the space-time sparse sampling to be constructed is obtained: for:

[0069]

[0070] In this embodiment, using the estimated array output signal covariance and space-time directional derivative matrix, the rank minimization problem of constructing the angle-frequency joint distribution P estimation includes: In order to make the sum in formula (17) close to the integral, GH is usually set to be greater than (NM) 2 .therefore, is an underdetermined equation with infinite solutions. In this case, the traditional least squares method may not be able to effectively estimate P.

[0071] Fortunately, the angle-frequency joint distribution matrix P has a low rank property. Since angle and frequency are two unrelated quantities, the angle-frequency joint distribution matrix P of the estimated quantity can be expressed as where p k (θ)=[p k (θ 1 ),...,p k (θ G )] T , p k (f) = [p k (f 1 ),...,p k (f H )] T are discrete vectors of angle and frequency distribution, respectively, Since the rank of the vector is 1, we know that the matrix P k The rank of is also 1, so the rank of P is less than or equal to K; and the number of sources K is less than the number of discretizations G and H, so the angle-frequency joint distribution matrix P has a low rank property.

[0072] According to the low-rank property of the matrix P, the vectorized incoherently distributed broadband source signal covariance model formula (17) can be transformed into a rank minimization problem, thereby obtaining an estimate of P:

[0073]

[0074] Where rank(·) represents the rank function; the estimated quantity is Alternative s =rr n , problem (20) can be further regularized as:

[0075]

[0076] Among them, λ>0 is the regularization parameter.

[0077] In this embodiment, the rank minimization problem of the angle-frequency joint distribution estimation is transformed into a nuclear norm minimization problem, and the angle-frequency joint distribution is estimated using low-rank matrix recovery (LRMR). Since the low-rank minimization problem is an NP-hard problem and the rank function is non-convex and discrete, it is challenging to directly solve problem (21). In order to solve this problem, the nuclear norm is usually used as a convex relaxation of the rank function, so the convex relaxation form of the nuclear norm of problem (21) is:

[0078]

[0079] Among them, the nuclear norm σ i (P) represents the i-th singular value of the matrix P, where Q = min(G,H). in‖·‖ 2 is the 2-norm of the vector.

[0080] The nuclear norm minimization problem (22) is solved by convex optimization. In the present invention, based on the MATLAB convex optimization toolbox CVX, the nuclear norm minimization problem (22) is solved by convex set. The solution adopts the low rank matrix recovery (LRMR) algorithm, thereby recovering the low rank matrix P and obtaining the estimated value of the angle-frequency joint distribution matrix

[0081] In this embodiment, the effect of the present invention can be further illustrated by the following simulation results. The simulation experiment conditions are as follows: the angle distribution of two incoherently distributed broadband sources is set to be a uniform distribution and a Gaussian distribution, and the frequency distribution is uniform distribution. Then, the angle-frequency joint distribution is as follows:

[0082]

[0083] Among them, θ 0k and denote the center DOA and angular spread of the k-th source signal angular distribution, respectively, and f 0k and B k is the center frequency and frequency bandwidth of the broadband signal. For two sources, the key parameters for setting the angle-frequency joint distribution are (f 01 ,B 1 )=(12.5GHz,7GHz), (f 02 ,B 2 )=(5GHz,6GHz). The angle and frequency ranges are [20°,50°]×[1GHz,17GHz], and the discrete grid steps are 1° and 0.5GHz, respectively.

[0084] In order to study the performance of the STSS-LRMR method for angle-frequency joint distribution estimation using different sampling structures, the structure of STSS is set to space-time uniform sampling and coprime sampling. For fair comparison, for all sampling structures, the number of sensors in the spatial array is set to N = 21, and the number of time samples is M = 11. Specifically, for space-time coprime sampling, the space-time subarray parameters are set to N = N c1 +N c2 -1=9+13-1,M=M c1 +M c2 -1=5+7-1, where N c1 、N c2 -1 is the number of sensors in the two subarrays of the coprime array, M c1 and M c2 is the corresponding parameter of the time domain coprime array. For the space-time two-level nested sampling, the space-time subarray parameters are set to N = N n1 +N n2=9+12 and M=M n1 +M n2 =5+6, where N n1 and N n2 is the number of sensors in the two sub-arrays in the 2-level nested array, M n1 and M n2 is the corresponding parameter of the two-level nested array in the time domain. For the LRMR algorithm, the normalization parameter λ is set to 0.5. In addition, in order to illustrate that the STSS structure can effectively solve the problem of estimation ambiguity, the performance is compared with the LRMR algorithm based on spatial uniform linear array sampling.

[0085] Figure 3 and Figure 4 The true and estimated angle-frequency joint distributions are shown, respectively. Figure 4 As shown in (a), the LRMR method based on uniform linear array cannot effectively estimate the angle-frequency joint distribution. This is because the one-dimensional linear array cannot uniquely determine the DOA and frequency, which leads to estimation ambiguity. Figure 4 (b) shows that the STSS-LRMR method can estimate the angle-frequency joint distribution based on space-time uniform sampling. This shows that the proposed space-time sampling structure can effectively solve the problem of DOA and frequency joint estimation ambiguity, and verifies the effectiveness of the proposed method for angle-frequency joint distribution estimation. Figure 4 (c)–(d) show that the angle-frequency joint distribution estimated by the proposed method based on space-time coprime and nested sampling is consistent with the true distribution. This is because the sparse sampling structure has more degrees of freedom than the uniform sampling structure, thus improving the performance of parameter estimation.

[0086] This simulation experiment mainly illustrates the accuracy of the angle-frequency joint distribution estimation of the STSS-LRMR method proposed in the present invention when using different space-time sampling structures. And the performance is compared with the previous LRMR method based on two-dimensional spatial array (L-type uniform linear array) sampling and the SBL method based on space-time coprime sampling. For different estimation methods, the same number of sensors N=15 and the number of sparse time sampling M=7 are set. For the proposed STSS-LRMR method, space-time uniform sampling, coprime sampling and two-level nested sampling are used again. In coprime and nested sampling, the parameters of the spatial and temporal subarrays are set to N c1 =N n1 =11,N c2 =N n2 +1=5,M c1 =M n1 =3, and M c2 =M n2+1=5. For the LRMR method based on spatial uniform array, two spatial Nyquist sampling structures are selected, one is a uniform linear array and the other is a two-dimensional L-shaped uniform linear array. The sensor spacing is set to d s In addition, the number of snapshots is set to B = 2000, and the other parameters are the same as the above example. Based on 100 Monte Carlo experiments, the performance of each estimation method for angle-frequency joint distribution estimation is evaluated by normalized mean square error (NMSE), where NMSE is:

[0087]

[0088] Where M = 100 is the number of Monte Carlo experiments. represents the estimated value of P in the i-th Monte Carlo experiment.

[0089] This experiment analyzes the change of NMSE of angle-frequency joint distribution estimation with signal-to-noise ratio SNR. Figure 5 It can be seen that, except for the LRMR method based on uniform linear array, the NMSE results of other methods decrease with the increase of SNR. This is because the low-rank matrix recovery algorithm uses a one-dimensional spatial linear array and cannot uniquely determine the DOA and frequency, resulting in an ambiguous problem in the estimation of the joint distribution. The estimation results of the LRMR method based on a two-dimensional L-shaped linear array show that the use of a two-dimensional spatial array can effectively decouple the DOA and frequency parameters in the direction vector and solve the estimation ambiguity problem, but the two-dimensional spatial array may increase the cost of array installation. The estimation results of the invented STSS-LRMR method based on space-time uniform sampling show that the space-time sampling structure can also solve the ambiguity problem. Compared with the use of a two-dimensional spatial array, the space-time sampling structure only requires one-dimensional spatial array sampling, the structure is simpler, and the required hardware cost is lower. When the STSS-LRMR method adopts a sparse sampling structure, that is, space-time coprime sampling and nested sampling, the estimated NMSE is smaller than other methods, indicating that the invented method combines the advantages of the STSS framework and the LRMR algorithm and can more accurately estimate the angle-frequency joint distribution.

[0090] In this embodiment, the estimated angle-frequency joint distribution can determine the source signal frequency type, and can further identify the target; it can be used for target positioning and determining the target orientation.

[0091] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for estimating the angle-frequency joint distribution of incoherently distributed broadband sources based on space-time sparse sampling, characterized in that: include: S1, constructing a spatial and temporal sparse sampling structure; The incoherently distributed broadband source signal is collected through a space-time sparse sampling structure; S2, estimating the covariance of the array output signal obtained based on space-time sparse sampling, and vectorizing the covariance; S3, constructing a space-time directional derivative matrix based on the vectorized covariance; S4, constructing the rank minimization problem of angle-frequency joint distribution estimation based on the covariance of array output signals and space-time directional derivative matrix; S5. The rank minimization problem of the angle-frequency joint distribution estimation is transformed into a nuclear norm minimization problem, and the nuclear norm minimization problem is solved to obtain an estimate of the angle-frequency joint distribution matrix.

2. The method for estimating the angle-frequency joint distribution of an incoherently distributed broadband source based on space-time sparse sampling according to claim 1, characterized in that: The space-time sparse sampling structure is a spatial sparse linear array containing N sensors, and each sensor obtains M sparse time sampling signals.

3. The method for estimating the angle-frequency joint distribution of an incoherently distributed broadband source based on space-time sparse sampling according to claim 1, characterized in that: Estimating the covariance of the array output signal includes: obtaining the Gaussian white noise variance of the signal; calculating the covariance R of the array output signal based on space-time sparse sampling according to the source signal and the Gaussian white noise variance; estimating the covariance R to obtain the covariance estimator Calculate the covariance estimator of the array output signal based on the covariance estimator of the array output signal and the variance of Gaussian white noise 4. The method for estimating the angle-frequency joint distribution of an incoherently distributed broadband source based on space-time sparse sampling according to claim 1, characterized in that: Constructing the space-time directional derivative matrix includes: deriving the covariance of the source signal; reconstructing the cross-correlation kernel according to the newly derived covariance; simplifying the newly derived covariance according to the reconstructed cross-correlation kernel; vectorizing the simplified source signal covariance; and constructing the space-time directional derivative matrix according to the vectorized covariance.

5. The method for estimating the angle-frequency joint distribution of an incoherently distributed broadband source based on space-time sparse sampling according to claim 1, characterized in that: The rank minimization problem of constructing the angle-frequency joint distribution estimation includes: constructing the angle-frequency joint distribution matrix P according to the array output signal covariance and the space-time directional derivative matrix; estimating the angle-frequency joint distribution matrix P, and regularizing the estimation result.

6. The method for estimating the angle-frequency joint distribution of an incoherently distributed broadband source based on space-time sparse sampling according to claim 5, characterized in that: Regularization of the estimation results includes: in, is the regularized estimator, P is the angle-frequency joint distribution matrix, λ is the regularization parameter, rank is the rank, is the directional derivative matrix, vec(.) is to stack the matrix column by column into a column vector, is the vectorized covariance, and ‖·‖2 is the vector 2-norm.

7. The method for estimating the angle-frequency joint distribution of incoherently distributed broadband sources based on space-time sparse sampling according to claim 1, characterized in that: The rank minimization problem is transformed into the nuclear norm minimization problem: Where P is the angle-frequency joint distribution matrix, λ is the regularization parameter, f(.) is the error of the array output signal, |.| * is the nuclear norm of the matrix, Q is the smaller value of the number of rows and columns of the matrix P, σ i (P) is the i-th singular value of the matrix P, is the directional derivative matrix, vec(.) is to stack the matrix column by column into a column vector, is the vectorized covariance, and ‖·‖2 is the vector 2-norm.

8. The method for estimating the angle-frequency joint distribution of an incoherently distributed broadband source based on space-time sparse sampling according to claim 1, characterized in that: Solving the nuclear norm minimization problem includes solving the nuclear norm minimization problem using a low-rank matrix recovery algorithm.

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