阅读说明：本技术 一种基于深度展开网络的混合源定位方法及系统 (Mixed source positioning method and system based on deep expansion network ) 是由 刘振 苏晓龙 户盼鹤 刘天鹏 彭勃 刘永祥 黎湘 于 2021-07-21 设计创作，主要内容包括：本发明公开了一种基于深度展开网络的混合源定位方法及系统,方法包括：S1、计算嵌套对称阵列下的混合源相位差矩阵；S2、将混合源相位差矩阵的副对角线元素输入至波达方向深度展开网络,计算混合源的波达方向；S3、利用波达方向深度展开网络的输出信息计算距离向量,并将距离向量输入至自动编码器；S4、将自动编码器的输出输入至距离深度展开网络,对混合源进行识别并计算近场源的距离。本发明相较于传统神经网络,深度展开网络的参数具有可解释性,对于偏离网格的波达方向和距离参数具有泛化能力,相较于基于四阶累积量的模型驱动类方法,本发明计算复杂度小,运算效率高。(The invention discloses a mixed source positioning method and a system based on a deep expansion network, wherein the method comprises the following steps: s1, calculating a mixed source phase difference matrix under the nested symmetric array; s2, inputting the secondary diagonal elements of the mixed source phase difference matrix into a depth of arrival expansion network, and calculating the direction of arrival of the mixed source; s3, calculating a distance vector by using output information of the DOA depth expansion network, and inputting the distance vector to an automatic encoder; and S4, inputting the output of the automatic encoder to a distance depth expansion network, identifying the mixed source and calculating the distance of the near-field source. Compared with the traditional neural network, the method has interpretability of the parameters of the deep expansion network, has generalization capability on the direction of arrival and distance parameters of the deviated grid, and has small calculation complexity and high operation efficiency compared with a model driving method based on fourth-order cumulant.)

1. A mixed source positioning method based on a deep expansion network is characterized by comprising the following steps:

s1, calculating a mixed source phase difference matrix under the nested symmetric array;

s2, inputting the secondary diagonal elements of the mixed source phase difference matrix into a depth of arrival expansion network, and calculating the direction of arrival of the mixed source;

s3, calculating a distance vector by using output information of the DOA depth expansion network, and inputting the distance vector to an automatic encoder;

and S4, inputting the output of the automatic encoder to a distance depth expansion network, identifying the mixed source and calculating the distance of the near-field source.

2. The hybrid source localization method based on the deep unfolding network of claim 1, wherein in step S1,

the nested symmetrical array comprises 2M +1 array elementsDenotes the m-th₁The phase of the kth peak in the spectrum of the individual elements,denotes the m-th₂Phase of the kth peak in the frequency spectrum of an array element, m₁,m₂-M, 2, -1,0,1,2, M, K1, 2, K representing the number of peaks in the spectrum, K also being the number of mixing sources, the mth being calculated using the following equation₁An array element and m₂Phase difference of kth peak in frequency spectrum of array element

By phase differenceForming a k-th mixed-source phase difference matrix U of (2M +1) × (2M +1) dimensions_kComprises the following steps:

3. the hybrid source localization method based on the deep unfolding network of claim 2, wherein the step S2 specifically comprises:

first, a phase difference matrix U is formed_kVectorizing the real part and the imaginary part of the sub diagonal element to obtain a vector

Wherein, y_k＝[u_-M,M,k … u_-1,1,k u_0,0,k u_1,-1,k … u_M,-M,k]^T，(·)^TRepresenting vector transposition, real (·) representing real part operation, and imag (·) representing imaginary part operation;

then, willThe input direction of arrival deeply expands the network to obtain the output of the networkFor the kth mixed source direction-of-arrival spatial spectrum, L_θRepresenting the number of layers of the network, then performing spectral peak search on the spatial spectrum of the direction of arrival, and determining the estimated value of the direction of arrival of the kth mixed source according to the position corresponding to the spectral peak

4. The method of claim 3, wherein the layer 1 output of the DOA deep unfolding network is:

first_θThe output of the layer is:

l_θ＝2,3,...,L_θ，h_st(. epsilon.) represents a nonlinear transformation function, h_st(β, ε) ═ sgn (β) < > max (| β | - ε,0), sgn (·) indicates a sign function, as indicates a Hadamard product, and the initialization parameters of the network are:

ε(θ)＝0.05

wherein α (θ) is 0.9/δ (θ), and δ (θ) representsI (theta) represents an identity matrix,representing a redundant dictionary matrix of directions of arrival:

B(θ)＝[b(θ₁) b(θ₂) … b(θ_p) … b(θ_P)]

whereinP represents the number of sampling points in the direction of arrival, λ represents the wavelength of the near-field source,denotes the position of the m3 th array element, m₃＝-M,...,-2,-1,0,1,2,...,M

5. The method for hybrid source localization based on deep unfolding network of claim 4, further comprising training the deep unfolding network before using the direction of arrival, wherein the training uses stochastic gradient descent to update the network parameters Ψ (θ), Φ (θ), and ε (θ), and the optimized objective function is:

whereinRepresents the square of 2-norm, | ·| non-woven phosphor₁Represents the 1-norm and μ represents the regularization parameter.

6. The hybrid source localization method based on the deep unfolding network of claim 5, wherein the step S3 specifically comprises:

firstly, calculating a distance vector g of the kth mixed source according to a formula_k；

Whereinm₄＝-M,-M+1,...,-1，m₅＝m₄+1,m₄+2,...,0；

Then, the distance vector g is calculated according to the formula_kThe real part and the imaginary part of the vector are vectorized to obtain a vector

Finally, the vector is calculatedInputting an automatic encoder, and calculating to obtain the output of the automatic encoder

7. The hybrid source localization method based on the deep unfolding network of claim 6, characterized in that an automatic encoder needs to be trained before being used, the mean square error is used as a loss function in the training process, the adaptive moment estimation is used for parameter updating, and a linear rectification function is used as an activation function.

8. The hybrid source localization method based on the deep unfolding network of claim 1, wherein the step S4 specifically comprises:

outputting an autoencoderThe input distance deeply expands the network to obtain the output of the networkFor the kth mixed source range spatial spectrum, L_rIndicating the number of layers of the network;

distance space spectrumIf no peak value appears, the mixed source is a far-field source, and if the distance space spectrum isWhen a peak occurs, the hybrid source is a near-field source.

9. The deep unfolding network based hybrid source localization method of claim 8, wherein the output of layer 1 of said distance deep unfolding network is

First_rThe output of the layer is

Wherein l_r＝2,3,...,L_r；

The initialization parameters of the distance-depth expansion network are as follows:

ε(r)＝0.05

wherein α (r) is 0.9/δ (r), and δ (r) representsI (r) represents an identity matrix,representing a distance redundant dictionary matrix:

B(r)＝[b(r₁) b(r₂) … b(r_Q)]

wherein the content of the first and second substances, r_qrepresents distance samples in space, Q is 1,2, …, Q represents the number of distance sample points.

10. A system of the hybrid source localization method based on the deep-developed network according to any one of claims 1 to 9, comprising:

the mixed source phase difference matrix module is used for calculating a mixed source phase difference matrix under the nested symmetric array;

the first input module is used for inputting the secondary diagonal elements of the mixed source phase difference matrix into the DOA depth expansion network and calculating the DOA of the mixed source;

the second input module is used for calculating a distance vector by utilizing output information of the depth expansion network in the direction of arrival and inputting the distance vector to the automatic encoder;

the identification module is used for inputting the output of the automatic encoder to the distance depth expansion network, identifying the mixed source and calculating the distance of the near-field source;

the mixed source phase difference matrix module, the first input module, the second input module and the identification module are connected in sequence.

Technical Field

The present invention relates to the field of array signal processing and machine learning technologies, and in particular, to a method and a system for hybrid source localization based on a deep-unfolding network.

Background

The positioning of the radiation source plays an important role in proximity fuses and passive radars. Far-field sources in space need to be described by the direction of arrival, while near-field sources in space need to be described by the direction of arrival and distance parameters. The deep expansion network models the iteration step of the iterative compressed sensing algorithm into a neural network layer, and the multilayer network is cascaded into a complete network structure, wherein the parameters of the iterative compressed sensing algorithm can be set as the initialization parameters of the network. Compared with the traditional deep neural network structure, the parameter of the deep expansion network has interpretability, and the generalization capability of the network is improved.

Compared with a document 1 of 'mixed-near-field and surface-field source localization real-time array [ J ]' (Digital Signal Processing,2018,73: pages 16 to 23), a nested symmetric array is adopted to realize the positioning of a far-field and a near-field mixed source, compared with a uniform linear array, the method increases the aperture of the array under the condition of the same number of array elements, can improve the parameter estimation precision of the mixed source, but needs to calculate fourth-order cumulant and has larger operand.

Compared with the traditional model-driven method, the method does not need to carry out eigenvalue decomposition on a covariance matrix and can reduce the calculation complexity and has small complexity, but the method is a 'black box model' and the parameters of the network do not have interpretability.

In contrast to document 3, "Direction-of-arrival estimation with circular array using compressed in 20GHz band [ J ]" (IEEEAntennas and Wireless Propagation metrics, 2021,20(5): pages 703 to 707), an Iterative Shrinkage Threshold Algorithm (ISTA) is developed into a network cascade form, so as to achieve estimation of far-field source arrival Direction. Compared with the traditional data-driven method based on machine learning, the method has the advantages that the network parameters are interpretable, so that the generalization capability is improved, but the method cannot realize mixed source positioning and cannot process complex signals.

In view of the above technical problems of the comparison documents, it is necessary to develop a hybrid source positioning method and system based on a deep-evolution network to solve the problems.

Disclosure of Invention

The invention aims to provide a mixed source positioning method and a mixed source positioning system based on a deep expansion network, which are used for overcoming the defects in the prior art.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a mixed source positioning method based on a deep expansion network comprises the following steps:

s1, calculating a mixed source phase difference matrix under the nested symmetric array;

s2, inputting the secondary diagonal elements of the mixed source phase difference matrix into a depth of arrival expansion network, and calculating the direction of arrival of the mixed source;

s3, calculating a distance vector by using output information of the DOA depth expansion network, and inputting the distance vector to an automatic encoder;

and S4, inputting the output of the automatic encoder to a distance depth expansion network, identifying the mixed source and calculating the distance of the near-field source.

Further, in step S1,

the nested symmetrical array comprises 2M +1 array elementsDenotes the m-th₁The phase of the kth peak in the spectrum of the individual elements,denotes the m-th₂Phase of the kth peak in the frequency spectrum of an array element, m₁,m₂-M, 2, -1,0,1,2, M, K1, 2, K representing the number of peaks in the spectrum, K also being the number of mixing sources, the mth being calculated using the following equation₁An array element and m₂Phase difference of kth peak in frequency spectrum of array element

By phase differenceForming a k-th mixed-source phase difference matrix U of (2M +1) × (2M +1) dimensions_kComprises the following steps:

further, the step S2 specifically includes:

first, a phase difference matrix U is formed_kVectorizing the real part and the imaginary part of the sub diagonal element to obtain a vector

Wherein, y_k＝[u_-M,M,k … u_-1,1,k u_0,0,k u_1,-1,k … u_M,-M,k]^T，(·)^TRepresenting vector transposition, real (·) representing real part operation, and imag (·) representing imaginary part operation;

then, willThe input direction of arrival deeply expands the network to obtain the output of the networkFor the kth mixed source direction-of-arrival spatial spectrum, L_θRepresenting the number of layers of the network, then performing spectral peak search on the spatial spectrum of the direction of arrival, and determining the estimated value of the direction of arrival of the kth mixed source according to the position corresponding to the spectral peak

Further, the layer 1 output of the direction-of-arrival depth unfolding network is:

first_θThe output of the layer is:

l_θ＝2,3,...,L_θ，h_st(. epsilon.) represents a nonlinear transformation function, h_st(β, ε) ═ sgn (β) < > max (| β | - ε,0), sgn (·) indicates a sign function, as indicates a Hadamard product, and the initialization parameters of the network are:

ε(θ)＝0.05

wherein α (θ) is 0.9/δ (θ), and δ (θ) representsI (theta) represents an identity matrix,representing a redundant dictionary matrix of directions of arrival:

B(θ)＝[b(θ₁) b(θ₂) … b(θ_p) … b(θ_P)]

whereinP is 1,2, …, P represents the number of sampling points in the direction of arrival, λ represents the wavelength of the near-field source,denotes the position of the m3 th array element, m₃＝-M,...,-2,-1,0,1,2,...,M

Further, before the network is deeply expanded by using the direction of arrival, training is further included, in the training, network parameters Ψ (θ), Φ (θ) and epsilon (θ) are updated by using random gradient descent, and an optimized objective function is as follows:

whereinRepresents the square of 2-norm, | ·| non-woven phosphor₁Represents the 1-norm and μ represents the regularization parameter.

Further, the step S3 specifically includes:

firstly, calculating a distance vector g of the kth mixed source according to a formula_k；

Whereinm₄＝-M，-M+1,...,-1，m₅＝m₄+1,m₄+2,...,0；

Then, the distance vector g is calculated according to the formula_kThe real part and the imaginary part of the vector are vectorized to obtain a vector

Finally, the vector is calculatedInputting an automatic encoder, and calculating to obtain the output of the automatic encoder

Further, the automatic encoder needs to be trained before being used, the mean square error is used as a loss function in the training process, the adaptive moment estimation is used for parameter updating, and the linear rectification function is used as an activation function.

Further, the step S4 is specifically:

outputting an autoencoderThe input distance deeply expands the network to obtain the output of the networkFor the kth mixed source range spatial spectrum, L_rRepresenting networksThe number of layers;

distance space spectrumIf no peak value appears, the mixed source is a far-field source, and if the distance space spectrum isWhen a peak occurs, the hybrid source is a near-field source.

Further, the output of layer 1 of the distance-depth expansion network is

First_rThe output of the layer is

Wherein l_r＝2,3,...,L_r；

The initialization parameters of the distance-depth expansion network are as follows:

ε(r)＝0.05

wherein α (r) is 0.9/δ (r), and δ (r) representsI (r) represents an identity matrix,representing a distance redundant dictionary matrix:

B(r)＝[b(r₁) b(r₂) … b(r_Q)]

wherein the content of the first and second substances, r_qrepresents distance samples in space, Q is 1,2, …, Q represents the number of distance sample points.

The invention also provides a system of the mixed source positioning method based on the deep expansion network, which comprises the following steps:

the mixed source phase difference matrix module is used for calculating a mixed source phase difference matrix under the nested symmetric array;

the first input module is used for inputting the secondary diagonal elements of the mixed source phase difference matrix into the DOA depth expansion network and calculating the DOA of the mixed source;

the second input module is used for calculating a distance vector by utilizing output information of the depth expansion network in the direction of arrival and inputting the distance vector to the automatic encoder;

the identification module is used for inputting the output of the automatic encoder to the distance depth expansion network, identifying the mixed source and calculating the distance of the near-field source;

the mixed source phase difference matrix module, the first input module, the second input module and the identification module are connected in sequence.

Compared with the prior art, the invention has the advantages that: compared with the traditional neural network, the method has interpretability of the parameters of the deep expansion network, has generalization capability on the direction of arrival and distance parameters of the deviated grid, and has small calculation complexity and high operation efficiency compared with a model driving method based on fourth-order cumulant.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a flow chart of a hybrid source positioning method based on a deep-scaling network according to the present invention.

Fig. 2 is a schematic structural view of a direction-of-arrival depth-expanded network according to the present invention.

Fig. 3 is a schematic structural diagram of an automatic encoder according to the present invention.

FIG. 4 is a schematic diagram of a distance-deep unfolding network according to the present invention.

FIG. 5 is a schematic diagram of a scenario for near field source localization using nested symmetric arrays.

FIG. 6 shows a mixed source direction-of-arrival spatial spectrum obtained using the present invention.

FIG. 7 is a mixed source range-space spectrum obtained using the present invention.

Fig. 8 shows the estimation results in different directions of arrival using the present invention.

Fig. 9 shows the estimation errors for different directions of arrival obtained with the present invention.

Fig. 10 shows the estimation results at different distances using the present invention.

FIG. 11 shows the estimation errors at different distances obtained using the present invention.

Detailed Description

The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the scope of the present invention will be more clearly and clearly defined.

Referring to fig. 1, the embodiment discloses a hybrid source positioning method based on a deep-unfolding network, comprising the following steps,

step S1, calculating a mixed source phase difference matrix under the nested symmetric array, specifically:

the known antenna array is a nested symmetrical arrangement, and comprises 2M +1 array elements. Is provided withDenotes the m-th₁The phase of the kth peak in the spectrum of the individual elements,denotes the m-th₂Phase of the kth peak in the frequency spectrum of an array element, m₁,m₂As can be seen from the practical situation, K represents the number of peaks in the frequency spectrum, and K is the number of mixing sources.

The m-th is calculated by using the following formula₁An array element and m₂Phase difference of kth peak in frequency spectrum of array element

By phase differenceForming a k-th mixed-source phase difference matrix U of (2M +1) × (2M +1) dimensions_kThe following were used:

in this embodiment, the antenna array is preferably nested with symmetric linear arrays, the sub diagonal elements of the phase difference matrix obtained by the array only contain direction-of-arrival information, and the aperture of the array is increased under the condition that the number of array elements is the same, so that the parameter estimation accuracy is improved.

Step S2, inputting the sub diagonal elements of the phase difference matrix into the depth of arrival expansion network, and calculating the direction of arrival of the hybrid source, specifically:

first, a phase difference matrix U is formed_kVectorizing the real part and the imaginary part of the sub diagonal element to obtain a vector

Wherein y is_k＝[u_-M,M,k … u_-1,1,k u_0,0,k u_1,-1,k … u_M,-M,k]^T，(·)^TDenotes vector transposition, real (-) denotes real part operation, and imag (-) denotes imaginary part operation.

Then, willThe input direction of arrival deeply expands the network to obtain the output of the networkI.e. the k-th mixed source direction-of-arrival spatial spectrum, L_θIndicating the number of layers of the network; then, the spectral peak search is carried out on the spatial spectrum of the direction of arrival, and the estimated value of the direction of arrival of the kth mixed source can be determined according to the position corresponding to the spectral peakThe structure of the DOA deep deployment network is shown in FIG. 2, where the output of layer 1 is

First_θThe output of the layer is

lθ-2,3,...,L_θ，h_st(. epsilon.) representsNon-linear transformation functions, i.e.

h_st(β,ε)＝sgn(β)⊙max(|β|-ε,0)

Wherein sgn (·) indicates a sign function, and indicates a Hadamard product, and the initialization parameters of the network are as follows:

ε(θ)＝0.05

wherein α (θ) is 0.9/δ (θ), and δ (θ) representsI (theta) represents an identity matrix,representing a redundant dictionary matrix of directions of arrival, namely:

B(θ)＝[b(θ₁) b(θ₂) … b(θ_p) … b(θ_P)]

whereinP is 1,2, …, P represents the number of sampling points in the direction of arrival, λ represents the wavelength of the near-field source,denotes the position of the m3 th array element, m₃＝-M,...,-2,-1,0,1,2,...,M。

It should be noted that, when the depth-of-arrival network is used, it must be trained first, and during the training, the network parameters Ψ (θ), Φ (θ), and ∈ (θ) are updated by using Stochastic gradient descent (i.e., SGD), and the optimized objective function is:

whereinRepresents the square of 2-norm, | ·| non-woven phosphor₁Represents the 1-norm and μ represents the regularization parameter.

Step S3, calculating a distance vector using output information of the depth-of-arrival expansion network, and inputting the distance vector to an automatic encoder, specifically including:

first, the distance vector g of the kth mixed source is calculated using the following equation_k：

Whereinm₄＝-M,-M+1,...,-1，m₅＝m₄+1,m₄+2,...,0。

Then, the distance vector g is calculated_kThe real part and the imaginary part of the vector are vectorized to obtain a vector

Finally, the vector is calculatedInputting an automatic encoder, and calculating to obtain the output of the automatic encoderAutoencoder As shown in FIG. 3, the autoencoder is composed of an encoder and a decoder, wherein the output of the encoderIs the input to the decoder, the output of the encoder is a round (M × (M +1)/4) × 1 vector, the output of the decoder is a round (M × (M +1)/2) × 1 vector, round (·) represents a rounding operation.

In this embodiment, the auto-encoder must be trained first, and if the kth hybrid source is a near-field source, the output of the auto-encoder is usedIs composed ofI.e. the output equals the input; if the k-th mixed source is a far-field source, the output of the automatic encoderAll of the elements of (1) are 0. In the training process, Mean Square Error (MSE) is used as a loss function, Adaptive Moment Estimation (Adam) is used for parameter updating, and a Linear rectification function (regulated Linear Unit, ReLU) is used as an activation function.

Step S4, inputting the output of the automatic encoder to the distance depth expansion network, identifying the mixed source, and calculating the distance of the near-field source, specifically including:

will be provided withThe input distance deeply expands the network to obtain the output of the networkI.e. the k-th mixed source range spatial spectrum, L_rIndicating the number of layers of the network.

Distance space spectrumIf no peak value appears, the mixed source is a far-field source; distance space spectrumIf a peak value appears, the mixed source is a near-field source, and the position corresponding to the spectral peak is the distance estimation value of the near-field sourceThe structure of the distance-deep expanded network is shown in FIG. 4, in which the output of layer 1 is

First_rThe output of the layer is

l_r＝2，3，...,L_r。

The initialization parameters of the network are as follows:

ε(r)＝0.05

wherein α (r) is 0.9/δ (r), δ (r) representsI (r) represents an identity matrix,representing distance redundant dictionary matrices, i.e.

B(r)＝[b(r₁) b(r₂) … b(r_Q)]

Wherein r_qRepresents distance samples in space, Q is 1,2, …, Q represents the number of distance sample points.

It is worth to be noted that, when the distance deep-expansion network is used, it must be trained first, and in the training, the SGD is used to update the network parameters Ψ (r), Φ (r), and ∈ (r), and the optimized objective function is:

the invention also provides a system of the mixed source positioning method based on the deep expansion network, which comprises the following steps: the mixed source phase difference matrix module is used for calculating a mixed source phase difference matrix under the nested symmetric array; the first input module is used for inputting the secondary diagonal elements of the mixed source phase difference matrix into the DOA depth expansion network and calculating the DOA of the mixed source; the second input module is used for calculating a distance vector by utilizing output information of the depth expansion network in the direction of arrival and inputting the distance vector to the automatic encoder; the identification module is used for inputting the output of the automatic encoder to the distance depth expansion network, identifying the mixed source and calculating the distance of the near-field source; the mixed source phase difference matrix module, the first input module, the second input module and the identification module are connected in sequence.

In order to verify the positioning performance of the invention on the near-field source, four simulation experiments are used for explanation.

Simulation experiment I

As shown in fig. 5, the two-stage nested symmetric linear array has an array element number of 17, where M is 8, the solid circle represents a first-stage sub-array, the hollow circle represents a second-stage sub-array, and the array element spacing of the second-stage sub-array is 5 times that of the first-stage sub-array. At intervals of 1 deg. and 1 lambda for wave reaching directions of-60 deg. and 60 deg. respectively]And a distance [5 λ,30 λ ]]Uniform sampling is performed to generate training samples for near-field sources. Number of layers L of DOA deep-developed network_θAnd number of layers L of the distance-depth expanded network_rBoth are 50, in the process of training two deep unfolding networks, the epoch is set to be 300, and the mini-batch is set to be 32; in training the auto encoder, epoch is set to 500 and mini-batch is set to 16.

Simulation experiment is used for verifying the effectiveness of the invention in locating and identifying the mixed source, and the experiment takes the example that the mixed source comprises a far-field source and a near-field source, wherein the far-field source is set to (10 °), the near-field source is set to (-20 °, 10 λ), fig. 6 is a direction-of-arrival spatial spectrum obtained by using the invention, fig. 7 is a distance spatial spectrum obtained by using the invention, wherein a solid line represents the far-field source spatial spectrum, and a dotted line represents the near-field source spatial spectrum. The wave arrival direction space spectrum and the distance space spectrum of the two radiation sources can be correctly matched, wherein the distance space spectrum of the far-field source has no peak value, the near-field source space spectrum has a peak value, and the position corresponding to the peak value is the near-field source distance, so that the invention can realize the positioning and identification of the mixed source.

Simulation experiment two

The simulation experiment was used to verify the generalization ability of the present invention to the direction of arrival estimation, in which the distance of the near field source was set to 10 λ, and 3 sets of test samples were generated in the airspace, the direction of arrival of the test sample set 1 was set to-59.99 °, -58.99 °, …, -0.99 °,0.01 °,1.01 °, …,59.01 °, the direction of arrival of the test sample set 2 was set to-59.90 °, -58.90 °, …, -0.90 °,0.10 °,1.10 °, …,59.10 °, the direction of arrival of the test sample set 3 was set to-59.70 °, -58.70 °, …, -0.70 °,0.30 °,1.30 °, …,59.30 °, and a total of 360 test samples. Fig. 8 is a view showing the estimation result of the direction of arrival obtained by the present invention, with the abscissa being the test sample number and the ordinate being the estimation result of the direction of arrival, and fig. 9 is a view showing the estimation error of the direction of arrival obtained by the present invention, with the abscissa being the test sample number and the ordinate being the estimation error of the direction of arrival. It can be seen that the direction of arrival of the deviated grid can be estimated into the adjacent grid, indicating that the method has generalization capability on the mixed source direction of arrival estimation.

Simulation experiment III

The simulation experiment is used for verifying the generalization ability of the invention to the estimation of the distance of the mixed source, in the experiment, the direction of arrival of the mixed source is set to be 30 degrees, 3 groups of test samples are generated in the airspace, the distance of the 1 st group of test samples is set to be 3.01 lambda, 4.01 lambda, … and 29.01 lambda, the distance of the 2 nd group of test samples is set to be 3.1 lambda, 4.1 lambda, … and 29.1 lambda, the distance of the 3 rd group of test samples is set to be 3.3 lambda, 4.3 lambda, … and 29.3 lambda, and the total number of the test samples is 81. Fig. 10 is a distance estimation result obtained by the present invention, the abscissa is a test sample number and the ordinate is a distance estimation result, fig. 11 is a distance estimation error obtained by the present invention, the abscissa is a test sample number and the ordinate is a distance estimation error. It can be seen that the distance from the grid can be estimated into the neighboring grid, indicating that the present invention has generalization capability to the mixed source distance estimation.

Simulation experiment four

The simulation experiment is used for verifying the operational efficiency of the invention and comparing with the calculation time of the mixed source positioning method based on the fourth-order cumulant of the comparison file 1. In the experiment, the mixed source comprises a far-field source and a near-field source, wherein the far-field source is set to be (30 degrees), the near-field source is set to be (-20 degrees and 10 lambda), under the same operation platform, the mixed source can be positioned and identified by the two methods, the calculation time of the invention is 0.352s, and the calculation time of the comparison document 1 is 3.613s, which indicates that the operation efficiency of the invention is high.

Although the embodiments of the present invention have been described with reference to the accompanying drawings, various changes or modifications may be made by the patentees within the scope of the appended claims, and within the scope of the invention, as long as they do not exceed the scope of the invention described in the claims.