CN112769441A - VDES receiving collision signal separation method based on random near-end gradient tensor decomposition - Google Patents

Abstract

The invention discloses a VDES collision signal separation method based on random near-end gradient tensor decomposition, which is suitable for VDES collision signal separation under the underdetermined or positive determined condition (the number of observation signals is less than or equal to the number of source signals), and specifically comprises the following steps: firstly, sampling and digital down-conversion processing are carried out on VDES received signals to obtain observation signals of each subsystem; after the preprocessing is completed, establishing a generalized covariance matrix set, dividing a tensor stacked by decompressing the matrix set by using a Tucker to obtain a kernel tensor, then optimizing a kernel tensor solving process by using a random near-end gradient algorithm, and inverting the obtained mixed matrix to obtain a separation matrix; and performing frame header detection, frequency offset estimation and demodulation processing on the separation signals calculated by the separation matrix to obtain a VDES subsystem signal data frame. According to the method, the tensor is compressed by using the Tucker decomposition, the calculation complexity is reduced, the time for solving the factor matrix is reduced while the decomposition precision is improved by using the random near-end gradient algorithm, and the received signals of the VDES system can be processed in real time.

Description

VDES receiving collision signal separation method based on random near-end gradient tensor decomposition

Technical Field

The invention belongs to the technical field of very high frequency data exchange systems in wireless communication, and particularly relates to a VDES collision signal separation method based on random near-end gradient tensor decomposition.

Background

An Automatic Identification System (AIS) for ships is used as a main tool for marine communication and an important guarantee for navigation safety, and provides services such as Identification information and position reports for ships. However, the number of ships is increasing year by year, the number of ships in some important water areas and ports is obviously increased, the demand of communication traffic is further expanded, the AIS link is not burdened, and the channel occupancy rate is obviously increased.

In response to the above problems, the international maritime standards association and the international telecommunications union have together proposed a new generation of maritime data exchange system in 2015: very high frequency Data Exchange system (VHF Data Exchange, VDES). The VDES system not only can relieve the overload pressure of the link of the current AIS system, but also is added with two subsystems of Application Specific Message (ASM) and very high frequency Data Exchange (VDE) on the basis of keeping the basic functions of the AIS system, so that the content and the form of transmitted Data are richer, and the communication requirement proposed by the international maritime organization is met. The industry has now regarded the VDES system as the subsequent evolution direction of the AIS system, and future VDES systems will be responsible for maritime communication and ensuring safe sailing.

However, in practical applications, when the satellite-borne AIS receiver receives data, signal collision occurs very frequently. Although the appearance of the satellite-borne VDES system relieves the link load to a certain extent, the problem of information loss caused by signal collision still exists. The ultra-large field of view of the satellite-borne VDES receiver far exceeds a self-organization area, and ships in different self-organization areas can send VDES signals in the same time slot, so that the signal collision problem is caused; or the shipborne transmitter reserves different time slots and transmits signals from different time slot units, but because the path lengths of the signals are different greatly, the signals subjected to time delay are simultaneously received by the receiver, and signal collision is generated. The collision signal is easy to cause the loss of the ship information, and the ship information is about the navigation safety, so the collision separation problem of the satellite-borne received signal becomes an important problem to be solved urgently in system application, and attention must be paid and must be solved.

Research on mixed signal separation has been a hot issue in the field of signal processing. In 2005, a.ferro et al proposed a mixed signal Blind Identification (FOBIUM) algorithm based on Fourth-order Cumulant based on a boundary Identification of an underestimated mixture, but the calculation process was too complicated; in 2008, l.d. lathauwer and Jos diphine proposed a simpler and more convenient algorithm for mixed signal Blind Identification based on Second-order Covariance (SOBIUM), which simplifies the calculation process but leaves the separation accuracy to be improved. In 2019, the Tongtong performs Separation research on multi-channel receiving collision signals, and provides a variable stride length Adaptive decomposition algorithm (EASI) based on hierarchical iteration, wherein the convergence rate of the EASI algorithm is higher than that of the traditional EASI algorithm.

The problem of separating collision signals received by a satellite-borne VDES system is a key problem to be solved urgently, but the research center of gravity of the current scholars is always put on the separation of collision signals under the conditions of adequacy or overdetermination, the research on the separation method under the conditions of underdetermined is less, the traditional separation algorithm cannot meet the requirement that the collision of multiple signals can be separated under the conditions of adequacy and underdetermined, most of the separation algorithms are simple and traditional, and the separation effect is unsatisfactory.

The invention relates to a Chinese patent with the patent application number of CN202010490681.X and the invention name of a collision feedback-based shipborne VDES access protocol implementation method, which divides signals into three channels according to a message priority redefining part to shunt messages, then modifies a time slot structure in VDES to divide feedback bits for feedback collision, and a ship broadcasts and senses collision time slot numbers through the collision bits, thereby reducing the problem of signal collision. The method needs to continuously monitor and broadcast conflict bits, and has poor real-time performance; the time slot structure is occupied by increasing the collision bit; signals sent by different time slots cannot be avoided, and collision may still occur due to delay caused by different transmission paths, so that the method cannot practically solve the problem of signal collision.

The invention relates to a Chinese patent with the patent application number of CN201410228651.6 and the name of 'a collision signal processing method for a satellite-borne AIS system', which carries out synchronization and channel estimation on a received signal according to known information in a frame structure, detects to obtain a single-path signal, reconstructs the single-path signal, subtracts the single-path signal from the AIS received signal, and repeats the steps on the obtained signal until no signal can be detected.

Disclosure of Invention

The invention aims to provide a VDES collision signal separation method based on random near-end gradient tensor decomposition.

The technical scheme for realizing the purpose of the invention is as follows: a VDES collision signal separation method based on random near-end gradient tensor decomposition comprises the following steps:

step 1, receiving a VDES collision signal, and processing the VDES collision signal to obtain an observation signal of each subsystem;

step 2, performing centralization and whitening pretreatment on the N paths of observation signals obtained in the step 1 to obtain a whitened mixed signal matrix;

step 3, establishing a generalized covariance matrix set between the observation signal and the source signal, compressing a tensor stacked by the matrix set by using Tucker decomposition to obtain a nuclear tensor, solving the nuclear tensor by using CP decomposition, optimizing the CP decomposition process by using a random near-end gradient algorithm to obtain an estimate of a mixed matrix, and inverting the mixed matrix to obtain a separation matrix;

step 4, multiplying the separation matrix obtained in the step 3 by the mixed signal matrix obtained in the step 2 to obtain a separation signal; and performing frame header detection, frequency offset estimation and demodulation decoding processing on the N paths of separated signals to obtain a data frame of each subsystem signal of the VDES.

Preferably, the VDES collision signal is received and processed, and the specific process of obtaining the observation signal of each subsystem is as follows:

and receiving the VDES collision signal by the shared antenna array, obtaining a plurality of paths of received signals through sampling of an analog-to-digital converter, and performing digital down-conversion and channel separation processing to respectively obtain observation signal matrixes of the AIS subsystem, the ASM subsystem and the VDE subsystem.

Preferably, the N paths of observation signals obtained in step 1 are subjected to centering and whitening preprocessing, and the obtained whitened mixed signal matrix specifically comprises:

removing the mean value of the observation signal matrix X;

for the signal after mean value removal

The covariance matrix of (2) is subjected to eigenvalue decomposition, i.e.

Sigma is

The eigenvalues of the covariance matrix of (1) are diagonal matrices of diagonal elements, U is

An orthogonal matrix formed by the eigenvectors of the covariance matrix;

obtaining a whitened mixed signal matrix:

V＝∑^-1/2U^T。

preferably, a generalized covariance matrix set between the observation signal and the source signal is established, the tensor stacked by the matrix set is compressed by using the Tucker decomposition to obtain a kernel tensor, and the specific process of solving the kernel tensor by using the CP decomposition is as follows:

3-1, obtaining an observation signal generalized covariance matrix set by using linear transformation characteristics of generalized covariance for K processing points, and stacking the observation signal generalized covariance matrix set to be a tensor to establish a tensor decomposition model;

step 3-2, compressing the tensor obtained in the step 3-1 by using Tucker decomposition to obtain a nuclear tensor;

3-3, setting an optimal objective function for decomposing the kernel tensor, setting the maximum iteration times and initially searching the step length;

step 3-4, evaluating the gradient of the target function in the step 3-3, introducing an adjusting factor, iterating the factor matrix of the nuclear tensor by utilizing the gradient and the adjusting factor to obtain a factor matrix of the next iteration, and updating the search step length;

3-5, repeating the steps 3-4 until the target function reaches a set value or reaches a set iteration number, and obtaining the estimation of the mixing matrix;

and 3-6, inverting the mixed matrix to obtain a separation matrix.

Preferably, the specific process of establishing the generalized covariance matrix set and stacking to obtain the tensor in step 3-1 is as follows:

establishing a generalized covariance matrix for the K processing points to obtain:

in the formula, Ψ_XFor observing the signal generalized covariance matrix, Ψ_SIs a source signal generalized covariance matrix, (-)^TFor transpose operator, A^TThe method is characterized in that the method is a transposition of a mixing matrix A, tau is a processing point and represents a data point expanded by using a Taylor series when a generalized characteristic function needs to be calculated;

stacking K matrixes to obtain tensor x epsilon R^M×M×KEach element thereof is represented as:

defining a matrix D ∈ R^K×NSo that the n-th element of the k-th row corresponds to the diagonal matrix Ψ_S[A^Tτ_k]The (n, n) th element of (i.e. the

The overwrite tensor element values are:

wherein, a_inAnd a_jnAre all the values of the elements in the mixing matrix A, d_knIs the value of an element of the matrix D.

Preferably, the specific process of compressing the tensor χ by using the Tucker decomposition in the step 3-2 is as follows:

fixing two factor matrixes in the Tucker decomposition as an identity matrix I epsilon R^M×MExpressed as:

χ＝γ×₁I×₂I×₃U

wherein γ ∈ R^M×M×LAs the nuclear tensor, U ∈ R^K×LIs a column unitary matrix, a_nN is the product of tensor and matrix, named n-mode product;

expressed as the Kronecker product of the matrix:

wherein, χ₍₃₎、γ₍₃₎Modulo-3 matrix of tensors χ and γ,

represents the Kronecker product;

the nuclear tensor is determined as:

γ＝χ×₁I×₂I×₃U^T＝χ×₃U^T

the nuclear tensor γ standard decomposition expression is:

in the formula (I), the compound is shown in the specification,

the outer product operation of the representative vector is performed,

and

respectively, the mixed matrix A and the matrix D are compressed,

and

is a matrix

And

the column vector of (2).

Preferably, the specific process of setting the optimal objective function f (θ) in step 3-3 is as follows:

setting the optimal objective function as

Wherein | · | purple sweet_FFor Frobenius norm, the target function is expanded by n mode and rewritten as

Wherein f (θ) is f (A)₍₁₎,…,A_(M)) Abbreviation of (A), H_(n)To remove A_(n)Khatri-Rao products of the matrix of extrinsic residue factors, θ and H_(n)Respectively expressed as:

θ＝[vec(A₍₁₎)^T，…，vec(A_(M))^T]^T

preferably, the specific process of step 3-4 is:

step 3-4-1, using

The gradient estimate for f (theta) is expressed,

then

In the formula, u_(n)A certain fiber of the nuclear tensor gamma, and r is the iteration number;

step 3-4-2, introducing a regulating factor h for promoting an optimization structure_n(A_(n)) The expression is

Step 3-4-3, obtaining a factor matrix of the next iteration by using the latest gradient obtained in the step 3-4-1 and the step 3-4-2

Step 3-4-4, updating step length alpha of search direction^(r)The updated formula is

Wherein beta is 10^-6。

Compared with the prior art, the invention has the following remarkable advantages: 1) the method adopts the VDES collision signal separation method based on the random near-end gradient tensor decomposition to realize the separation of the collision signals under the appropriate condition (the number of the observation signals is equal to the number of the source signals) and the under-determined condition (the number of the observation signals is less than the number of the source signals), can obtain the recovery signals of N paths of source signals at the same time of one-time reception, and has wider applicability; 2) the method is suitable for collision signals of AIS, ASM and VDE subsystems in the VDES system, the separation principle and the separation process are the same, and compared with the traditional separation method, the method has more signal types capable of being separated; 3) the method adopts the Tucker decomposition to compress the established generalized covariance matrix number sets of the observation signal and the source signal, reduces the times of tensor decomposition and simplifies the calculation process; 4) the invention introduces the process of optimizing CP decomposition by a random near-end gradient algorithm, improves the precision of solving the factor matrix while accelerating the optimization speed of the objective function, and has better global searching performance and real-time performance.

The present invention is described in further detail below with reference to the attached drawing figures.

Drawings

FIG. 1 is a flow chart of the present invention.

FIG. 2 is a flow chart showing a specific process of step 3 of the present invention.

Detailed Description

In a known satellite-borne VDES receiver, signals are received through M channels, and the signals are subjected to linear aliasing in a transmission process and are interfered by noise, which includes: and X is AS + N, wherein X is the observed signals of M paths obtained by processing, S is N paths of unknown source signals, M is less than or equal to N, and N is a noise signal.

As shown in fig. 1 and fig. 2, a method for separating VDES received collision signals based on random near-end gradient tensor decomposition includes the following steps:

step 1, receiving VDES collision signals by a shared antenna array, then obtaining multipath received signals through sampling of an analog-to-digital converter, and performing digital down-conversion and channel separation processing to obtain observation signal matrixes of AIS, ASM and VDE subsystems respectively. Let each subsystem observe signal as X ∈ R^M×TThe source signal is S ∈ R^N×TThe M is the number of the observation signals X, the N is the number of the source signals S, and the T is the number of data sampling points, wherein the value of the M is smaller than or equal to the value of the N, namely, the underdetermined or proper condition is met;

and 2, performing centralization processing on the N paths of observation signals obtained in the step 1 to enable the signals to have unit variance, and performing whitening processing on the signals to eliminate correlation among the signals.

In a further embodiment, the observation signal matrix X is de-averaged, and the de-averaged signal is used

Is shown, i.e.

To pair

The covariance matrix of (2) is subjected to eigenvalue decomposition, i.e.

Sigma is

The eigenvalues of the covariance matrix of (1) are diagonal matrices of diagonal elements, U is

The orthogonal matrix is formed by the eigenvectors of the covariance matrix. Then there is a whitening matrix of V ═ Σ^-1/2U^TWhitened mixed signal matrix

And 3, establishing a generalized covariance matrix set between the observation signal and the source signal, compressing a tensor stacked by the generalized covariance matrix set by using Tucker decomposition to obtain a nuclear tensor, and solving the nuclear tensor by using CP decomposition. A random near-end gradient algorithm is introduced to optimize the CP decomposition process, matrix iteration is accelerated, and decomposition precision is improved. Finally, an estimate of the mixing matrix a is obtained. And (5) inverting the mixed matrix to obtain a separation matrix W.

As shown in fig. 2, the specific steps are as follows:

step 3-1, utilizing linear transformation characteristics of the generalized covariance to obtain an observation signal generalized covariance matrix psi_XA functional relationship, called kernel function, is established between the observed signal and the source signal. Calculating kernel functions of the K processing points to obtain a matrix set, and establishing a tensor decomposition model, wherein the specific process comprises the following steps:

establishing a generalized covariance matrix for the K processing points to obtain

In the formula, Ψ_XFor observing the signal generalized covariance matrix, Ψ_SIs a source signal generalized covariance matrix, (-)^TFor transpose operator, A^TFor the transpose of the mixing matrix a, τ is the processing point, which represents the data point that is expanded using the taylor series when the generalized eigenfunction needs to be calculated.

Stacking K generalized covariance matrixes to obtain tensor x epsilon R^M×M×KEach element thereof is represented as:

defining a matrix D ∈ R^K×NSo that the n-th element of the k-th row corresponds to the diagonal matrix Ψ_S[A^Tτ_k]The (n, n) th element of (i.e. the

The tensor element values are rewritten as:

wherein, a_inAnd a_jnAre all the values of the elements in the mixing matrix A, d_knIs the value of an element of the matrix D.

Step 3-2, compressing the tensor χ obtained in the step 3-1 by using Tucker decomposition to obtain a core tensor γ, wherein the specific process is as follows:

fixing two factor matrixes in the Tucker decomposition as an identity matrix I epsilon R^M×MI.e. the tensor χ is subjected to the Tucker-1 decomposition, expressed as

χ＝γ×₁I×₂I×₃U

Wherein γ ∈ R^M×M×LAs the nuclear tensor, U ∈ R^K×LIs a column unitary matrix, a_nAnd n is the product of tensor and matrix, namely n-mode product, 2 and 3. Expressed as the Kronecker product of the matrix:

wherein, χ₍₃₎、γ₍₃₎Modulo-3 matrix of tensors χ and γ,

representing the Kronecker product.

The nuclear tensor is determined as:

γ＝χ×₁I×₂I×₃U^T＝χ×₃U^T

after U is obtained, the kernel tensor can be calculated by the above formula, so that the tensor χ of M × K is compressed into the kernel tensor γ of M × L, and then the kernel tensor γ is subjected to standard canonical decomposition to solve the hybrid matrix a. The gamma standard decomposition expression is

In the formula (I), the compound is shown in the specification,

the outer product operation of the representative vector is performed,

and

respectively, the mixed matrix A and the matrix D are compressed,

and

is a matrix

And

the column vector of (2). After completing the pair matrix

After the estimation, it needs to be decompressed to finally obtain the mixed matrix a, and since both factor matrices decomposed by Tucker-1 are identity matrices, the mixed matrix a can be obtained from the following formula

The intermediate decompression obtains a mixing matrix A:

it can be seen that the pair matrix derived from the kernel tensor

Is also an estimate of the mixing matrix a.

3-3, setting an optimal objective function f (theta) for decomposing the nuclear tensor gamma, and setting the maximum iteration times r_maxInitial search step size α^(r)|_r＝0The value is between 0.1 and 0.001, wherein the specific process of setting the optimal objective function f (theta) is as follows:

setting the optimal objective function as

Wherein | · | purple sweet_FIs Frobenius norm. And (3) performing n-mode expansion on the target function, and rewriting as:

wherein f (θ) is f (A)₍₁₎,…,A_(M)) Abbreviation of (A), H_(n)To remove A_(n)Khatri-Rao products of the matrix of extrinsic residue factors, θ and H_(n)Are respectively represented as

θ＝[vec(A₍₁₎)^T，…，vec(A_(M))^T]^T

Step 3-4, solving gradient estimation of the objective function f (theta) obtained in the step 3-3

And introducing a regulating factor h_n(A_(n)) Iterating the factor matrix of the kernel tensor by utilizing the gradient and the adjustment factor to obtain the factor matrix of the next iteration

And updating the search step size a (^r+1)The specific process is as follows:

step 3-4-1, using

The gradient estimate for f (theta) is expressed,

then

In the formula, u_(n)Is a certain fiber of the nuclear tensor gamma, and r is the iteration number.

Step 3-4-2, introducing a regulating factor h for promoting an optimization structure_n(A_(n)) The expression is

Step 3-4-3, obtaining a factor matrix of the next iteration by using the latest gradient, namely the adjustment factor, obtained in the step 3-4-1 and the step 3-4-2

Step 3-4-4, updating step length alpha of search direction^(r)The updated formula is

Wherein beta is 10^-6。

3-5, repeating the steps 3-4 until the target function reaches a set value or reaches a set iteration number, and obtaining the final estimation of the mixing matrix A;

and 3-6, inverting the mixed matrix A to obtain a separation matrix W.

Step 4, multiplying the final separation matrix W obtained in the step 3 with the mixed signal moment Z obtained in the step 2 to obtain a separation signal

For N paths of separated signals

And performing frame header detection, frequency offset estimation and demodulation decoding processing to obtain data frames of signals of each subsystem of the VDES.

The generalized covariance matrix set is compressed by using the Tucker decomposition, and the random near-end gradient is introduced to accelerate the CP decomposition calculation process, so that the tensor decomposition method for separating the VDES subsystem collision signals is obtained, the tensor decomposition method has applicability to separation of each subsystem collision signal of the VDES under the underdetermined and appropriate conditions, and the application range is wide.

The following is described in detail with reference to the examples:

examples

The specific conditions in this example are: the VDES collision signal is received by the shared antenna array, the number of the subsystem source signals is set to be 4, namely N is 4, the number of the observation signals is set to be 3, namely M is 3, and the receiving of the collision signal under the condition of underdetermined condition is met. After the four VDES source signals collide and reach a receiver, the three receiving signals are separated by using the collision signal separation method based on the random near-end gradient tensor decomposition, the transmitted source signal waveform and the separated signal waveform are compared, at the moment, the signal-to-noise ratio (SNR) is 10dB, and the signal amplitude values are all subjected to normalization processing. The two waveforms are basically consistent, the distortion is small, and the collision signals under the underdetermined condition are well separated.

The correlation coefficient can still reach more than 0.9 when the signal-to-noise ratio is low, and gradually tends to 1 along with the increase of the signal-to-noise ratio, thereby showing that the invention has better separation precision on the collision signals under the underdetermined condition.

The bit error rate gradually goes to 0 along with the increase of the signal-to-noise ratio, thereby illustrating that the invention has good separation effect on the received VDES collision signal.

The embodiment shows that the random near-end gradient tensor decomposition collision signal separation method has good separation performance and separation precision on the under-determined collision signal, and is suitable for the VDES satellite-borne receiving system.

Claims (8)

1. A VDES collision signal separation method based on random near-end gradient tensor decomposition is characterized by comprising the following steps:

step 1, receiving a VDES collision signal, and processing the VDES collision signal to obtain an observation signal of each subsystem;

step 2, performing centralization and whitening pretreatment on the N paths of observation signals obtained in the step 1 to obtain a whitened mixed signal matrix;

step 3, establishing a generalized covariance matrix set between the observation signal and the source signal, compressing a tensor stacked by the matrix set by using Tucker decomposition to obtain a nuclear tensor, solving the nuclear tensor by using CP decomposition, optimizing the CP decomposition process by using a random near-end gradient algorithm to obtain an estimate of a mixed matrix, and inverting the mixed matrix to obtain a separation matrix;

step 4, multiplying the separation matrix obtained in the step 3 by the mixed signal matrix obtained in the step 2 to obtain a separation signal; and performing frame header detection, frequency offset estimation and demodulation decoding processing on the N paths of separated signals to obtain a data frame of each subsystem signal of the VDES.

2. The method for separating VDES collision signals based on random near-end gradient tensor decomposition as recited in claim 1, wherein the VDES collision signals are received and processed, and the specific process of obtaining the observation signals of each subsystem is as follows:

and receiving the VDES collision signal by the shared antenna array, obtaining a plurality of paths of received signals through sampling of an analog-to-digital converter, and performing digital down-conversion and channel separation processing to respectively obtain observation signal matrixes of the AIS subsystem, the ASM subsystem and the VDE subsystem.

3. The method for separating a VDES collision signal based on random near-end gradient tensor decomposition as recited in claim 1, wherein the N observation signals obtained in step 1 are preprocessed by centering and whitening, and the obtained whitened mixed signal matrix specifically includes:

removing the mean value of the observation signal matrix X;

for the signal after mean value removal

The covariance matrix of (2) is subjected to eigenvalue decomposition, i.e.

Sigma is

The eigenvalues of the covariance matrix of (1) are diagonal matrices of diagonal elements, U is

An orthogonal matrix formed by the eigenvectors of the covariance matrix;

obtaining a whitened mixed signal matrix:

V＝∑^-1/2U^T。

4. the VDES collision signal separation method based on stochastic near-end gradient tensor decomposition as recited in claim 1, wherein a generalized covariance matrix set between the observed signal and the source signal is established, a tensor stacked by the matrix set is compressed by using Tucker decomposition to obtain a nuclear tensor, and the specific process of solving the nuclear tensor by using CP decomposition comprises the following steps:

3-1, obtaining an observation signal generalized covariance matrix set by using linear transformation characteristics of generalized covariance for K processing points, and stacking the observation signal generalized covariance matrix set to be a tensor to establish a tensor decomposition model;

step 3-2, compressing the tensor obtained in the step 3-1 by using Tucker decomposition to obtain a nuclear tensor;

3-3, setting an optimal objective function for decomposing the kernel tensor, setting the maximum iteration times and initially searching the step length;

step 3-4, evaluating the gradient of the target function in the step 3-3, introducing an adjusting factor, iterating the factor matrix of the nuclear tensor by utilizing the gradient and the adjusting factor to obtain a factor matrix of the next iteration, and updating the search step length;

3-5, repeating the steps 3-4 until the target function reaches a set value or reaches a set iteration number, and obtaining the estimation of the mixing matrix;

and 3-6, inverting the mixed matrix to obtain a separation matrix.

5. The method for separating a VDES collision signal based on random near-end gradient tensor decomposition as recited in claim 4, wherein the specific process of establishing a generalized covariance matrix set and stacking the generalized covariance matrix set to obtain a tensor in step 3-1 is as follows:

establishing a generalized covariance matrix for the K processing points to obtain:

in the formula, Ψ_XFor observing the signal generalized covariance matrix, Ψ_SIs a source signal generalized covariance matrix, (-)^TFor transpose operator, A^TThe method is characterized in that the method is a transposition of a mixing matrix A, tau is a processing point and represents a data point expanded by using a Taylor series when a generalized characteristic function needs to be calculated;

stacking K matrixes to obtain tensor x epsilon R^M×M×KEach element thereof is represented as:

defining a matrix D ∈ R^K×NSo that the n-th element of the k-th row corresponds to the diagonal matrix Ψ_S[A^Tτ_k]The (n, n) th element of (i.e. the

The overwrite tensor element values are:

wherein, a_inAnd a_jnAre all the values of the elements in the mixing matrix A, d_knIs the value of an element of the matrix D.

6. The VDES collision signal separation method based on stochastic near-end gradient tensor decomposition as recited in claim 4, wherein the step 3-2 of compressing tensor χ by using Tucker decomposition comprises the following specific steps:

fixing two factor matrixes in the Tucker decomposition as an identity matrix I epsilon R^M×MExpressed as:

χ＝γ×₁I×₂I×₃U

wherein γ ∈ R^M×M×LAs the nuclear tensor, U ∈ R^K×LIs a column unitary matrix, a_nN is the product of tensor and matrix, named n-mode product;

expressed as the Kronecker product of the matrix:

wherein, χ₍₃₎、γ₍₃₎Modulo-3 matrix of tensors χ and γ,

represents the Kronecker product;

the nuclear tensor is determined as:

γ＝χ×₁I×₂I×₃U^T＝χ×₃U^T

the nuclear tensor γ standard decomposition expression is:

in the formula (I), the compound is shown in the specification,

the outer product operation of the representative vector is performed,

and

respectively, the mixed matrix A and the matrix D are compressed,

and

is a matrix

And

the column vector of (2).

7. The method for separating a VDES collision signal based on random near-end gradient tensor decomposition as recited in claim 4, wherein the specific process of setting the optimal objective function f (θ) in the step 3-3 is as follows:

setting the optimal objective function as

Wherein | · | purple sweet_FFor Frobenius norm, the target function is expanded by n mode and rewritten as

Wherein f (θ) is f (A)₍₁₎,…,A_(M)) Abbreviation of (A), H_(n)To remove A_(n)Khatri-Rao products of the matrix of extrinsic residue factors, θ and H_(n)Respectively expressed as:

θ＝[vec(A₍₁₎)^T,…,vec(A_(M))^T]^T

8. a VDES collision signal separation method based on random near-end gradient tensor decomposition as set forth in claim 4, wherein the specific process of the step 3-4 is as follows:

step 3-4-1, using

The gradient estimate for f (theta) is expressed,

then

In the formula, u_(n)A certain fiber of the nuclear tensor gamma, and r is the iteration number;

step 3-4-2, introducing a regulating factor h for promoting an optimization structure_n(A_(n)) The expression is

Step 3-4-3, obtaining a factor matrix of the next iteration by using the latest gradient obtained in the step 3-4-1 and the step 3-4-2

Step 3-4-4, updating step length alpha of search direction^(r)More, moreThe new formula is

Wherein beta is 10^-6。

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