A blind source separation method for joint stationary correlation source signals

Abstract

This invention relates to a blind source separation method for jointly stationary correlated source signals, belonging to the field of signal processing. Firstly, based on a linear model for blind source separation, this invention proposes fundamental assumptions about the model. Then, it decomposes the observed signal into a regular component and a predictable component, and studies a method for extracting useful information from the predictable component. Based on this method, the mixing matrix is ​​estimated, and the separation of correlated source signals is achieved. This invention decomposes the observed signal into a regular component and a predictable component, extracting useful information from the predictable component, thus solving the problem that traditional blind source separation methods, based on the assumption that source signals are independent or uncorrelated, cannot separate correlated source signals.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, specifically relating to a blind source separation method for joint stationary correlated source signals. Background Technology

[0002] The Blind Source Separation (BSS) problem requires consideration of specific assumptions about the source signals when prior knowledge is lacking. Many BSS algorithms consider the statistical properties of the source signals, the most common being the statistical independence of the source signals. These methods aim to find a separation process that achieves the most independent outputs. Another approach is to consider the uncorrelation of the source signals, which utilizes the temporal correlation of the source signals (second-order blind identification) and employs the joint diagonalization of the correlation matrix.

[0003] Another approach to the BSS algorithm is to achieve blind source separation by tracking some prior features of the source signal; CMA is one important technique in this regard. Other methods utilize the properties of the hybrid matrix; for example, the structure of an antenna array can create a special structure for the hybrid matrix. Typical examples of this approach are the MUSIC and ESPIRIT algorithms. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] The technical problem to be solved by the present invention is how to provide a blind source separation method for jointly stationary correlated source signals, so as to solve the problem that traditional blind source separation methods, which are based on the assumption that the source signals are independent or uncorrelated, cannot separate correlated source signals.

[0006] (II) Technical Solution

[0007] To address the aforementioned technical problems, this invention proposes a blind source separation method for joint stationary correlation source signals, which includes the following steps:

[0008] S1. Calculate the correlation function of the observed signal:

[0009] S2. Calculate the spectral density function:

[0010] S3. Extract the spectral components corresponding to the predictable parts from the spectral density function:

[0011] S4. Remove the terms corresponding to the common frequency components from the spectral density function:

[0012] S5. Calculate the correlation function of the expected value:

[0013] S6. Construct the correlation matrix:

[0014] S7. Apply the SOBI method;

[0015] S8. Obtain the mixing matrix A and the source signal s(t).

[0016] (III) Beneficial Effects

[0017] This invention proposes a blind source separation method for joint stationary correlated source signals. The observed signal is decomposed into a regular part and a predictable part, and useful information is extracted from the predictable part. This solves the problem that traditional blind source separation methods, which are based on the assumption that the source signals are independent or uncorrelated, cannot separate correlated source signals. Attached Figure Description

[0018] Figure 1 This is the overall flowchart of the present invention. Detailed Implementation

[0019] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0020] This invention proposes a blind source separation method for jointly stationary correlated source signals, which does not require consideration of the special structure of the source signals or the mixing matrix. First, based on a linear model for blind source separation, fundamental assumptions about the model are proposed. Then, the observed signal is decomposed into a regular part and a predictable part, and a method for extracting useful information from the predictable part is investigated. Based on this method, the mixing matrix is ​​estimated, and the separation of correlated source signals is achieved.

[0021] The overall steps of the blind source separation method based on joint stationary correlated source signals are as follows: Figure 1 As shown,

[0022] The specific steps are as follows:

[0023] S1. Calculate the correlation function of the observed signal:

[0024] S2. Calculate the spectral density function:

[0025] S3. Extract the spectral components corresponding to the predictable parts from the spectral density function:

[0026] S4. Remove the terms corresponding to the common frequency components from the spectral density function:

[0027] S5. Calculate the correlation function of the expected value:

[0028] S6. Construct the correlation matrix:

[0029] S7. Apply the SOBI method;

[0030] S8. Obtain the mixing matrix A and the source signal s(t).

[0031] 3.1 Model and Assumptions

[0032] Suppose there are d signals s1(t), ..., s2(t). d (t) represents d signal sources from different locations.

[0033] x(t) = a1s1(t) + ... + a d s d (t)+n(t)

[0034] therefore

[0035] x(t)=y(t)+n(t)=A·s(t)+n(t)

[0036] in These are observation signals obtained from m sensors. It is a source signal composed of d unknown source signals. It is an additive noise signal. It is a mixed matrix.

[0037] The following assumptions are made about this model:

[0038] (1) Each component in s(t) is a stationary random process with zero mean;

[0039] (2) n(t) is a stationary random process with zero mean and is independent of the source signal;

[0040] (3) The mixed matrix A is full rank;

[0041] (4) The source signals are jointly stationary, but it is not required that the source signals are mutually independent or uncorrelated.

[0042] 3.2 Decomposition of Observed Signals

[0043] The observed signal can be represented in the following model form:

[0044]

[0045] in It is a mixture matrix. Therefore,

[0046] x i (t)=α i s1(t)+β i s2(t)+ni (t), i = 1, 2, ...

[0047] The conventional and predicted parts of the source signal can be represented as s, respectively. ir (t) and s ip (t)(i=1,2:

[0048] s i (t)=s ip (t)+s ir (t)

[0049] in

[0050]

[0051]

[0052] Where {a K} and {b L} are orthogonal random variables, {ω 1K},{ω 2L} is a frequency set.

[0053] Since the normal and predictive parts of any signal are orthogonal, we can obtain

[0054] x i (t)=x ip (t)+x ir (t)+n i (t), i = 1, 2, ...

[0055] in

[0056] x ip (t)=α i s 1p (t)+β i s 2p (t), i = 1, 2, ...

[0057] x ir (t)=α i s 1r (t)+β i s 2r (t), i = 1, 2, ...

[0058] therefore,

[0059]

[0060] Where {d iq} are orthogonal random variables, {ω q}={ω 1K}∪{ω 2L}

[0061] As can be seen from the above, any observed signal consists of a conventional part and a predictable part, and these are linear combinations of the conventional part and the predictable part of the source signal, respectively.

[0062] 3.3 Calculate the correlation function

[0063] The correlation function of the observed signal is

[0064]

[0065] Where N0 is the variance of the noise. and These are the correlation functions for the regular part and the predictable part, respectively.

[0066] 3.4 Calculation of Spectral Density

[0067] The rate spectral density function of the observed signal is:

[0068]

[0069] in,

[0070]

[0071] It can be seen that the spectral function of the predictable part is a pure impulse component, so these components can be detected and separated from the spectral function of the observed signal.

[0072] 3.5 Extracting the spectral density of the predictable portion

[0073] {Ω n} represents the frequency set, and the predictable part of the observed signal can be written as:

[0074]

[0075]

[0076] therefore,

[0077]

[0078] therefore

[0079]

[0080] 3.6 Spectral density after removing common frequency components

[0081] Remove the terms corresponding to the common frequency components from the spectral density function, i.e. The second part of the function yields

[0082]

[0083] 3.7 Calculate the correlation function of the expected value

[0084] The expected correlation function is

[0085]

[0086] Among them, F -1 {·} represents the inverse Fourier transform.

[0087] 3.8 Constructing the correlation matrix

[0088] because and If they are unrelated, the following matrix form can be obtained.

[0089]

[0090] Where H represents the complex conjugate transpose.

[0091]

[0092] 3.9 Applying the SOBI Method

[0093] The SOBI (Second-order blind identification) algorithm is used to calculate the orthogonal matrix T and the identity matrix U.

[0094] The orthogonal matrix T is

[0095]

[0096] Where μ1 and μ2 are used as The eigenvalues ​​are v1 and v2, which are the eigenvectors corresponding to the eigenvalues.

[0097] When τ≠0, applying the orthogonal matrix T, the correlation matrix can be written as:

[0098]

[0099] therefore,

[0100]

[0101] 3.10 Calculating the Mixture Matrix and Source Signals: The mixture matrix can be obtained from the identity matrix U.

[0102] A = T -1 ·U

[0103] Therefore, the source signal is

[0104] s(t)=A -1 ·x(t)

[0105] 4. Beneficial effects

[0106] By decomposing the observed signal into a regular part and a predictable part, and extracting useful information from the predictable part, this method solves the problem that traditional blind source separation methods, which are based on the assumption that source signals are independent or uncorrelated, cannot separate correlated source signals.

[0107] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A blind source separation method for joint stationary correlated source signals, characterized in that, The method includes the following steps: S1. Calculate the correlation function of the observed signal: S2. Calculate the spectral density function: S3. Extract the spectral components corresponding to the predictable parts from the spectral density function: S4. Remove the terms corresponding to the common frequency components from the spectral density function: S5. Calculate the correlation function of the expected value: S6. Construct the correlation matrix: S7. Apply the SOBI method; S8. Obtain the mixing matrix A and the source signal s(t); in, Suppose there are d signals s1(t), ..., s2(t) d (t) represents d signal sources from different locations. x(t)=a1s1(t)+…+a d s d (t)+n(t) therefore x(t)=y(t)+n(t)=A·s(t)+n(t) in These are observation signals obtained from m sensors. It is a source signal composed of d unknown source signals. It is an additive noise signal. It is a mixed matrix; Assumption: Each component in s(t) is a stationary random process with zero mean; n(t) is a stationary random process with zero mean, and is independent of the source signal; The mixed matrix A is full rank; The source signals are jointly stationary, but it is not required that the source signals are independent or uncorrelated. The observed signal can be represented in the following model form: in It is a mixture matrix; therefore, x i (t)=α i s1(t)+β i s2(t)+n i (t),i=1,2,… The conventional and predicted parts of the source signal can be represented as s, respectively. ir (t) and s ip (t), i = 1, 2: s i (t)=s ip (t)+s ir (t) in Where {a K } and {b L } are orthogonal random variables, {ω 1K },{ω 2L } is a frequency set; Since the normal and predictive parts of any signal are orthogonal, we can obtain x i (t)=x ip (t)+x ir (t)+n i (t),i=1,2,… in x ip (t)=α i s 1p (t)+β i s 2p (t),i=1,2,… x ir (t)=α i s 1r (t)+β i s 2r (t),i=1,2,… therefore, Where {d iq } are orthogonal random variables, {ω q }={ω 1K }∪{ω 2L }; In step S1, the correlation function of the observed signal is: Where N0 is the variance of the noise. and These are the correlation functions for the conventional part and the predictable part, respectively; In step S2, the rate spectral density function of the observed signal is: in, In step S3, {Ω n } represents the frequency set, and the predictable part of the observed signal can be written as: therefore, therefore In step S4, the terms corresponding to the common frequency components in the spectral density function are removed, i.e. The second part of the function yields In step S5, the desired correlation function is: Among them, F -1 {·} denotes the inverse Fourier transform; In step S6, because and Unrelated, the following matrix form can be obtained. Where H represents the complex conjugate transpose. Steps S7 and S8 specifically include: applying the second-order blind identification SOBI algorithm to calculate the orthogonal matrix T and the identity matrix U; The orthogonal matrix T is Where μ1 and μ2 are used as The eigenvalues ​​are v1 and v2 are the eigenvectors corresponding to the eigenvalues. When τ≠0, applying the orthogonality matrix T, the correlation matrix is ​​written as follows: therefore, The mixture matrix is ​​obtained from the identity matrix U. A=T -1 ·U Therefore, the source signal is s(t)=A -1 ·x(t)。

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