阅读说明：本技术 一种基于多策略矩阵重构的自适应信源数估计方法 (self-adaptive source number estimation method based on multi-strategy matrix reconstruction ) 是由 陈章 柳永祥 施伟 吴昊 刘斌 周强 于 2019-09-18 设计创作，主要内容包括：本发明公开了一种基于多策略矩阵重构的自适应信源数估计方法。该方法为：首先利用均匀线性天线阵列接收相干信号,计算观测信号的协方差矩阵；然后根据两种不同策略对观测信号的协方差矩阵R<Sub>x</Sub>进行Toeplitz矩阵重构处理,得到具有Toeplitz性质的协方差矩阵R<Sub>S1</Sub>以及R<Sub>S2</Sub>；接着利用R<Sub>x</Sub>、R<Sub>S1</Sub>和R<Sub>S2</Sub>对信号源的相干类型进行联合估计；然后利用R<Sub>S1</Sub>和R<Sub>S2</Sub>的特征值下降比在不同相干信号条件下的统计分布特性,针对不同相干类型的信源设计对应的数据过滤与融合策略；最后采用基于特征值分解法对处理后的数据进行信源数估计。本发明具有方法简单、信源数估计准确率高、抗噪声能力强、鲁棒性好的优点,能够估计信源相干类型。(The invention discloses an self-adaptive source number estimation method based on multi-strategy matrix reconstruction x Performing Toeplitz matrix reconstruction processing to obtain a covariance matrix R with Toeplitz property S1 And R S2 (ii) a Followed by the use of R x 、R S1 And R S2 Carrying out joint estimation on the coherence type of the signal source; then use R S1 And R S2 The characteristic value reduction ratio of the signal source is calculated according to the statistical distribution characteristics of the signal source under different coherent signal conditions, and corresponding data filtering and fusion strategies are designed aiming at the signal sources with different coherent types; and finally, performing information source number estimation on the processed data by adopting a characteristic value-based decomposition method. The invention has the advantages of simple method, high accuracy of information source number estimation, and noise resistanceThe method has the advantages of strong force and good robustness, and can estimate the information source coherence type.)

1, A self-adaptive source number estimation method based on multi-strategy matrix reconstruction, characterized by comprising the following steps:

step 1, carrying out T times of observation, receiving signals by utilizing a uniform linear antenna array, and calculating a covariance matrix set { R ] of an observed signal x_x}_T；

Step 2, adopting two different strategies to carry out covariance matrix R on observation signals_xPerforming Toeplitz matrix reconstruction processing to obtain a covariance matrix R with Toeplitz property_S1And R_S2Further obtaining Toeplitz weightSet of construction matrices { R }_S1}_TAnd { R_S2}_T；

Step 3, mixing { R_x}_T、{R_S1}_TAnd { R_S2}_TInputting the data to an information source number estimator g (R) based on a eigenvalue decomposition method, and carrying out independent estimation for T times to obtain an estimated value { V }_x,V_S1,V_S2}；

Step 4, utilizing { V_x,V_S1,V_S2Performing joint estimation on the source coherence type, and outputting a source coherence type estimation value CF: CF ═ C_dWhen is expressed as an independent source case, CF ═ C_cTime indicates the existence of a coherent source condition;

step 5, if CF ═ C_dThen, it is judged as V_xThe estimated value of the information source number is obtained, and the algorithm is ended; otherwise, the Toeplitz reconstruction matrix set { R }_S1}_TAnd { R_S2}_TInputting the input into an extended output value estimator h (R) to obtain an estimation set { h (R)_S1)}_TAnd { h (R)_S2)}_T；

Step 6, estimating a set { h (R) of the estimation_S1)}_TAnd { h (R)_S2)}_TPerforming data filtering processing to obtain a set { V (R)_S1)}_TAnd { V (R)_S2)}_T；

Step 7, set { V (R) }_S1)}_TAnd { V (R)_S2)}_TPerforming weighted fusion processing to obtain a set V_f；

Step 8, set V_fThe value K with the most occurrence times is the estimation result of the information source number;

and 9, outputting the information source number estimation result.

2. The method of claim 1, wherein the step 1 comprises performing T observations, receiving signals with a uniform linear antenna array, and calculating a covariance matrix set { R } of observed signals x_x}_TThe method comprises the following steps:

setting the antenna array to N spacing distancesD, all the elements are isotropic, the problem of antenna mutual coupling does not exist, the fast beat number of the received signal is M, and the observation signal vector received by the antenna array is expressed as X ═ X₁,x₂,…,x_NAnd calculating a covariance matrix R of the observed signal according to formula (1)_x：

Carrying out T times of observation to obtain a covariance matrix set { R_x}_TWherein T is more than or equal to 1; x (t)_i) Represents t_iThe observation signal received by the time-of-day antenna array, R represents the covariance matrix R_xOf (1).

3. The method as claimed in claim 1, wherein the covariance matrix R of the observed signal is determined by two different strategies in step 2_xPerforming Toeplitz matrix reconstruction processing to obtain a covariance matrix R with Toeplitz property_S1And R_S2The method comprises the following steps:

toeplitz matrix R reconstructed according to error minimum difference transformation strategy_S1The following were used:

wherein C is_S1(m) is calculated from equation (3):

wherein r is_i,i+mRepresenting the coherence coefficient between the ith source and the (i + m) th source, (r)_i,i+m)^*Represents taking r_i,i+mConjugation of (1); n represents the number of array elements in the antenna array;

toeplitz matrix R reconstructed according to standard virtual linear array differential transformation strategy_S2The following were used:

wherein C is_S2(m) is calculated from equation (5):

wherein r is_1,1+mRepresents the coherence coefficient between the 1 st source and the 1+ m sources, (r)_1,1+m)^*Represents taking r_1,1+mConjugation of (1);

from a set of covariance matrices R_x}_TObtaining a Toeplitz reconstruction matrix set { R_S1}_TAnd { R_S2}_T。

4. The method of claim 1, wherein { R } is used in step 3_x}_T、{R_S1}_TAnd { R_S2}_TInputting the data to an information source number estimator g (R) based on a eigenvalue decomposition method, and carrying out independent estimation for T times to obtain an estimated value { V }_x,V_S1,V_S2The method concretely comprises the following steps:

step 3.1, carrying out eigenvalue decomposition on the input signal covariance matrix to calculate eigenvalues, and sequencing from large to small to obtain an eigenvalue set { lambda₁,λ₂,...,λ_N}；

Step 3.2, calculate the reduction ratio ρ of the adjacent eigenvalues according to equation (6)_i：

Obtaining a ratio set [ rho ] containing N-1 elements from the characteristic value set_i|i＝1,2,...,N-1}；

Step 3.3, the estimator g (R) outputs the serial number value V corresponding to the maximum value in the ratio set, and the expression is as follows:

will { R_x}_T、{R_S1}_TAnd { R_S2}_TInputting the data to an information source number estimator g (R) based on a characteristic value decomposition method, and carrying out independent estimation for T times to respectively obtain corresponding estimation values V_x、V_S1、V_S2。

5. The method of claim 1, wherein the step 4 utilizes { V } V_x,V_S1,V_S2Performing joint estimation on the source coherence type, and outputting a source coherence type estimation value CF, specifically as follows:

the formula of the coherent type joint estimation is as follows:

if V_x＝V_S1If the signal source type is judged to be independent, th state mark C is output_d；

If V_x1 and V_S1≠V_S2If so, the signal source is judged to be a complete coherent signal source type, and a second state mark C is output_c；

If V_xNot equal to 1, and V_S1≠V_S2If yes, the method is judged as a partial coherent source type, and a third state mark C is output_dc。

6. The adaptive source number estimation method based on multi-strategy matrix reconstruction as claimed in claim 1, wherein the Toeplitz reconstruction matrix set { R ] in step 5_S1}_TAnd { R_S2}_TInputting the input into an extended output value estimator h (R) to obtain an estimation set { h (R)_S1)}_TAnd { h (R)_S2)}_TThe method comprises the following steps:

expanding the output value of the estimator g (R), and expanding the output value from the sequence number of the output maximum reduction ratio to the sequence number corresponding to the first two values of the maximum reduction ratio, namely:

ρ_i、ρ_jis the adjacent eigenvalue reduction ratio.

7. The method as claimed in claim 1, wherein the estimation set { h (R) is the estimation set of the pairs in step 6_S1)}_TAnd { h (R)_S2)}_TPerforming data filtering processing to obtain a set { V (R)_S1)}_TAnd { V (R)_S2)}_TThe formula is as follows:

all values in the original set equal to 1 and N-1 are rejected according to equation (10).

8. The method of claim 1, wherein the set { V (R) is set in step 7_S1)}_TAnd { V (R)_S2)}_TPerforming weighted fusion processing to obtain a set V_fThe formula is as follows:

{V_f}＝w₁{V(R_S1)}+w₂{V(R_S2)} (11)

wherein the weight value w₁And w₂Is a positive integer, w being a fully coherent source condition₁<w₂(ii) a Under partially coherent source conditions, w₁>w₂。

Technical Field

The invention belongs to the technical field of signal source number estimation algorithms, and particularly relates to self-adaptive signal source number estimation methods based on multi-strategy matrix reconstruction.

Background

Most existing array signal DOA estimation algorithms need to know a priori knowledge about the number of incident signals, however, in practical scenarios, especially in non-cooperative passive localization applications, the number of signal sources is usually unpredictable. Since most model bases of DOA algorithms are based on feature decomposition and subspace estimation, the number of sources directly determines the composition of the subspace. Therefore, before estimating the azimuth angle of the signal source, the source number needs to be estimated.

The characteristic value solution method and the information theory method can only estimate the number of independent signal sources and cannot estimate signals with coherence or strong correlation, the estimation of the number of the information sources with coherence or strong correlation can adopt a smooth rank sequence method and a Gauss circle method, wherein the smooth rank sequence method is similar to a space smooth decorrelation method, research shows that the performance of the smooth rank sequence method is better when the signal-to-noise ratio is larger and the number of fast beats is more, and the Gauss circle method does not need to estimate the information source number by using the characteristic value and has better estimation performance under the condition of low signal-to-noise ratio.

Disclosure of Invention

The invention aims to provide self-adaptive source number estimation methods based on multi-strategy matrix reconstruction, which have high source number estimation accuracy, strong anti-noise capability and good robustness, and can estimate the source coherence type.

kinds of self-adapting information source number estimation method based on multi-strategy matrix reconstruction, including the following steps:

step 1, carrying out T times of observation, receiving signals by utilizing a uniform linear antenna array, and calculating a covariance matrix set { R ] of an observed signal x_x}_T；

Step 2, adopting two different strategies to carry out covariance matrix R on observation signals_xPerforming Toeplitz matrix reconstruction processing to obtain a covariance matrix R with Toeplitz property_S1And R_S2And further obtaining a Toeplitz reconstruction matrix set { R_S1}_TAnd { R_S2}_T；

Step 3, mixing { R_x}_T、{R_S1}_TAnd { R_S2}_TInputting the data to an information source number estimator g (R) based on a eigenvalue decomposition method, and carrying out independent estimation for T times to obtain an estimated value { V }_x,V_S1,V_S2}；

Step 4, utilizing { V_x,V_S1,V_S2Performing joint estimation on the source coherence type, and outputting a source coherence type estimation value CF: CF ═ C_dWhen is expressed as an independent source case, CF ═ C_cTime indicates the existence of a coherent source condition;

step 5, if CF ═ C_dThen, it is judged as V_xThe estimated value of the information source number is obtained, and the algorithm is ended; otherwise, the Toeplitz reconstruction matrix set { R }_S1}_TAnd { R_S2}_TInputting the input into an extended output value estimator h (R) to obtain an estimation set { h (R)_S1)}_TAnd { h (R)_S2)}_T；

Step 6, estimating a set { h (R) of the estimation_S1)}_TAnd { h (R)_S2)}_TPerforming data filtering processing to obtain a set { V (R)_S1)}_TAnd { V (R)_S2)}_T；

Step 7, set { V (R) }_S1)}_TAnd { V (R)_S2)}_TPerforming weighted fusion processing to obtain a set V_f；

Step 8, set V_fThe value K with the most occurrence times is the information sourceThe result of the estimation of the number;

and 9, outputting the information source number estimation result.

, performing T observations as described in step 1, receiving signals with a uniform linear antenna array, and calculating a covariance matrix set { R } of observed signals x_x}_TThe method comprises the following steps:

the antenna array is set to be composed of N array elements with the interval distance of d, all the array elements are isotropic, the problem of antenna mutual coupling does not exist, the fast beat number of a received signal is M, and an observation signal vector received by the antenna array is represented as X ═ X { (X)₁,x₂,…,x_NAnd calculating a covariance matrix R of the observed signal according to formula (1)_x：

Carrying out T times of observation to obtain a covariance matrix set { R_x}_TWherein T is more than or equal to 1; x (t)_i) Represents t_iThe observation signal received by the time-of-day antenna array, R represents the covariance matrix R_xOf (1).

step, the covariance matrix R of the observed signal in step 2 is determined by two different strategies_xPerforming Toeplitz matrix reconstruction processing to obtain a covariance matrix R with Toeplitz property_S1And R_S2The method comprises the following steps:

toeplitz matrix R reconstructed according to error minimum difference transformation strategy_S1The following were used:

wherein C is_S1(m) is calculated from equation (3):

wherein r is_i,i+mRepresenting the coherence coefficient between the ith source and the (i + m) th source,(r_i,i+m)^*represents taking r_i,i+mConjugation of (1); n represents the number of array elements in the antenna array;

toeplitz matrix R reconstructed according to standard virtual linear array differential transformation strategy_S2The following were used:

wherein C is_S2(m) is calculated from equation (5):

wherein r is_1,1+mRepresents the coherence coefficient between the 1 st source and the 1+ m sources, (r)_1,1+m)^*Represents taking r_1,1+mConjugation of (1);

from a set of covariance matrices R_x}_TObtaining a Toeplitz reconstruction matrix set { R_S1}_TAnd { R_S2}_T。

Step , step 3 describes converting { R_x}_T、{R_S1}_TAnd { R_S2}_TInputting the data to an information source number estimator g (R) based on a eigenvalue decomposition method, and carrying out independent estimation for T times to obtain an estimated value { V }_x,V_S1,V_S2The method concretely comprises the following steps:

step 3.1, carrying out eigenvalue decomposition on the input signal covariance matrix to calculate eigenvalues, and sequencing from large to small to obtain an eigenvalue set { lambda₁,λ₂,...,λ_N}；

Step 3.2, calculate the reduction ratio ρ of the adjacent eigenvalues according to equation (6)_i：

Obtaining a ratio set [ rho ] containing N-1 elements from the characteristic value set_i|i＝1,2,...,N-1}；

Step 3.3, the estimator g (R) outputs the serial number value V corresponding to the maximum value in the ratio set, and the expression is as follows:

will { R_x}_T、{R_S1}_TAnd { R_S2}_TInputting the data to an information source number estimator g (R) based on a characteristic value decomposition method, and carrying out independent estimation for T times to respectively obtain corresponding estimation values V_x、V_S1、V_S2。

step, step 4 said utilizing { V_x,V_S1,V_S2Performing joint estimation on the source coherence type, and outputting a source coherence type estimation value CF, specifically as follows:

the formula of the coherent type joint estimation is as follows:

if V_x＝V_S1If the signal source type is judged to be independent, th state mark C is output_d；

If V_x1 and V_S1≠V_S2If so, the signal source is judged to be a complete coherent signal source type, and a second state mark C is output_c；

If V_xNot equal to 1, and V_S1≠V_S2If yes, the method is judged as a partial coherent source type, and a third state mark C is output_dc。

step, set Toeplitz reconstruction matrix { R } in step 5_S1}_TAnd { R_S2}_TInputting the input into an extended output value estimator h (R) to obtain an estimation set { h (R)_S1)}_TAnd { h (R)_S2)}_TThe method comprises the following steps:

expanding the output value of the estimator g (R), and expanding the output value from the sequence number of the output maximum reduction ratio to the sequence number corresponding to the first two values of the maximum reduction ratio, namely:

ρ_i、ρ_jis the adjacent eigenvalue reduction ratio.

, the set of estimates { h (R) } from step 6_S1)}_TAnd { h (R)_S2)}_TPerforming data filtering processing to obtain a set { V (R)_S1)}_TAnd { V (R)_S2)}_TThe formula is as follows:

all values in the original set equal to 1 and N-1 are rejected according to equation (10).

Further , the step 7 will assemble V (R)_S1)}_TAnd { V (R)_S2)}_TPerforming weighted fusion processing to obtain a set V_fThe formula is as follows:

{V_f}＝w₁{V(R_S1)}+w₂{V(R_S2)} (11)

wherein the weight value w₁And w₂Is a positive integer, w being a fully coherent source condition₁<w₂(ii) a Under partially coherent source conditions, w₁>w₂。

Compared with the prior art, the invention has the remarkable advantages that: (1) the method has the advantages that the characteristics that the performances have complementarity under different coherent information source conditions by utilizing two matrix reconstruction strategies, and accurate estimation of the information source number under any coherent condition is realized by a strategy combination method; (2) the array degree of freedom does not need to be sacrificed, and compared with the traditional coherent information source number estimation method, the method has higher accuracy under the condition of low signal-to-noise ratio; (3) the type of coherence of the source can be estimated.

Drawings

FIG. 1 is a schematic flow chart of an adaptive source number estimation method based on multi-strategy matrix reconstruction according to the present invention.

Detailed Description

The invention is further described in detail in connection with the figures and the detailed description.

With reference to fig. 1, the adaptive source number estimation method based on multi-strategy matrix reconstruction of the present invention includes the following steps:

step 1, carrying out T times of observation, receiving signals by utilizing a uniform linear antenna array, and calculating a covariance matrix set { R ] of an observed signal x_x}_T(ii) a The method comprises the following specific steps:

the antenna array is set to be composed of N array elements with the interval distance of d, all the array elements are isotropic, the problem of antenna mutual coupling does not exist, the fast beat number of a received signal is M, and an observation signal vector received by the antenna array is represented as X ═ X { (X)₁,x₂,…,x_NAnd calculating a covariance matrix R of the observed signal according to formula (1)_x：

Carrying out T times of observation to obtain a covariance matrix set { R_x}_TWherein T is more than or equal to 1; x (t)_i) Represents t_iThe observation signal received by the time-of-day antenna array, R represents the covariance matrix R_xOf (1).

Step 2, adopting two different strategies to carry out covariance matrix R on observation signals_xPerforming Toeplitz matrix reconstruction processing to obtain a covariance matrix R with Toeplitz property_S1And R_S2And further obtaining a Toeplitz reconstruction matrix set { R_S1}_TAnd { R_S2}_TThe method comprises the following steps:

observing the covariance matrix R of the array signals when coherence exists in the incident signals_xThe method is not nonsingular any more, namely the condition of rank deficiency occurs, the rank deficiency of the covariance matrix can cause the signal feature vector to be dispersed into a noise subspace, the orthogonality of the signal subspace and the noise subspace is damaged, so the rank of the covariance matrix needs to be recovered through a decorrelation algorithm_xTo carry outThe Toeplitz matrix is reconstructed to obtain a covariance matrix R with Toeplitz property_S1And R_S2。

Obtaining a Toeplitz matrix R reconstructed according to the error minimum difference transformation strategy according to a formula (2)_S1：

Wherein C is_S1(m) is calculated from equation (3):

wherein r is_i,i+mRepresenting the coherence coefficient between the ith source and the (i + m) th source, (r)_i,i+m)^*Represents taking r_i,i+mConjugation of (1); n represents the number of array elements in the antenna array;

toeplitz matrix R obtained from formula (2)_S1Covariance matrix R with original observed signal_xHas the smallest euclidean distance, i.e. the error of the reconstructed matrix is smallest.

Obtaining a Toeplitz matrix R reconstructed according to a standard virtual linear array differential transformation strategy according to a formula (4)_S2：

Wherein C is_S2(m) is calculated from equation (5):

wherein r is_1,1+mRepresents the coherence coefficient between the 1 st source and the 1+ m sources, (r)_1,1+m)^*Represents taking r_1,1+mConjugation of (1);

the Toeplitz matrix reconstructed according to the strategy standard virtual linear array differential transformation strategy can be equivalent to a covariance matrix of a standard linear array into which independent signals are incident when the information sources are completely coherent.

From a set of covariance matrices R_x}_TObtaining a Toeplitz reconstruction matrix set { R_S1}_TAnd { R_S2}_T。

Step 3, mixing { R_x}_T、{R_S1}_TAnd { R_S2}_TInputting the data to an information source number estimator g (R) based on a eigenvalue decomposition method, and carrying out independent estimation for T times to obtain an estimated value { V }_x,V_S1,V_S2The method concretely comprises the following steps:

wherein the estimator g (R) is a source number estimator based on eigenvalue decomposition, and the estimation process is as follows:

step 3.1, carrying out eigenvalue decomposition on the input signal covariance matrix R to calculate eigenvalues, and sequencing from large to small to obtain an eigenvalue set { lambda₁,λ₂,...,λ_N}；

And 3.2, calculating the descending ratio of the adjacent characteristic values according to the formula (6):

obtaining a ratio set [ rho ] containing N-1 elements from the characteristic value set_i|i＝1,2,...,N-1}；

Step 3.3, the estimator g (R) outputs the serial number value V corresponding to the maximum value in the ratio set, and the expression is as follows:

will { R_x}_T、{R_S1}_TAnd { R_S2}_TInputting the data to an information source number estimator g (R) based on a characteristic value decomposition method, and carrying out independent estimation for T times to respectively obtain corresponding estimation values V_x、V_S1、V_S2。

When the input is the covariance matrix set, the output result is the V value with the largest number of occurrences.

Step 4, utilizing { V_x,V_S1,V_S2Performing joint estimation on the source coherence type, and outputting a source coherence type estimation value CF: CF ═ C_dWhen is expressed as an independent source case, CF ═ C_cTime is expressed as the presence of coherent source conditions:

the formula of the coherent type joint estimation is as follows:

if V_x＝V_S1If the signal source type is judged to be independent, th state mark C is output_d；

If V_x1 and V_S1≠V_S2If so, the signal source is judged to be a complete coherent signal source type, and a second state mark C is output_c；

If V_xNot equal to 1, and V_S1≠V_S2If yes, the method is judged as a partial coherent source type, and a third state mark C is output_dc。

Step 5, if CF ═ C_dThen, it is judged as V_xThe estimated value of the information source number is obtained, and the algorithm is ended; otherwise, the Toeplitz reconstruction matrix set { R }_S1}_TAnd { R_S2}_TInputting the input into an extended output value estimator h (R) to obtain an estimation set { h (R)_S1)}_TAnd { h (R)_S2)}_TThe method comprises the following steps:

expanding the output value of the estimator g (R), and expanding the output value from the sequence number of the output maximum reduction ratio to the sequence number corresponding to the first two values of the maximum reduction ratio, namely:

ρ_i、ρ_jis the adjacent eigenvalue reduction ratio.

Step 6, estimating a set { h (R) of the estimation_S1)}_TAnd { h (R)_S2)}_TPerforming data filtering processing to obtain a set { V (R)_S1)}_TAnd { V (R)_S2)}_TThe formula is as follows:

all values in the original set equal to 1 and N-1 are rejected according to equation (10).

Step 7, set { V (R) }_S1)}_TAnd { V (R)_S2)}_TPerforming weighted fusion processing to obtain a set V_fThe formula is as follows:

{V_f}＝w₁{V(R_S1)}+w₂{V(R_S2)} (11)

wherein the weight value w₁And w₂Is a positive integer, w being a fully coherent source condition₁<w₂(ii) a Under partially coherent source conditions, w₁>w₂。

Step 8, set V_fAnd the value K with the largest occurrence number is the estimation result of the information source number.

And 9, outputting the information source number estimation result.

Through the steps, the information source number estimation under the conditions of information source irrelevance and coherent information sources can be realized, and the coherent type of the information source can be estimated.

In conclusion, the information source number estimation method based on multi-strategy matrix reconstruction provided by the invention has high estimation accuracy under the conditions of independent information sources and coherent information sources, has strong anti-noise interference capability and robustness, and is easy to realize in engineering.