CN105182299B - Non-orthogonal joint diagonalization echo signal processing method based on multiple spin matrix - Google Patents
Non-orthogonal joint diagonalization echo signal processing method based on multiple spin matrix Download PDFInfo
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- CN105182299B CN105182299B CN201510401321.7A CN201510401321A CN105182299B CN 105182299 B CN105182299 B CN 105182299B CN 201510401321 A CN201510401321 A CN 201510401321A CN 105182299 B CN105182299 B CN 105182299B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/28—Details of pulse systems
- G01S7/285—Receivers
- G01S7/292—Extracting wanted echo-signals
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/35—Details of non-pulse systems
- G01S7/352—Receivers
- G01S7/354—Extracting wanted echo-signals
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Abstract
The embodiment of the present invention provides a kind of non-orthogonal joint diagonalization echo signal processing method based on multiple spin matrix, can avoid the appearance of singular solution, improve computational efficiency.This method includes：(1) matrix element is extracted；(2) intermediary matrix is constructed；(3) cost function is minimized；(4) the first spin matrix under given position parameter value is sought；(5) each covariance matrix in the covariance complex matrix set of echo-signal is updated with the first spin matrix tried to achieve in (4), new matrix group is obtained.Same above-mentioned steps (1), (2), (3), extract the element of homography in new matrix group, construct intermediary matrix, minimize cost function；(6) the second spin matrix under given position parameter value is sought；(7) value of all location parameters has been updated, Joint diagonalization factor matrix is obtained.
Description
Technical field
The present invention relates to blind signal processing field, more particularly to a kind of non-orthogonal joint diagonalization based on multiple spin matrix
Echo signal processing method.
Background technology
Various information are filled with nature and actual life.In order to obtain useful information therefrom, it is necessary to
The data containing the information are obtained, information is obtained by handling these data.The data for usually containing information are often multiple
The mixing of composition, it is difficult to handle, and the characteristic of signal transmission passage is also very complicated.Therefore, needed for being extracted from mass data
Composition, and then the signal processing method of useful information is obtained, become to solve the powerful of this problem.
Blind source separating (Blind Source Separation, BSS) is just a process that.It is used as signal transacting
Important component in subject, there is very important theory significance and practical value.Because irrelevance is assumed and counts
Independence assumption both has generality, agrees with the physical mechanism that a large amount of source signals are produced again, therefore blind source separate technology has succeeded
Apply in many fields, as one of powerful for solving numerous signal processing problems.
Blind source separate technology is developed so far, and many scholars it is also proposed some effective methods.There is scholar to be based on Jacobi
(Jacobi) rotate, realize Joint diagonalization, estimation separation matrix is so as to the method for realizing source signal separation.There is scholar to be based on source
The non-white characteristic of signal, objective matrix group is used as using the multiple different tests correlation matrixes of observation signal, it is proposed that based on second order system
SOBI (Second-order Blind Indification) method of metering, such algorithm usually requires that aliasing to be estimated
Matrix or separation matrix are unitary matrice, it is therefore desirable to carry out whitening processing to observation signal.But albefaction is carried out to observation signal
Can not possibly accurately it be realized during processing, and the extra error thus introduced can not be disappeared by ensuing orthogonal Joint diagonalization algorithm
Remove.
The content of the invention
It is a kind of based on the nonopiate of multiple spin matrix it is an object of the invention to propose for above-mentioned the deficiencies in the prior art
Joint diagonalization echo signal processing method.
The technical scheme is that in the case where source signal and transmission signal parameters are unknown, according to input source signal
Statistical property, the source signal of each statistical iteration is isolated merely with observation signal.Propose a kind of based on F- norm costs
The complex field non-orthogonal joint diagonalization method that the Givens rotations of function and Hyperbolic rotate, passes through continuous Givens
Rotation and hyperbolic rotations, realize the Joint diagonalization of complicated target matrix group.Combined estimator Givens spin moments of the present invention
All parameters of battle array and hyperbolic spin matrixs, it is to avoid the appearance of singular solution, improve computational efficiency.And finally give
Non-orthogonal joint diagonalization covariance complex matrix diagonal on element be from source signal (i.e. radar echo signal)
The useful signal of middle extraction.
To reach above-mentioned purpose, the present invention, which is adopted the following technical scheme that, to be achieved.
A kind of non-orthogonal joint diagonalization echo signal processing method based on multiple spin matrix, comprises the following steps：
Step 1, radar receives echo-signal, and according to receiving the sequencing of the echo-signal by the echo-signal
It is grouped, the covariance complex matrix of every group of echo-signal is determined as the first covariance complex matrix, so as to obtain multiple first
Covariance complex matrix, the multiple first covariance complex matrix has in identical dimension, and each first covariance complex matrix
Element indicated by location parameter；
Step 2, the first covariance complex matrix set is constituted using each first covariance complex matrix as element；
Step 3, according to the designated value of location parameter, position described in the multiple first covariance complex matrix is extracted respectively
Element indicated by the designated value of parameter, and construct the first cost function；
Step 4, first cost function is solved, the first spin matrix is obtained；
Step 5, the multiple first covariance complex matrix is multiplied with first spin matrix respectively, obtained after multiplication
Multiple second covariance complex matrix, the multiple second covariance complex matrix constitutes the second covariance complex matrix set；
Step 6, according to the designated value of the location parameter, extract respectively each second in the second covariance complex matrix set
The element that the designated value of location parameter described in covariance complex matrix is indicated；
Step 7, the position according to each second covariance complex matrix in the second covariance complex matrix set is joined
The element that several designated values is indicated, constructs the second cost function；
Step 8, second cost function is solved, the second spin matrix is obtained；
Step 9, each second covariance complex matrix and second spin moment in the second covariance complex matrix set
Battle array is multiplied, and multiple 3rd covariance complex matrix are obtained after multiplication, and the multiple 3rd covariance complex matrix constitutes the 3rd covariance
Complex matrix set；
Step 10, the designated value of the location parameter is changed, by the 3rd covariance complex matrix aggregate assignment to described
First covariance complex matrix set, then circulation performs step 3 to step 9, until having traveled through all location parameters, obtains final
The 3rd covariance complex matrix set；
Step 11, if at least one in the parameter of first spin matrix or the parameter of second spin matrix expires
The corresponding pre-determined threshold of foot, then each 3rd covariance complex matrix in the 3rd final covariance complex matrix set be
Covariance complex matrix to every group of echo-signal carries out the result of non-orthogonal joint diagonalization；
If the parameter of first spin matrix and the parameter of second spin matrix are unsatisfactory for corresponding default simultaneously
Thresholding, then continue cycling through execution step 3 to step 10, until the parameter and second spin matrix of first spin matrix
Parameter at least one meet pre-determined threshold.
The features of the present invention and further it is improved to：
(1) step 2 is specially：
The first covariance complex matrix set is constituted using each first covariance complex matrix as elementThe first covariance complex matrix setInclude multiple first covariance complex matrix Mk(i=1,
2 ..., K), wherein, Mk(i=1,2 ..., K) is the complex matrix of M × M dimensions.
(2) in step 3 location parameter (p, q) value is as follows successively：
(p, q)=(1,2), (1,3) ..., (1, M), (2,3) ..., (2, M) ..., (M-1, M)
(3) cost function is constructed in step 3 and specifically includes following sub-step：
(3a) remembers each first covariance complex matrix M in the first covariance complex matrix setkPth row q column elements be mk
(p, q), is usedRepresent mkThe real part of (p, q), is usedRepresent mkThe void of (p, q)
Portion；
(3b) makes
Construct two intermediary matrixs：
(3c) makesThen construct the first cost function as follows：
Wherein, J=diag ([- 11 1]), R1It is the matrix of one 3 × 3.
(4) step 4 specifically includes following sub-step：
(4a) passes through solution matrix (R1, J) generalized eigenvalue, obtain the minimum positive corresponding characteristic vector u=of characteristic value
[u1 u2 u3]T；
(4b), for the value of specified location parameter (p, q), the parameter of the first spin matrix is expressed as：
(4c) determines the first spin matrix S according to the parameter of first spin matrix1(p, q, θ1, y1),
Wherein, the first spin matrix is defined asH (p, q, α, y)
For multiple Hyperbolic spin matrixs, G (p, q, β, θ) is multiple Givens spin matrixs.
(5) step 5 is specifically included：
Second covariance complex matrix collection is combined intoWherein the second covariance complex matrix Mk'=S1(p,
Q, θ1, y1)MkS1(p, q, θ1, y1)H(i=1,2 ..., K).
(6) step 7 specifically includes following sub-step：
(7a) remembers each second covariance complex matrix M in the second covariance complex matrixk' pth row q column elements be mk′
(p, q), is usedRepresent mk' (p, q) real part, is usedRepresent mk' (p, q)
Imaginary part；
(7b) makes
Construct four intermediary matrixs：
(7c) makesThen construct the second cost function as follows：
Wherein, R2It is the matrix of one 3 × 3.
(7) step 8 specifically includes following sub-step：
(8a) passes through solution matrix (R2, J) generalized eigenvalue, obtain the minimum positive corresponding characteristic vector v=of characteristic value
[v1 v2 v3]T；
(8b), for the value of specified location parameter (p, q), the parameter of the second spin matrix is expressed as：
(8c) determines the second spin matrix S according to the parameter of second spin matrix2(p, q, θ2, y2),
Wherein, the second spin matrix is defined asH (p,
Q, α, are y) multiple Hyperbolic spin matrixs, G (p, q, β, θ) is multiple Givens spin matrixs.
(8) step 9 is specifically included：
3rd covariance complex matrix collection is combined intoWherein the 3rd covariance complex matrix Mk"=S2(p,
Q, θ1, y1)Mk′S2(p, q, θ1, y1)H(i=1,2 ..., K).
The present invention compared with prior art have it is following a little：(1) it is traditional based on least square fitting cost function
Blind Signal Separation method, such as UWEDGE-c algorithms, although can also realize Blind Signal Separation, but the algorithm not only needs estimation to join
Close diagonalization factor matrix, in addition it is also necessary to estimate one group of diagonal matrix, and the value of these matrixes is typically institute in Blind Signal Separation
It is unconcerned, this increase that will cause operand and estimate parameter.Also relate to the computing of matrix inversion, operand
It is larger, it can also amplify evaluated error, influence performance.The method of the present invention is to be based on F- norm cost functions, is not related to Matrix Calculating
It is inverse, operand is not only substantially reduced, estimation performance is also improved；(2) with traditional orthogonal Joint diagonalization method, for example
SOBI algorithms, it usually needs whitening processing is carried out to observation signal.Due to the influence of truncated error and noise etc., objective matrix
There is error in estimation, this causes albefaction inaccurate, and the extra error being thus introduced into can not be eliminated in ensuing processing.This
Invention uses non-orthogonal joint diagonalization method, can be prevented effectively from the adverse effect of whitening stage generation, improve accuracy.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is the accompanying drawing used required in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with
Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is implementation process schematic diagram provided in an embodiment of the present invention；
Fig. 2 is the schematic flow sheet of diagonalization provided in an embodiment of the present invention；
Fig. 3 is the GBL (global refusal level) of experiment one with NER change curve；
Fig. 4 is the GBL (global refusal level) of experiment one with the change curve of matrix number；
Fig. 5 is the GBL (global refusal level) of experiment one with the change curve of iterations；
Fig. 6 is the CF (cost function value) of experiment one with the change curve of iterations；
Fig. 7 is the GBL (global refusal level) of experiment two with the change curve of SNR (signal to noise ratio)；
Fig. 8 is the source signal planisphere of experiment two；
Fig. 9 is the reception signal constellation (in digital modulation) figure of experiment two；
Figure 10 is the separation signal constellation (in digital modulation) figure of experiment two.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
In order to preferably introduce technical scheme, first describe non-orthogonal joint diagonalization and its need to solve
The problem of.
The covariance complex matrix set of known one group of echo-signalWherein Mk(i=1,2 ...,
K) be M × M dimension complex matrix, then non-orthogonal joint diagonalization need solve the problem of be exactly：Obtain so that matrix V MkVH(k=
1 ..., K) it is diagonal matrix, while so that the minimum Joint diagonalization factor matrix V of F- norms cost function, wherein ()H
The conjugate transposition of representing matrix or vector.
Joint diagonalization factor matrix V is the complex matrix of M × M dimension, and it can be analyzed to a series of multiplying for spin matrixs
Product form：
Joint diagonalization factor matrix V initial value is V0, make V0=I, I here is unit matrix, wherein symbol ∏ tables
Show continued product.
Take different location parameters (p, q) that the Joint diagonalization factor matrix V after updating, usually, position can be tried to achieve
Following the example of for parameter (p, q) is as follows：
(p, q)=(1,2), (1,3) ..., (1, M), (2,3) ..., (2, M) ..., (M-1, M)
(p, q) completes all of above value, represents the wheel renewal completed to Joint diagonalization factor matrix V.
Wherein, the first spin matrix S1(p, q, θ1, y1) be expressed as：
Second spin matrix S2(p, q, θ2, y2) be expressed as：
SymbolThe meaning be defined as.Solution the has been reformed into the problem of Joint diagonalization factor matrix V is to solve for
One spin matrix S1(p, q, θ1, y1) and the second spin matrix S2(p, q, θ2, y2) the problem of.
(p, q, α y) are Hyperbolic spin matrixs, G (p, q, β, θ) is Givens spin matrixs, they diagonal to H
Line element is 1 outside (p, p) and (q, q) individual element, and off diagonal element is except (p, q) and (q, p) individual member
It is 0 outside plain.P, q are location parameters, α, y, and β, θ is rotation parameter.
Now, for each location parameter (p, q) (p=1 ..., M-1, q=p+1 ..., M), it could set up one kind
Simplified F- norm cost functions：
Wherein, symbol ∑ is summation symbol, | | it is absolute value sign, mk(p, q) is matrix Mk(p, q) individual member
Element, mk(q, p) is matrix Mk(q, p) individual element.This cost function is minimized to determine the parameter θ of spin matrix, y, to solve
First spin matrix S1(p, q, θ1, y1) and the second spin matrix S2(p, q, θ2, y2), and then obtain Joint diagonalization factor matrix
V。
Known by formula (1), Joint diagonalization factor matrix V is obtained by being decomposed into the continued product form of many spin matrixs,
And the storage of spin matrix can waste substantial amounts of internal memory, therefore in the covariance complex matrix set of echo-signalV can be also updated during renewal, iterative processing is done equivalent to it, to save memory headroom.
Description based on more than to non-orthogonal joint diagonalization, technical scheme may be summarized to be：By continuous
Givens rotation and Hyperbolic rotation, i.e., the value to (p, q) is continually scanned for, and continues to optimize F- norm cost functions,
And to each covariance complex matrix M in the covariance complex matrix set of echo-signal1..., MKAnd Joint diagonalization factor square
Battle array V is updated, and each spin matrix for making cost function minimum finally is done into continued product, Joint diagonalization factor matrix is produced
V.Implement process includes as shown in Figure 1：
(1) matrix element is extracted；(2) intermediary matrix is constructed；(3) cost function is minimized；(4) ask under now (p, q) value
The first spin matrix S1(p, q, θ1, y1)；(5) with the first spin matrix S tried to achieve in (4)1(p, q, θ1, y1) update echo letter
Number covariance complex matrix setIn each covariance matrix, i.e. Mk'=S1(p, q, θ1, y1)
MkS1(p, q, θ1, y1)H, obtain new matrix group M1' ..., MK′.Same above-mentioned steps (1), (2), (3), are extracted in new matrix group
The element of homography, constructs intermediary matrix, minimizes cost function；(6) the second spin matrix S under now (p, q) value is sought2
(p, q, θ2, y2)；(7) value (p=1 ..., M-1, q=p+1 ..., M) of all (p, q) has been updated, Joint diagonalization is obtained
Factor matrix V.
It should be noted that the method that provides of the present invention pass through it is each in the covariance complex matrix set to echo-signal
Covariance complex matrix M1..., MKIt is updated, you can reach and nonopiate joint pair is carried out to the covariance complex matrix of echo-signal
The purpose of angling, because Joint diagonalization factor matrix V is a highly useful matrix, therefore, is realizing the present invention to returning
While the covariance complex matrix of ripple signal carries out the purpose of non-orthogonal joint diagonalization, Joint diagonalization factor square has also been solved
Battle array V.
With reference to Fig. 2, the embodiments of the invention provide a kind of non-orthogonal joint diagonalization method based on spin matrix, including
Following steps：
Step 1, radar receives echo-signal, and according to receiving the sequencing of the echo-signal by the echo-signal
It is grouped, the covariance complex matrix of every group of echo-signal is determined as the first covariance complex matrix, so as to obtain multiple first
Covariance complex matrix.
The multiple first covariance complex matrix has the element in identical dimension, and each first covariance complex matrix
Indicated by location parameter.
Step 2, the first covariance complex matrix set is constituted using each first covariance complex matrix as element.
The first covariance complex matrix set is constituted using each first covariance complex matrix as elementThe first covariance complex matrix setInclude multiple first covariance complex matrix Mk(i=1,
2 ..., K), wherein, Mk(i=1,2 ..., K) is the complex matrix of M × M dimensions.
Step 3, according to the designated value of location parameter, location parameter described in each first covariance complex matrix is extracted
Designated value indicated by element, and construct the first cost function.
Usually, the value order of location parameter (p, q) is as follows successively：
(p, q)=(1,2), (1,3) ..., (1, M), (2,3) ..., (2, M) ..., (M-1, M).
The first cost function is constructed in step 3 and specifically includes following sub-step：
(3a) remembers each first covariance complex matrix M in the first covariance complex matrix setkPth row q column elements be mk
(p, q), is usedRepresent mkThe real part of (p, q), is usedRepresent mkThe void of (p, q)
Portion；
(3b) makes
Construct two intermediary matrixs：
(3c) makesThen construct the first cost function as follows：
Wherein, J=diag ([- 11 1]), R1It is the matrix of one 3 × 3.
Step 4, first cost function is solved, the first spin matrix is obtained.
Step 4 specifically includes following sub-step：
(4a) passes through solution matrix (R1, J) generalized eigenvalue, obtain the minimum positive corresponding characteristic vector u=of characteristic value
[u1 u2 u3]T；
(4b), for the value of specified location parameter (p, q), the parameter of the first spin matrix is expressed as：
(4c) determines the first spin matrix S according to the parameter of first spin matrix1(p, q, θ1, y1),
Wherein, the first spin matrix is defined asH (p, q, α, y)
For multiple Hyperbolic spin matrixs, G (p, q, β, θ) is multiple Givens spin matrixs.
Step 5, the multiple first covariance complex matrix is multiplied with first spin matrix respectively, obtained after multiplication
Multiple second covariance complex matrix, the multiple second covariance complex matrix constitutes the second covariance complex matrix set
The first Joint diagonalization factor matrix is also multiplied with first spin matrix simultaneously, obtains the second Joint diagonalization
Factor matrix, the first Joint diagonalization factor matrix is unit matrix.
Update the first covariance complex matrix setAnd the first Joint diagonalization factor matrix V.To the multiple square of the first covariance
Battle array setIn each first covariance complex matrix Mk(i=1,2 ..., K), with the first rotation tried to achieve
Torque battle array S1(p, q, θ1, y1) be updated, i.e. Mk'=S1(p, q, θ1, y1)MkS1(p, q, θ1, y1)H, obtain the second covariance and answer
Set of matricesSimultaneously to the first Joint diagonalization factor matrix V0Also it is updated, i.e. V '=S1(p,
Q, θ1, y1)V0, obtain the second Joint diagonalization factor matrix V '.
Step 6, according to the designated value of the location parameter, extract each in the second covariance complex matrix set respectively
Element described in second covariance complex matrix indicated by the designated value of location parameter.
Step 7, the position according to each second covariance complex matrix in the second covariance complex matrix set is joined
Element indicated by several designated values, constructs the second cost function.
Step 7 specifically includes following sub-step：
(7a) remembers each second covariance complex matrix M in the second covariance complex matrixk' pth row q column elements be mk′
(p, q), is usedRepresent mk' (p, q) real part, is usedRepresent mk' (p, q)
Imaginary part；
(7b) makes
Construct four intermediary matrixs：
(7c) makesThen construct the second cost function as follows：
Wherein, R2It is the matrix of one 3 × 3.
Step 8, second cost function is solved, the second spin matrix is obtained.
Step 8 specifically includes following sub-step：
(8a) passes through solution matrix (R2, J) generalized eigenvalue, obtain the minimum positive corresponding characteristic vector v=of characteristic value
[v1 v2 v3]T；
(8b), for the value of specified location parameter (p, q), the parameter of the second spin matrix is expressed as：
(8c) determines the second spin matrix S according to the parameter of second spin matrix2(p, q, θ2, y2),
Wherein, the second spin matrix is defined asH (p,
Q, α, are y) multiple Hyperbolic spin matrixs, G (p, q, β, θ) is multiple Givens spin matrixs.
Step 9, each second covariance complex matrix and second spin moment in the second covariance complex matrix set
Battle array is multiplied, and multiple 3rd covariance complex matrix are obtained after multiplication, and the multiple 3rd covariance complex matrix constitutes the 3rd covariance
Complex matrix set.
The second Joint diagonalization factor matrix is also multiplied with first spin matrix simultaneously, obtains the 3rd Joint diagonalization
Factor matrix.
Update the second covariance complex matrix setAnd the second Joint diagonalization factor matrix V '.It is multiple to the second covariance
Set of matricesIn each second covariance complex matrix Mk' (i=1,2 ..., K) is updated, i.e.,Set of matrices after renewal is the 3rd covariance complex matrix setThe second Joint diagonalization factor matrix V ' is also updated simultaneously, the second joint pair after renewal
Angling factor matrix V ' is denoted as the 3rd Joint diagonalization factor matrix V ", i.e. the 3rd Joint diagonalization factor matrix V "=S2(p,
Q, θ2, y2)V′。
Step 10, the designated value of the location parameter is changed, by the 3rd covariance complex matrix aggregate assignment to described
First covariance complex matrix set, then circulation performs step 3 to step 9, until having traveled through all location parameters, obtains final
The 3rd covariance complex matrix set.
The 3rd covariance complex matrix aggregate assignment is given after the first covariance complex matrix set, in addition it is also necessary to by institute
State the 3rd Joint diagonalization factor matrix and be assigned to the first Joint diagonalization factor matrix, then circulation perform step 3 to
Step 9, until having traveled through the value of all location parameters, the 3rd final Joint diagonalization factor matrix and the final the 3rd are obtained
Covariance complex matrix set.
For one group of specified location parameter (p, q) value, by trying to achieve the first spin matrix S1(p, q, θ1, y1) and second
Spin matrix S2(p, q, θ2, y2), corresponding 3rd covariance matrix of this group of location parameter (p, q) and this group of position can be obtained
The corresponding 3rd Joint diagonalization factor of parameter (p, q).Value (p, q)=(1,2) of all location parameters (p, q) is completed,
(1,3) ..., (1, M), (2,3) ..., (2, M) ..., (M-1, M) is referred to as completing a wheel scan.
Step 11, if at least one in the parameter of first spin matrix or the parameter of second spin matrix expires
The corresponding pre-determined threshold of foot, then each 3rd covariance complex matrix in the 3rd final covariance complex matrix set be
Covariance complex matrix to every group of echo-signal carries out the result of non-orthogonal joint diagonalization；
If the parameter of first spin matrix and the parameter of second spin matrix are unsatisfactory for corresponding default simultaneously
Thresholding, then continue cycling through execution step 3 to step 10, until the parameter and second spin matrix of first spin matrix
Parameter at least one meet pre-determined threshold.
You need to add is that, it is necessary to judge whether this method restrains after a wheel scan is completed.
Specifically, in formula (2) and formula (3), taking less value in sin (θ) and sinh (y), i.e. min { sin (θ), sinh
(y) }, judge whether min { sin (θ), sinh (y) } is less than required threshold value ξ, if min { sin (θ), sinh (y) } compares
Threshold value ξ is small, then it is assumed that convergence；If bigger than threshold value ξ, then it is assumed that not converged, it is necessary to proceed next wheel scan, Zhi Daoshou
Hold back.
If algorithm is not converged, the 3rd tried to achieve covariance matrix set of above one wheel is accordingly assigned to the first association
Variance matrix set；The 3rd Joint diagonalization factor is assigned to the first Joint diagonalization factor, above step is then proceeded to, directly
To algorithmic statement.
After above-mentioned steps are all finished, the value of the 3rd Joint diagonalization factor is required V, and the 3rd covariance is answered
Each 3rd covariance complex matrix in set of matrices is exactly to carry out anon-normal to the covariance complex matrix of every group of echo-signal
Hand over the matrix (result for carrying out Blind Signal Separation) after Joint diagonalization.
L-G simulation test is contrasted：
In order to further illustrate the superiority of the more traditional Blind Signal Separation method of the present invention, following two l-G simulation tests are done.
System model：Use global refusal level (the Global Rejection of the performance parameter commonly used in blind separation algorithm
Level, GRL) carry out the validity of measure algorithm：
For the ease of comparing, in all experiments, if meetingThen think that algorithm is received
Hold back, stop iteration, here,Represent the estimate of kth time iteration.Greatest iteration (scanning) number of times of each algorithm is set to 200
It is secondary.
Experiment one：
Construct one group of M × M objective matrix group R (k)=A diag (λ1..., λ (k)M(k))AH+ Δ R (k) (k=
1 ..., K).The duplicate ratio of error free matrix entries and error matrix F- norms is defined, i.e.,To weigh the disturbance of noise.Make M=5, K=12, aliasing matrix A,
Diagonal matrix and error matrix Δ R (l) real and imaginary parts are to randomly generate, and are obeyedNormal distribution.At the beginning of method
Value is set as IM.The curve that Fig. 3 changes for the GRL of UWEDGE-c methods and the inventive method with NER, Fig. 4 is UWEDGE-c side
The curve that the GRL of method and the inventive method changes with matrix number, it can be seen that method of the invention is more deemed-to-satisfy4 than UWEDGE-c
Can be more preferably.The curve that Fig. 5 changes for the GBL of the inventive method with iterations, Fig. 6 is the CF of the inventive method with iterations
The curve of change, it can be seen that method of the invention has good constringency performance.
Experiment two：
Consider 4 zero-means, the complex value source signals of statistical iteration,
s1(t)=sin (3200 π t)+i cos (1900 π t),
s2(t)=sin (180 π t)+i sin (400 π t),
s3(t)=sin (20 π t) sin (600 π t)+i cos (20 π t) cos (600 π t),
s4(t)=sin [600 π t+6 cos (120 π t)]+i cos (900 π t),
This 4 signals are received by 4 sensors, and reception signal is X=AS+N.Wherein, channel impulse response is by complex matrix A
Represent, its real and imaginary parts is obeyedNormal distribution；Source signal S=[s (1) ..., s (T)], here, s (t)=[s1
(t) s2(t) s3(t) s4(t)]T；Noise matrix N=randn (4, T)+irandn (4, T), sample number T=1000.Produce 10
Individual objective matrix.Defining signal to noise ratio snr isFig. 7 is UWEDGE-c methods and the inventive method
The curve that GRL changes with SNR, wherein, each SNR value carries out 100 Monte Carlo experiments, it can be seen that side of the invention
Method is more preferable than UWEDGE-c method performances.Fig. 8 is the planisphere of source signal, and Fig. 9 is receives the planisphere of signal, and Figure 10 is separation
The planisphere of signal, it can be seen that method of the invention has a good constringency performance, and can recover source signal well,
With good separating property.
The foregoing is only a specific embodiment of the invention, but protection scope of the present invention is not limited thereto, any
Those familiar with the art the invention discloses technical scope in, change or replacement can be readily occurred in, should all be contained
Cover within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (6)
1. a kind of non-orthogonal joint diagonalization echo signal processing method based on multiple spin matrix, it is characterised in that the side
Method comprises the following steps：
Step 1, radar receives echo-signal, and is carried out the echo-signal according to the sequencing for receiving the echo-signal
Packet, determines the covariance complex matrix of every group of echo-signal as the first covariance complex matrix, so as to obtain multiple first association sides
Poor complex matrix, the multiple first covariance complex matrix has the member in identical dimension, and each first covariance complex matrix
Element is indicated by location parameter；
Step 2, the first covariance complex matrix set is constituted using each first covariance complex matrix as element；Will be described every
Individual first covariance complex matrix constitutes the first covariance complex matrix set as elementThe first association side
Poor complex matrix setInclude multiple first covariance complex matrix Mk(i=1,2 ..., K), wherein, Mk(i=1,2 ...,
K) be M × M dimension complex matrix；
Step 3, according to the designated value of location parameter, location parameter described in the multiple first covariance complex matrix is extracted respectively
Designated value indicated by element, and construct the first cost function；
Wherein, value is as follows successively for location parameter (p, q)：
(p, q)=(1,2), (1,3) ..., (1, M), (2,3) ..., (2, M) ..., (M-1, M)
The first cost function is constructed to specifically include：
(3a) remembers each first covariance complex matrix M in the first covariance complex matrix setkPth row q column elements be mk(p,
Q), useRepresent mkThe real part of (p, q), is usedRepresent mkThe imaginary part of (p, q)；
(3b) makes
Construct two intermediary matrixs：
(3c) makesThen construct the first cost function as follows：
Wherein, J=diag ([- 11 1]), R1It is the matrix of one 3 × 3, Cpq 1(θ1,y1) it is the first cost function, θ1,y1
For the first spin matrix rotation parameter, m'k(p, q) is the second covariance complex matrix Mk' pth row q column elements, m'k
(q, p) is the second covariance complex matrix Mk' q row pth column elements, u be matrix (R1, J) the positive corresponding spy of characteristic value of minimum
Levy vector；
Step 4, first cost function is solved, the first spin matrix is obtained；
Step 5, the multiple first covariance complex matrix is multiplied with first spin matrix respectively, obtains multiple after multiplication
Second covariance complex matrix, the multiple second covariance complex matrix constitutes the second covariance complex matrix set；
Step 6, according to the designated value of the location parameter, each second association side in the second covariance complex matrix set is extracted respectively
The element that the designated value of location parameter described in poor complex matrix is indicated；
Step 7, the location parameter according to each second covariance complex matrix in the second covariance complex matrix set
The element that designated value is indicated, constructs the second cost function；
Step 8, second cost function is solved, the second spin matrix is obtained；
Step 9, each second covariance complex matrix and the second spin matrix phase in the second covariance complex matrix set
Multiply, multiple 3rd covariance complex matrix are obtained after multiplication, the multiple 3rd covariance complex matrix constitutes the multiple square of the 3rd covariance
Battle array set；
Step 10, change the designated value of the location parameter, described first is given by the 3rd covariance complex matrix aggregate assignment
Covariance complex matrix set, then circulation performs step 3 to step 9, until traveled through all location parameters, obtains final the
Three covariance complex matrix set；
Step 11, if at least one in the parameter of first spin matrix or the parameter of second spin matrix is met pair
The pre-determined threshold answered, then each 3rd covariance complex matrix in the 3rd final covariance complex matrix set is to institute
The covariance complex matrix for stating every group of echo-signal carries out the result of non-orthogonal joint diagonalization；
If the parameter of first spin matrix and the parameter of second spin matrix are unsatisfactory for corresponding pre-determined threshold simultaneously,
Execution step 3 is then continued cycling through to step 10, until the parameter and the ginseng of second spin matrix of first spin matrix
At least one in number meets corresponding pre-determined threshold.
2. the non-orthogonal joint diagonalization echo signal processing method according to claim 1 based on multiple spin matrix, its
It is characterised by, step 4 specifically includes following sub-step：
(4a) passes through solution matrix (R1, J) generalized eigenvalue, obtain the minimum positive corresponding characteristic vector u=[u of characteristic value1 u2
u3]T；Matrix (R1, J) and it is by matrix R1The matrix constituted with matrix J；
(4b), for the value of specified location parameter (p, q), the parameter of the first spin matrix is expressed as：
(4c) determines the first spin matrix S according to the parameter of first spin matrix1(p,q,θ1,y1),
Wherein, the first spin matrix is defined as(p, q, α are y) multiple to H
Hyperbolic spin matrixs, α=0, y=y1, G (p, q, β, θ) is multiple Givens spin matrixs, β=0, θ=θ1。
3. the non-orthogonal joint diagonalization echo signal processing method according to claim 1 based on multiple spin matrix, its
It is characterised by, step 5 is specifically included：
Second covariance complex matrix setWherein the second covariance complex matrix Mk'=S1(p,q,θ1,y1)
MkS1(p,q,θ1,y1)H(k=1,2 ..., K), wherein, Mk(i=1,2 ..., K) it is the first covariance complex matrix setIn
Comprising the first covariance complex matrix, S1(p,q,θ1,y1) it is the first spin matrix.
4. the non-orthogonal joint diagonalization echo signal processing method according to claim 1 based on multiple spin matrix, its
It is characterised by, step 7 specifically includes following sub-step：
(7a) remembers each second covariance complex matrix M in the second covariance complex matrixk' pth row q column elements be mk' (p, q),
WithRepresent mk' (p, q) real part, is usedRepresent mk' (p, q) imaginary part；
(7b) makes
Construct four intermediary matrixs：
(7c) makesThen construct the second cost function as follows：
Wherein, R2It is the matrix of one 3 × 3, Cpq 2(θ2,y2) it is the second cost function, θ2,y2It is the rotation of the second spin matrix
Turn parameter, m "k(p, q) is the 3rd covariance complex matrix Mk" pth row q column elements, m "k(q, p) is the multiple square of the second covariance
Battle array Mk" q row pth column elements, v be matrix (R2, J) the positive corresponding characteristic vector of characteristic value of minimum.
5. the non-orthogonal joint diagonalization echo signal processing method according to claim 4 based on multiple spin matrix, its
It is characterised by, step 8 specifically includes following sub-step：
(8a) passes through solution matrix (R2, J) generalized eigenvalue, obtain the minimum positive corresponding characteristic vector v=[v of characteristic value1 v2
v3]T；Matrix (R2, J) and it is by matrix R2The matrix constituted with matrix J；
(8b), for the value of specified location parameter (p, q), the parameter of the second spin matrix is expressed as：
(8c) determines the second spin matrix S according to the parameter of second spin matrix2(p,q,θ2,y2),
Wherein, the second spin matrix is defined asH(p,q,α,y)
For multiple Hyperbolic spin matrixs, α=pi/2, y=y2, G (p, q, β, θ) is multiple Givens spin matrixs, β=pi/2, θ=θ2。
6. the non-orthogonal joint diagonalization echo signal processing method according to claim 5 based on multiple spin matrix, its
It is characterised by, step 9 is specifically included：
3rd covariance complex matrix collection is combined intoWherein the 3rd covariance complex matrix Mk"=S2(p,q,θ1,
y1)Mk′S2(p,q,θ1,y1)H(i=1,2 ..., K), Mk' (k=1,2 ..., K) it is the second covariance complex matrix setIn the second covariance complex matrix for including, S2(p,q,θ2,y2) it is the second spin matrix.
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