CN109901111A - Near-field sound source localization method based on Partial Least Squares Regression - Google Patents
Near-field sound source localization method based on Partial Least Squares Regression Download PDFInfo
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Abstract
Partial Least Squares Regression near-field sound source localization method can effectively solve the problems, such as the multiple correlation between variable；Even linear array receives the L group that K narrowband, non-gaussian, steady near-field sound source signal generate in training section and receives data, each group of reception data are made to obtain corresponding covariance matrix after covariance, it extracts the upper triangle element of data covariance matrix and carries out standardization, and training sample signal source collection is standardized, extracted ingredient number is determined according to Cross gain modulation, to obtain satisfied estimation model；Test data is estimated using trained near-field sound source Partial Least-Squares Regression Model, estimates the angle and distance of measuring sound source；The extracted ingredient of Partial Least Squares Regression can summarize the information in independent variable system well and explain dependent variable well, and the noise jamming in removal system, and the angle and distance of prediction has very high precision.
Description
Technical field
The invention belongs to array signal processing technology more particularly to a kind of near-field sound source of Partial Least Squares Regression are fixed
Position method.
Background technique
Angle of arrival (DOA, Direction of Arrival) estimates the signal Mutual coupling that is otherwise known as, and is array letter
One important research direction of number process field.Traditional near field sources DOA estimation method has two step MUSIC methods, broad sense
ESPRIT method and other improved methods.Two step MUSIC methods utilize the orthogonality of signal subspace and noise subspace
Realize the positioning of target, but two traditional step MUSIC approach applications come with some shortcomings place when estimation of parameters of near field sources,
Such as using spectrum peak search make it is computationally intensive, when information source be coherent when will appear rank defect damage so that can not differentiate, in low letter
Estimated accuracy when making an uproar than being separated by closer to information source angle under situation declines rapidly.Broad sense ESPRIT method estimates signal
There is a problem of similar.
Partial Least Squares Regression (Partial least squares regression, PLSR) method, is to answer in recent years
Actual needs and generate and a Multielement statistical analysis method for having a broad applicability of development.Partial Least Squares Regression provides
A kind of multivariate response is to the regression modeling methods of more independents variable, especially when, there are when high correlation, use is partially minimum between variable
Two, which multiply recurrence, is modeled, and analysis conclusion is relatively reliable, and globality is stronger.Partial Least Squares Regression can efficiently solve change
Multiple correlation problem between amount is also suitble to carry out regression modeling in the case where sample size is less than variable number.It is returning
In analysis, this variable multiple correlation can often seriously endanger parameter Estimation, expand model error, and damage model is steady
Property.Partial Least Squares Regression in such a way that data information is decomposed and is screened, efficiently extract it is explanatory to system most
Strong generalized variable rejects the interference of multiple correlation information and uninterpreted semantic information, to overcome variable multiple correlation
In the defects of system modelling.For such as incoherent letter of shortcoming existing for two step MUSIC methods, broad sense ESPRIT method
Number low signal-to-noise ratio lower angle resolution ratio difference and the problems such as coherent can not be handled, partial least-square regression method of the invention
It is to extract the independent variable ingredient for meeting error condition after standardizing sample data, establish independent variable and extracted independent variable
The regression equation of ingredient, the regression equation between dependent variable and extracted independent variable ingredient, to obtain independent variable and because becoming
Regression equation between amount.Using the covariance matrix of the L group near field source signal received as independent variable, angle and distance conduct
Dependent variable, using the estimation model of partial least-square regression method available signal characteristic matrix and angle, distance.This for
Incoherent signal DOA estimation under low signal-to-noise ratio has good precision, while also also having good essence to coherent signal estimation
Degree.This method has many advantages not available for traditional homing method, its meaning is clear, calculates simple, time saving, modeling effect
Fruit is good, explanatory strong, and application range is considerably beyond engineering technology and economic management field.
Summary of the invention
The object of the present invention is to provide a kind of near-field sound source localization method based on Partial Least Squares Regression.
To achieve the goals above, the present invention takes following technical solution:
Near-field sound source localization method based on Partial Least Squares Regression, it is narrow using scalar sound pressure sensor array received K
The steady near-field sound source of band, non-gaussian.Receiving array obtains in the following manner: arbitrarily choosing a little in space as reference axis
Origin position o, from left to right by the origin horizontal line be x-axis, perpendicular to the horizontal straight line be z-axis, that is, assume
Sound source is incident from xoz plane, and the angle of k-th of incident sound source and z-axis isValue range be [- pi/2, pi/2],
To x-axis forward direction respectively with d=λ at coordinate originmin/ 4 place M array element, λ at equal intervalsminFor the most small echo in incident sound source
It is long, array element from left to right successively labeled as [1,2 ... m ... M]；
Steps are as follows for near-field sound source localization method based on Partial Least Squares Regression:
Step 1: receiving K narrowband, non-height using the uniform linear array that array number is M as signal receiving array
This, steady near-field sound source signal, the L group sample signal generated from the angular range and distance range where near-field sound source signal
Set Y=[y1, y2..., yl..., yL], L group signal receives data acquisition system X=[X1, X2..., XL]；
By l group sample signalIt is incident on receiving array
On, the l group signal that dimension is M × N is obtained after n times sample receives data Xl；It finally obtains L group signal and receives data
Set X=[X1, X2..., Xl... XL]；Indicate the angle of k-th of signal source and z-axis in l group sample data, rlkIt indicates
Distance of k-th of signal source to coordinate origin in l group sample data；
Step 2: receiving each of data acquisition system X X to signall, seek matrix covariance Rl=XlXl H/ N, to obtaining
Each covariance matrix RlIt is normalized and extracts the feature vector R ' that triangle element constitutes l group signall, thus
To eigenvectors matrix R '=[R ' of sample data set1, R '2..., R 'l..., R 'L]T；By the feature of obtained sample data
Vector matrix intersects sampling and obtains the eigenvectors matrix Re ' of training sample data and the eigenvectors matrix of test sample data
Rp ' two parts, Re ' include the E sampling feature vectors for training, and Rp ' includes the P sampling feature vectors for test,
Wherein, P=L-E；The eigenvectors matrix of training sample data is Re '=[Re '1, Re '2..., Re 'e..., Re 'E]T, test
The eigenvectors matrix of sample data is Rp '=[Rp '1, Rp '2..., Rp 'p..., Rp 'P]T；Training signal corresponding to them
Source set and testing source set Ye=[ye 1, ye 2..., ye e..., ye E] and Yp=[yp 1, yp 2..., yp p..., yp P]；Wherein,
(·)HThe conjugate transposition of representing matrix, ()TThe transposition of representing matrix；
Step 3: the eigenvectors matrix Re ' to training sample is standardized, the feature after being standardized to
Moment matrix Re " and standardized training signal source collection is combined into Ye "；
1) standardization is made to the eigenvectors matrix Re ' of obtained training sample, first asks all samples in each spy
Average value in sign allows each element in matrix to subtract the mean value on the character pair, then does normalized square mean, it is known that each
Upper Order Triangular Elements in feature vector are known asIt is a, it enablesThe eigenvectors matrix Re ' of training sample
Are as follows:
Standardization are as follows:
Wherein, average value
Training sample eigenvectors matrix after obtained standardization is Re ":
2) using such as 1) by the way of training signal source set Ye is standardized, obtain standardized training signal source collection
It is combined into Ye "；
Wherein,With r "ekIt is angle and distance of k-th of signal after standardization in e-th of training sample
?；
Step 4: modeled using Partial Least Squares Regression, obtain standardized training sample eigenvectors matrix Re " with
The PLS regression model of standardized training signal source set Ye "；
Specific step is as follows for Partial Least Squares Regression modeling:
1) the matrix u=[u that the C ingredient of Re " is constituted is extracted1, u2..., uc-1..., uC]；
Assuming that being extracted C (C≤A) a ingredient, then c-th of ingredient is uc=Re "c-1wc(wherein when c is 1, Re "c-1For
Re "), Re "c-1It indicates Re " to the residual matrix Re for the regression equation for being extracted c-1 ingredient "c-1=Re "-u1p1 T+u2p2 T
+…+uc-1pc-1 T, wcIt is Re "c-1First axis, it is a unit vector, i.e., | | wc| |=1, to matrixIt carries out feature decomposition and acquires the corresponding feature vector of maximum eigenvalue to be wc；Finally obtain Re "=
u1p1 T+u2p2 T+…+ucpc T+…+uCpC T+Re″C, regression coefficient vector is
2) Ye is found out " to the regression equation coefficient υ of the ingredient u of extraction；
Ye " regression equation to ingredient u is Ye "=u υ+Ye "C, wherein coefficient υ=u-1Ye ", Ye "CIndicate residual matrix,
u-1Indicate the inverse matrix of u；
3) the ingredient u that should be extracted is determined using cross validation test1..., uC, ingredient number is C；
Calculating is extracted the error sum of squares SS (c) of Ye after c ingredient "；Remember estimating for z-th of element of e-th of sample point
Evaluation isYe″ezIndicate Ye "zTrue value on e-th of sample point；Ye " can then be definedzError sum of squaresWherein, Ye "zIndicate the z column vector of Ye ", the error sum of squares of Ye "
It calculates and casts out the predicted value PRESS (c) that e-th of sample point extracts Ye " after c ingredient every time, cast out every time e-th
Observation models remaining E-1 observation with partial least-square regression method, and considers to extract returning for c ingredient fitting
Return formula, then e-th of the sample point cast out is substituted into be fitted regression equation, obtain Ye "zOn e-th of sample point
Estimated valueYe″zThe z column vector of representing matrix Ye ", Ye "ezIndicate Ye "zTrue value on e-th of sample point,
The above verifying is repeated to get Ye " when extracting c ingredient for e=1,2 ..., EzEstimated error sum of squaresThe estimated error sum of squares of Ye "
Definition Cross gain modulation is Qc 2=1-PRESS (c)/SS (c-1), modeling each step calculating terminate before, into
Row cross validation test, if specified have Q in c stepc 2< G, then model reaches required precision, can stop extract component；If
Qc 2>=G indicates the u that c step is extractedcThe contributrion margin of ingredient is significant, and Ying Jixu c+1 step calculates, and finally obtains and to be extracted
Component number is C, under normal circumstances, can use G=0.0975；
4) according to Cross gain modulation, satisfied regression equation is obtained；
The regression equation form of Ye " about Re ", i.e. Ye "=β Re "+Ye " are obtained after extracting C ingredientCz, wherein β=w*
υ, υ=Re "/u,w* cIndicate w*C column, Ye "CzIt is residual matrix Ye "CZ column；
5) factor beta ' and constant term b of original regression equation are calculated；
Distinguished about the mean value of independent variable and dependent variable by step 3 what the process that sample data is standardized was found out
ForStandard deviationOur available original recurrence sides
The factor beta of journey ' and constant term b,
6) original regression equation is obtained
Wherein,It indicatesThe e row of matrix, Re 'eIndicate the e row of Re ', β 'eIndicate the e row of β '；
Step 5: being tested test sample eigenvectors matrix Rp ' to obtain estimation angle and distance
It will be obtained in original regression equation that Rp ' substitution step 4 obtains:
Wherein,It indicatesPth row, Rp 'pIndicate the pth row of Rp ', β 'pIndicate the pth row of β '；
The present invention carries out array parameter estimation using partial least-square regression method, by the sample data after standardization
Collection extracts the independent variable ingredient for meeting error condition, establishes the regression equation of independent variable Yu extracted independent variable ingredient, because becoming
Regression equation between amount and extracted independent variable ingredient, to obtain the regression equation between independent variable and dependent variable, partially
Least-squares regression approach can estimate angle and distance simultaneously, and the distance and angle estimated has calculating process simple, estimation
The advantages of time is short, can reach good estimated accuracy.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
Having needs attached drawing to be used to do simple introduction in technical description, it should be apparent that, the accompanying drawings in the following description is only the present invention
Some embodiments for those of ordinary skill in the art without creative efforts, can also basis
These attached drawings obtain other attached drawings.
Fig. 1 is the schematic diagram of scalar of embodiment of the present invention sound pressure sensor array；
Fig. 2 is the flow chart of the method for the present invention；
Fig. 3 is fitted figure of the method for the present invention angle estimation with sampling number；
Fig. 4 is fitted figure of the method for the present invention distance estimations with sampling number；
Fig. 5 is the method for the present invention angle estimation scatter plot；
Fig. 6 is the method for the present invention distance estimations scatter plot；
Fig. 7 is the method for the present invention angle estimation root-mean-square error with signal-to-noise ratio change curve；
Fig. 8 is the method for the present invention distance estimations root-mean-square error with signal-to-noise ratio change curve；
Fig. 9 is the change curve of two step MUSIC methods and the method for the present invention angle estimation root-mean-square error with signal-to-noise ratio；
Specific embodiment
In order to above and other objects of the present invention, feature and advantage can be become apparent from, the embodiment of the present invention is cited below particularly,
And cooperate appended diagram, it is described below in detail.
The object of the present invention is to provide a kind of near-field sound source localization method based on Partial Least Squares Regression.
To achieve the goals above, the present invention takes following technical solution:
Near-field sound source localization method based on Partial Least Squares Regression, it is narrow using scalar sound pressure sensor array received K
The steady near-field sound source of band, non-gaussian.Receiving array obtains in the following manner: arbitrarily choosing a little in space as reference axis
Origin position o, from left to right by the origin horizontal line be x-axis, perpendicular to the horizontal straight line be z-axis, that is, assume
Sound source is incident from xoz plane, and the angle of k-th of incident sound source and z-axis isValue range be [- pi/2, pi/2],
To x-axis forward direction respectively with d=λ at coordinate originmin/ 4 place M array element, λ at equal intervalsminFor the most small echo in incident sound source
Long, array element is from left to right successively labeled as [1,2 ..., m ..., M]；
Steps are as follows for near-field sound source localization method based on Partial Least Squares Regression:
Step 1: receiving K narrowband, non-height using the uniform linear array that array number is M as signal receiving array
This, steady near-field sound source signal, the L group sample signal generated from the angular range and distance range where near-field sound source signal
Set Y=[y1, y2..., yl..., yL], L group signal receives data acquisition system X=[X1, X2..., XL]；
By l group sample signalIt is incident on receiving array
On, the l group signal that dimension is M × N is obtained after n times sample receives data Xl；It finally obtains L group signal and receives data
Set X=[X1, X2..., Xl... XL]；Indicate the angle of k-th of signal source and z-axis in l group sample data, rlkIt indicates
Distance of k-th of signal source to coordinate origin in l group sample data；
Step 2: receiving each of data acquisition system X X to signall, seek matrix covariance Rl=XlXl H/ N, to obtaining
Each covariance matrix RlIt is normalized and extracts the feature vector R ' that triangle element constitutes l group signall, thus
To eigenvectors matrix R '=[R ' of sample data set1, R '2..., R 'l..., R 'L]T；By the feature of obtained sample data to
Moment matrix intersects sampling and obtains the eigenvectors matrix Re ' of training sample data and the eigenvectors matrix of test sample data
Rp ' two parts, Re ' include the E sampling feature vectors for training, and Rp ' includes the P sampling feature vectors for test,
Wherein, P=L-E；The eigenvectors matrix of training sample data is Re '=[Re '1, Re '2..., Re 'e..., Re 'E]T, test
The eigenvectors matrix of sample data is Rp '=[Rp '1, Rp '2..., Rp 'p..., Rp 'P]T；Training signal corresponding to them
Source set and testing source set Ye=[ye 1, ye 2..., ye e..., ye E] and Yp=[yp 1, yp 2..., yp p..., yp P]；Its
In, ()HThe conjugate transposition of representing matrix, ()TThe transposition of representing matrix；
Step 3: the eigenvectors matrix Re ' to training sample is standardized, the feature after being standardized to
Moment matrix Re " and standardized training signal source collection is combined into Ye "；
1) standardization is made to the eigenvectors matrix Re ' of obtained training sample, first asks all samples in each spy
Average value in sign allows each element in matrix to subtract the mean value on the character pair, then does normalized square mean, it is known that each
Upper Order Triangular Elements in feature vector are known asIt is a, it enablesThe eigenvectors matrix Re ' of training sample
Are as follows:
Standardization are as follows:
Wherein, average value
Training sample eigenvectors matrix after obtained standardization is Re ":
2) using such as 1) by the way of training signal source set Ye is standardized, obtain standardized training signal source collection
It is combined into Ye "；
Wherein,With r "ekIt is angle and distance of k-th of signal after standardization in e-th of training sample
?；
Step 4: modeled using Partial Least Squares Regression, obtain standardized training sample eigenvectors matrix Re " with
The PLS regression model of standardized training signal source set Ye "；
Specific step is as follows for Partial Least Squares Regression modeling:
1) the matrix u=[u that the C ingredient of Re " is constituted is extracted1, u2..., uc-1..., uC]；
Assuming that being extracted C (C≤A) a ingredient, then c-th of ingredient is uc=Re "c-1wc(wherein when c is l, Re "c-1For
Re "), Re "c-1It indicates Re " to the residual matrix Re for the regression equation for being extracted c-1 ingredient "c-1=Re "-u1p1 T+u2p2 T
+…+uc-1pc-1 T, wcIt is Re "c-1First axis, it is a unit vector, i.e., | | wc| |=1, to matrixIt carries out feature decomposition and acquires the corresponding feature vector of maximum eigenvalue to be wc；Finally obtain Re "=
u1p1 T+u2p2 T+…+ucpc T+…+uCpC T+Re″C, regression coefficient vector is
2) Ye is found out " to the regression equation coefficient υ of the ingredient u of extraction；
Ye " regression equation to ingredient u is Ye "=u υ+Ye "C, wherein coefficient υ=u-1Ye ", Ye "CIndicate residual matrix,
u-1Indicate the inverse matrix of u；
3) the ingredient u that should be extracted is determined using cross validation test1..., uC, ingredient number is C；
Calculating is extracted the error sum of squares SS (c) of Ye after c ingredient "；Remember estimating for z-th of element of e-th of sample point
Evaluation isYe″ezIndicate Ye "zTrue value on e-th of sample point；Ye " can then be definedzError sum of squaresWherein, Ye "zIndicate the z column vector of Ye ", the error sum of squares of Ye "
It calculates and casts out the predicted value PRESS (c) that e-th of sample point extracts Ye " after c ingredient every time, cast out every time e-th
Observation models remaining E-1 observation with partial least-square regression method, and considers to extract returning for c ingredient fitting
Return formula, then e-th of the sample point cast out is substituted into be fitted regression equation, obtain Ye "zOn e-th of sample point
Estimated valueYe″zThe z column vector of representing matrix Ye ", Ye "ezIndicate Ye "zTrue value on e-th of sample point,
The above verifying is repeated to get Ye " when extracting c ingredient for e=1,2 ..., EzEstimated error sum of squaresThe estimated error sum of squares of Ye "
Definition Cross gain modulation is Qc 2=1-PRESS (c)/SS (c-1), modeling each step calculating terminate before, into
Row cross validation test, if specified have Q in c stepc 2< G, then model reaches required precision, can stop extract component；If
Qc 2>=G indicates the u that c step is extractedcThe contributrion margin of ingredient is significant, and Ying Jixu c+1 step calculates, and finally obtains and to be extracted
Component number is C, under normal circumstances, can use G=0.0975；
4) according to Cross gain modulation, satisfied regression equation is obtained；
The regression equation form of Ye " about Re ", i.e. Ye "=β Re "+Ye " are obtained after extracting C ingredientCz, wherein β=w*
υ, υ=Re "/u,w* cIndicate w*C column, Ye "CzIt is residual matrix Ye "CZ column；
5) factor beta ' and constant term b of original regression equation are calculated；
Distinguished about the mean value of independent variable and dependent variable by step 3 what the process that sample data is standardized was found out
ForStandard deviationOur available original recurrence sides
The factor beta of journey ' and constant term b,
6) original regression equation is obtained
Wherein,It indicatesThe e row of matrix, Re 'eIndicate the e row of Re ', β 'eIndicate the e row of β '；
Step 5: being tested test sample eigenvectors matrix Rp ' to obtain estimation angle and distance
It will be obtained in original regression equation that Rp ' substitution step 4 obtains:
Wherein,It indicatesPth row, Rp 'pIndicate the pth row of Rp ', β 'pIndicate the pth row of β '；
In abovementioned steps, K indicates that number of sources, k=1,2 ..., K indicate the label of signal source, m=1,2 ..., M
The label of expression array element, l=1,2 ..., L expression number of samples, e=1,2 ..., E expression training sample number, p=1,
2 ..., P indicates test sample number, a=1, the columns of 2 ..., A representing matrix Re ", z=1,2 ..., Z representing matrix Ye "
Columns, C indicate institute's extract component number, c=1,2 ..., C.
The present invention carries out array parameter estimation using partial least-square regression method, by PLSR method to feature samples square
Battle array and output angle and distance matrix carry out constituents extraction, establish the multiple linear of angle and distance matrix Yu feature samples matrix
Regression equation.Training pattern is obtained for estimating angle and distance parameter；The method of the present invention passes through Cross gain modulation extract component,
So that operand greatly reduces, angle and distance information can be efficiently estimated.
Effect of the invention can be further illustrated by simulation result below:
Two near fields, narrowband, the steady sound-source signal of non-gaussian are incident on scalar sound pressure sensor array shown in FIG. 1,
The receiving array is made of M=9 array element, and signal frequency is set as [fs/ 8, fs/ 10], fsIt is sample frequency, is divided into d=between array element
λmin/ 4, λminBe frequency be fsThe corresponding wavelength of/8 signals, number of snapshots 200, noise are white Gaussian noise；Training sample data
Angle intervalDistance interval Δ r=0.09 λmin, train the section of angle to be located at [- pi/2, pi/2], training distance
Section be located at [1.5 λmin, 2.5 λmin], sample data is 175 groups, sample data intersected into sampling and is divided into two parts, a part
For training, another part is for testing；Fig. 3 and Fig. 4 be respectively the method for the present invention for the angle of test sample data and away from
From fit solution, as can be seen from the figure estimated value and true value are very close, illustrate that the method for the present invention can effectively be estimated
The angle and distance of near field source signal；Fig. 5 and Fig. 6 is the scatter plot of angle and distance estimation, it can be seen that angle and distance
Estimated value illustrates the validity of the method for the present invention close to true value；Fig. 7 and Fig. 8 is the angle of signal source one and signal source two
Degree and distance root mean square Error Graph, the angle and distance root-mean-square error of two signal sources estimates all identical, curve co-insides, selected
One angle and distance of signal source be [15 °, 2.025 λmin], two angle and distance information of signal source be [20 °, 2.115 λmin],
Signal source one and signal source two be not in training area, as can be seen from the figure root-mean-square error very little, the method for the present invention for
Angle and distance all has very high estimated accuracy, illustrates that the method for the present invention has good Generalization Capability；Fig. 9 is two steps
The estimation angle root-mean-square error figure of MUSIC method and the method for the present invention, as can be seen from the figure two step MUSIC algorithms are low
There is very big error for angle estimation under signal-to-noise ratio, and the method for the present invention has very high estimated accuracy, performance is substantially better than
Two step MUSIC methods；
The above described is only a preferred embodiment of the present invention, limitation in any form not is done to the present invention, though
So the present invention has been disclosed as a preferred embodiment, and however, it is not intended to limit the invention, any technology people for being familiar with this profession
Member, without departing from the scope of the present invention, when the technology contents using the disclosure above are modified or are modified
For the equivalent embodiment of equivalent variations, but anything that does not depart from the technical scheme of the invention content, according to the technical essence of the invention
Any simple modification, equivalent change and modification to the above embodiments, all of which are still within the scope of the technical scheme of the invention.
Claims (1)
1. the near-field sources localization method based on Partial Least Squares Regression, it is characterised in that:
Near-field sound source localization method based on Partial Least Squares Regression, using K narrowband of scalar sound pressure sensor array received, non-
The steady near-field sound source of Gauss；Receiving array obtains in the following manner: arbitrarily choosing some original as reference axis in space
Point position o is from left to right x-axis by the horizontal line of the origin, is z-axis perpendicular to the horizontal straight line, is i.e. hypothesis sound source
Incident from xoz plane, the angle of k-th of incident sound source and z-axis isValue range be [- pi/2, pi/2], in coordinate
To x-axis forward direction respectively with d=λ at originmin/ 4 place M array element, λ at equal intervalsminFor the minimum wavelength in incident sound source, array element
From left to right successively it is labeled as [1,2 ..., m ..., M]；
Steps are as follows for near-field sound source localization method based on Partial Least Squares Regression:
Step 1: receiving K narrowband using the uniform linear array that array number is M as signal receiving array, non-gaussian, putting down
Steady near-field sound source signal, the L group sample signal set Y generated from the angular range and distance range where near-field sound source signal
=[y1, y2..., yl..., yL], L group signal receives data acquisition system X=[X1, X2..., XL]；
By l group sample signalIt is incident on receiving array, by n times
The l group signal that dimension is M × N is obtained after sampling receives data Xl；It finally obtains L group signal and receives data acquisition system X=[X1,
X2..., Xl..., XL]；Indicate the angle of k-th of signal source and z-axis in l group sample data, rlkIndicate l group sample
Distance of k-th of signal source to coordinate origin in data；
Step 2: receiving each of data acquisition system X X to signall, seek matrix covariance Rl=XlXl H/ N, to each of obtaining
Covariance matrix RlIt is normalized and extracts the feature vector R ' that triangle element constitutes the 1st group of signall, to obtain sample
Eigenvectors matrix R '=[R ' of data set1, R '2..., R 'l..., R 'L]T；By the eigenvectors matrix of obtained sample data
Intersect eigenvectors matrix Rp ' two for sampling the eigenvectors matrix Re ' and test sample data that obtain training sample data
Point, Re ' includes the E sampling feature vectors for training, and Rp ' includes the P sampling feature vectors for test, wherein P=
L-E；The eigenvectors matrix of training sample data is Re '=[Re '1, Re '2..., Re 'e..., Re 'E]T, test sample data
Eigenvectors matrix be Rp '=[Rp '1, Rp '2..., Rp 'p..., Rp 'P]T；Corresponding to them training signal source set and
Testing source set Ye=[ye 1, ye 2..., ye e..., ye E] and Yp=[yp 1, yp 2..., yp p..., yp P]；Wherein, ()HTable
Show the conjugate transposition of matrix, ()TThe transposition of representing matrix；
Step 3: the eigenvectors matrix Re ' to training sample is standardized, the feature vector square after being standardized
Battle array Re " and standardized training signal source collection is combined into Ye "；
1) standardization is made to the eigenvectors matrix Re ' of obtained training sample, first asks all samples in each feature
Average value, allow each element in matrix to subtract the mean value on the character pair, then do normalized square mean, it is known that each feature
Upper Order Triangular Elements on vector are known asIt is a, it enablesThe eigenvectors matrix Re ' of training sample are as follows:
Standardization are as follows:
Wherein, average value
Training sample eigenvectors matrix after obtained standardization is Re ":
2) using such as 1) by the way of training signal source set Ye is standardized, obtain standardized training signal source collection and be combined into
Ye″；
Wherein,With r "ekIt is angle and distance item of k-th of the signal in e-th of training sample after standardization；
Step 4: modeling using Partial Least Squares Regression, standardized training sample eigenvectors matrix Re " and standardization are obtained
Training signal source set Ye " PLS regression model；
Specific step is as follows for Partial Least Squares Regression modeling:
1) the matrix u=[u that the C ingredient of Re " is constituted is extracted1, u2..., uc-1..., uC]；
Assuming that being extracted C (C≤A) a ingredient, then c-th of ingredient is uc=Re "c-1wc(wherein when c is 1, Re "c-1For Re "),
Re″c-1It indicates Re " to the residual matrix Re for the regression equation for being extracted c-1 ingredient "c-1=Re "-u1p1 T+u2p2 T+…+uc- 1Pc-1 T, wcIt is Re "c-1First axis, it is a unit vector, i.e., | | wc| |=1, to matrix
It carries out feature decomposition and acquires the corresponding feature vector of maximum eigenvalue to be wc；Finally obtain Re "=u1p1 T+u2p2 T+…+ucpc T
+…+uCpC T+Re″C, regression coefficient vector is
2) Ye is found out " to the regression equation coefficient υ of the ingredient u of extraction；
Ye " regression equation to ingredient u is Ye "=u υ+Ye "C, wherein coefficient υ=u-1Ye ", Ye "CIndicate residual matrix, u-1Table
Show the inverse matrix of u；
3) the ingredient u that should be extracted is determined using cross validation test1..., uC, ingredient number is C；
Calculating is extracted the error sum of squares SS (c) of Ye after c ingredient "；Remember the estimated value of z-th of element of e-th of sample point
ForYe″ezIndicate Ye "zTrue value on e-th of sample point；Ye " can then be definedzError sum of squaresWherein, Ye "zIndicate the z column vector of Ye ", the error sum of squares of Ye "
It calculates and casts out the predicted value PRESS (c) that e-th of sample point extracts Ye " after c ingredient every time, cast out e-th of observation every time
Value, remaining E-1 observation is modeled with partial least-square regression method, and considers to extract the regression equation of c ingredient fitting,
Then e-th of the sample point cast out is substituted into be fitted regression equation, obtains Ye "zEstimated value on e-th of sample pointYe″zThe z column vector of representing matrix Ye ", Ye "ezIndicate Ye "zTrue value on e-th of sample point, for e=
1,2 ..., E repeat the above verifying to get Ye " when extracting c ingredientzEstimated error sum of squaresThe estimated error sum of squares of Ye "
Definition Cross gain modulation is Qc 2=1-PRESS (c)/SS (c-1) is handed over before each step calculating of modeling terminates
Validity check is pitched, if specified have Q in c stepc 2< G, then model reaches required precision, can stop extract component；If Qc 2≥
G indicates the u that c step is extractedcThe contributrion margin of ingredient is significant, and Ying Jixu c+1 step calculates, and finally obtains the ingredient to be extracted
Number is C, under normal circumstances, can use G=0.0975；
4) according to Cross gain modulation, satisfied regression equation is obtained；
The regression equation form of Ye " about Re ", i.e. Ye "=β Re "+Ye " are obtained after extracting C ingredientCz, wherein β=w*υ, υ
=Re "/u,w* cIndicate w*C column, Ye "CzIt is residual matrix Ye "CZ column；
5) factor beta ' and constant term b of original regression equation are calculated；
It is respectively to the mean value about independent variable and dependent variable that the process that sample data is standardized is found out by step 3Standard deviation
The factor beta of our available original regression equations ' and constant term b,
6) original regression equation is obtained
Wherein,It indicatesThe e row of matrix, Re 'eIndicate the e row of Re ', β 'eIndicate the e row of β '；
Step 5: being tested test sample eigenvectors matrix Rp ' to obtain estimation angle and distance
It will be obtained in original regression equation that Rp ' substitution step 4 obtains:
Wherein,It indicatesPth row, Rp 'pIndicate the pth row of Rp ', β 'pIndicate the pth row of β '；
In abovementioned steps, K indicates that number of sources, k=1,2 ..., K indicate that the label of signal source, m=1,2 ..., M indicate
The label of array element, l=1,2 ..., L indicate that number of samples, e=1,2 ..., E indicate training sample number, p=1,2 ..., P
Expression test sample number, a=1, the columns of 2 ..., A representing matrix Re ", z=1, the columns of 2 ..., Z representing matrix Ye ",
C indicates institute's extract component number, c=1,2 ..., C.
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