CN109901101A - Based on the relatively prime array method for estimating angle of arrival of coherent signal of electromagnetic vector sensor - Google Patents
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Abstract
The invention proposes a kind of relatively prime array method for estimating angle of arrival of coherent signal of electromagnetic vector sensor, mainly solving the problems, such as the virtual array of relatively prime battle array in existing method, there are the estimations of information loss and coherent caused by hole；The relatively prime array of electromagnetic vector sensor is constructed as receiving array；The relatively prime array received data of electromagnetic vector sensor are divided into 6 submatrix data, submatrix data covariance matrix vector quantization and de-redundancy；The reception data of uniform submatrix virtual array are constructed by filling array element；Solve the Toeplitz covariance matrix that uniform submatrix virtual array receives signal；Full rank Toeplitz matrix after obtaining decorrelation LMS by arithmetic mean simultaneously carries out feature decomposition, and MUSIC method is utilized to realize the angle-of- arrival estimation of signal；The method of the present invention can realize the angle-of- arrival estimation of coherent signal in the case where signal source number is greater than physics element number of array, improve the estimated accuracy and estimation number of angle of arrival.
Description
Technical field
The invention belongs to field of signal processing, more particularly to one kind to be based on the relatively prime array coherent signal of electromagnetic vector sensor
Angle-of- arrival estimation method.
Background technique
Angle of arrival (direction of arrival, DOA) estimation is an important branch in array signal processing field,
It refers to using array antenna received airspace signal, and is handled by the collection of letters number of modern signal processing interface differential technique, realizes
The DOA of signal estimates.Traditional DOA estimation mainly estimates signal by multiple signal classification (MUSIC) method, rotation invariant technology
Parameter (ESPRIT) method and its deriving method carry out.The DOA algorithm for estimating of current most of classics is all confined to uniform line
Battle array, array number total for one are the uniform linear array of N, the maximum airspace mesh that can be identified using traditional DOA estimation method
Marking number is N-1.In practice, target number in airspace is greater than array number situation and happens occasionally, using less than target number
Traditional DOA estimation method of uniform linear array will fail.Simultaneously even linear array in order to avoid angle of arrival it is fuzzy, the battle array of array
First spacing be all necessarily less than or equal to incoming signal half times of wavelength, limit array aperture.In order to improve the freedom of DOA estimation
Degree and resolution ratio, the geometry for changing array is an effective method, therefore is come with the nonuniform array that less array element forms
Estimation starts to receive more and more attention compared with multiple source.
Relatively prime battle array can increase the freedom degree of DOA estimation under the premise of element number of array is certain, thus start to receive wide
General concern.Relatively prime array is made of the sparse homogenous linear submatrix that two array numbers are respectively M, N, and wherein M, N are relatively prime whole
Number.Relatively prime battle array is mainly derived by virtual signal of equal value to realize that DOA estimates by the existing DOA estimation method based on relatively prime battle array
Meter, since the Virtual array number for including in virtual array is greater than actual bay number, freedom degree has been obtained effectively
It is promoted.Relatively prime battle array provides the thinned array architectural schemes an of systematization, thus also reduce to a certain extent array element it
Between mutual lotus root effect.But belong to nonuniform noise from the virtual array that relatively prime battle array is derived, wherein uniform portion can only be intercepted
Divide and handled, has lost partial information；And most methods are all based on the estimation of incoherent signal, and in actual environment
There are coherent signals.For existing methods deficiency, the present invention proposes a kind of relevant based on the relatively prime array of electromagnetic vector sensor
Signal direction of arrival estimation method reduces information loss using filling array element method, utilizes electromagnetic vector sensor submatrix space
Invariable rotary characteristic realizes the angle-of- arrival estimation of coherent signal, therefore this method not only increases the freedom degree of DOA estimation and divides
Resolution；And the estimation of coherent signal is realized on this basis.
Summary of the invention
The present invention proposes a kind of based on the relatively prime array method for estimating angle of arrival of coherent signal of electromagnetic vector sensor.
Implementation of the invention includes the following:
Step 1: construction one is made of the one-dimensional relatively prime array of electromagnetic vector sensor M+N-1 array element, wherein M and N is
Relatively prime integer, the relatively prime array of electromagnetic vector sensor are made of a pair of sparse homogenous linear subarray, and first submatrix includes M
A spacing is the array element of Nd, and element position 0, Nd ..., (M-1) Nd, second subarray includes the battle array that N number of spacing is Md
Member, element position 0, Md ..., (N-1) Md, d are incoming signal minimum half-wavelength；
Step 2: receiving K from different directions using the relatively prime array of electromagnetic vector sensor as receiving array
Far field narrow band signal source θ1, θ2..., θK, data will be received and be divided into x, y, z axis direction electric and magnetic fields totally 6 submatrix data, t times
The reception signal that snap obtains is respectively X1, X2, X3, X4, X5, X6, and calculates 6 submatrix data covariance matrix and be respectively
Rx1、Rx2、Rx3、Rx4、Rx5、Rx6；
Step 3: obtaining new single snap by 6 submatrix data covariance matrix vector quantizations receives signal data, remove superfluous
Remaining equivalence virtual signal obtains the virtual signal of equal value of 6 non-homogeneous virtual submatrixs:
(3a) vector quantization covariance matrix stacks gradually each column of covariance matrix to form a new column vector,
It obtains new single snap and receives signal data；
The position difference set D of (3b) calculating submatrix array elements={ usi-usj, wherein usi, usjRespectively indicate s-th of subarray
The position coordinates of i-th and j-th array element, DsThe element position difference set for indicating s-th of submatrix, by DsBattle array of the d as virtual array
First position coordinates obtain 6 redundant virtual arrays；
Repetition array element in (3c) removal redundant virtual array obtains irredundant non-homogeneous virtual array, corresponds to of equal value empty
It is quasi- to receive signal Z1, Z2, Z3, Z4, Z5, Z6；
Step 4: the equivalence for constructing uniform virtual array is virtual to receive signal, in the missing array element of non-homogeneous virtual array
Partially supplement receives the array element data that signal is 0, and the equivalent single snap for obtaining corresponding to 6 uniform virtual submatrixs receives data
Y1,Y2,Y3,Y4,Y5,Y6；
Step 5: receiving data configuration Toeplitz data using equivalent single snap of 6 uniform virtual submatrixs of construction
Covariance matrix Rz1、Rz2、Rz3、Rz4、Rz5、Rz6；
Data configuration Toeplitz covariance matrix is received using equivalent single snap of 6 uniform virtual arrays of construction
Rz1、Rz2、Rz3、Rz4、Rz5、Rz6It is specific as follows: by taking x-axis direction electric field submatrix as an example, to remember that the element number of array of uniform virtual array is
L1, due to the array be with zero position at array element it is symmetrical, so center array element is theA array element, x-axis side
It can be constructed in the Toeplitz matrix of electric field submatrix:
Wherein,<Y1>lIt indicates that equivalence corresponding to first of the array element of first virtual sub-array receives signal, similarly may be used
Obtain Rz2、Rz3、Rz4、Rz5、Rz6；
Step 6: construction only includes the matrix H of 0 and 1 element；
Matrix H dimension and Rz1It is identical, because being filled with zero reception data, R when filling array elementz1In there are neutral element,
As matrix Rz1In some position element be 0, then the element of opposite position is also 0 in matrix H, the element of remaining position of matrix H
Value is 1；
Step 7: solving and Toeplitz data covariance matrix Rz1、Rz2、Rz3、Rz4、Rz5、Rz6The smallest low-rank of difference
Toeplitz matrix RT1、RT2、RT3、RT4、RT5、RT6；
R is solved by taking x-axis direction electric field submatrix as an exampleT1, solved and met using CVX Optimization ToolboxThe smallest positive semidefinite matrix RT1, whereinRepresenting matrix RT1
In element multiplication in each element and matrix H on corresponding position；||·||FFor Frobenius norm, Tr () indicates square
The mark of battle array, μ is regularization parameter, according to seeking RT1Same mode obtains RT2、RT3、RT4、RT5、RT6；
Step 8: carrying out the estimation that arithmetic mean realizes coherent signal to 6 low-rank Toeplitz matrixes that solution obtains；
The arithmetic average for calculating 6 low-rank Toeplitz matrixes obtains full rank Toeplitz matrix
Full rank Toeplitz matrixFeature decomposition is carried out, obtains angle-of- arrival estimation using MUSIC method
I=1 in abovementioned steps, 2 ..., M+N-1, j=1,2 ..., M+N-1 indicate the element number of array of relatively prime array, s=1,
2 ..., 6 indicate the number of submatrix, and l=1,2 ..., L1 indicate that the element number of array of uniform virtual array, k=1,2 ..., K indicate letter
The number in number source.
The invention has the following advantages that
(1) present invention shifts virtual Domain onto and is handled by way of electromagnetic vector sensor is lined up relatively prime battle array, thus
Improve the freedom degree and resolution ratio of DOA estimation；
(2) present invention may make reconstructed results and true value difference using the reconstruction that Toeplitz characteristic carries out covariance matrix
It is different smaller, to improve the performance of DOA estimation method；
(3) present invention passes through Space Rotating decorrelation LMS according to the Space Rotating invariant feature of electromagnetic vector sensor submatrix
Processing restores the order of data covariance, to realize the estimation of coherent signal.
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 flow chart of the method for the present invention；
Fig. 2 is the structural schematic diagram of the relatively prime array of the method for the present invention；
Fig. 3 is the sparse uniform subarray structural schematic diagram of a pair that the present invention forms relatively prime array；
Fig. 4 is the structural schematic diagram of non-homogeneous virtual array in the present invention；
Fig. 5 is the schematic diagram that the uniform virtual array obtained after array element is inserted into the present invention；
Fig. 6 is the space power spectrum schematic diagram of the mentioned method of the present invention.
Specific embodiment
Referring to the drawings, implementation of the invention is described in further detail.
Referring to Fig.1, steps are as follows for realization of the invention:
Step 1: construction one is made of the one-dimensional relatively prime array of electromagnetic vector sensor M+N-1 array element, reference Fig. 2,
Middle M and N is relatively prime integer, which is made of a pair of sparse homogenous linear subarray, referring to Fig. 3, first submatrix packet
The array element for being Nd containing M spacing, element position 0, Nd ..., (M-1) Nd, second subarray include that N number of spacing is Md's
Array element, element position 0, Md ..., (N-1) Md, d are incoming signal minimum half-wavelength；
Step 2: receiving K from different directions using the relatively prime array of electromagnetic vector sensor as receiving array
Far field narrow band signal source θ1, θ2..., θK, data will be received and be divided into x, y, z axis direction electric and magnetic fields totally 6 submatrix data, t times
For the reception signal that snap obtains to be respectively X1, X2, X3, X4, X5, X6, thus calculating covariance matrix is respectively Rx1、Rx2、
Rx3、Rx4、Rx5、Rx6；
Step 3: obtaining new single snap by 6 covariance matrix vector quantizations receives signal data, removal redundancy is of equal value empty
Quasi- signal obtains the virtual signal of equal value of non-homogeneous virtual array:
(3a) vector quantization covariance matrix stacks gradually each column of covariance matrix to form a new column vector,
It obtains new single snap and receives signal data；
The position difference set D of (3b) calculating submatrix array elements={ usi-usj, wherein usi, usjRespectively indicate s-th of subarray
The position coordinates of i-th and j-th array element, DsThe element position difference set for indicating s-th of submatrix, by DsBattle array of the d as virtual array
First position coordinates obtain 6 redundant virtual arrays；
Repetition array element in (3c) removal redundant virtual array obtains irredundant non-homogeneous virtual array, right referring to Fig. 4
Answer virtual reception signal Z1, Z2, Z3, Z4, Z5, Z6 of equal value；
Step 4: the equivalence for constructing uniform virtual array is virtual to receive signal, in the missing array element of non-homogeneous virtual array
Part supplement receives the array element data that signal is 0, obtains corresponding to 6 uniform virtual arrays, referring to Fig. 5, equivalent list snap
Receiving data is Y1, Y2, Y3, Y4, Y5, Y6；
Step 5: receiving the association side data configuration Toeplitz using equivalent single snap of 6 uniform virtual arrays of construction
Poor matrix Rz1、Rz2、Rz3、Rz4、Rz5、Rz6；
Data configuration Toeplitz covariance matrix is received using equivalent single snap of 6 uniform virtual submatrixs of construction
Rz1、Rz2、Rz3、Rz4、Rz5、Rz6It is specific as follows: by taking x-axis direction electric field submatrix as an example, to remember that the element number of array of uniform virtual array is
L1, since the array is with the symmetrical structure of zero position array element, so center array element is theA array element, first
The Toeplitz matrix of a submatrix can be constructed in:
Wherein,<Y1>lIt indicates that equivalence corresponding to first of the array element of first virtual sub-array receives signal, similarly may be used
Obtain Rz2、Rz3、Rz4、Rz5、Rz6；
Step 6: construction only includes the matrix H of 0 and 1 element；
Matrix H dimension and Rz1It is identical, because being filled with zero reception data, R when filling array elementz1In there are neutral element,
As matrix Rz1In some position element be 0, then the element of opposite position is also 0 in matrix H, the element of remaining position of matrix H
Value is 1；
Step 7: solving and Toeplitz data covariance matrix Rz1、Rz2、Rz3、Rz4、Rz5、Rz6The smallest low-rank of difference
Toeplitz matrix RT1、RT2、RT3、RT4、RT5、RT6；
R is solved by taking x-axis direction electric field submatrix as an exampleT1, solved and met using CVX Optimization ToolboxThe smallest positive semidefinite matrix RT1, whereinRepresenting matrix RT1
In element multiplication in each element and matrix H on corresponding position；||·||FFor Frobenius norm, Tr () indicates square
The mark of battle array, μ is regularization parameter, according to seeking RT1Same mode obtains RT2、RT3、RT4、RT5、RT6；
Step 8: carrying out the estimation that arithmetic mean realizes coherent signal to 6 low-rank Toeplitz matrixes that solution obtains；
The arithmetic average for calculating 6 low-rank Toeplitz matrixes obtains full rank Toeplitz matrix
Full rank Toeplitz matrixFeature decomposition is carried out, obtains angle-of- arrival estimation using MUSIC method
Nonuniform noise compensation is a uniform array by the method for insertion array element by one aspect of the present invention, avoids house
Former array non-uniform part bring information loss is abandoned, freedom degree and resolution ratio are improved；On the other hand it is passed by electromagnetic vector
The vectorial property of sensor realizes the estimation of coherent signal.
The invention is further described below with reference to simulation example；
Simulation example:
Relatively prime array parameter is chosen for M=3, N=5, i.e., relatively prime array shares M+N-1=6 physics array element；It is assumed that incident
Narrow band signal number is 10, and wherein coherent signal has 3, and incoherent signal has 7, and incident direction [- 50 °, -40 °, -
30 °, -20 °, -10 °, 0 °, 10 °, 20 °, 30 °, 40 °], signal-to-noise ratio 10dB, number of snapshots t=1024, regularization parameter μ are 2.5
×10-3/((log t)2log(M+N-1))。
Fig. 2 gives the relatively prime battle array structural schematic diagram of construction, and as can be seen from the figure array element is non-evenly arranged, this
Arrangement mode has the advantages that very much；Fig. 3 gives the uniform sparse subarray of a pair of relatively prime battle array, as can be seen from the figure each
The array element interval of submatrix is greater than half wavelength, and the interval of array and array number have certain relationship, thereby may be ensured that construction
Relatively prime array has bigger array aperture and freedom degree；Fig. 4 gives the non-homogeneous void obtained after covariance matrix vector quantization
The structural schematic diagram of matroid column, it is as can be seen from the figure virtual after array element be non-homogeneous array element, if only choosing its uniform portion
Array element loss will be had by dividing；Fig. 5 gives the schematic diagram of the uniform virtual array obtained after insertion array element, and white circle expression is filled out in figure
Fill array element；Fig. 6 is the space power spectrum schematic diagram of the mentioned method of the present invention, and wherein vertical dotted line represents the reality of incident signal source
Direction, as can be seen from the figure 10 spectral peaks accurately appear in sense, illustrate that the method for the present invention can effectively be told
10 incoming signals, the signal number 10 that can be differentiated is greater than array number 6, and coherent signal also can accurately estimate angle of arrival,
And conventional uniform linear array can only at most differentiate 5 signal sources using 6 physics array elements, the method for the present invention improves freedom degree, can
Realize decorrelation LMS on the basis of increasing freedom degree.
In conclusion the method for the present invention takes full advantage of the reception information on non-homogeneous virtual array, it can be in signal source
Number realizes being effectively estimated for incoming signal in the case where being greater than physics element number of array, and the maximum for increasing DOA estimation can be estimated
Several and resolution ratio；In addition, the present invention estimates for giving effective coherent signal there are the case where coherent signal in actual environment
The angle of arrival of coherent signal can be effectively estimated by the inventive method for meter method.
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 (5)
1. one kind is based on the relatively prime array method for estimating angle of arrival of coherent signal of electromagnetic vector sensor comprising the steps of:
Step 1: construction one is made of the one-dimensional relatively prime array of electromagnetic vector sensor M+N-1 array element, wherein M and N is relatively prime
Integer, the relatively prime battle array of electromagnetic vector sensor are made of a pair of sparse homogenous linear subarray, and first submatrix includes M spacing
For the array element of Nd, element position 0, Nd ..., (M-1) Nd, second subarray includes the array element that N number of spacing is Md, battle array
First position is 0, Md ..., and (N-1) Md, d are incoming signal minimum half-wavelength；
Step 2: receiving the K far fields from different directions using the relatively prime array of electromagnetic vector sensor as receiving array
Narrow band signal source θ1, θ2..., θK, data will be received and be divided into x, y, z axis direction electric and magnetic fields totally 6 submatrix data, t snap
For the reception signal of acquisition to be respectively X1, X2, X3, X4, X5, X6, thus calculating covariance matrix is respectively Rx1、Rx2、Rx3、Rx4、
Rx5、Rx6；
Step 3: obtaining new single snap by 6 submatrix data covariance matrix vector quantizations receives signal data, removal redundancy etc.
Valence virtual signal obtains the virtual signal of equal value of non-homogeneous virtual array:
(3a) vector quantization covariance matrix stacks gradually each column of covariance matrix to form a new column vector, obtain
New single snap receives signal data；
(3b) calculates submatrix element position difference set Ds={ usi-usj, wherein usi, usjRespectively indicate i-th of s-th of subarray
With the position coordinates of j-th of array element, DsThe element position difference set for indicating s-th of submatrix, by DsArray element position of the d as virtual array
Coordinate is set, 6 redundant virtual submatrixs are obtained；
Repetition array element in (3c) removal redundant virtual array obtains 6 irredundant non-homogeneous virtual submatrixs, corresponds to of equal value empty
It is quasi- to receive signal Z1, Z2, Z3, Z4, Z5, Z6；
Step 4: the equivalence for constructing uniform virtual array is virtual to receive signal, in the missing array element part of non-homogeneous virtual array
Supplement receives the array element data that signal is 0, obtain corresponding to 6 uniform virtual submatrixs equivalent single snap receive data Y1, Y2,
Y3,Y4,Y5,Y6；
Step 5: receiving data configuration Toeplitz covariance square using equivalent single snap of 6 uniform virtual submatrixs of construction
Battle array Rz1、Rz2、Rz3、Rz4、Rz5、Rz6；
Step 6: construction only includes the matrix H of 0 and 1 element；
Step 7: solving and Toeplitz covariance matrix Rz1、Rz2、Rz3、Rz4、Rz5、Rz6The smallest low-rank Toeplitz of difference
Matrix RT1、RT2、RT3、RT4、RT5、RT6；
Step 8: carrying out the estimation that arithmetic mean realizes coherent signal to 6 low-rank Toeplitz matrixes that solution obtains；
I=1 in abovementioned steps, 2 ..., M+N-1, j=1,2 ..., M+N-1 indicate the element number of array of relatively prime array, s=1,
2 ..., 6 indicate the number of submatrix.
2. according to claim 1 be based on the relatively prime array method for estimating angle of arrival of coherent signal of electromagnetic vector sensor, step
Equivalent single snap of 6 uniform virtual submatrixs in rapid five using construction receives data configuration Toeplitz covariance matrix Rz1、
Rz2、Rz3、Rz4、Rz5、Rz6It is specific as follows: by taking x-axis direction electric field submatrix as an example, remember that the element number of array of uniform virtual array is L1,
Since the array is with the symmetrical structure of zero position array element, so center array element is theA array element, x-axis direction
The Toeplitz matrix of electric field submatrix can be constructed in:
Wherein,<Y1>lIt indicates that equivalence corresponding to first of the array element of first virtual sub-array receives signal, similarly can be obtained
Rz2、Rz3、Rz4、Rz5、Rz6, wherein l=1,2 ..., L1 indicate the element number of array of uniform virtual array.
3. according to claim 1 be based on the relatively prime array method for estimating angle of arrival of coherent signal of electromagnetic vector sensor, step
Rapid six construction only includes the matrix H of 0 and 1 element, specific as follows: matrix H dimension and Rz1It is identical, because being filled with when filling array element
Zero receives data, so Rz1In there are neutral elements, as matrix Rz1In some position element be 0, then opposite position in matrix H
Element be also 0, the element value of remaining position of matrix H is 1.
4. according to claim 1 be based on the relatively prime array method for estimating angle of arrival of coherent signal of electromagnetic vector sensor, step
Rapid seven solve and Toeplitz covariance matrix Rz1、Rz2、Rz3、Rz4、Rz5、Rz6The smallest low-rank Toeplitz matrix R of differenceT1、
RT2、RT3、RT4、RT5、RT6It is specific as follows: to solve R by taking x-axis direction electric field submatrix as an exampleT1, solved using CVX Optimization Toolbox full
FootThe smallest positive semidefinite matrix RT1, whereinRepresenting matrix
RT1In element multiplication in each element and matrix H on corresponding position；||·||FFor Frobenius norm, Tr () is indicated
The mark of matrix, μ are regularization parameter, according to seeking RT1Same mode obtains RT2、RT3、RT4、RT5、RT6。
5. according to claim 1 be based on the relatively prime array method for estimating angle of arrival of coherent signal of electromagnetic vector sensor, step
Rapid eight pairs solve 6 obtained low-rank Toeplitz matrixes and carry out the estimation specific steps that arithmetic mean realizes coherent signal are as follows:
5.1) arithmetic average for calculating 6 low-rank Toeplitz matrixes, obtains full rank Toeplitz matrix
5.2) full rank Toeplitz matrix is obtained to above-mentionedFeature decomposition is carried out, obtains angle-of- arrival estimation using MUSIC methodWherein, the number of k=1,2 ..., K expression signal source.
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