CN107576951A - Wave arrival direction estimating method based on nested type Electromagnetic Vector Sensor Array - Google Patents
Wave arrival direction estimating method based on nested type Electromagnetic Vector Sensor Array Download PDFInfo
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Abstract
The invention discloses a kind of Wave arrival direction estimating method based on nested type Electromagnetic Vector Sensor Array, mainly solve the problems, such as between each electromagnetic component of Electromagnetic Vector Sensor Array in the prior art that mutual coupling is more serious and Electromagnetic Vector Sensor Array hardware realize it is complicated.Its implementation process is：Construct nested type Electromagnetic Vector Sensor Array；There is blur estimation value using what ESPRIT algorithms obtained target direction cosine；There is blur estimation value to match target direction cosine；Using the vector cross-products algorithm of single Split type electric magnetic vector sensor obtain target direction cosine without blur estimation value；There is blur estimation value to carry out ambiguity solution target direction cosine, and do triangulo operation, obtain the estimating two-dimensional direction-of-arrival value of extraterrestrial target.Present invention reduces the mutual coupling between each electromagnetic component and hard-wired complexity, extends the aperture of whole array, improves angle measurement accuracy, and the angle of target is positioned available for radar.
Description
Technical field
The invention belongs to signal processing technology field, more particularly to a kind of Wave arrival direction estimating method, available for radar pair
The angle positioning of target.
Background technology
Electromagnetic Vector Sensor Array radar is to adapt to a kind of New System for great potential that modern war is suggested
Radar.Compared with conventional arrays, Electromagnetic Vector Sensor Array can perceive the electromagnetic component of incidence wave in different directions, so as to
Extract more information such as to polarize, and the domain information that polarizes is combined with spatial information (si), can further improve signal multi-Dimensional parameters
Estimation and the performance of signal detection.Therefore in recent decades, the object space angle estimation based on Electromagnetic Vector Sensor Array by
The extensive concern of people is arrived.The electromagnetism that three orthogonal electrical dipoles and three orthogonal magnet rings overlapped by phase center form is sweared
Quantity sensor can measure the three-dimensional electric field component and three-dimensional magnetic field component of incoming signal, and referred to as concurrent formula electromagnetic vector senses
Device.For this concurrent formula electromagnetic vector sensor, professor K.T.Wong proposes a kind of for the electromagnetic vector sensor
New DOA estimation method --- vector cross-products algorithm, this method can not be related to the phase difference between frequency domain information and antenna, so as to
Estimate for the DOA of arrowband and broadband signal.But the concurrent formula electromagnetic vector sensor that this phase center overlaps needs each
There is very strict electromagnetic isolation, this is not easy to realize within hardware between electromagnetic component.Therefore, Split type electric magnetic vector passes
Sensor is suggested, and each component is spatially separated into a segment distance, to reduce the mutual coupling of each component and hard-wired complexity.
But because each component of Split type electric magnetic vector sensor is spatially separated, phase shift factor is introduced, therefore can not be direct
Target DOA estimation is carried out using vector cross-products algorithm.
2011, professor K.T.Wong proposed a kind of Split type electric magnetic vector sensor based on parallel lines structure, into
Work(realizes application of the vector cross-products DOA algorithm for estimating in Split type electric magnetic vector sensor, but this method is to element position
It is required that it is relatively strict, and this method only discuss situation of the vector cross-products algorithm in single Split type electric magnetic vector sensor,
Its applicable cases in an array is not discussed.
Because array angle measurement accuracy is directly proportional to array aperture, in general even linear array ULA, array element spacing is not more than
λ/2, so array aperture is subject to certain restrictions.On the other hand, P.P.Vaidyanathan proposes nested type array, the nested type
Array is made up of two or more homogenous linear submatrixs with different array element spacing, and other submatrixs in addition to the first submatrix
Array element spacing is all much larger than λ/2, and the mutual coupling between each array element is smaller, and in the case of identical array unit number,
Array aperture is greater than even linear array ULA, and angle measurement accuracy is also higher.But it is single pole that research before, which concentrates on array element,
Change the situation of antenna, the electromagnetic information of collection is simultaneously imperfect, and does not discuss using Split type electric magnetic vector sensor as nesting
The situation of the antenna element of formula array.
2014, Keyong Han, which are proposed, a kind of to be combined concurrent formula electromagnetic vector sensor with even linear array ULA
Array, the estimation to target DOA is realized using the method for tensor, but because the array element of the array is concurrent formula electromagnetism arrow
Quantity sensor, the mutual coupling between each component of electromagnetic vector sensor is larger, and by the array aperture of even linear array in itself and
Array element spacing is not more than the influence of λ/2, and the mutual coupling between each electromagnetic vector sensor has had a strong impact on target DOA estimation
Can, in addition, DOA of this method using tensor estimation target, amount of calculation are relatively large.
To sum up, no matter single Split type electric magnetic vector sensor or nested type array can correctly estimate the ripple of target
Up to direction, but all there is certain limitation, and by electromagnetic vector sensor apply to the array of common form then due to by
To the influence of the mutual coupling between the mutual coupling between each component of electromagnetic vector sensor and each electromagnetic vector sensor, cause target
The estimated accuracy of direction of arrival declines.
The content of the invention
The present invention is directed to above-mentioned the deficiencies in the prior art, proposes a kind of and based on nested type Electromagnetic Vector Sensor Array
Wave arrival direction estimating method, to reduce the mutual coupling between electromagnetic vector sensor, improve the estimated accuracy of target direction of arrival.
To achieve the above object, the present invention incite somebody to action both according to electromagnetic vector sensor and the respective advantage of nested type array
It is combined, its technical scheme is as follows：
1) nested type Electromagnetic Vector Sensor Array is constructed：
Given array element number N, by preceding n1Individual array element is set using D as array element spacing along certain direction, is obtained uniformly
First submatrix C1s, rear n of the linear array ULA as nested type Electromagnetic Vector Sensor Array2Individual array element is using mD as array element spacing
Set in same direction, obtain second submatrix C2s of the even linear array ULA as nested type Electromagnetic Vector Sensor Array, wherein, m
=n1+ 1, and have n1+n2=N, each array element place a Split type electric magnetic vector sensor, obtain nested type electromagnetism
Spectra of acoustic vector sensor array A, D are more than λ/2, and λ is electromagnetic wavelength；
2) by the reception data X (t) of nested type Electromagnetic Vector Sensor Array by C2 points of the first submatrix C1 and the second submatrix
For X1And X (t)2(t) two parts；
3) data X is received to two parts1And X (t)2(t) two groups are estimated with invariable rotary subspace ESPRIT algorithms respectively
There is fuzzy target y-axis direction cosines estimateWithAnd two groups of estimates
Signal subspace Es corresponding to respectively1And Es2, wherein K is target number；
4) two groups of target y-axis direction cosines estimates to estimating in 3)WithMatched, and according to pairing order pair signal subspace Es corresponding with estimate1And Es2Progress
Match somebody with somebody, obtain the estimate of the array manifold matrix of nested type Electromagnetic Vector Sensor Array；
5) steering vector of remaining array element in the estimate of array manifold matrix in addition to referential array unit is entered
Row phase compensation, and the steering vector of remaining array element after compensation is synthesized to the separate type electromagnetism at referential array unit
On the steering vector of vector sensor, the guiding of the Split type electric magnetic vector sensor at the referential array unit after being synthesized
Vector；
6) guiding of the Split type electric magnetic vector sensor at referential array unit after the synthesis obtained in step 5) is utilized
Vector, it is relatively low but without fuzzy target y-axis direction cosines estimate that one group of precision is obtained by vector cross-products algorithmWith one group of x-axis direction cosines estimateAnd two groups have fuzzy target x-axis side
To cosine estimateWith
7) two groups are obtained to step 4) fuzzy target y-axis direction cosines estimateTwo are obtained with step 6)
Group has fuzzy target x-axis direction cosines estimateAmbiguity solution is carried out, obtains one group without fuzzy target x-axis direction
Cosine high accuracy estimateWith one group without fuzzy target y-axis direction cosines high accuracy estimate
8) to without fuzzy target x-axis direction cosines high accuracy estimateIt is high with the fuzzy target y-axis direction cosines of nothing
Accuracy extimate valueTriangulo operation is done, obtains the two-dimensional space direction of arrival information of targetWhereinIt is l-th of target
Azimuth estimate,It is the angle of pitch estimate of l-th of target.
It is of the invention that there is advantages below compared with existing array structure and existing algorithm：
1) compared with even linear array, the arrangement mode of the array element of array of the present invention uses the knot of nested type array
Structure, possesses bigger array aperture in the case of same array element number, and the angle measurement accuracy of array is higher；
2) compared with common Electromagnetic Vector Sensor Array, each array element of array of the present invention is one
Split type electric magnetic vector sensor, and the spacing between array element is bigger, reduces in reception signal between electromagnetic component
Mutual coupling and electromagnetic vector sensor hardware itself complexity；
3) compared with the algorithm of existing Electromagnetic Vector Sensor Array, the present invention is being maintained using each array list
All electromagnetic informations of member reduce operand and complexity with the basis of the characteristics of can estimating multiple targets simultaneously.
Brief description of the drawings
Fig. 1 is the implementation process figure of the present invention；
Fig. 2 is the geometry schematic diagram of single Split type electric magnetic vector sensor in the present invention；
Fig. 3 is the array configuration structural representation in the present invention；
Fig. 4 is the simulation result schematic diagram once estimated target two dimensional angle with the present invention；
Fig. 5 be in the present invention to the root-mean-square error of different directions cosine estimate compared with Between Signal To Noise Ratio figure；
Fig. 6 is to reach side to array of the present invention and the target two dimension ripple of two homogenous linear Electromagnetic Vector Sensor Arrays
To angle estimation value root-mean-square error compared with Between Signal To Noise Ratio figure, two of which homogenous linear Electromagnetic Vector Sensor Array
Array element number it is identical with array of the present invention, array element spacing is respectively D and mD；
Fig. 7 is to reach side to array of the present invention and the target two dimension ripple of two homogenous linear Electromagnetic Vector Sensor Arrays
Root-mean-square error and fast umber of beats relations comparison chart to angle estimation value, two of which homogenous linear Electromagnetic Vector Sensor Array
Array element number it is identical with array of the present invention, array element spacing is respectively D and mD；
Fig. 8 is to reach side to array of the present invention and the target two dimension ripple of two homogenous linear Electromagnetic Vector Sensor Arrays
To angle estimation value root-mean-square error compared with the first submatrix C1 array element spaced relationship figure, two of which homogenous linear electromagnetism
The array element number of spectra of acoustic vector sensor array is identical with array of the present invention, and array element spacing is respectively D and mD.
Embodiment
The implementation process and effect of the present invention are further described referring to the drawings.
Reference picture 1, step is as follows for of the invention realizing：
Step 1, according to single Split type electric magnetic vector Sensor Design nested type Electromagnetic Vector Sensor Array.
Reference picture 2, single Split type electric magnetic vector sensor are divided into：Electric dipole Ex parallel to x-axis, parallel to y-axis
Electric dipole Ey, the electric dipole Ez parallel to z-axis, the magnet ring Hx perpendicular to x-axis, the magnet ring Hy perpendicular to y-axis and vertical
In this six components of the magnet ring Hz of z-axis, Δx,yEx and Ey spacing is represented, and Hx and Hy spacing is also equal to Δx,y, Δy,zTable
Show Ey and Ez spacing, and Hy and Hz spacing is also equal to Δy,z；
Given array element number N, according to the position of the structure design array element of nested type array, by all arrays
Unit is divided into former and later two parts：First submatrix C1 and the second submatrix C2, wherein：
With preceding n1Spacing of the individual array element using D between array element, even linear array ULA conducts are constructed along the y-axis direction
First submatrix C1, the position of its array element is [0, D, 2D ..., (n1- 1) D], it is used as reference by 0 array element of position
Array element；
With remaining n2Spacing of the individual array element using mD between array element, along phase Tongfang after the first submatrix C1
It is as the second submatrix C2, the position of its array element to construction even linear array ULA：
[n1D,(n1+m)D,(n1+2m)D,...,(n1+(n2- 1) m) D], wherein, m=n1+ 1, and have n1+n2=N, D are more than
λ 2, λ are electromagnetic wavelength；
N number of Split type electric magnetic vector sensor is placed according to the array element position of following nested type array, obtained
Nested type Electromagnetic Vector Sensor Array, as shown in figure 3, the position of the wherein array element of nested type array is as follows：[0,D,
2D,...,(n1-1)D,n1D,(n1+m)D,(n1+2m)D,...,(n1+(n2-1)m)D]。
Step 2, according to the nested type Electromagnetic Vector Sensor Array of construction, nested type Electromagnetic Vector Sensor Array is obtained
Reception data X (t).
2.1) by nested type Electromagnetic Vector Sensor Array, the steering vector for obtaining the array is
Wherein, the steering vector of the Split type electric magnetic vector sensor at a expressions referential array unit, its expression are as follows：
Wherein,
(ex,ey,ez) x-axis, the electric field component that y-axis and z-axis receive, (h are represented respectivelyx,hy,hz) x-axis, y are represented respectively
The magnetic-field component that axle and z-axis receive, φ ∈ [0,2 π), θ ∈ [0, π] represent azimuth and the angle of pitch of incoming signal respectively,
Azimuth is signal and x-axis forward direction angle, and the angle of pitch is signal and z-axis forward direction angle, and γ ∈ [0, pi/2], η ∈ [- π, π] are respectively
Represent that polarization explement and the polarization phases of incoming signal are poor, u=sin θ cos θ represent direction cosines of the incoming signal along x-axis, v=
Sin θ sin φ represent direction cosines of the incoming signal along y-axis, and w=cos θ represent direction cosines of the incoming signal along z-axis, ⊙ tables
Show that Hadamard is accumulated, (xh,yh,zh) represent that the Split type electric magnetic vector sensor at referential array unit is put perpendicular to x-axis
Magnet ring Hx position coordinates；
2.2) according to the steering vector of nested type Electromagnetic Vector Sensor Array, the reception data X (t) of this array is obtained：
Assuming that there is K mutually incoherent narrowband target signals to incide the array, then its whole array received signal mode
Type is represented by：
Wherein, blThe steering vector corresponding to l-th of signal, l=1 are represented, 2 ..., K, n (t) represent that average is zero, side
Difference isWhite complex gaussian noise, and, B=[b uncorrelated to incoming signal1,b2,...,bl,...,bK] it is array manifold square
Battle array, signal phasor is s (t)=[s1(t),s2(t),...,sl(t),...,sK(t)]T, sl(t) l-th of incoming signal is represented,
()TThe transposition of vector is represented, t represents sampling time t=t1,t2,...,tL, the fast umber of beats of L expressions.
Step 3, according to two submatrixs C1 and C2 array element position, the first submatrix C1 and the second submatrix C2 are respectively obtained
Reception data covariance matrixWith
According to two submatrixs C1 and C2 division, by the data X (t) of array received=[X (t1),X(t2),...,X(tL)]
It is divided into X1(t)=[X1(t1),X1(t2),...,X1(tL)] and X2(t)=[X2(t1),X2(t2),...,X2(tL)] two parts, profit
The covariance matrix of this two groups of reception data is obtained with maximal possibility estimationWith()HThe conjugate transposition of representing matrix.
Step 4, according to the first submatrix C1 and the covariance matrix of the second submatrix C2 reception dataWithObtain
One submatrix C1 signal subspace matrix Es1With the second submatrix C2 signal subspace matrix Es2。
To the first submatrix C1 reception data covariance matrixEigenvalues Decomposition is done, and takes its K maximum characteristic value
Corresponding characteristic vector forms the first submatrix C1 signal subspace matrix Es1；
To the second submatrix C2 reception data covariance matrixEigenvalues Decomposition is done, and takes its K maximum characteristic value
Corresponding characteristic vector forms the second submatrix C2 signal subspace matrix Es2。
Step 5, according to the first submatrix C1 signal subspace matrix Es1, utilize invariable rotary subspace ESPRIT algorithms
Obtain one group of periodically fuzzy y-axis direction cosines estimate
5.1) a is madelRepresent that the Split type electric magnetic vector sensor at referential array unit is sweared to the guiding of l-th of target
Amount,Represent n before the first submatrix C11- 1 array element is to l-th target
Steering vector,Represent n after the first submatrix C11- 1 array element
To the steering vector of l-th of target；
For single target, by the first submatrix C1 preceding n1- 1 array element and rear n1The sky that -1 array element is formed
Between rotational invariance be reflected on steering vector, its form is：
5.2) makeFor n before the first submatrix C11Array corresponding to -1 array element
Flow pattern matrix,For n after the first submatrix C11Array manifold corresponding to -1 array element
Matrix；
For all targets, by the first submatrix C1 preceding n1- 1 array element and rear n1The sky that -1 array element is formed
Between rotational invariance be deformed into matrix form：
Wherein,For the first submatrix C1 invariable rotary factor matrix；
5.3) according to signal subspace this property identical with the space of its steering vector, following relational expression is obtained：
Es1=B1T1
Wherein B1Represent the first submatrix C1 array manifold matrix, T1It is the invariable rotary factor matrix with the first submatrix C1Corresponding unique nonsingular matrix；
By relational expressionSubstitute into Es1=B1T1, obtain following relational expression：
Wherein, Es1,2Represent n after the first submatrix C11Signal subspace matrix, Es corresponding to -1 array element1,1Represent
N before first submatrix C11Signal subspace matrix corresponding to -1 array element, and have
5.4) according to the first submatrix C1 signal subspace matrix Es1, isolate preceding n1Signal corresponding to -1 array element
Subspace matrices Es1,1With rear n1Signal subspace matrix Es corresponding to -1 array element1,2, according to relational expressionObtain the first intermediate variable
5.5) it is rightEigenvalues Decomposition is carried out, its characteristic value is exactly the first submatrix C1 invariable rotary factor matrix's
Diagonal element, according to the condition of D ＞ λ/2, obtain one group of periodically fuzzy y-axis direction cosines with total least square method and estimate
Value：
Step 6, according to the second submatrix C2 signal subspace matrix Es2, utilize invariable rotary subspace ESPRIT algorithms
Obtain one group of periodically fuzzy y-axis direction cosines estimate
6.1) makeFor preceding n2- 1 array list
First steering vector to l-th of target,For
N afterwards2Steering vector of -1 array element to l-th of target；
For single target, by the second submatrix C2 preceding n2N after -1 array element and the second submatrix C22- 1 array list
The Space Rotating consistency that member is formed is reflected on steering vector, and its form is：
6.2) makeFor n before the second submatrix C22Array corresponding to -1 array element
Flow pattern matrix,For n after the second submatrix C22Array manifold corresponding to -1 array element
Matrix；
For all targets, by the second submatrix C2 preceding n2N after -1 array element and the second submatrix C22- 1 array list
The Space Rotating consistency that member is formed is deformed into matrix form：
Wherein,For the second submatrix C2 invariable rotary factor square
Battle array；
6.3) according to signal subspace this property identical with the space of its steering vector, following relational expression is obtained：
Es2=B2T2,
Wherein B2Represent the second submatrix C2 array manifold matrix, T2It is the invariable rotary factor matrix with the second submatrix C2Corresponding unique nonsingular matrix；
By relational expressionSubstitute into Es2=B2T2, obtain following relational expression：
Wherein, Es2,2Represent n after the second submatrix C22Signal subspace matrix, Es corresponding to -1 array element2,1Represent
N before second submatrix C22Signal subspace matrix corresponding to -1 array element, and have
6.4) according to the second submatrix C2 signal subspace matrix Es2, isolate n before the second submatrix C22- 1 array element
Corresponding signal subspace matrix Es2,1With n after the second submatrix C22Signal subspace matrix Es corresponding to -1 array element2,2,
According to relational expressionObtain the second intermediate variable
6.5) it is rightEigenvalues Decomposition is carried out, its characteristic value is exactly the second submatrix C2 invariable rotary factor matrix's
Diagonal element, according to the condition of mD ＞ D ＞ λ/2, one group of periodically fuzzy y-axis direction cosines is obtained with total least square method
Estimate：
Step 7, according toWithDiagonal entry pairWithMatched.
Due toWithEstimation be two relatively independent processes, so they
Between not automatic matching, therefore need before ambiguity solution operation is done using them pairWithMatched.
Due toIt is basisDiagonal entryIn l-th of target at the first submatrix C1 because of array list
Space D between member and caused phase differenceObtain,In each target sequence number put in order
WithDiagonal entry in each target sequence number put in order it is identical；It is basisDiagonal entryIn
L-th of target in the second submatrix C2 because of the spacing mD between array element and caused by phase differenceObtain,In each target sequence number put in order withDiagonal entry in each target sequence number the phase that puts in order
Together, therefore can incite somebody to actionWithMarriage problem translate intoDiagonal entry andThe pairing of diagonal entry ask
Topic.
Diagonal entry andDiagonal entry pairing according to the second submatrix C2 array element spacing mD
Realized with m times of relation of the first submatrix C1 array element space D, its step is as follows：
7.1) set a target at the first submatrix C1 because of array element space D and caused by true phase difference as Λ1=
2g1π+φ1, wherein φ1For Λ1The phase difference that can actually measure, g1For Λ1With φ1Between the cycle fuzzy number that differs, if
The target at the second submatrix C2 because of array element spacing mD and caused by phase difference be Λ2=2g2π+φ2, φ2For Λ2It is actual
The phase difference that can be measured is φ2, g2For Λ2With φ2Between the cycle fuzzy number that differs；
According to the second submatrix C2 array element spacing mD and m times of relation of the first submatrix C1 array element space D, obtain
To m Λ1=Λ2Relational expression；
7.2) by relational expression m Λ1=Λ2Obtain equation below：
m×(2g1π+φ1)=2g2π+φ2,
The equation is deformed, the relational expression after being deformed as follows：
mφ1=2 π (g2-mg1)+φ2
According to the relational expression and the property of exponential function after deformation, following relational expression is obtained：
7.3) according to relational expressionIt is rightDiagonal entryAll it is m times
Side, and successively withDiagonal entryContrasted one by one, selection difference minimum match, and obtains
Diagonal entry andDiagonal entry pairing order；
7.4) basis obtainsDiagonal entry andDiagonal entry pairing order, to two groups of target y
Direction of principal axis cosine estimateWithIn putting in order for each target sequence number re-start sequence, complete pairWith's
Pairing.
Step 8, according to the first submatrix C1 signal subspace matrix Es1With the second submatrix C2 signal subspace matrix Es2
WithWithPairing order, obtain the steering vector synthesis of all electromagnetic vector sensors in addition to referential array unit
The result on steering vector at referential array unitWith
8.1) it is rightWithAfter carrying out feature decomposition, its characteristic vector constitutes nonsingular matrix T1And T2, according to
WithPairing result it is right respectivelyWithColumn vector and nonsingular matrix T1And T2Column vector matched, according to
The relation of signal subspace matrix and array manifold matrix in ESPRIT algorithmsWithObtain array
Flow pattern matrix B1And B2EstimateWith
8.2) guiding of all electromagnetic vector sensors in addition to the electromagnetic vector sensor at referential array unit is sweared
Amount carries out phase compensation, to carry out relevant addition, so as to be synthesized to the Split type electric magnetic vector sensing at referential array unit
On the steering vector of device, compensation rate is the phase shift factor of each electromagnetic vector sensor, obtains the institute in addition to referential array unit
The steering vector for having electromagnetic vector sensor is synthesized to the result on the steering vector at referential array unit：
Wherein, c1And c2It is different complex constants,
Step 9, according toWithWith vector cross-products algorithm, the precision for obtaining one group of u is relatively low but without fuzzy estimateThe fuzzy estimate with two groups of u degree of precision but presence periodicityWithAnd one group of v precision is relatively low but without fuzzy estimate
9.1) it is rightWithThe normalized vector cross product of electric field component and magnetic-field component is carried out respectively, and its result is as follows：
OrderFinal vector as the Split type electric magnetic vector sensor at referential array unit is pitched
Product result, passes through plComposition：
It is relatively low but without fuzzy u, v, w estimates to obtain precision：
Wherein | | expression takes absolute value；
9.2) makeObtain
According toComposition, obtain direction cosines u of the target along x-axis two groups of degree of precision but exist periodically fuzzy
EstimateWith
Step 10, according toIt is rightWithAmbiguity solution is carried out, obtains v high accuracy and without fuzzy estimate
10.1) it is precision is relatively low but without fuzzy y-axis direction cosines estimateAs solution precision compared with
Y-axis direction cosines estimate that is high but being obscured in the presence of periodicityReference value, v first precision be higher
And without fuzzy estimateObtained by following ambiguity solution equation：
Wherein, Expression rounds up,Expression rounds downwards；
10.2) willY-axis direction cosines estimation that is higher as solution precision but being obscured in the presence of periodicity
ValueReference value, v it is final high accuracy and without fuzzy estimateBy following solution
Fuzzifying equation obtains：
Wherein,
Step 11, according toIt is rightWithAmbiguity solution is carried out, obtains u high accuracy and without fuzzy estimate
11.1) it is precision is relatively low but without fuzzy x-axis direction cosines estimateAs solution precision compared with
X-axis direction cosines estimate that is high but being obscured in the presence of periodicityReference value, u first precision be higher
And without fuzzy estimateObtained by following ambiguity solution equation：
Wherein,
11.2) willX-axis direction cosines estimation that is higher as solution precision but being obscured in the presence of periodicity
ValueReference value, u it is final high accuracy and without fuzzy estimateBy following solution
Fuzzifying equation obtains：
Wherein,
Step 12, according to u high accuracy without fuzzy high-precision estimateHigh accuracy with v is without fuzzy
EstimateObtain azimuth and the angle of pitch estimate of target
It is rightWithMake following triangulo operation：
Obtain the estimating two-dimensional direction-of-arrival information of targetWhereinIt is the azimuth estimate of l-th of target,It is the angle of pitch estimate of l-th of target.
The effect of the present invention is further illustrated by following Computer Simulation.
1. simulated conditions
If array element number is 10, step 1 in above-mentioned embodiment construction array, array element position for [0,
1,2,3,4,5,11,17,23,29], the first submatrix C1 is made up of array element [0,1,2,3,4], and the second submatrix C2 is by array list
First [5,11,17,23,29] are formed, if C1 array element spacing is 6 λ, then C2 array element spacing is 36 λ.
A Split type electric magnetic vector sensor is placed at each array element；Sweared for any one separate type electromagnetism
Quantity sensor, wherein the distance between three electric dipoles are Δx,y=Δy,z=5 λ, if the separate type at referential array unit
Electromagnetic vector sensor is located at the Split type electric magnetic vector sensor of origin, its magnetic perpendicular to x-axis for an electric dipole Ey
Ring Hx coordinate isThe nested type Electromagnetic Vector Sensor Array such as Fig. 3 institutes constructed
Show.
Being located in same range cell has K=3 uncorrelated targets, and the azimuth of target is φ=(42 °, 55 °, 28 °),
The angle of pitch is θ=(20 °, 60 °, 45 °), and polarization explement is γ=(45 °, 30 °, 55 °), polarization phases difference for η=(90 °,
120°,70°).Fast umber of beats is L=200, and signal to noise ratio SNR=15dB, 200 times Monte-Carlo is tested.
2. emulation content
Emulation 1：Effectiveness of the invention is emulated.
Under above-mentioned simulated conditions, estimated result is as shown in Figure 4 to be estimated to the 2-d direction finding of target.
The present invention can correctly estimate azimuth and the angle of pitch this two dimensional angle of target as can be seen from Figure 4
Information.
Emulation 2：The root-mean-square error of different directions cosine estimate and the relation of signal to noise ratio of the present invention are emulated.
Under above-mentioned simulated conditions, if signal to noise ratio snr is a class value, to the equal of different directions cosine estimate of the invention
The relation of square error and signal to noise ratio is emulated, as a result as shown in Figure 5.
From fig. 5, it can be seen that due to array of the present invention, in the aperture in y-axis direction, extension is much larger than in x-axis direction
Aperture extends, so when signal to noise ratio is higher than the signal-noise ratio threshold of ambiguity solution, will height along the direction cosines v of y-axis estimated accuracy
In the estimated accuracy of the direction cosines u along x-axis.
Emulation 3：Respectively to the array of the present invention and the target of two homogenous linear Electromagnetic Vector Sensor Arrays shown in Fig. 3
The root-mean-square error of two dimensional angle estimate and the relation of signal to noise ratio are emulated.
Under above-mentioned simulated conditions, if the array element number and Fig. 3 of two homogenous linear Electromagnetic Vector Sensor Arrays
Shown array of the present invention is identical, and the array element spacing of array is respectively D and mD, and signal to noise ratio snr is a class value, to shown in Fig. 3
The target two dimensional angle estimate of array of the present invention and two homogenous linear Electromagnetic Vector Sensor Arrays it is square
Root error and the relation of signal to noise ratio are emulated, simulation result such as Fig. 6, wherein, Fig. 6 (a) be array of the present invention shown in Fig. 3 and
The root-mean-square error of azimuth estimate and the relations comparison chart of signal to noise ratio of two homogenous linear Electromagnetic Vector Sensor Arrays,
Fig. 6 (b) is the equal of the angle of pitch estimate of the array of the present invention and two homogenous linear Electromagnetic Vector Sensor Arrays shown in Fig. 3
The relations comparison chart of square error and signal to noise ratio.
From Fig. 6 (a) and Fig. 6 (b) as can be seen that when signal to noise ratio is less than the signal-noise ratio threshold of ambiguity solution, ambiguity solution failure,
Azimuth and the angle of pitch of target can not correctly be estimated, and after increasing to the signal-noise ratio threshold of ambiguity solution with signal to noise ratio, angle measurement
Performance optimizes rapidly, and angle measurement accuracy improves with the raising of signal to noise ratio.
In addition, by the array of the present invention shown in Fig. 3 compared with two homogenous linear Electromagnetic Vector Sensor Arrays, Fig. 3 institutes
The ambiguity solution signal-noise ratio threshold of the array of the present invention shown is lower, and when signal to noise ratio is higher than the signal-noise ratio threshold of ambiguity solution, it is identical
The angle measurement accuracy of array of the present invention in the case of signal to noise ratio shown in Fig. 3 is higher than other two kinds of arrays.
Emulation 4：To the array of the present invention shown in Fig. 3 and the target two dimension of two homogenous linear Electromagnetic Vector Sensor Arrays
The root-mean-square error and the relation of fast umber of beats of direction of arrival angle estimate are emulated.
Under above-mentioned simulated conditions, if the array element number and Fig. 3 of two homogenous linear Electromagnetic Vector Sensor Arrays
Shown array of the present invention is identical, and the array element spacing of array is respectively D and mD, and fast umber of beats L is a class value, to shown in Fig. 3
Array of the present invention and two homogenous linear Electromagnetic Vector Sensor Arrays target two dimensional angle estimate it is equal
The relation of square error and fast umber of beats is emulated, simulation result such as Fig. 7, wherein, Fig. 7 (a) is the array of the present invention shown in Fig. 3
With the root-mean-square error and the Relationship Comparison of fast umber of beats of the azimuth estimate of two homogenous linear Electromagnetic Vector Sensor Arrays
Figure, Fig. 7 (b) is the angle of pitch estimate of the array of the present invention and two homogenous linear Electromagnetic Vector Sensor Arrays shown in Fig. 3
Root-mean-square error and fast umber of beats relations comparison chart.
From Fig. 7 (a) and Fig. 7 (b) as can be seen that the angle measurement accuracy of the array of the present invention shown in Fig. 3 is with the increasing of fast umber of beats
Improve greatly, and in the case of identical fast umber of beats, the angle measurement accuracy of the array of the present invention shown in Fig. 3 is higher than other two kinds of battle arrays
Row.
Emulation 5：To the array of the present invention shown in Fig. 3 and the target two dimension of two homogenous linear Electromagnetic Vector Sensor Arrays
The relation of the root-mean-square error of direction of arrival angle estimate and the first submatrix C1 array element space D is emulated.
Under above-mentioned simulated conditions, if the array element number and Fig. 3 of two homogenous linear Electromagnetic Vector Sensor Arrays
Shown array of the present invention is identical, and the array element spacing of array is respectively D and mD, the first submatrix C1 array element space D
For a class value, to the array of the present invention shown in Fig. 3 and the target two-dimensional space of two homogenous linear Electromagnetic Vector Sensor Arrays
Estimation angle root-mean-square error and D relation are emulated, simulation result such as Fig. 8, wherein, Fig. 8 (a) is this hair shown in Fig. 3
The root-mean-square error of azimuth estimate and D Relationship Comparison of bright array and two homogenous linear Electromagnetic Vector Sensor Arrays
Figure, Fig. 8 (b) is the angle of pitch estimate of the array of the present invention and two homogenous linear Electromagnetic Vector Sensor Arrays shown in Fig. 3
Root-mean-square error and D relations comparison chart.
From Fig. 8 (a) and Fig. 8 (b) as can be seen that within the specific limits, with the first submatrix C1 array element space D
Increase, the angle measurement accuracy of the array of the present invention shown in Fig. 3 is held essentially constant, because the precision of angle measurement depends mainly on the
Two level submatrix C2 array element spacing mD, and the second submatrix C2 array element spacing mD exceeds array element spacing door
Limit, the angle measurement accuracy using mD as the homogenous linear Electromagnetic Vector Sensor Array of array element spacing can not be with the first submatrix
The increase of C1 array element space D and increase, so the increase of the array element space D with the first submatrix C1, shown in Fig. 3
The angle measurement accuracy of array of the present invention be held essentially constant.And as D increase, submatrix C1 array element space D also exceed
Array element spacing thresholding, the angle measurement accuracy of the array of the present invention shown in Fig. 3 deteriorate rapidly, be maintained at quickly one it is relatively low
Scope.
In addition, than two homogenous linear electromagnetic vector sensors of the array pitch thresholding of the array of the present invention shown in Fig. 3
Array is higher, under identical array element space D, the homogenous linear electromagnetic vector sensor array using mD as array element spacing
The array element spacing mD of row is more than array element spacing thresholding, and angle measurement accuracy is maintained at a relatively low scope, and for D
For the homogenous linear Electromagnetic Vector Sensor Array of array element spacing, if D is not more than array element spacing thresholding, but due to this
The aperture of array is relatively small, and its angle measurement accuracy is also relative low, if D is more than array element spacing thresholding, its angle measurement accuracy
It is rapid to deteriorate, it is maintained at a relatively low scope.So when D is not higher than array element spacing thresholding, in of identical first
Under battle array C1 array element space D, than two homogenous linear electromagnetic vectors of angle measurement accuracy of the array of the present invention shown in Fig. 3 pass
Sensor array is higher.
To sum up, the advantage of present invention comprehensive utilization electromagnetic vector sensor and nested type array, electromagnetic vector biography is reduced
Complexity in the mutual coupling and hardware of each component of sensor, expands the aperture of whole array, and two-dimensional angular can be provided to extraterrestrial target
Estimated information is spent, improves the angle measurement performance of array.
Claims (8)
1. a kind of Wave arrival direction estimating method based on nested type Electromagnetic Vector Sensor Array, including：
1) nested type Electromagnetic Vector Sensor Array is constructed：
Given array element number N, by preceding n1Individual array element is set using D as array element spacing along certain direction, obtains even linear array
First submatrix C1s, rear n of the ULA as nested type Electromagnetic Vector Sensor Array2Individual array element is array element spacing along phase using mD
Equidirectional setting, second submatrix C2s of the even linear array ULA as nested type Electromagnetic Vector Sensor Array is obtained, wherein, m=n1
+ 1, and have n1+n2=N, each array element place a Split type electric magnetic vector sensor, obtain nested type electromagnetic vector
Sensor array A, D are more than λ/2, and λ is electromagnetic wavelength；
2) it is X by C2 points of the first submatrix C1 and the second submatrix by the reception data X (t) of nested type Electromagnetic Vector Sensor Array1
And X (t)2(t) two parts；
3) data X is received to two parts1And X (t)2(t) estimating two groups with invariable rotary subspace ESPRIT algorithms respectively has mould
The target y-axis direction cosines estimate of pasteWithAnd two groups of estimate difference
Corresponding signal subspace Es1And Es2, wherein K is target number；
4) two groups of target y-axis direction cosines estimates to being estimated in step 3)WithMatched, and according to pairing order pair signal subspace Es corresponding with estimate1And Es2Progress
Match somebody with somebody, obtain the estimate of the array manifold matrix of nested type Electromagnetic Vector Sensor Array；
5) to remaining array element in the estimate of the array manifold matrix obtained in step 4) in addition to referential array unit
Steering vector carries out phase compensation, and the steering vector of remaining array element after compensation in addition to referential array unit is synthesized to
On the steering vector of Split type electric magnetic vector sensor at referential array unit, at the referential array unit after being synthesized
The steering vector of Split type electric magnetic vector sensor；
6) steering vector of the Split type electric magnetic vector sensor in step 5) after obtained synthesis at referential array unit is utilized,
It is relatively low but without fuzzy target y-axis direction cosines estimate that one group of precision is obtained by vector cross-products algorithm
With one group of x-axis direction cosines estimateAnd two groups have fuzzy target x-axis direction cosines estimateWith
7) two groups of the pairing completion obtained to step 4) have fuzzy target y-axis direction cosines estimateAnd step
6) two groups obtained have fuzzy target x-axis direction cosines estimateAmbiguity solution is carried out, obtains one group without fuzzy
Target x-axis direction cosines high accuracy estimateWith one group without fuzzy target y-axis direction cosines high accuracy estimate
8) to without fuzzy target x-axis direction cosines high accuracy estimateThe fuzzy target y-axis direction cosines high accuracy with nothing
EstimateTriangulo operation is done, obtains the two-dimensional space direction of arrival information of targetWhereinIt is the side of l-th of target
Parallactic angle estimate,It is the angle of pitch estimate of l-th of target.
2. according to the method described in claim 1, data X is received to two parts wherein in step 3)1And X (t)2(t) use respectively
Invariable rotary subspace ESPRIT algorithms, which estimate two groups, fuzzy target y-axis direction cosines estimate
WithCarry out as follows：
Data X 3a) is received according to the first submatrix C11(t) and the second submatrix C2 reception data X2(t) this two groups, are calculated respectively to connect
Receive the covariance matrix of dataWith
<mrow>
<msub>
<mover>
<mi>R</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>L</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>X</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msubsup>
<mi>X</mi>
<mn>1</mn>
<mi>H</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
<mrow>
<msub>
<mover>
<mi>R</mi>
<mo>^</mo>
</mover>
<mn>2</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>L</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>L</mi>
</munderover>
<msub>
<mi>X</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msubsup>
<mi>X</mi>
<mn>2</mn>
<mi>H</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
Wherein, X1(t)=[X1(t1),X1(t2),...X1(ti)...,X1(tL)],
X2(t)=[X2(t1),X2(t2),...X2(ti)...,X2(tL)], i=1,2 ... L, L are fast umber of beats,；
3b) respectively to 3a) in obtained covariance matrixWithEigenvalues Decomposition is done, and takes K maximum in characteristic value respectively
Characteristic vector corresponding to individual characteristic value forms the first submatrix C1 signal subspace matrix Es1With the second submatrix C2 signal subspace
Space matrix Es2；
3c) according to 3b) in obtained the first submatrix C1 signal subspace Es1, isolate preceding n1Believe corresponding to -1 array element
Work song space matrix Es1,1With rear n1Signal subspace matrix Es corresponding to -1 array element1,2, according to invariable rotary subspace
ESPRIT algorithms draw Es1,1With Es1,2Following relational expression：
<mrow>
<msub>
<mi>Es</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>Es</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>&Psi;</mi>
<mi>v</mi>
<mn>1</mn>
</msubsup>
</mrow>
<mrow>
<msubsup>
<mi>&Psi;</mi>
<mi>v</mi>
<mn>1</mn>
</msubsup>
<mo>=</mo>
<msup>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<msubsup>
<mi>&Phi;</mi>
<mi>v</mi>
<mn>1</mn>
</msubsup>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
</mrow>
Wherein,It is the first intermediate variable,For the first submatrix C1 invariable rotary factor matrix,vlFor the y-axis direction cosines actual value of l-th of target, l
=1,2 ..., K, j be imaginary unit, diag [] represents that using the element in vector be diagonal entry construction square formation, T1Be with
First submatrix C1 invariable rotary factor matrixCorresponding unique nonsingular matrix；
Total least square method 3d) is utilized, solves 3c) inRelational expression obtainsIt is rightCarry out characteristic value
Decompose, its characteristic value is exactlyDiagonal entry, and according to the condition of D ＞ λ/2, obtain one group of degree of precision and week be present
The fuzzy target y-axis direction cosines estimate of phase property：
<mrow>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mn>1</mn>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mo>&angle;</mo>
<mrow>
<mo>(</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msubsup>
<mi>&Phi;</mi>
<mi>v</mi>
<mn>1</mn>
</msubsup>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mi>l</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
<mi>D</mi>
<mo>/</mo>
<mi>&lambda;</mi>
</mrow>
</mfrac>
<mo>,</mo>
<mi>l</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>K</mi>
</mrow>
3e) according to 3b) in obtained the second submatrix C2 signal subspace Es2, isolate preceding n2Believe corresponding to -1 array element
Work song space matrix Es2,1With rear n2Signal subspace matrix Es corresponding to -1 array element2,2, according to invariable rotary subspace
ESPRIT algorithms draw Es2,1With Es2,2Following relational expression：
<mrow>
<msub>
<mi>E</mi>
<mrow>
<mi>s</mi>
<mn>2</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>E</mi>
<mrow>
<mi>s</mi>
<mn>2</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<msubsup>
<mi>&Psi;</mi>
<mi>v</mi>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msubsup>
<mi>&Psi;</mi>
<mi>v</mi>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msup>
<msub>
<mi>T</mi>
<mi>2</mi>
</msub>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<msubsup>
<mi>&Phi;</mi>
<mi>v</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>T</mi>
<mn>2</mn>
</msub>
</mrow>
Wherein,It is the second intermediate variable,For the second submatrix C2 invariable rotary factor matrix,T2It is the invariable rotary factor with the second submatrix C2
MatrixCorresponding unique nonsingular matrix；
Total least square method 3f) is utilized, solves 3e) inRelational expression obtainsIt is rightCarry out characteristic value
Decompose, its characteristic value is exactlyDiagonal entry, and according to the condition of mD ＞ D ＞ λ/2, obtain one group of higher precision and deposit
In the target y-axis direction cosines estimate that periodicity is fuzzy：
<mrow>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mo>&angle;</mo>
<mrow>
<mo>(</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msubsup>
<mi>&Phi;</mi>
<mi>v</mi>
<mn>2</mn>
</msubsup>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mi>l</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
<mi>m</mi>
<mi>D</mi>
<mo>/</mo>
<mi>&lambda;</mi>
</mrow>
</mfrac>
<mo>,</mo>
<mi>l</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>K</mi>
<mo>.</mo>
</mrow>
3. according to the method for claim 1, to two groups of target y-axis direction cosines estimates wherein in step 4)WithMatched, carried out according to the following rules：
4a) according to the first submatrix C1 invariable rotary factor matrix
Diagonal entryIn l-th of target at the first submatrix C1 because of the space D between array element and caused by phase
Potential differenceThe estimate of the y-axis direction cosines of l-th of the target estimated isWhereinIn each target sequence number put in order withDiagonal entry in each target sequence number the phase that puts in order
Together；
4b) according to the second submatrix C2 invariable rotary factor matrix
Diagonal entryIn l-th of target in the second submatrix C2 because of the spacing mD between array element and caused by
Phase differenceThe estimate of the y-axis direction cosines of l-th of the target estimated isWhereinIn each target sequence number put in order withDiagonal entry in each target sequence number the phase that puts in order
Together；
It is 4c) right according to the following rulesDiagonal entry andDiagonal entry match：
4c1) set a target at the first submatrix C1 because of array element space D and caused by true phase difference as Λ1=2g1π+
φ1, wherein φ1For Λ1The phase difference that can actually measure, g1For Λ1With φ1Between the cycle fuzzy number that differs；
4c2) set the target at the second submatrix C2 because of array element spacing mD and caused by true phase difference as Λ2=2g2π+
φ2, φ2For Λ2The phase difference that can actually measure, g2For Λ2With φ2Between the cycle fuzzy number that differs；
4c3) according to the second submatrix C2 array element spacing mD and m times of relation of the first submatrix C1 array element space D, obtain
To m Λ1=Λ2Relational expression, thus relational expression obtain equation below：
m×(2g1π+φ1)=2g2π+φ2
The equation is deformed, the relational expression after being deformed as follows：
mφ1=2 π (g2-mg1)+φ2
According to the relational expression and the property of exponential function after deformation, following relational expression is obtained：
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&phi;</mi>
<mn>1</mn>
</msub>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mi>m</mi>
</msup>
<mo>=</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>&pi;</mi>
<mo>(</mo>
<msub>
<mi>g</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>mg</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&phi;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
</msup>
<mo>=</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&phi;</mi>
<mn>2</mn>
</msub>
</mrow>
</msup>
<mo>;</mo>
</mrow>
4c4) according to relational expressionWillDiagonal entryM powers are all done, according to
It is secondary withDiagonal entryContrasted one by one, selection difference minimum match, and obtainsDiagonal
Element andDiagonal entry pairing order；
4d) according to 4c) obtainDiagonal entry andDiagonal entry pairing order, to two groups of target y-axis sides
To cosine estimateWithMatched.
4. according to the method described in claim 1, according to pairing order pair signal corresponding with estimate wherein in step 4)
Subspace Es1And Es2Matched, carried out according to the following rules：
According to signal subspace matrix Es1Column vector the invariable rotary factor matrix to put in order with the first submatrix C1's
The one-to-one relation to put in order and signal subspace matrix Es of target sequence number in diagonal entry2Column vector row
Row order and the second submatrix C2 invariable rotary factor matrixDiagonal entry in target sequence number put in order one by one
Corresponding relation, will signal subspace matrix Es corresponding with estimate1And Es2Column vector put in order according to two groups of mesh
Mark y-axis direction cosines estimateWithPairing order resequence, realize and estimate
Signal subspace Es corresponding to evaluation1And Es2Matching.
5. according to the method for claim 1, to removing referential array in the estimate of array manifold matrix wherein in step 5)
The steering vector of remaining array element outside unit carries out phase compensation, obtains all electromagnetic vectors in addition to referential array unit
The steering vector of sensor is synthesized to the result on the steering vector at referential array unit, carries out as follows：
<mrow>
<msubsup>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
<mn>1</mn>
</msubsup>
<mo>=</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>n</mi>
<mn>1</mn>
</msub>
</munderover>
<msub>
<mover>
<mi>B</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
<mo>{</mo>
<mo>&lsqb;</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>1</mn>
<mo>&rsqb;</mo>
<mo>:</mo>
<mo>&lsqb;</mo>
<mn>6</mn>
<mi>n</mi>
<mo>&rsqb;</mo>
<mo>}</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&Phi;</mi>
<mi>v</mi>
<mn>1</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>*</mo>
</msup>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<msub>
<mi>e</mi>
<mi>l</mi>
</msub>
</mrow>
<mrow>
<msubsup>
<mover>
<mi>b</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>n</mi>
<mn>2</mn>
</msub>
</munderover>
<msub>
<mover>
<mi>B</mi>
<mo>^</mo>
</mover>
<mn>2</mn>
</msub>
<mo>{</mo>
<mo>&lsqb;</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>1</mn>
<mo>&rsqb;</mo>
<mo>:</mo>
<mo>&lsqb;</mo>
<mn>6</mn>
<mi>n</mi>
<mo>&rsqb;</mo>
<mo>}</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&Phi;</mi>
<mi>v</mi>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>*</mo>
</msup>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&Phi;</mi>
<mi>v</mi>
<mn>1</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>*</mo>
</msup>
<mo>&rsqb;</mo>
</mrow>
<msub>
<mi>n</mi>
<mn>1</mn>
</msub>
</msup>
<msub>
<mi>e</mi>
<mi>l</mi>
</msub>
</mrow>
Wherein, c1And c2It is different complex constants, To pass throughMeter
The estimate of the first submatrix C1 calculated array manifold matrix,To pass throughThe the second submatrix C2's calculated
The estimate of array manifold matrix.
6. according to the method for claim 1, wherein the step 6), is carried out as follows：
6a) to the steering vector of the Split type electric magnetic vector sensor at the referential array after synthesisWithElectric field point is done respectively
The normalized vector cross product of amount and magnetic-field component, has：
<mrow>
<msubsup>
<mi>p</mi>
<mi>l</mi>
<mn>1</mn>
</msubsup>
<mo>=</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>h</mi>
</msub>
<msub>
<mi>u</mi>
<mi>l</mi>
</msub>
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<msub>
<mi>y</mi>
<mi>h</mi>
</msub>
<msub>
<mi>v</mi>
<mi>l</mi>
</msub>
<mo>+</mo>
<msub>
<mi>z</mi>
<mi>h</mi>
</msub>
<msub>
<mi>w</mi>
<mi>l</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>u</mi>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mrow>
<mo>(</mo>
<mn>2</mn>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>u</mi>
<mi>l</mi>
</msub>
</mrow>
</msup>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>ve</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
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<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>u</mi>
<mi>l</mi>
</msub>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>we</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mfrac>
<mrow>
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<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<msub>
<mi>u</mi>
<mi>l</mi>
</msub>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
<mrow>
<msubsup>
<mi>p</mi>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>h</mi>
</msub>
<msub>
<mi>u</mi>
<mi>l</mi>
</msub>
<mo>+</mo>
<msub>
<mi>y</mi>
<mi>h</mi>
</msub>
<msub>
<mi>v</mi>
<mi>l</mi>
</msub>
<mo>+</mo>
<msub>
<mi>z</mi>
<mi>h</mi>
</msub>
<msub>
<mi>w</mi>
<mi>l</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>u</mi>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mrow>
<mo>(</mo>
<mn>2</mn>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>u</mi>
<mi>l</mi>
</msub>
</mrow>
</msup>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>ve</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>u</mi>
<mi>l</mi>
</msub>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>we</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<msub>
<mi>u</mi>
<mi>l</mi>
</msub>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
OrderFinal vector cross-products knot as the Split type electric magnetic vector sensor at referential array unit
Fruit；
6b) pass through plComposition to obtain precision relatively low but without fuzzy u, v, w rough estimate evaluations：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<mo>|</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>p</mi>
<mi>l</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mn>1</mn>
</msub>
<mo>|</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<mo>|</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>p</mi>
<mi>l</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msub>
<mo>|</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>w</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<mo>|</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>p</mi>
<mi>l</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mn>3</mn>
</msub>
<mo>|</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein | | expression takes absolute value；
6c) makeObtain
<mrow>
<msubsup>
<mi>p</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>u</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>v</mi>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mi>u</mi>
</mrow>
</msup>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>we</mi>
<mrow>
<mi>j</mi>
<mfrac>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mi>&lambda;</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>u</mi>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
According toComposition, obtain direction cosines u of the target along x-axis two groups of degree of precision but periodically fuzzy estimation be present
ValueWith
<mrow>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mn>1</mn>
</msubsup>
<mo>=</mo>
<mfrac>
<mi>&lambda;</mi>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</mfrac>
<mfrac>
<mn>1</mn>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
</mfrac>
<mo>&angle;</mo>
<mo>{</mo>
<mfrac>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msubsup>
<mi>p</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
<mo>&rsqb;</mo>
</mrow>
<mn>2</mn>
</msub>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
</mfrac>
<mo>}</mo>
</mrow>
<mrow>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<mfrac>
<mi>&lambda;</mi>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</mfrac>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>&angle;</mo>
<mo>{</mo>
<mfrac>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msubsup>
<mi>p</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
<mo>&rsqb;</mo>
</mrow>
<mn>3</mn>
</msub>
<msubsup>
<mi>w</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
</mfrac>
<mo>}</mo>
<mo>.</mo>
</mrow>
7. according to the method for claim 1, wherein the step 7), is carried out as follows：
It is 7a) that precision is relatively low but without fuzzy y-axis direction cosines estimateIt is higher but deposit as solution precision
In the y-axis direction cosines estimate that periodicity is fuzzyReference value, v first precision be higher and without mould
The estimate of pasteObtained by following ambiguity solution equation：
<mrow>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>x</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mn>1</mn>
</msubsup>
<mo>+</mo>
<msub>
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<mi>m</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
<mi>&lambda;</mi>
<mo>/</mo>
<mi>D</mi>
<mo>,</mo>
<msub>
<mover>
<mi>m</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
<mo>=</mo>
<mi>arg</mi>
<munder>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
</munder>
<mo>|</mo>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mn>1</mn>
</msubsup>
<mo>-</mo>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
<mi>&lambda;</mi>
<mo>/</mo>
<mi>D</mi>
<mo>|</mo>
</mrow>
Wherein, Expression rounds up,Expression rounds downwards；
7b) willY-axis direction cosines estimate that is higher as solution precision but being obscured in the presence of periodicityReference value, v it is final high accuracy and without fuzzy estimateBy following solution mould
Paste equation obtains：
<mrow>
<msub>
<mover>
<mi>v</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
</msub>
<mo>=</mo>
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<mi>v</mi>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msub>
<mover>
<mi>m</mi>
<mo>^</mo>
</mover>
<mn>2</mn>
</msub>
<mi>&lambda;</mi>
<mo>/</mo>
<mi>m</mi>
<mi>D</mi>
<mo>,</mo>
<msub>
<mover>
<mi>m</mi>
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</mover>
<mn>2</mn>
</msub>
<mo>=</mo>
<mi>arg</mi>
<munder>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
</munder>
<mo>|</mo>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>x</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>v</mi>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
<mi>&lambda;</mi>
<mo>/</mo>
<mi>m</mi>
<mi>D</mi>
<mo>|</mo>
</mrow>
Wherein,
It is 7c) that precision is relatively low but without fuzzy x-axis direction cosines estimateIt is higher but deposit as solution precision
In the x-axis direction cosines estimate that periodicity is fuzzyReference value, u first precision be higher and without mould
The estimate of pasteObtained by following ambiguity solution equation：
<mrow>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>x</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mn>1</mn>
</msubsup>
<mo>+</mo>
<msub>
<mover>
<mi>m</mi>
<mo>^</mo>
</mover>
<mn>3</mn>
</msub>
<mi>&lambda;</mi>
<mo>/</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mover>
<mi>m</mi>
<mo>^</mo>
</mover>
<mn>3</mn>
</msub>
<mo>=</mo>
<mi>arg</mi>
<munder>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
<msub>
<mi>m</mi>
<mn>3</mn>
</msub>
</munder>
<mo>|</mo>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mn>0</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mn>1</mn>
</msubsup>
<mo>-</mo>
<msub>
<mi>m</mi>
<mn>3</mn>
</msub>
<mi>&lambda;</mi>
<mo>/</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>|</mo>
</mrow>
Wherein,
7d) willX-axis direction cosines estimate that is higher as solution precision but being obscured in the presence of periodicityReference value, u it is final high accuracy and without fuzzy estimateBy following solution mould
Paste equation obtains：
<mrow>
<msub>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msub>
<mover>
<mi>m</mi>
<mo>^</mo>
</mover>
<mn>4</mn>
</msub>
<mi>&lambda;</mi>
<mo>/</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<msub>
<mover>
<mi>m</mi>
<mo>^</mo>
</mover>
<mn>4</mn>
</msub>
<mo>=</mo>
<mi>arg</mi>
<munder>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
<msub>
<mi>m</mi>
<mn>4</mn>
</msub>
</munder>
<mo>|</mo>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>x</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msub>
<mi>m</mi>
<mn>4</mn>
</msub>
<mi>&lambda;</mi>
<mo>/</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>|</mo>
</mrow>
Wherein,
8. according to the method for claim 1, to estimating in high precision without fuzzy target x-axis direction cosines wherein in step 8)
ValueThe fuzzy target y-axis direction cosines high accuracy estimate with nothingTriangulo operation is done, is carried out by following formula：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mover>
<mi>&theta;</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
</msub>
<mo>=</mo>
<mi>a</mi>
<mi>r</mi>
<mi>c</mi>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mo>(</mo>
<msqrt>
<mrow>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mover>
<mi>v</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
<mn>2</mn>
</msubsup>
</mrow>
</msqrt>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>&phi;</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
</msub>
<mo>=</mo>
<mi>arctan</mi>
<mo>(</mo>
<mfrac>
<msubsup>
<mover>
<mi>v</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
<mn>2</mn>
</msubsup>
<msubsup>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mi>l</mi>
<mn>2</mn>
</msubsup>
</mfrac>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>l</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>K</mi>
</mrow>
It is exactly the estimating two-dimensional direction-of-arrival information of l-th of target, whereinIt is the side of l-th of target
Parallactic angle estimate,It is the angle of pitch estimate of l-th of target.
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| CN109254272A (en) * | 2018-09-27 | 2019-01-22 | 中国人民解放军空军工程大学 | A kind of bidimensional angle estimating method of concurrent formula polarization MIMO radar |
| CN109738853A (en) * | 2018-11-21 | 2019-05-10 | 南京航空航天大学 | A kind of angle and polarization estimate method of the relatively prime battle array of electromagnetic vector based on rotational invariance |
| CN111208471A (en) * | 2020-03-02 | 2020-05-29 | 重庆大学 | Method for estimating direction of arrival of few-snapshot non-linearly polarized electromagnetic waves |
| CN113985485A (en) * | 2021-09-29 | 2022-01-28 | 中国矿业大学 | Method for tracking coal rock dynamic disaster source positioning by passive source electromagnetic radiation |
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| CN111208471A (en) * | 2020-03-02 | 2020-05-29 | 重庆大学 | Method for estimating direction of arrival of few-snapshot non-linearly polarized electromagnetic waves |
| CN111208471B (en) * | 2020-03-02 | 2023-01-13 | 重庆大学 | Method for estimating direction of arrival of few-snapshot non-linearly-polarized electromagnetic waves |
| CN113985485A (en) * | 2021-09-29 | 2022-01-28 | 中国矿业大学 | Method for tracking coal rock dynamic disaster source positioning by passive source electromagnetic radiation |
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