CN106842114A - Target direction of arrival acquisition methods based on root MUSIC algorithms - Google Patents

Target direction of arrival acquisition methods based on root MUSIC algorithms Download PDF

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CN106842114A
CN106842114A CN201611247927.0A CN201611247927A CN106842114A CN 106842114 A CN106842114 A CN 106842114A CN 201611247927 A CN201611247927 A CN 201611247927A CN 106842114 A CN106842114 A CN 106842114A
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matrix
frequency spectrum
radar
spatial frequency
vector
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王彤
夏月明
王娟
吴建新
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae

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  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
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Abstract

The invention discloses a kind of target direction of arrival acquisition methods based on root MUSIC algorithms, thinking is：Determine that radar includes N number of array element, and determine the beam forming matrix B in the range of detections of radar, N is included in the beam forming matrix B in the range of the detections of radarsIndividual echo signal；It is then determined that the spatial frequency spectrum regional extent of the beam forming matrix in the range of detections of radar, and by the spatial frequency spectrum regional extent to be spaced ε and be evenly dividing be M spatial frequency spectrum region, the 1st window vector matrix in window vector matrix T and the 1st of spatial frequency spectrum region spatial frequency spectrum region is calculated successively to be estimated；The sample covariance matrix for calculating radar return data is estimated, it is rightFeature decomposition is carried out, and calculates the sample covariance matrix estimation of radar return data successivelyNoise subspace matrixWith the noise covariance matrix V of the beam forming matrix in the range of detections of radar, and then N in the beam forming matrix B in the range of detections of radar is obtainedsThe individual respective direction of arrival of echo signal.

Description

Target direction of arrival acquisition methods based on root-MUSIC algorithms
Technical field
The invention belongs to Radar Technology field, more particularly to a kind of target direction of arrival based on root-MUSIC algorithms is obtained Method is taken, i.e., the target direction of arrival acquisition methods of multiple signal classification (root-MUSIC) algorithm based on rooting, it is adaptable to Determine the target direction of arrival of any wave beam.
Background technology
The direction of arrival DOA of target estimates have great importance in Array Signal Processing, in past nearly 40 years, There has been proposed the direction of arrival DOA algorithm for estimating of a series of target；Wherein, MUSIC algorithms are due to the high-resolution of its own Ability is widely used.However, traditional MUSIC algorithms realize needing being carried out in whole angular range it is one-dimensional or many Dimension search, amount of calculation is very big.In order to reduce amount of calculation, there has been proposed root-MUSIC algorithms, but its amount of calculation is battle array The cube of first number, and the increase of array number can bring bigger amount of calculation；At the same time, it is contemplated that traditional beam space The advantage for the treatment of, such as amount of calculation are low, and the SNR that resolution target needs is low, there has been proposed beam space MUSIC algorithms, study table Bright, in the outer null characteristic of the common band of Wave beam forming, such as beam forming matrix is discrete fourier to beam space MUSIC algorithms The situation of DFT matrixes is converted, the amount of calculation of the realization of beam space root-MUSIC algorithms is only the cube of numbers of beams, jointly The outer null characteristic of band it is typically unpractical.
The content of the invention
It is computationally intensive for traditional beam space root-MUSIC algorithms, and conditional to beam forming matrix ask Topic, it is an object of the invention to propose a kind of target direction of arrival acquisition methods based on root-MUSIC algorithms, this kind is based on The target direction of arrival acquisition methods of root-MUSIC algorithms realize beam space using the rooting of many window low order real polynomials Root-MUSIC, lower compared to traditional algorithm amount of calculation, the result of estimation is more stable, and is applicable to any beam forming matrix The determination of middle target direction of arrival.
To achieve the above object, the present invention is adopted the following technical scheme that and is achieved.
A kind of target direction of arrival acquisition methods based on root-MUSIC algorithms, comprise the following steps：；
Step 1, determines radar, and the radar includes N number of array element, and determines the beam forming matrix in the range of detections of radar B, includes N in the beam forming matrix B in the range of the detections of radarsIndividual echo signal；
It is then determined that the spatial frequency spectrum regional extent of the beam forming matrix in the range of detections of radar, and by the space frequently Spectrum regional extent is M spatial frequency spectrum region to be spaced ε and be evenly dividing, and order is arranged, whereinM=2Nb- 1, Nb Represent the wave beam number that beam forming matrix B is included, N, Nb, M, ε be respectively integer more than 0；
Step 2, selection order arrange after the 1st spatial frequency spectrum region in M spatial frequency spectrum region, and be calculated the 1 window vector matrix T in spatial frequency spectrum region, and then it is calculated the 1st window vector matrix estimation in spatial frequency spectrum region
Step 3, determines that the echo data that radar is received is X, is then calculated the sampling association side of radar return data Difference Matrix EstimationSample covariance matrix to radar return data is estimatedFeature decomposition is carried out, and is calculated radar The sample covariance matrix of echo data is estimatedNoise subspace matrix
Step 4, using beam forming matrix B and the sample covariance matrix of radar return data in the range of detections of radar EstimateNoise subspace matrixThe noise covariance matrix of the beam forming matrix being calculated in the range of detections of radar V；
Step 5 is all of right by what is included in the noise covariance matrix V of the beam forming matrix in the range of detections of radar Angle element constructs column vector v；
Step 6, determines the M transformation matrix W in spatial frequency spectrum region, and according to column vector v and the 1st spatial frequency spectrum region Window vector matrix estimateIt is calculated intermediary matrix D；
Then, line translation is entered to middle matrix D using the transformation matrix W in M spatial frequency spectrum region, obtains M space frequently The corresponding M groups low order real polynomial coefficient in spectrum region；
Step 7, according to the corresponding M groups low order real polynomial coefficient in M spatial frequency spectrum region, correspondence obtains M equation, its In m-th equation befl-1It is the independent variable of l-1 power, f0=1, γmlIt is m group low order real polynomials L level numbers in coefficient, L conjugate root is obtained after solving m-th equation, and each conjugate root includes real part and imaginary part, then Imaginary part is selected to meet the N' of sets requirement in L conjugate rootsIndividual conjugate root, the sets requirement is that imaginary part modulus value is less than 10-6 Conjugate root, the N'sIndividual each self-corresponding real part of conjugate root, corresponds to the beam forming matrix B in the range of detections of radar respectively Interior NsThe sine value of the respective space angle of individual echo signal, and the NsThe sine value of the respective angle of individual echo signal, it is right respectively Should be N in the beam forming matrix B in the range of detections of radarsThe individual respective direction of arrival of echo signal；
Wherein, the echo signal number for being included in the beam forming matrix B in the range of detections of radar is empty with L conjugate root Portion meet sets requirement conjugate root number it is equal and correspond.
The present invention has advantages below：
First, higher order polynomial is decomposed into multigroup lower order polynomial expressions by the present invention, is dropped by the rooting of low order real polynomial Low computation complexity, improves processing capability in real time；In addition, being only applicable to DFT Wave beam forming squares compared to traditional root-MUSIC The situation of battle array, the inventive method can be applied to any wave beam.
Second, the inventive method reduces the complexity of beam space root-MUSIC algorithms using the rooting of many window real polynomials Degree, and the amount of calculation problem for traditional beam space root-MUSIC algorithms under big array case, by higher order polynomial Multigroup lower order polynomial expressions are decomposed into, computation complexity is reduced by the rooting of low order real polynomial, improve processing capability in real time.
3rd, generally need to be reduced using the taper such as adding window method in practical operation compared to traditional root-MUSIC Secondary lobe, and then suppress interference, therefore traditional root-MUSIC is only applicable to DFT beam forming matrixs；Compared to traditional root- MUSIC, the inventive method considers in low-angle region the correlation of (as in -3dB beam angles) steering vector, the small angle Any steering vector can be using the low order real polynomial of its correspondence spatial frequency come approximate in degree region so that the inventive method Can be realized using the rooting of multigroup low order real polynomial, lower compared to traditional algorithm amount of calculation, the result of estimation is more stable, and It is applicable to any beam forming matrix.
Brief description of the drawings
The present invention is described in further detail with reference to the accompanying drawings and detailed description.
Fig. 1 is a kind of target direction of arrival acquisition methods flow chart based on root-MUSIC algorithms of the invention；
Fig. 2 is steering vector approximate error figure under different rank；
Fig. 3 is that ideally many algorithms estimate angle on target RMSE comparison diagrams；
Fig. 4 is many algorithms estimation angle on target RMSE comparison diagrams in the case of taper.
Specific embodiment
Reference picture 1, is a kind of target direction of arrival acquisition methods flow chart based on root-MUSIC algorithms of the invention； The target direction of arrival acquisition methods based on root-MUSIC algorithms, comprise the following steps：
Step 1, determines radar, and the radar includes N number of array element, and determines the beam forming matrix in the range of detections of radar B, includes N in the beam forming matrix B in the range of the detections of radarsIndividual echo signal, subscript behalf signal signal, and Beam forming matrix B in the range of the detections of radar includes N'bIndividual column vector, each of which column vector is provided to thunder The weighted vector set up to the space angle of middle correspondence beam position,Represent N × NbThe complex field of rank Matrix, ∈ represents and belongs to, NbThe wave beam number that beam forming matrix B is included is represented, subscript b represents wave beam beam；N≥Nb≥Ns。
It is then determined that the spatial frequency spectrum regional extent of the beam forming matrix in the range of detections of radar is
[-Nb/N Nb/ N], and by the spatial frequency spectrum regional extent [- Nb/N Nb/ N] it is evenly dividing as M is empty with being spaced ε Between spectral regions, and order arrange, whereinM=2Nb- 1, N, Nb、Ns, M, ε be respectively integer more than 0.
Step 2, the 1st spatial frequency spectrum region after selection order arrangement in M spatial frequency spectrum region, and utilize a most young waiter in a wineshop or an inn Multiply method and be calculated the 1st window vector matrix T in spatial frequency spectrum region,
T=[t1,t2,…tL+1], T ∈ C(2N-1)×(L+1), C(2N-1)×(L+1)Represent the complex field square of (2N-1) × (L+1) ranks Battle array, L represents the multinomial top step number of setting, L >=3；And then be calculated the window vector matrix in the 1st spatial frequency spectrum region and estimate Meter
Step 2 to implement sub-step as follows：
The 1st spatial frequency spectrum region after 2.1 selections order arrangement in M spatial frequency spectrum region, the 1st space is frequently Spectrum region includes several frequencies, chooses wherein Q frequency, and the frequency of q-th frequency is designated as into f respectivelyq, by q-th frequency The corresponding extension steering vector of frequency of point is designated as On Mark T represents transposition, and N represents the element number of array that radar is included, and e represents exponential function.
The 2.2 corresponding extension steering vectors of frequency for being calculated q-th frequency using least square methodLow order Real polynomial is approximate, i.e., T∈C(2N-1)×(L+1), C(2N-1)×(L+1)Represent (2N-1) × (L+ 1) complex-field matrix of rank, T is the 1st window vector matrix in spatial frequency spectrum region, is ∑ ζ (fq) take corresponding arrow during minimum value Moment matrix；∑ζ(fq) be q-th frequency the corresponding extension steering vector of frequencyLow order real polynomial approximate mistake Difference,fqIt is the corresponding extension steering vector of the frequency of q-th frequencyL rank multinomials arrow Amount,L represents the multinomial top step number of setting, L >=3, fqIt is q-th frequency of frequency, q ∈ { 1,2 ..., Q }, Q is the frequency points of selection in the 1st spatial frequency spectrum region.
2.3 are calculated the 1st window vector matrix in spatial frequency spectrum region estimates F=[f1,…,fq,…,fQ], q ∈ { 1,2 ..., Q }, Q are the 1st spatial frequency spectrum The frequency points chosen in region, subscript T represents transposition, and subscript -1 represents inversion operation.
The window vector matrix in the 1st spatial frequency spectrum region is estimatedComprising L+1 column vector,
T is designated as respectively1,t2,…,th,…,tL+1, h ∈ { 1,2 ..., L+1 }, thRepresent the 1st window in spatial frequency spectrum region Vector matrix is estimatedIn h-th column vector, L represents the multinomial top step number of setting.
Step 3, determines that the echo data that radar is received is X, k-th sampling in the echo data that radar is received Data are designated as X (k), k-th sampled data X (k) in the echo data that the radar is received be N × 1 tie up column vector, k ∈ 1, 2,3 ..., K }, the sampling number that K is included for echo data X that radar is received；Then it is calculated adopting for radar return data Sample covariance matrix Subscript H represents conjugate transposition operation.
Sample covariance matrix to radar return data is estimatedCarry out feature decomposition, respectively obtain N " individual characteristic value and Each self-corresponding characteristic vector of the individual characteristic values of N "；By N " individual characteristic value by order arrangement from big to small, and respectively by preceding NsIt is individual Big characteristic value is estimated as the sample covariance matrix of radar return dataDiagonal matrixBy preceding NsIndividual big feature It is worth each self-corresponding characteristic vector to estimate as the sample covariance matrix of radar return dataSignal subspace matrix By N "-NsIndividual characteristic value is estimated as the sample covariance matrix of radar return dataNoise subspace diagonal matrix By N "-NsIndividual each self-corresponding characteristic vector of characteristic value is estimated as the sample covariance matrix of radar return dataNoise Subspace matricesI.e. the sample covariance matrix of radar return data is estimatedMeet after carrying out feature decomposition：→ represent and the sample covariance matrix of radar return data is estimatedCarry out Eigenvalues Decomposition； The individual characteristic value of the echo signal total number and N included in the M spatial frequency spectrum interval " is by choosing after order arrangement from big to small The big characteristic value number for taking is equal.
Step 4, using beam forming matrix B and the sample covariance matrix of radar return data in the range of detections of radar EstimateNoise subspace matrixThe noise covariance matrix of the beam forming matrix being calculated in the range of detections of radar V, For the sample covariance matrix of radar return data is estimatedNoise subspace matrix, subscript H Represent conjugate transposition operation.
Step 5 is all of right by what is included in the noise covariance matrix V of the beam forming matrix in the range of detections of radar Angle element construction column vector v, ell rice spy's Hermitian column vectors symmetrical centered on the column vector v, and by column vector v In k-th element be designated as vk,{ 1 ..., N'}, N' are the element number that column vector v is included to k ∈；Column vector The element number that v is included is equal with the element number of array that radar is included.
Step 6, determines M transformation matrix W, the W=[w in spatial frequency spectrum region1,w2,...,wm,...wM], wmIt is m-th The transformation vector in spatial frequency spectrum region,
wm=[e-j2π(N-1)(m-1)ε,e-j2π(N-2)(m-1)ε,…1,…ej2π(N-2)(m-1)ε,ej2π(N-1)(m-1)ε]T。
According to the M transformation matrix W in spatial frequency spectrum region, the window vector matrix in column vector v and the 1st spatial frequency spectrum region EstimateIntermediary matrix D is calculated,
L ∈ { 1,2 ..., L+1 }, tl Represent that the 1st window vector matrix in spatial frequency spectrum region is estimatedIn l-th column vector, L represents the multinomial most high-order of setting Number；1L+1Represent by the L+1 1 row vector for constituting,Crow internal medicine product is represented, ⊙ represents Hadamard's product.
Then, line translation is entered to middle matrix D using the transformation matrix W in M spatial frequency spectrum region, obtains M space frequently The corresponding M groups low order real polynomial coefficient in spectrum region, wherein m group low order real polynomials coefficient is γm,
γm=[γm1,γm2,…,γml,…γm(L+1)], γmlIt is the l levels in m group low order real polynomial coefficients Number,M ∈ { 1,2,3 ..., M },
L ∈ { 1,2,3 ..., L+1 }, L represent the multinomial top step number of setting, L >=3；Subscript T represents transposition.
Step 7, according to the corresponding M groups low order real polynomial coefficient in M spatial frequency spectrum region, correspondence obtains M equation, its In m-th equation befl-1It is the independent variable of l-1 power, f0=1, γmlIt is m group low order real polynomials L level numbers in coefficient, L conjugate root is obtained after solving m-th equation, and each conjugate root includes real part and imaginary part, then Imaginary part is selected to meet the N' of sets requirement in L conjugate rootsIndividual conjugate root, the sets requirement is imaginary part close to 0, i.e., empty Portion's modulus value is less than 10-6Or smaller conjugate root, the N'sIndividual each self-corresponding real part of conjugate root, corresponds to detections of radar model respectively N in beam forming matrix B in enclosingsThe sine value of the respective angle of individual echo signal, and the NsThe respective space of individual echo signal The sine value of angle, corresponds to N in the beam forming matrix B in the range of detections of radar respectivelysThe individual respective ripple of echo signal reaches Direction.
Wherein, the echo signal number for being included in the beam forming matrix B in the range of detections of radar is empty with L conjugate root Portion meet sets requirement conjugate root number it is equal and correspond.
Effect of the invention can be further illustrated by following emulation experiment.
(1) emulation experiment data explanation
Using the even linear array of radar array number N=32 in emulation, ideally, Wave beam forming utilizes Nb=3 DFT Matrix, there is two information sources in Beam Domain frequency band, and angle is respectively -2 degree and 1 degree, single information source SNR=15dB, order of a polynomial Number L=5；Using Taylor's window of -30dB in the case of taper, other specification is constant
(2) simulation result and analysis
Shown in Fig. 2, Fig. 3 and Fig. 4, Fig. 2 is steering vector approximate error figure under different rank to simulation result of the invention； Fig. 3 is that ideally many algorithms estimate angle on target RMSE comparison diagrams；Fig. 4 is many algorithms estimation target in the case of taper Angle RMSE comparison diagrams.
Fig. 2 shows that error is reduced with the increase of exponent number, and when exponent number is more than 4, error is in tolerance interval；Fig. 3 Show RMSE reduces as SNR increases, and the inventive method is lower compared to other two kinds of algorithm amounts of calculation, but in all SNR The performance almost same with other two kinds of algorithms can be obtained.As seen from Figure 4, due to traditional Beam Domain root-MUSIC It is not attainable in the case of taper, is not contrasted herein, Fig. 4 shows that the inventive method compares Beam Domain frequency spectrum MUSIC Algorithm amount of calculation is lower, but can obtain almost same performance in all SNR.
In sum, emulation experiment demonstrates correctness of the invention, validity and reliability.
Obviously, those skilled in the art can carry out various changes and modification without deviating from essence of the invention to the present invention God and scope；So, if these modifications of the invention and modification belong to the scope of the claims in the present invention and its equivalent technologies Within, then the present invention is also intended to comprising these changes and modification.

Claims (7)

1. a kind of target direction of arrival acquisition methods based on root-MUSIC algorithms, it is characterised in that comprise the following steps：
Step 1, determines radar, and the radar includes N number of array element, and determines the beam forming matrix B in the range of detections of radar, institute State in the beam forming matrix B in the range of detections of radar comprising NsIndividual echo signal；
It is then determined that the spatial frequency spectrum regional extent of the beam forming matrix in the range of detections of radar, and by the spatial frequency spectrum area Domain scope is M spatial frequency spectrum region to be spaced ε and be evenly dividing, and order is arranged, whereinM=2Nb- 1, NbRepresent The wave beam number that beam forming matrix B is included, N, Nb, M, ε be respectively integer more than 0；
Step 2, the 1st spatial frequency spectrum region after selection order arrangement in M spatial frequency spectrum region, and it is calculated the 1st The window vector matrix T in spatial frequency spectrum region, and then it is calculated the 1st window vector matrix estimation in spatial frequency spectrum region
Step 3, determines that the echo data that radar is received is X, is then calculated the sampling covariance square of radar return data Battle array is estimatedSample covariance matrix to radar return data is estimatedFeature decomposition is carried out, and is calculated radar return number According to sample covariance matrix estimateNoise subspace matrix
Step 4, the sample covariance matrix using the beam forming matrix B in the range of detections of radar and radar return data is estimatedNoise subspace matrixThe noise covariance matrix V of the beam forming matrix being calculated in the range of detections of radar；
Step 5, all of diagonal element that will be included in the noise covariance matrix V of the beam forming matrix in the range of detections of radar Element construction column vector v；
Step 6, determines the M transformation matrix W in spatial frequency spectrum region, and according to column vector v and the 1st window in spatial frequency spectrum region Vector matrix is estimatedIt is calculated intermediary matrix D；
Then, line translation is entered to middle matrix D using the transformation matrix W in M spatial frequency spectrum region, obtains M spatial frequency spectrum area The corresponding M groups low order real polynomial coefficient in domain；
Step 7, according to the corresponding M groups low order real polynomial coefficient in M spatial frequency spectrum region, correspondence obtains M equation, wherein the M equation befl-1It is the independent variable of l-1 power, f0=1, γmlIt is m group low order real polynomial coefficients In l level numbers, obtain L conjugate root after solving m-th equation, each conjugate root includes real part and imaginary part, then individual in L Imaginary part is selected to meet the N' of sets requirement in conjugate rootsIndividual conjugate root, the sets requirement is that imaginary part modulus value is less than 10-6Conjugation Root, the N'sIndividual each self-corresponding real part of conjugate root, corresponds to N in the beam forming matrix B in the range of detections of radar respectivelysIndividual mesh The sine value of the mark respective angle of signal, and the NsThe sine value of the respective space angle of individual echo signal, corresponds to thunder respectively N in up to the beam forming matrix B in detection rangesThe individual respective direction of arrival of echo signal；
Wherein, the echo signal number for being included in the beam forming matrix B in the range of detections of radar expires with imaginary part in L conjugate root The conjugate root number of sufficient sets requirement is equal and corresponds.
2. a kind of target direction of arrival acquisition methods based on root-MUSIC algorithms as claimed in claim 1, its feature exists In, in step 1, the beam forming matrix B in the range of the detections of radar,Represent N × NbRank is answered Field matrix, ∈ represents and belongs to, NbRepresent the wave beam number that beam forming matrix B is included；N≥Nb≥Ns；
The spatial frequency spectrum regional extent of the beam forming matrix in the range of the detections of radar is
[-Nb/N Nb/ N], and by the spatial frequency spectrum regional extent [- Nb/N Nb/ N] to be spaced ε and be evenly dividing it is M spatial frequency spectrum Region,M=2Nb- 1, N, Nb、Ns, M, ε be respectively integer more than 0.
3. a kind of target direction of arrival acquisition methods based on root-MUSIC algorithms as claimed in claim 1, its feature exists In the sub-step of step 2 is：
The 1st spatial frequency spectrum region after 2.1 selections order arrangement in M spatial frequency spectrum region, the 1st spatial frequency spectrum area Domain includes several frequencies, chooses wherein Q frequency, and the frequency of q-th frequency is designated as into f respectivelyq, by q-th frequency The corresponding extension steering vector of frequency is designated as
Subscript T represents transposition, and N represents thunder Up to comprising element number of array, e represents exponential function；
The 2.2 corresponding extension steering vectors of frequency for being calculated q-th frequency using least square methodLow order it is real many Item formula is approximate, i.e.,
T∈C(2N-1)×(L+1), C(2N-1)×(L+1)The complex-field matrix of (2N-1) × (L+1) ranks is represented, T is the 1st The window vector matrix in individual spatial frequency spectrum region, ζ (fq) be q-th frequency the corresponding extension steering vector of frequencyIt is low The approximate error of rank real polynomial,fqIt is the corresponding extension steering vector of the frequency of q-th frequencyL rank multinomial vectors,L represents the multinomial top step number of setting, L >=3, fqIt is q The frequency of individual frequency, q ∈ { 1,2 ..., Q }, Q are the frequency points of selection in the 1st spatial frequency spectrum region；
2.3The 1st window vector matrix in spatial frequency spectrum region is calculated to estimate F =[f1,…,fq,…,fQ], q ∈ { 1,2 ..., Q }, Q are the frequency points of selection in the 1st spatial frequency spectrum region, subscript T tables Show transposition, subscript -1 represents inversion operation；The window vector matrix in the 1st spatial frequency spectrum region is estimatedComprising L+1 row Vector, is designated as respectively
t1,t2,…,th,…,tL+1, h ∈ { 1,2 ..., L+1 }, thRepresent that the 1st window vector matrix in spatial frequency spectrum region is estimatedIn h-th column vector, L represents the multinomial top step number of setting, L >=3.
4. a kind of target direction of arrival acquisition methods based on root-MUSIC algorithms as claimed in claim 1, its feature exists In in step 3, the sample covariance matrix of the radar return data is estimated X (k) is K-th sampled data in the echo data that radar is received, k-th sampled data in the echo data that the radar is received X (k) is that column vector is tieed up in N × 1, the sampling number that k ∈ { 1,2,3 ..., K }, K are included for echo data X that radar is received, on Mark H represents conjugate transposition operation；
The sample covariance matrix of the radar return data is estimatedNoise subspace matrixIt obtains process：
Sample covariance matrix to radar return data is estimatedFeature decomposition is carried out, N is respectively obtained " individual characteristic value and N " it is individual Each self-corresponding characteristic vector of characteristic value；By N " individual characteristic value by order arrangement from big to small, and respectively by preceding NsIt is individual big Characteristic value is estimated as the sample covariance matrix of radar return dataDiagonal matrixBy preceding NsIndividual big characteristic value is each Self-corresponding characteristic vector is estimated as the sample covariance matrix of radar return dataSignal subspace matrixWill N”-NsIndividual characteristic value is estimated as the sample covariance matrix of radar return dataNoise subspace diagonal matrixWill N”-NsIndividual each self-corresponding characteristic vector of characteristic value is estimated as the sample covariance matrix of radar return dataNoise Space matrixI.e. the sample covariance matrix of radar return data is estimatedMeet after carrying out feature decomposition： → represent and the sample covariance matrix of radar return data is estimatedCarry out Eigenvalues Decomposition；The M spatial frequency spectrum interval In the echo signal total number that includes and N " individual characteristic value is by the big characteristic value number chosen after order arrangement from big to small It is equal.
5. a kind of target direction of arrival acquisition methods based on root-MUSIC algorithms as claimed in claim 4, its feature exists In, in step 4, the noise covariance matrix V of the beam forming matrix in the range of the detections of radar, its expression formula is： For the sample covariance matrix of radar return data is estimatedNoise subspace matrix, subscript H tables Show conjugate transposition operation.
6. a kind of target direction of arrival acquisition methods based on root-MUSIC algorithms as claimed in claim 4, its feature exists In in steps of 5, k-th element in the vector v being designated as into vk,{ 1 ..., N'}, N' are sweared k ∈ for row The element number that amount v is included；The element number that column vector v is included is equal with the element number of array that radar is included.
7. a kind of target direction of arrival acquisition methods based on root-MUSIC algorithms as claimed in claim 4, its feature exists In, in step 6, the corresponding M groups low order real polynomial coefficient in the M spatial frequency spectrum region, it obtains process and is：
Determine M transformation matrix W, the W=[w in spatial frequency spectrum region1,w2,...,wm,...wM], wmIt is m-th spatial frequency spectrum area The transformation vector in domain,
wm=[e-j2π(N-1)(m-1)ε,e-j2π(N-2)(m-1)ε,…1,…ej2π(N-2)(m-1)ε,ej2π(N-1)(m-1)ε]T；
According to M the transformation matrix W and column vector v in spatial frequency spectrum region, intermediary matrix D is calculated,L ∈ { 1,2 ..., L+1 }, tlRepresent the 1st The window vector matrix in spatial frequency spectrum region is estimatedIn l-th column vector, L represents the multinomial top step number of setting；1L+1Represent By the L+1 1 row vector for constituting,Crow internal medicine product is represented, ⊙ represents Hadamard's product；
Then, line translation is entered to middle matrix D using the transformation matrix W in M spatial frequency spectrum region, obtains M spatial frequency spectrum area The corresponding M groups low order real polynomial coefficient in domain, wherein m group low order real polynomials coefficient is γm,
γm=[γm1,γm2,…,γml,…γm(L+1)], γmlIt is the l level numbers in m group low order real polynomial coefficients,M ∈ { 1,2,3 ..., M },
L ∈ { 1,2,3 ..., L+1 }, L represent the multinomial top step number of setting, L >=3；Subscript T represents transposition.
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CN108008386A (en) * 2017-11-22 2018-05-08 电子科技大学 A kind of distance based on single snap MUSIC algorithms is to processing method
CN108089147A (en) * 2017-12-07 2018-05-29 西南电子技术研究所（中国电子科技集团公司第十研究所） Improved shortwave unit localization method
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CN109799486B (en) * 2019-01-09 2022-12-13 西安科技大学 Self-adaptive sum and difference beam forming method
CN109975807A (en) * 2019-03-27 2019-07-05 东南大学 A kind of reduced order subspace angle-measuring method suitable for millimeter wave trailer-mounted radar
CN109975807B (en) * 2019-03-27 2022-03-18 东南大学 Dimension reduction subspace angle measurement method suitable for millimeter wave vehicle-mounted radar
CN110161489A (en) * 2019-05-21 2019-08-23 西安电子科技大学 A kind of strong and weak signals direction-finding method based on pseudo- frame
CN110161489B (en) * 2019-05-21 2022-11-01 西安电子科技大学 Strong and weak signal direction finding method based on pseudo frame
CN111551924A (en) * 2020-06-10 2020-08-18 重庆圭研科技有限公司 Digital signal processing method

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