CN108680894A - A kind of mixing field signal source locating method based on reconstruct cumulant matrices - Google Patents
A kind of mixing field signal source locating method based on reconstruct cumulant matrices Download PDFInfo
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Abstract
The present invention provides a kind of mixing field signal source locating method based on reconstruct cumulant matrices, which includes the following steps：The covariance matrix R of step S1. calculating observation signals；Step S2. calculates far-field signal DOA estimated values；Step S3. reconstructs far field cumulant matrices according to far-field signal DOA estimated values；Step S4. separation near-field components and far field component；Step S5. utilizes ESPRIT algorithms, and near-field signals DOA estimated values are calculated；Step S6. is worth to distance of near field estimated value using near-field signals DOA estimations.The present invention is using mixing rank statistic, compared to second-order statistics quantity algorithm, overcomes Gauusian noise jammer and the problem of degree of freedom halves, and compared to fourth-order cumulant quantity algorithm, the DOA estimation near field for exempting from search is realized, algorithm complexity is reduced；Using space difference, far field cumulant matrices are reconstructed, realize being precisely separating for far field and near-field signals component.
Description
Technical field
The invention belongs to fields in terms of passive orientation of information source, and in particular to a kind of mixing field based on reconstruct cumulant matrices
Signal source locating method.
Background technology
Passive orientation of information source refers to utilizing array signal processing method, and it is fixed to estimate DOA or distance of target information source etc.
Position parameter, the technology of information source spatial position is determined with this.In recent years, passive orientation of information source is grinding for array signal processing field
Study carefully one of hot spot.There is very important effect in many civil and military fields such as radar, sonar, communication and seismic survey.
With the rapid development of information technology, mixing field orientation of information source receives more and more attention.Radar, sonar,
The fields such as auditory localization and electronic reconnaissance, echo signal are usually coexisted by far field source and near field sources and are formed.In such a case, it mixes
The positional parameter of target information source will not only be estimated by closing field orientation of information source algorithm, also be precisely separating far field and Near-field sources.It is former
First pure far field or pure near-field source localization method of estimation has been no longer desirable for above-mentioned environment.Thus, research mixing field information source is fixed
Position method has important practical significance and wide application prospect.
Mixing field signal source locating method at present can be roughly divided into two classes according to using statistic different：It is to be based on two first
The mixing source location algorithm of rank statistic, as based on second-order statistic oblique projection algorithm (MBODS) and based on space difference
Mixing source location algorithm.For above two algorithm because using second-order statistic, computation complexity is relatively low, but can not eliminate the shadow of noise
It rings, and suffers from the shortcomings that degree of freedom halves；Followed by the mixing source location algorithm based on Higher Order Cumulants, it is such as tired based on quadravalence
Two step MUSIC algorithms (TSMUSIC) of accumulated amount and the mixing source location algorithm based on steering vector orthogonality.Two kinds of above-mentioned calculations
Method, by selecting symmetrical sensor to detach DOA and distance parameter, avoids two-dimentional combined parameters and estimates because using fourth order cumulant
Meter, and the influence of Gaussian noise is eliminated, improve estimated accuracy.But that there is calculated loads is big for Higher Order Cumulants, increases
The shortcomings that algorithm computation complexity.
In addition to two above-mentioned class algorithms, compressed sensing technology and thinned array are also introduced into the research of mixing field orientation of information source
In.For example, the mixing source location algorithm based on sparse signal reconfiguring, the mixing rank mixing field orientation of information source based on thinned array is calculated
Method and mixing source location algorithm based on symmetrical nested array.Because using compressed sensing technology, document [Mixed Sources
Localization Based on Sparse Signal Reconstruction] in algorithm have high-resolution, to making an uproar
The advantages that sound is insensitive and is not necessarily to information source number prior information.Document [Mixed-Order MUSIC Algorithm for
Localization of Far-Field and Near-Field Sources][Mixed near-field and far-
Field source localization utilizing symmetricnestedarray] because using thinned array, array
Aperture is more than the uniform array of same array number, realizes further increasing for estimated accuracy.However, three kinds of above-mentioned algorithms are all
Have the shortcomings that computation complexity is high.Therefore, on the basis of ensureing estimated accuracy, the mixing source positioning for studying low complex degree is calculated
Method is very necessary.
Invention content
It is an object of the invention to overcome the deficiencies in the prior art, and provide a kind of mixing based on reconstruct cumulant matrices
Field signal source locating method, far field and Near-field sources are precisely separating to reach, and under conditions of ensureing estimated accuracy, realizing reduces calculating
The purpose of complexity.
In order to achieve the above objects and other related objects, the present invention provides a kind of mixing field based on reconstruct cumulant matrices
Signal source locating method, the localization method include the following steps：
The covariance matrix R of step S1. calculating observation signals；
Step S2. calculates far-field signal DOA estimated values；
Step S3. reconstructs far field cumulant matrices according to far-field signal DOA estimated values；
Step S4. separation near-field components and far field component；
Step S5. utilizes ESPRIT algorithms, and near-field signals DOA estimated values are calculated；
Step S6. is worth to distance of near field estimated value using near-field signals DOA estimations.
Preferably, the step S2 includes following sub-step：
Step S21. carries out feature decomposition to the covariance matrix R of observation signal,
Wherein, ΣsIt is the diagonal matrix of K × K dimensions, UsIt is that (2M+1) × K dimensional signal are empty
Between, ΣnIt is the diagonal matrix of (2M+1-K) × (2M+1-K) dimensions, UnIt is (2M+1) × (2M+1-K) dimension noise subspaces, K is battle array
First number is the signal number of the antenna array receiver of 2M+1, ()HIndicate conjugate transposition；
Step S22. sets the distance parameter r of two-dimentional MUSIC spectrum peak searches formula to r=∞, by two-dimentional MUSIC spectral peaks
Search is converted to one-dimensional MUSIC spectrum peak searches, obtains K-K1A far-field signal DOA estimated values and range estimation
Preferably, the step S3 includes following sub-step：
Step S31. constructions contain only the fourth order cumulant matrix C of DOA information1；
Wherein, C4s,NWith C4s,FThe respectively fourth order cumulant kurtosis matrix of near-field signals and far-field signal, BNWith BFRespectively near field point
The virtual array flow pattern of amount and far field component；
Step S32. obtains the fourth order cumulant kurtosis of far-field signal according to the far-field signal DOA estimated values in step S2
Estimated value
Step S33. reconstructs far field cumulant matrices according to the fourth order cumulant kurtosis estimated value of far-field signal Wherein,Indicate the estimated value of the virtual array flow pattern of far field component,ForConjugate transposition.
Preferably, the step S4 includes following sub-step：
Step S41. utilizes fourth order cumulant matrix C1Subtract far field cumulant matrices CF, obtain near field cumulant matrices CN；
Step S42., which is calculated, obtains fourth order cumulant matrix C1Estimated value
Step S43. utilizes fourth order cumulant matrix C1Estimated valueSubtract far field cumulant matricesIt is tired to obtain near field
Accumulated amount Matrix Estimation value Wherein,EsIt is (2M+1) × K
The signal subspace of dimension, ΔsIt is the diagonal matrix of K × K dimensions, IK×KIndicate the unit matrix of K × K,Indicate EsConjugate transposition,Indicate fourth order cumulant matrix C1Acquisition matrix, I2M+1Indicate the unit matrix of 2M+1 dimensions,Indicate fourth order cumulant matrix
C1Diagonal entry error estimated value.
Preferably, the step S5 includes following sub-step：
Step S51. is by near field cumulant matrices CNIn BNIt is divided into B1And B2Two parts, B2=B1Φ wherein,For the displacement factor of respective column；
Step S52. is near field cumulant matrices CNFeature decomposition is carried out, C is obtainedNSignal subspace Es,N, by signal subspace
Space Es,NIt is divided into E1And E2Two parts, Es,N=BNT, T K1×K1Non-singular matrix；
There is E1=B1T and E2=B2T=B1Φ T, then E2=E1Ψ, wherein Ψ=T-1ΦT。
Step S53. solves the estimated value of matrix Ψ using TLS-ESPRIT algorithmsAnd then obtain DOA estimation near field
Value
Wherein, { λk, k=1 ..., K1It is matrixCharacteristic value.
Preferably, the utilization near-field signals DOA estimates that being worth to distance of near field estimated value is specially：
By near field DOA estimated valuesIt substitutes into two dimension MUSIC spectrum peak searches, obtains corresponding one-dimensional
MUSIC spectrum peak searchesAnd then obtain corresponding distance of near field estimated value
As described above, a kind of mixing field signal source locating method based on reconstruct cumulant matrices of the present invention, has following
Advantageous effect：
The present invention overcomes Gauusian noise jammer and freedom using mixing rank statistic compared to second-order statistics quantity algorithm
The problem of degree halves, and compared to fourth-order cumulant quantity algorithm, the DOA estimation near field for exempting from search is realized, algorithm complexity is reduced
Degree；Using space difference, far field cumulant matrices are reconstructed, realize being precisely separating for far field and near-field signals component.
Description of the drawings
Fig. 1 is that schematic diagram is arranged in array of the present invention；
Fig. 2 is the root-mean-square error of embodiment of the present invention emulation experiment mixing field DOA with SNR variation relation schematic diagrames；
Fig. 3 is that the mean square error of embodiment of the present invention emulation experiment mixing field near field sources distance is shown with SNR variation relations
It is intended to；
The root-mean-square error that Fig. 4 is embodiment of the present invention emulation experiment mixing field DOA is illustrated with number of snapshots variation relation
Figure；
Fig. 5 is the mean square error of embodiment of the present invention emulation experiment mixing field near field sources distance with number of snapshots variation relation
Schematic diagram；
Fig. 6 is the flow chart of the method for the present invention.
Specific implementation mode
Illustrate that embodiments of the present invention, those skilled in the art can be by this specification below by way of specific specific example
Disclosed content understands other advantages and effect of the present invention easily.The present invention can also pass through in addition different specific realities
The mode of applying is embodied or practiced, the various details in this specification can also be based on different viewpoints with application, without departing from
Various modifications or alterations are carried out under the spirit of the present invention.It should be noted that in the absence of conflict, following embodiment and implementation
Feature in example can be combined with each other.
It should be noted that the diagram provided in following embodiment only illustrates the basic structure of the present invention in a schematic way
Think, component count, shape and size when only display is with related component in the present invention rather than according to actual implementation in schema then
Draw, when actual implementation kenel, quantity and the ratio of each component can be a kind of random change, and its assembly layout kenel
It is likely more complexity.
As shown in fig. 6, the present embodiment provides a kind of mixing field signal source locating methods based on reconstruct cumulant matrices, including
Following steps：
The covariance matrix R of step S1. calculating observation signals
One one-dimensional even linear array as shown in Figure 1 is set, array center is phase reference point, shares 2M+1 array element,
λ/4 array pitch d=.K wavelength of the array received is the steady independence in narrowband and non-zero kurtosis signal of λ, considers K1A near field
Signal source and K-K1A far-field signal source.Noise on array elements is zero-mean additive white Gaussian noise, and noise independently of
Signal.
The data that m-th of array element is received in t moment can be expressed as：
Wherein, sk(t) k-th of signal source, n are indicatedm(t) white Gaussian noise in m-th of array element of expression, and am,kIndicate the
The array manifold element of k-th of signal of m array element pair, can be further represented as：
Wherein, ωkAnd φkThere is following form：
Wherein, λ is signal wavelength, θkAnd rkIt is the DOA and distance parameter of k-th of signal.
Array observation data, which are expressed as matrix form, is：
X (t)=AS (t)+N (t) (5)
Wherein, X (t)=[x-M(t),…,x0(t),…,xM(t)]TTo observe data vector, S (t)=[s1(t),…,sK
(t)]TFor signal source data vector, A=[a (θ1,r1),…,a(θK,rK)] it is array manifold matrix, a (θk,rk)=
[a-M,k,…,a0,k,…,aM,k]TFor steering vector, N (t)=[n-M(t),…,n0(t),…,nM(t)]TFor noise vector.
In actual operation, the calculation formula of the covariance matrix R of observation data X (t) is：
Wherein, N is number of snapshots.
Step S2. calculates far-field signal DOA estimated values；
Specifically,
To covariance matrix R feature decompositions, have
Wherein, ΣsIt is the diagonal matrix of K × K dimensions, includes the K maximum eigenvalue of covariance matrix R；UsIt is (2M+1)
× K dimensional signals subspace is turned by the corresponding feature vector of K maximum eigenvalue of covariance matrix R；ΣnIt is (2M+1-K)
The diagonal matrix of × (2M+1-K) dimensions, includes the 2M+1-K minimal eigenvalue of R；UnIt is (2M+1) × (2M+1-K) dimension noises
Subspace is turned by the corresponding feature vector of 2M+1-K minimal eigenvalue of R.
Two-dimentional MUSIC spectrum peak searches formula is：
Wherein, the search ranges signal DOA are [- pi/2, pi/2], and signal distance search range is that near-field signals distance domain adds
It is just infinite.By the way that distance parameter r=∞ are arranged so that two-dimensional search is converted to one-dimensional MUSIC spectrum peak searches：
By one-dimensional MUSIC spectrum peak searches, K-K can be obtained1A DOA estimation in far-field value and range estimation
Step 3：Far field cumulant matrices are reconstructed according to far-field signal DOA estimated values；
Array elements observation data fourth order cumulant calculation formula be：
Wherein,For the kurtosis of k-th of signal source, m, n, p, q ∈ [- M, M],
And symbol ()*Indicate complex conjugate.
By selecting the observation data of symmetrical array element, one can be constructed and only retain parameter ωkFourth order cumulant matrix
C1, i.e. Matrix C1In contain only DOA information.It enablesWithThen Matrix C1 A element
For：
The matrix dimension is (2M+1) × (2M+1), and matrix form is：
C1=BC4sBH(12)
Wherein,B=[b (θ1),…,b(θK)] be virtual array manifold matrix, then
Its virtual steering vector is
It further derives, C1Near-field components and far field component two parts can be divided into, matrix expression is：
Wherein, CNWith CFNear-field components and far field component matrix are indicated respectively,With
It is followed successively by near field virtual array manifold and far field virtual array manifold matrix,WithFor the fourth order cumulant kurtosis matrix of near-field signals and far-field signal.
Using the DOA estimation in far-field value previously obtained, far field cumulant matrices can be reconstructed：
Wherein,For the far field virtual array manifold of reconstruct, and far-field signal fourth order cumulant
Kurtosis estimated value can be calculated by following formula：
Wherein, symbol ()+Indicate M-P generalized inverses.
Step 4：Detach near-field components and far field component
By the fourth order cumulant matrix C obtained in step 31With the far field cumulant matrices of reconstructIt can be calculated
Near field cumulant matrices.
CN=C1-CF (16)
To obtain accurate near field cumulant matrices estimated value, need to fourth order cumulant matrix C1Make at error correction
Reason.For convenience of analysis, fourth order cumulant matrix C is only considered1The error of diagonal entry, and assume the error one of diagonal entry
It causes, then fourth order cumulant matrix C1Sampling matrixIt can be defined as
Wherein, ε is fourth order cumulant matrix C1Diagonal entry error, CnFor fourth order cumulant matrix C1Error component.
To sampling matrixFeature decomposition is carried out, then
Wherein, ΔsIt is the diagonal matrix of K × K dimensions, containsK maximum eigenvalue.EsIt is the signal of (2M+1) × K dimensions
Subspace.ΔnIt is the diagonal matrix of (2M+1-K) × (2M+1-K) dimensions, includes near field cumulant matrices C12M+1-K most
Small characteristic value；EnIt is (2M+1) × (2M+1-K) dimensional signal subspace, by near field cumulant matrices C12M+1-K minimal characteristic
It is worth corresponding feature vector to be turned into.
Fourth order cumulant matrix C as a result,1Accurate estimated valueIt can be calculated by following formula：
Wherein, C1Diagonal entry error ε be estimated as2M+1-K minimal eigenvalue mean value.
It further derives, near field cumulant matrices estimated valueFor
Step 5：Using ESPRIT algorithms, near-field signals DOA estimated values are calculated；
By step 3 it is found that near field cumulant matrices CNMatrix form be
By BNIt is divided into B1And B2Two parts, such as following formula
Wherein,
With
Observe b1(ωk) and b2(ωk) expression formula is it is found that b2(ωk) can be by b1(ωk) indicate：
Therefore, B1And B2Between relationship be：
B2=[b1(ω1),…,b1(ωK1)] Φ=B1Φ (24)
Wherein,
To near field cumulant matrices CNFeature decomposition is carried out, then
Wherein, Λs,NIt is K1×K1The diagonal matrix of dimension includes near field cumulant matrices CNK1A maximum eigenvalue.
Es,NIt is (2M+1) × K1Dimensional signal subspace, by near field cumulant matrices CNK1The corresponding feature vector of a maximum eigenvalue
At.Λs,NIt is (2M+1-K1)×(2M+1-K1) dimension diagonal matrix, include near field cumulant matrices CN2M+1-K1It is a most
Small characteristic value；En,NIt is (2M+1) × (2M+1-K1) dimensional signal subspace, by near field cumulant matrices CN2M+1-K1A minimum
The corresponding feature vector of characteristic value is turned into.
Similar to BN, Es,NAlso E can be divided into1And E2Two parts, such as following formula
Because of Es,NWith BNIt can be turned into the same space, so there will necessarily be a K1×K1Non-singular matrix T, has
Therefore, E1And E2It is represented by
E1=B1T (28)
E2=B2T=B1ΦT (29)
So E2It can be by E1Expression
E2=E1Ψ (30)
Wherein, Ψ=T-1ΦT.Therefore matrix Ψ is similar to matrix Φ, and the characteristic value of the two is identical.Only require Ψ spy
Value indicative can further obtain parameter ωk, can also obtain DOA estimation near field value.
The near field cumulant matrices estimated value previously obtainedFormula (25) is substituted into, E can be obtained1And E2Estimated value
WithIt willWithIt is configured to matrixTo its singular value decomposition, it is 2K to find out dimension1×2K1Right singular value to
Moment matrix V, then V is resolved into four K1×K1Part, such as
According to overall lowest mean square criterion, the estimated value of Ψ is：
Therefore, DOA estimation near field can be obtained by following formula：
Wherein, λkForCharacteristic value.
Step 6：It is worth to distance of near field estimated value using near-field signals DOA estimations.
By near field DOA estimated valuesIt substitutes into two dimension MUSIC spectrum peak searches, can be obtained corresponding one-dimensional
MUSIC spectrum peak searches:
Therefore, the corresponding distance of near field is estimated as：
The present invention be for it is existing based on high complexity issue present in the location algorithm of fourth order cumulant mixing source with
Degree of freedom halves in mixing source location algorithm based on second-order statistic deficiency and propose.Mixing source proposed by the present invention is fixed
Position algorithm uses second-order statistic and fourth order cumulant simultaneously using even linear array and mixing rank statistic.First, by observing
Its covariance matrix is calculated in signal, and with two-dimentional MUSIC algorithms, it is just infinite that distance parameter in steering vector, which is arranged, is made
Two-dimensional search is converted into linear search, obtains far field information source DOA estimations；Then, the observation data for selecting symmetrical array element calculate four
Rank cumulant obtains the special fourth order cumulant matrix without distance parameter, realizes DOA and distance parameter separation.According to estimation
Far field DOA information, calculating reconstruct corresponding far field cumulant matrices.Tire out in the far field that reconstruct is subtracted by special cumulant matrices
Accumulated amount matrix obtains pure near field cumulant matrices, realizes accurately distinguishing for far field and near field；Isolated near field is accumulated again
Moment matrix uses ESPRIT algorithms, estimates near field DOA information；Finally, DOA estimation near field is substituted into two dimension MUSIC algorithms,
Search obtains corresponding distance of near field estimation.
A kind of mixing field orientation of information source algorithm based on reconstruct cumulant matrices proposed by the present invention, is precisely separating with reaching
Far field and Near-field sources under conditions of ensureing estimated accuracy, realize the purpose for reducing computation complexity.
For the performance of verification algorithm, present embodiment designs two groups of emulation experiments.First group of experiment is proposed algorithm, TS-
In the case where number of snapshots are 400, DOA is with distance estimations root-mean-square error with the change of signal-to-noise ratio for MUSIC algorithms and MBODS algorithms
Change relationship.And second group of experiment is proposed algorithm, TS-MUSIC algorithms and MBODS algorithms under conditions of signal-to-noise ratio is 15dB,
DOA is with distance estimations root-mean-square error with the variation relation of number of snapshots.
The random experiments number of two groups of experiments is 500, and even linear array used is identical, array number 9, array pitch d
=λ 4, near field range are 1.7536 λ ＜ r ＜, 8 λ.Incident signal number K=2, wherein each comprising near-field signals and far-field signal
One.Signal parameter is respectively (θ1,r110 ° of)={, 3.5 λ } and (θ2,r245 ° of)={ ,+∞ }.The result difference of two groups of experiments
As shown in Fig. 2,3,4,5.
Therefore, the present invention not only improves the estimated accuracy of DOA and distance, can accurately distinguish near field and far-field signal,
And the DOA estimation near field for exempting from search is realized, reduce the complexity of algorithm.
The above-described embodiments merely illustrate the principles and effects of the present invention, and is not intended to limit the present invention.It is any ripe
The personage for knowing this technology can all carry out modifications and changes to above-described embodiment without violating the spirit and scope of the present invention.Cause
This, institute is complete without departing from the spirit and technical ideas disclosed in the present invention by those of ordinary skill in the art such as
At all equivalent modifications or change, should by the present invention claim be covered.
Claims (6)
1. it is a kind of based on reconstruct cumulant matrices mixing field signal source locating method, which is characterized in that the localization method include with
Lower step：
The covariance matrix R of step S1. calculating observation signals；
Step S2. calculates far-field signal DOA estimated values；
Step S3. reconstructs far field cumulant matrices according to far-field signal DOA estimated values；
Step S4. separation near-field components and far field component；
Step S5. utilizes ESPRIT algorithms, and near-field signals DOA estimated values are calculated；
Step S6. is worth to distance of near field estimated value using near-field signals DOA estimations.
2. a kind of mixing field signal source locating method based on reconstruct cumulant matrices according to claim 1, feature exist
In the step S2 includes following sub-step：
Step S21. carries out feature decomposition to the covariance matrix R of observation signal,
Wherein, ΣsIt is the diagonal matrix of K × K dimensions, UsIt is (2M+1) × K dimensional signals subspace,
ΣnIt is the diagonal matrix of (2M+1-K) × (2M+1-K) dimensions, UnIt is (2M+1) × (2M+1-K) dimension noise subspaces, K is array number
For the signal number of the antenna array receiver of 2M+1, ()HIndicate conjugate transposition；
Step S22. sets the distance parameter r of two-dimentional MUSIC spectrum peak searches formula to r=∞, by two-dimentional MUSIC spectrum peak searches
One-dimensional MUSIC spectrum peak searches are converted to, K-K is obtained1A far-field signal DOA estimated values and range estimation
3. a kind of mixing field signal source locating method based on reconstruct cumulant matrices according to claim 2, feature exist
In the step S3 includes following sub-step：
Step S31. constructions contain only the fourth order cumulant matrix C of DOA information1；Wherein,
C4s,NWith C4s,FThe respectively fourth order cumulant kurtosis matrix of near-field signals and far-field signal, BNWith BFRespectively near-field components with
The virtual array flow pattern of far field component；
Step S32. obtains the fourth order cumulant kurtosis estimation of far-field signal according to the far-field signal DOA estimated values in step S2
Value
Step S33. reconstructs far field cumulant matrices according to the fourth order cumulant kurtosis estimated value of far-field signal Wherein,Indicate the estimated value of the virtual array flow pattern of far field component,ForConjugate transposition.
4. a kind of mixing field signal framing method based on reconstruct cumulant matrices according to claim 3, feature exist
In the step S4 includes following sub-step：
Step S41. utilizes fourth order cumulant matrix C1Subtract far field cumulant matrices CF, obtain near field cumulant matrices CN；
Step S42., which is calculated, obtains fourth order cumulant matrix C1Estimated value
Step S43. utilizes fourth order cumulant matrix C1Estimated valueSubtract far field cumulant matricesObtain near field cumulant
Matrix Estimation valueWherein,EsIt is (2M+1) × K dimensions
Signal subspace, ΔsIt is the diagonal matrix of K × K dimensions, IK×KIndicate the unit matrix of K × K,Indicate EsConjugate transposition,
Indicate fourth order cumulant matrix C1Acquisition matrix, I2M+1Indicate the unit matrix of 2M+1 dimensions,Indicate fourth order cumulant matrix C1
Diagonal entry error estimated value.
5. a kind of mixing field signal framing method based on reconstruct cumulant matrices according to claim 3, feature exist
In the step S5 includes following sub-step：
Step S51. is by near field cumulant matrices CNIn BNIt is divided into B1And B2Two parts, B2=B1Φ wherein,For the displacement factor of respective column；
Step S52. is near field cumulant matrices CNFeature decomposition is carried out, C is obtainedNSignal subspace Es,N, by signal subspace
Es,NIt is divided into E1And E2Two parts, Es,N=BNT, T K1×K1Non-singular matrix；
There is E1=B1T and E2=B2T=B1Φ T, then E2=E1Ψ, wherein Ψ=T-1ΦT。
Step S53. solves the estimated value of matrix Ψ using TLS-ESPRIT algorithmsAnd then obtain DOA estimation near field value
Wherein, { λk, k=1 ..., K1It is matrixCharacteristic value.
6. a kind of mixing field signal framing method based on reconstruct cumulant matrices according to claim 3, feature exist
In the utilization near-field signals DOA estimations are worth to distance of near field estimated value and are specially：
By near field DOA estimated valuesIt substitutes into two dimension MUSIC spectrum peak searches, obtains corresponding one-dimensional MUSIC spectrums
Peak is searched forAnd then obtain corresponding distance of near field estimated valuek
∈[1,K1]。
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| CN109870670A (en) * | 2019-03-12 | 2019-06-11 | 西北工业大学 | A kind of mixed signal method for parameter estimation based on array reconfiguration |
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| CN113032721A (en) * | 2021-03-11 | 2021-06-25 | 哈尔滨工程大学 | Far-field and near-field mixed signal source parameter estimation method with low computation complexity |
| CN113032721B (en) * | 2021-03-11 | 2022-11-01 | 哈尔滨工程大学 | Far-field and near-field mixed signal source parameter estimation method with low computation complexity |
| CN113702899A (en) * | 2021-08-03 | 2021-11-26 | 哈尔滨工程大学 | Covariance difference propagation algorithm based on phase fraction low-order moment |
| CN113702899B (en) * | 2021-08-03 | 2023-09-29 | 哈尔滨工程大学 | Propagation algorithm of covariance difference based on phase fraction low-order moment |
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