CN107422299A - A kind of mixed source localization method and mixed source alignment system - Google Patents

A kind of mixed source localization method and mixed source alignment system Download PDF

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CN107422299A
CN107422299A CN201710307612.9A CN201710307612A CN107422299A CN 107422299 A CN107422299 A CN 107422299A CN 201710307612 A CN201710307612 A CN 201710307612A CN 107422299 A CN107422299 A CN 107422299A
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signal source
array
matrix
incident
amplitude
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崔晗
刘佟
彭文娟
汪茂稳
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Huizhou University
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Huizhou 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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/04—Position of source determined by a plurality of spaced direction-finders

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  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

The invention discloses a kind of mixed source localization method, including：A fourth order cumulant matrix is built according to the reception data of uniform linear array model, the Two-dimensional electron angle of mixed source is estimated one by one respectively；The covariance matrix of reception data to the Array Model carries out feature decomposition, and the width for estimating the Array Model mutually responds；The Fuzzy Phase during width mutually responds is eliminated using multiple correction array elements；The Two-dimensional electron angular estimation, width mutually respond estimation, Fuzzy Phase eliminates three big processes and is iterated computing until convergence, obtains width and mutually respond diagonal matrix and the convergency value at Two-dimensional electron angle；Judge incoming signal Source Type, export the positioning result of incident signal source.Present invention also offers a kind of mixed source alignment system.Implement technical scheme provided by the invention, can effectively reduce computation complexity, shorten the positioning trip time, while near field and far field mixed source are positioned, improve positional accuracy and the scope of application.

Description

Mixed signal source positioning method and mixed signal source positioning system
Technical Field
The present invention relates to the field of signal source positioning technologies, and in particular, to a hybrid signal source positioning method and a hybrid signal source positioning system.
Background
The signal source positioning technology, which can be simply understood as determining the direction and position of a desired useful signal, is widely applied to the fields of communication, radio astronomy, seismic exploration, radar, medicine and the like. The current signal source positioning technology can be divided into far field source positioning and near field source positioning according to the distance between a signal source and a receiving array.
For a far-field signal source, an incoming wave signal of a receiving array is in the form of a plane wave, and the position of the signal source at the moment is determined by the direction of arrival (DOA), as shown in fig. 1, when the far-field signal source is positioned, an incident angle θ needs to be estimated. For near field signal sources, the incoming wave signal traveling through the receiving array is propagated as a spherical wave, as shown in FIG. 2, from the direction of arrival (DOA) and the distance rkTo jointly determine the location of the near field signal source k.
In signal source positioning, the prior art generally estimates the signal source orientation parameters by building an ideal array model. Assume that there are K narrow-band independent mixed signal sources incident on a uniform symmetric linear array (as shown in fig. 2) composed of 2M +1 array elements, and the array element spacing is d ≦ λ/4, where λ is the incident signal wavelength. For an ideal array model, when the center of the array (i.e. array element 0) is set as a phase reference point, the signal received by the mth array element is:
where K denotes the number of incident signal sources, sk(t) denotes that the k-th frequency is fkPhase of gammakAmplitude of σskOf the narrowband source signal nm(t) means zero mean and σ powern 2M is-M, …, M is an array element index, N is 0,1, …, N is a sampling point of time t, N is a snapshot number, ω iskAndcalled two-dimensional electronic angle, which are the direction angles theta of the kth signal sourcekAnd a distance rkAre defined as:
ωk＝-2πdsin(θk)/λ (2)
wherein if the k-th incident source is a far-field incident signal
According to equation (1), the (2M +1) × 1-dimensional received data for the entire array can be written as a matrix multiplication of the form:
wherein, the definition of each matrix is as follows:
X(t)＝[x-M(t),x-M+1(t),…,xM(t)]T(5)
N(t)＝[n-M(t),n-M+1(t),…,nM(t)]T(6)
S(t)＝[s1(t),s2(t),…,sK(t)]T(7)
ω＝[ω1,ω2,…,ωK](8)
and isFor the array model matrix:
wherein:
to meet the development requirements of electronic detection and voice communication, signal source positioning technology needs to adapt to more complex environmental conditions. However, most of the research is focused on the positioning of a single signal source (far-field signal source or near-field signal source). Moreover, existing research on the situation of the near-field incident source is basically established under the assumption that the array is an ideal situation (i.e., an ideal array model); however, with the expansion of the practical application range, incident signals are complex and various, mixed signals existing in both far-field and near-field signal sources are common, and inevitable array errors will be caused due to factors such as the humidity of the surrounding environment, the change of temperature, the vibration of the array, the aging of active devices and the like, so that the actual array flow pattern will deviate from an ideal array model and have certain disturbance or deviation.
In summary, the existing source localization solution has various defects, including: the near-field source positioning method usually needs to perform multi-dimensional search and calculation of a plurality of high-order cumulant matrixes, and needs to perform two-dimensional parameter matching, so that the calculation complexity is high, and the calculation time is long; the method is not suitable for the positioning of a mixed signal source with a near-field signal source and a far-field signal source existing simultaneously; an array error exists; the phase ambiguity of the array phase response estimate is not taken into account. At this time, the positioning performance of the system may be seriously deteriorated or even failed, which makes its application greatly limited.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a mixed signal source positioning technical scheme, which is suitable for positioning a far-field mixed signal source and a near-field mixed signal source at the same time, and reduces parameter dimension, thereby effectively reducing the calculation complexity, shortening the positioning operation time, realizing amplitude and phase response correction of the whole array, and improving the positioning performance and the application range.
To solve the foregoing technical problem, in one aspect, an embodiment of the present invention provides a method for positioning a hybrid signal source, including:
s1: constructing a fourth-order cumulant matrix according to the received data of the uniform linear array model, and respectively estimating two-dimensional electronic angles of the mixed signal source of the array model one by one on the basis of the fourth-order cumulant matrix to obtain a first-dimensional electronic angle and a second-dimensional electronic angle;
s2: according to the first dimension electron angle and the second dimension electron angle, carrying out characteristic decomposition on a covariance matrix of received data of the array model, and estimating the amplitude-phase response of the array model; the amplitude-phase response comprises an amplitude response and a phase response;
s3: eliminating fuzzy phases in the amplitude-phase response by using a plurality of correction array elements, and estimating an amplitude-phase response diagonal matrix;
s4: correcting the received data of the uniform linear array by using the amplitude-phase response matrix, reconstructing the fourth-order cumulant matrix, and re-estimating the two-dimensional electronic angle of the mixed signal source based on the fourth-order cumulant matrix;
s5: judging whether the iterative operation is converged; if yes, outputting the array amplitude-phase response diagonal matrix and the convergence value of the two-dimensional electronic angle of the mixed signal source, and executing the step S6; if not, returning to execute the step S2;
s6: and judging the type of an incident signal source in the mixed signal source by using the second-dimension electronic angle convergence value of the mixed signal source, and outputting the positioning result of the incident signal source.
In one implementation, the steps S1 and S4 include:
calculating a covariance matrix of the whole array according to the received data of the uniform linear array model; performing eigenvalue decomposition on the covariance matrix to obtain corresponding signal subspace estimation and noise subspace estimation;
correcting the received data of the whole array according to the array amplitude-phase response diagonal matrix;
constructing a fourth-order cumulant matrix according to the initialized or corrected received data of the uniform linear array model: array element serial numbers in the fourth-order cumulant matrix are symmetrical, so that the matrix only comprises a first-dimension electron angle;
performing eigenvalue decomposition on the fourth-order cumulant matrix to obtain corresponding fourth-order cumulant signal subspace estimation;
respectively obtaining first-dimension electronic angles corresponding to a plurality of incident sources by utilizing the fourth-order cumulant signal subspace estimation and applying an ESPRIT algorithm;
constructing MUSIC spectrums which are in one-to-one correspondence with the first-dimension electron angles of the multiple incident sources according to the noise subspace estimation and the estimated first-dimension electron angles of the multiple incident sources; and performing one-dimensional spectral peak search on the MUSIC spectrum to obtain second-dimensional electronic angles in one-to-one correspondence with the first-dimensional electronic angles.
Preferably, the step S3 includes:
selecting two correction array elements subjected to phase correction in the uniform linear array model, and respectively calculating the ambiguity error of the first-dimension electronic angle and the ambiguity error of the second-dimension electronic angle;
estimating the fuzzy phase of the phase response of the array model according to the fuzzy error of the first-dimension electronic angle and the fuzzy error of the second-dimension electronic angle;
and estimating the unique amplitude-phase response of each array element by eliminating the fuzzy phase of the phase response of each array element of the array model, and obtaining the amplitude-phase response diagonal matrix after eliminating the fuzzy phase.
Preferably, the step S6 includes: when the convergence estimation value of a second-dimension electron angle of a certain incident signal source in the uniform linear array model is smaller than a preset value, judging that the current incident signal source is a far-field signal source; otherwise, the current incident signal source is determined to be the near field signal source.
Further, the step S6 includes:
when the kth signal source is a near-field incident source, the output wave direction isIncident distance ofAs a result of the positioning of the current incident signal source;
when the k signal source is a far-field incident source, the wave arrival direction of the k signal source is outputAs a result of the positioning of the current incident signal source;
wherein,a convergence estimate for the first dimension electron angle for the kth signal source;a convergence estimate for a second dimension electron angle for a kth signal source; k is more than or equal to 1 and less than or equal to K, K is the number of incident sources, d is the array element interval, and lambda is the incident signal wavelength.
On the other hand, an embodiment of the present invention further provides a system for positioning a hybrid signal source, including:
the mixed signal source parameter estimation module is used for constructing a fourth-order cumulant matrix according to the received data of the uniform linear array model, and respectively estimating the two-dimensional electronic angles of the mixed signal source of the array model one by one on the basis of the fourth-order cumulant matrix to obtain a first-dimensional electronic angle and a second-dimensional electronic angle;
the array amplitude-phase response estimation module is used for performing characteristic decomposition on a covariance matrix of received data of the array model according to the first-dimension electronic angle and the second-dimension electronic angle to estimate amplitude-phase response of the array model; the amplitude-phase response comprises an amplitude response and a phase response;
the array fuzzy phase elimination module is used for eliminating fuzzy phases in the amplitude-phase response by utilizing a plurality of correction array elements and estimating an amplitude-phase response diagonal matrix;
the mixed signal source parameter estimation module is further configured to correct the received data of the uniform linear array by using the amplitude-phase response matrix, reconstruct the fourth-order cumulant matrix, and re-estimate the two-dimensional electronic angle of the mixed signal source based on the fourth-order cumulant matrix;
the iteration convergence judging module is used for judging whether the iteration operations sequentially executed by the three modules are converged or not according to the iteration convergence condition; if the iteration is converged, outputting an array amplitude-phase response diagonal matrix and a convergence value of a two-dimensional electronic angle of the mixed signal source; otherwise, sending the re-estimated two-dimensional electronic angle to the array amplitude-phase response estimation module for iterative operation;
and the positioning result output module is used for judging the type of the incident signal source in the mixed signal source by utilizing the convergence value of the second-dimensional electronic angle of the final incident signal source and outputting the positioning result of the incident signal source according to the type of the incident signal source and the convergence value of the two-dimensional electronic angle of the final incident signal source.
In one implementation, the mixed signal source parameter estimation module includes:
the subspace estimation module is used for calculating a covariance matrix of the whole array according to the received data of the uniform linear array model; performing eigenvalue decomposition on the covariance matrix to obtain corresponding signal subspace estimation and noise subspace estimation;
the array received data correction module is used for correcting the received data of the whole array according to the array amplitude-phase response diagonal matrix;
a fourth order cumulant matrix construction module for constructing a fourth order cumulant matrix according to the initialized or corrected received data of the uniform linear array model: array element serial numbers in the fourth-order cumulant matrix are symmetrical, so that the matrix only comprises a first-dimension electron angle; and carrying out eigenvalue decomposition on the fourth-order cumulant matrix to obtain corresponding fourth-order cumulant signal subspace estimation;
the first-dimension electronic angle calculation module is used for utilizing the fourth-order cumulant signal subspace estimation and applying an ESPRIT algorithm to respectively obtain first-dimension electronic angles corresponding to a plurality of incident sources;
the second-dimension electronic angle calculation module is used for constructing MUSIC spectrums which are in one-to-one correspondence with the first-dimension electronic angles of the plurality of incident sources according to the noise subspace estimation and the estimated first-dimension electronic angles of the plurality of incident sources; and performing one-dimensional spectral peak search on the MUSIC spectrum to obtain second-dimensional electronic angles in one-to-one correspondence with the first-dimensional electronic angles.
Preferably, the array ambiguity phase elimination module comprises:
the ambiguity error calculation module is used for selecting two correction array elements which are subjected to phase correction in the uniform linear array model, and calculating the ambiguity error of the first-dimension electronic angle and the ambiguity error of the second-dimension electronic angle respectively;
the fuzzy phase estimation module is used for estimating a fuzzy phase of the phase response of the array model according to the fuzzy error of the first-dimension electronic angle and the fuzzy error of the second-dimension electronic angle;
and the amplitude-phase response updating module is used for estimating the unique amplitude-phase response of each array element by eliminating the fuzzy phase of the phase response of each array element of the array model, and obtaining the amplitude-phase response diagonal matrix after the fuzzy phase is eliminated.
Preferably, the positioning result output module includes:
the signal source type judging module is used for judging that the current incident signal source is a far-field signal source when the convergence estimation value of the second-dimension electron angle of a certain incident signal source in the uniform linear array model is smaller than a preset value; otherwise, the current incident signal source is determined to be the near field signal source.
Preferably, the positioning result output module further includes:
a positioning result calculation module for:
when the kth signal source is a near-field incident source, the output wave direction isIncident distance ofAs a result of the positioning of the current incident signal source;
when the k signal source is a far-field incident source, the wave arrival direction of the k signal source is outputAs a result of the positioning of the current incident signal source;
wherein,a convergence estimate for the first dimension electron angle for the kth signal source;a convergence estimate for a second dimension electron angle for a kth signal source; k is not less than 1 and not more than K, K isThe number of incident sources, d is the array element spacing, and λ is the incident signal wavelength.
The mixed signal source positioning technical scheme provided by the embodiment of the invention is suitable for uniform linear arrays, and the parameter dimension is reduced by constructing a special fourth-order cumulant matrix, so that the calculation complexity of the method is effectively reduced, the positioning operation time is shortened, a near-field and far-field mixed signal source can be positioned at the same time, the incoming wave direction is estimated for a far-field signal source, the incoming wave direction and the incident distance are estimated for a near-field signal source, the amplitude phase response correction of the whole array can be further realized by utilizing two correction array elements, and the signal source positioning problem under the condition that the incident distance of a signal source is uncertain and the array amplitude phase response has errors is solved. The technical scheme provided by the invention has the advantages of moderate calculated amount, short positioning time, no need of parameter matching, and improvement of positioning performance and application range.
Drawings
Fig. 1 is a schematic diagram of source location for a uniform linear array receiving far field signal source.
Fig. 2 is a schematic diagram of source locations for a uniform linear array receiving near field signal sources.
Fig. 3 is a flowchart illustrating the steps of an embodiment of a method for locating a hybrid signal source according to the present invention.
FIG. 4 is a schematic diagram of the composition of an embodiment of a uniform linear array model provided by the present invention.
Fig. 5 is a flowchart illustrating the steps of a hybrid signal source positioning method according to another embodiment of the present invention.
Fig. 6 is a schematic structural diagram of an embodiment of a hybrid signal source localization system provided by the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. The present invention will be described in further detail with reference to examples; it is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without any inventive effort, are within the scope of the present invention.
The technical scheme provided by the invention is established on the basis of a non-ideal array model to estimate the positioning result of the mixed signal source. Specifically, when a non-ideal array model is established for the mixed signal source positioning system, namely when the amplitude and phase response of the uniform linear array have errors, the array received data model is changed from the ideal array model to:
wherein,is an array model matrix defined as described in equation (10); s (n) matrix, N (n) matrix, ω matrix andthe matrix is defined in the same way as equations (6) to (9), where N is 0,1, …, N is the sampling point of time t, and N is the fast beat number; is an amplitude phase response diagonal matrix, which can be expressed as:
in this embodiment, let the central array element 0 be a reference array element, that is: g0＝1，The non-ideal amplitude response of 2M +1 array elements is g ═ g-M,g-M+1,…,g-1,g0,g1,…,gM-1,gM]The phase response is β ═ β-M, β-M+1,…,β-1,β0,β1,…,βM-1,βM]. The technical problem to be solved by the present invention is therefore to jointly estimate the input and output source orientation parameters ω from the array received signals x (N), N being 0,1, …, N,and array element amplitude phase responses g and β in non-ideal array models.
Example one
Referring to fig. 3, a flowchart of the steps of an embodiment of a method for locating a hybrid signal source according to the present invention is shown.
In this embodiment, the method for positioning a hybrid signal source mainly includes the following steps S1 to S6:
step S1: a fourth-order cumulant matrix is constructed according to the received data of a uniform linear array model (as shown in fig. 2), and the two-dimensional electron angles of the mixed signal source of the array model are respectively estimated one by one based on the fourth-order cumulant matrix to obtain a first-dimensional electron angle omega and a second-dimensional electron angleSpecifically, a special fourth-order cumulant matrix is constructed, and the matrix only comprises one-dimensional estimation parameters, so that the dimensionality of the parameters can be effectively reduced, the calculation complexity is reduced, and the positioning operation time is shortened.
In order to obtain more accurate parameter estimates from known information, initialization needs to be performed first. Initializing the amplitude-phase response matrix from known information (initialization may assume that an array model with 2M +1 array elements has an ideal amplitude-phase responseAt this timeAfter the array received data is corrected, a mixed signal source orientation parameter estimation algorithm based on a special cumulant matrix can be applied to estimate a two-dimensional electronic angle of a mixed incident source to obtain an initial estimation value
Specifically, in an ideal case, the fourth order cumulant of the uniform linear array model output can be defined as:
in the above formula, parameter c4,sk＝cum{sk(t),sk*(t),sk*(t),sk(t) } denotes the signal sk(t) kurtosis, superscript denotes complex conjugation due to array elements M, n, p, q ∈ [ -M, M]So that M-n, p-q ∈ [ -2M,2M [ ]]。
In order to reduce the amount of calculation and complexity, the embodiment of the invention may only reserve the parameter ω in the above formula in consideration of the symmetry of the array modelkRemoving the parametersNamely, require (m)2-n2)-(p2-q2) Thus, a special (2M +1) × (2M +1) -dimensional fourth-order accumulation amount matrix can be obtained according to the fourth-order accumulation amount calculation formula:
in this embodiment, the one-dimensional parameter ω is setkCalled the first dimension electron angle, and one-dimensional parametersReferred to as the second dimension electron angle. Therefore, in the embodiment of the present invention, the above equation (15) can be used to first estimate the one-dimensional parameter ω of any kth incident signal source in the arraykThen reuse omegakEstimating the corresponding other dimension parameter
In a preferred implementation, the step S1 includes: firstly, constructing a special fourth-order cumulant matrix according to the receiving data after the initialization of the uniform linear array model, wherein the construction method comprises the following steps: making the array element serial numbers in the fourth-order cumulant matrix symmetrical, so that the matrix only contains a first-dimension electron angle omega; then, carrying out eigenvalue decomposition on the fourth-order cumulant matrix to obtain a corresponding signal subspace estimation Es(ii) a Respectively obtaining first-dimension electronic angles corresponding to a plurality of incident sources by utilizing the fourth-order cumulant signal subspace estimation and applying an ESPRIT algorithm; calculating a covariance matrix of the whole array according to the received data of the uniform linear array model; performing eigenvalue decomposition on the covariance matrix to obtain corresponding signal subspace estimation and noise subspace estimation; constructing MUSIC spectrums which are in one-to-one correspondence with the first-dimension electron angles of the multiple incident sources according to the noise subspace estimation and the estimated first-dimension electron angles of the multiple incident sources; and performing one-dimensional spectral peak search on the MUSIC spectrum to obtain second-dimensional electronic angles in one-to-one correspondence with the first-dimensional electronic angles.
Specifically, in order to estimate the two-dimensional electron angle of each incident source, in step S1, the following two sub-steps S11 to S12 may be adopted to implement:
step S11: estimating a one-dimensional parameter ωk(first dimension electron angle) estimate
Writing the matrix C defined by equation (15) in the form of a matrix multiplication:
C＝BC4sBH(16)
wherein, B is a virtual flow pattern matrix:
B＝[b(ω1),…,b(ωk),…,b(ωK)](17)
the virtual steering vector is:
BHa conjugate transpose matrix representing matrix B; diagonal matrixWherein,is the fourth order cumulant of the kth signal source.
In this embodiment, eigenvalue decomposition is performed on matrix C:
C＝EΛEH＝EsΛsEs H+EnΛnEn H(19)
in the above equation (19), the symbol Λ is a diagonal matrix whose diagonal elements are eigenvalues, and the eigenvalues are sorted by λ1≥…≥λK＞λK+1≥…≥λ2M+1Then diagonal matrix Λs∈CK×KContaining the characteristic value lambda1，λ2，…，λK；Es∈C(2M+1)×KThe signal subspace of C is constructed for its corresponding eigenvector similarly, the diagonal matrix Λn∈C(2M+1-K)×(2M+1-K)Containing the characteristic value lambdaK+1，…，λ2M+1；En∈C(2M+1)×(2M+1-K)For its corresponding feature vector, formC noise subspace.
In this embodiment, the virtual flow pattern matrix B of equation (17) can be further decomposed into two matrices, the first matrix B1Composed of the first 2M rows of B, the second matrix B2Consisting of the last 2M rows of B. From equation (15), the first matrix is B1＝[b1(ω1),…,b1(ωk),...,b1(ωK)]Wherein the kth (K is more than or equal to 1 and less than or equal to K) is as follows:
the second matrix is B2＝[b2(ω1),...,b2(ωk),…,b2(ωK)]Wherein the kth (K is more than or equal to 1 and less than or equal to K) is as follows:
the following equations (20) and (21) can be derived:
B2＝B1Φ (22)
B1，B2the relationship of B to
Since range (B) is range (E)s) So that there is a non-singular matrix tauK×KSo that:
Es＝BΤ (25)
this means that the signal is emptyIn a room EsCan be decomposed equally into:
thus, Es1And Es2Corresponding to the first and the second directional matrixes B1，B2Namely:
Es1＝B1Τ，Es2＝B2Τ (27)
from the formulae (22), (27), it is possible to obtain:
Es2＝B2Τ＝B1ΦΤ＝B1ΤT-1ΦΤ2＝Es1Τ-1ΦΤ (28)
let Ψ equal to Es1 #Es2Wherein the symbol#Representing the pseudo-inverse of a matrix. Obtained from the above formula (28):
Ψ＝Τ-1ΦΤ (29)
in this embodiment, the value of Φ can be obtained by performing eigenvalue decomposition on Ψ, and then the parameter ω can be obtained by equation (23)k(K is not less than 1 and not more than K)
In this embodiment, the signal subspace E can be takensThe first 2M row of (A) obtains Es1Then selecting a signal subspace EsLast 2M line of (D) to obtain Es2CalculatingWherein the symbol # represents the pseudo-inverse of a matrix, the eigenvalue of psi is calculated, and half of the angle of the eigenvalue is taken to obtain the first dimension electron angle omega of K incident signalsk(K is more than or equal to 1 and less than or equal to K); calculating the covariance of the entire array based on the received data of the uniform linear array modelA difference matrix; and carrying out eigenvalue decomposition on the covariance matrix to obtain corresponding signal subspace estimation and noise subspace estimation.
Step S12: by applying a per-estimated parameterConstructing a Multiple SignalClassification (Multi-Signal Classification) spectral function to estimate another dimensional parameter corresponding thereto
To make a pair with the electron angle omegakCorresponding electron angleThe estimation can be performed using the covariance matrix R of the array received data x (n):
wherein R isS＝E{s(n)sH(n) is the covariance matrix of the incident signal source;
performing characteristic decomposition on the covariance matrix R of the array received data:
thereby obtaining mutually orthogonal signal subspaces USSum noise subspace UN. Since range (A) is range (U)S) Thus there is a non-singular matrix TK×KSo that:
the estimated near-field source parametersSubstituting a guide vectorThe kth signal source parameter can be constructed by the MUSIC methodSpectral function of (c):
the present embodiment is implemented by applying a per-estimated-parameter estimationConstructing a MUSIC spectral function, and performing one-dimensional spectral peak search through the formula (33) to obtain the kth signal source parameterIs estimated value ofThus avoiding estimating parametersThe pairing problem between the two. The embodiment of the invention reduces the parameter dimension by constructing a special fourth-order cumulant matrix, thereby effectively reducing the calculation complexity of the method and shortening the positioning operation time. Thus, the embodiment of the present invention has estimated two incident source orientation parameters ωk，Respectively corresponding estimated values ofAnd
further, the embodiment of the invention can also obtain the amplitude phase response g and the phase response beta of the array elements in the non-ideal array model through limited calculation.
Step S2: according to the first dimension electron angle omega and the second dimension electron angleAnd performing characteristic decomposition on the covariance matrix R of the received data of the array model, and estimating the amplitude-phase response of the array model, wherein the amplitude-phase response comprises an amplitude response g and a phase response β.
In particular implementation, when the array has amplitude phase response error, the covariance matrix R of the received data in the non-ideal array model will be transformed by equation (30) as:
performing characteristic decomposition on the mixed solution to obtain:
R＝UΛUH＝UsΛsUs H+UnΛnUn H(35)
thereby obtaining a signal subspace US. Since range (A) is range (U)s) The following can be deduced:
UsUs HA＝A (36)
namely:
defining a direction vectorComposed diagonal matrixAnd a (2M +1) × 1-dimensional vector consisting of diagonal elements of the amplitude-phase response diagonal matrix:
equation (36) can be written as:
k matrices WkK is 1,2, …, K, which adds to:
the correlation can be obtained from equation (39): the parameter pair (v,1) is Wk(K-1, 2, …, K), then (v, K) is the feature vector and feature value pair for W. Wherein, the eigenvalue K is the maximum eigenvalue of the matrix W, and v is the eigenvector corresponding to the maximum eigenvalue K. Therefore, in the embodiment of the present invention, the non-ideal amplitude response g ═ g of each array element can be obtained by calculating the eigenvector v corresponding to the maximum eigenvalue of W and then according to the correlation of the equation (38)-M,g-M+1,…,g-1,g0,g1,…,gM-1,gM]And, phase response β ═ β-M,β-M+1,…,β-1,β0,β1,…, βM-1,βM]Is estimated value ofAndin this embodiment, the combination of the magnitude response and the phase response is simply referred to as the magnitude-phase response.
Step S3: and eliminating the fuzzy phase in the amplitude-phase response estimation value by utilizing a plurality of correction array elements, and estimating an amplitude-phase response diagonal matrix.
In this embodiment, estimating the two-dimensional electron angle of the incident signal source by the non-ideal array model using the above steps produces ambiguity, which will cause the array phase response to deviate and only the array phase response to deviate. Therefore, in specific implementation, it is necessary to characterize the phase ambiguity error in the amplitude-phase response obtained by estimation, so as to obtain an amplitude-phase response diagonal matrix with higher accuracy, and thus obtain a more accurate amplitude-phase response. In a preferred implementation, the step S3 selects two array elements in the array model as the correction array elements.
Specifically, two correction array elements with phase correction are selected from the uniform linear array model, and the ambiguity error of the first-dimension electron angle ω and the second-dimension electron angle ω are calculated respectivelyAmbiguity error of (d); the ambiguity error according to the first dimension electron angle omega and the second dimension electron angleEstimating a fuzzy phase of the phase response of the array model; and estimating the unique amplitude-phase response of each array element by eliminating the fuzzy phase of the phase response of each array element of the array model, and obtaining the amplitude-phase response diagonal matrix after eliminating the fuzzy phase. In the specific implementation:
first, two unknown additive scalars can be used to characterize the ambiguity of the two-dimensional electronic angle estimate of the mixed-signal source parameter.
Specifically, the amplitude-phase response estimation of each array element in this embodiment is mainly performed according to a subspace method, that is, a range (a) range (U)s). Signal subspace UsThe equation solved is:
where the sum a is the array amplitude-phase response diagonal matrix and the array flow pattern matrix, matrix g, β, ω,are as defined in the array model above.
When present, is1≠2And A is1≠A2Satisfies the following conditions:
range(Us)＝range(1A1)＝range(2A2) (42)
whereinThen (1,A1) And (a)2,A2) Are solutions of equation (41). Therefore, equation (42) implies that there exists a non-singular matrix W satisfying the relationship:
1A1W＝2A2(43)
simplifying the above formula to obtain:
′A1W＝A2(44)
wherein,is a diagonal matrix. Line m of the above equation can be converted to K-1 equations:
wherein,representation matrix A1M-th row vector of, wkRepresenting the k column vector of the matrix W.Representation matrix A2Row m and column k. Equation (45) above can be expressed as:
wherein:
wherein a ismIs the m-th element, ω, of the array flow pattern vector aa,bRepresents omegaaThe number b of the element (a) of (b),to representWherein a is 1, 2.
For M ═ M, -M + 1.., M, i.e. 2M +1 array elements in the array model, one can obtain:
CA1w1-A1wk＝0,k＝2,...,K (48)
wherein:
thus, the above equation can be written in the form of a matrix multiplication:
whereinDefining a composite matrix B:
if w is1And wkWith a non-zero solution, the composite matrix B must be a rank-impairment matrix. Considering the special form of the array flow type matrix A, in the case of 2M +1 ≧ 2K, the rank deficiency of the composite matrix B means { ω ≧ 2K1+ω2,k-ω2,1,ω1Andmust contain repeating elements, and ω1Andthe repeated elements in (a) must correspond to the same source signal. Due to omega1Andare different from each other, and therefore, ω is1Andin which two elements ω are present, respectively1,m,ω1,nAndsatisfies the following conditions:
defining:
then omega2Andthe set of all element differences in (A) can be effectively represented as [ Delta omega ] respectively2,...,ΔωKAndsubstituting the set of these errors into the equation yields:
to obtain a non-zero solution of the matrix W, all of the above equations need to be solved, and W solved for all of the equations1The solution is the same, which means that the matrix ω is1There is an element, when it adds △ ωkWhile it is still the matrix ω1An element of (1); matrix arrayThere is an element, when it is addedWhile it is still a matrixAn element of (1). Suppose this element is the first element, e.g., ω1,1When Δ ω is added in sequence2,...,ΔωKω can be obtained1,2,…,ω1,K；Are added in sequence respectivelyCan obtainNamely: omega1,1+Δωk＝ω1,k,
According to △ omegakAndcan be obtained by defining (a):
wherein ω2,1-ω1,1Andis an unknown constant, the sum of the parameters is the signal source electronic angle omega andambiguity error of (d).
The above equation shows that the ambiguity of the two-dimensional electronic angle estimate of the mixed signal source parameter can be characterized by two unknown additive scalars. Observations have shown that these two unknown additive scalars also bias the array phase response.
Let G ═ diag { a () }, where:
by an array flow pattern matrixExpression, we can get:
it can be seen that the diagonal matrix G is the deviation of the array amplitude phase response matrix caused by the array flow pattern matrix. Because the elements of matrix G contain only phase factors, the ambiguity of the two-dimensional electronic angle estimate of the signal source only biases the array phase response, and the phase response ambiguity error for the m-th array element is:
Δβm＝m+m2(58)
suppose the true phase response of the m-th array element is βmThen the phase response estimate for the mth array element is:
therefore, the unknown scalar sum will introduce an indistinguishable error to the signal source two-dimensional electronic angle and array element phase response estimate, whereas a unique array element phase response estimate cannot be obtained based on the subspace relational equations alone. Therefore, other constraints must be introduced to eliminate ambiguity.
To solve this problem, in this embodiment, two correction array elements need to be introduced (i.e. the phase response of the array elements has been corrected in advance). Suppose that m is1And m2(m1,m2∈ (-M, -1) ∪ (1, M)) array elements have their phase response corrected, i.e.:
thus:
it is possible to obtain:
by the above two formulas, the signal source electronic angle ω and can be calculated according to the phase response estimated value of the correction array elementThe sum of the ambiguity errors; the fuzzy phase of the array phase response estimation can be calculated further according to the equation (58); by eliminating the fuzzy phase of the m-th array element phase response estimation, a unique array element amplitude phase response estimation can be obtained.
In a preferred implementation, the two-dimensional electron angle estimated last can be used in the amplitude-phase response estimationSubstitution into equation (39) yields:
where i denotes an estimated value after the ith iteration, and when i is 0, denotes an initial estimated value obtained at the time of initialization Representing the estimated value of the first dimension electron angle omega of the kth signal source after the ith iteration,representing the first dimension electron angle of the kth signal source after the ith iterationAn estimate of (d). Vector v returns the elements on the main diagonal of the diagonal matrix: v ═ diag { }; the function diag is used to extract the diagonal elements of the matrix. Therefore, the matrix W represented by equation (40) can also be expressed as the following expression:
therefore, v is the eigenvector corresponding to the maximum eigenvalue of the matrix W, that is, the magnitude-phase response g, β can be estimated by calculating the eigenvector v corresponding to the maximum eigenvalue of the obtained matrix W, specifically, after each element value of the eigenvector v is obtained by estimation, it can be known from equation (38) that the magnitude value of each element value of the eigenvector v is the non-ideal magnitude response g ═ g of each array element in the model-M,g-M+1,…,g-1,g0,g1,…,gM-1,gM]The phase value of each element value of the eigenvector v is the phase response β ═ β-M,β-M+1,…,β-1,β0,β1,…,βM-1,βM]. Therefore, the non-ideal amplitude response g corresponding to the estimated value of the characteristic vector v can be obtained sequentiallyiIs estimated value ofAnd phase response βiIs estimated value of
Further, to eliminate the phase ambiguity, assume that two sequence numbers are m1,m2The phase response of the array elements has been previously corrected so that the electron angles ω andthe sum of the ambiguity errors of (a) can then be based on two equations in equation (62)Andrespectively, so that the ambiguous phase error Δ β can be removed from the magnitude-phase response estimate according to equations (58) and (59)mThe latest estimate of the amplitude-phase response matrix defined in equation (13) is obtained
In this embodiment, the initial value of the array amplitude-phase response matrix is an identity matrix, because the estimated values of the hybrid signal source azimuth parameter and the array amplitude-phase response are estimated under the condition of having errors with each other, in order to obtain a stable and accurate estimation result, the estimation needs to be repeated continuously through iteration to reduce the errors of the two, and because the array phase response estimation has phase ambiguity, two correction array elements are needed to eliminate the ambiguity.
Step S4: using the amplitude-phase response matrixCorrecting the received data of the uniform linear array, reconstructing the fourth-order cumulant matrix, and re-estimating the two-dimensional electronic angle of the mixed signal source based on the fourth-order cumulant matrix
In practical implementation, the difference between the step S4 and the step S1 is that the step S1 performs two-dimensional electron angle estimation using the initialized received data when performing the iterative operation for the first time, and the step S4 performs estimation on the corrected received data and the reconstructed fourth-order cumulative quantity matrix. Specifically, firstly, correcting the received data of the whole array according to the array amplitude-phase response diagonal matrix; and constructing a fourth-order cumulant matrix according to the received data corrected by the uniform linear array model: array element serial numbers in the fourth-order cumulant matrix are symmetrical, so that the matrix only comprises a first-dimension electron angle; performing eigenvalue decomposition on the fourth-order cumulant matrix to obtain corresponding fourth-order cumulant signal subspace estimation; and obtaining a one-to-one corresponding second dimension electron angle by estimating the obtained first dimension electron angle. Other specific implementation processes are the same as step S1, and are not described herein again.
Step S5: judging whether the iterative operation is converged; if yes, outputting an array amplitude-phase response diagonal matrixAnd mixed signal source two-dimensional electronic angleAnd step S6 is performed; if not, the process returns to step S2.
Preferably, the criterion for determining convergence adopted in this embodiment is:
order toCalculating a parameter PiThe value of (c):
if Pi-1-PiIf ρ is greater than a preset positive minimum value, the iteration counter i is i +1, and the process returns to step S2 to repeat the iteration calculation; if Pi-1-PiStopping iterative computation when rho is less than or equal to rho, and obtaining the current estimation Namely the iterative computation result.
Step S6: and judging the type of an incident signal source in the mixed signal source by utilizing the second-dimension electronic angle convergence value of the mixed signal source, and outputting the positioning result of the incident signal source.
In the present embodiment, it is preferable that the convergence estimation value of the second-dimension electron angle of a certain incident signal source k in the uniform linear array modelWhen the current incident signal source is smaller than the preset value, judging that the current incident signal source is a far-field signal source; otherwise, the current incident signal source is determined to be the near field signal source. Specifically, two-dimensional electron angle estimation values are obtained through iterative convergence in the stepsThen, the estimated value obtained by the last iteration is obtainedMake a judgment if(setting a positive minimum ρ), the k-th incident source is a far field source, i.e., rk≈∞。
Preferably, when the kth signal source is a near-field incident source, the output has a direction of arrival ofIncident distance ofAs a result of the positioning of the current incident signal source; when the k signal source is a far-field incident source, the wave arrival direction of the k signal source is outputAs a result of the positioning of the current incident signal source; wherein,is the first dimension electron angle omega of the kth signal sourcekThe convergence estimation of (2);is the second dimension electron angle of the k signal sourceThe convergence estimation of (2); k is more than or equal to 1 and less than or equal to K, K is the number of incident sources, d is the array element interval, and lambda is the incident signal wavelength.
The method for positioning the near-field and far-field mixed signal source with the self-correcting function has the advantages that: the technical scheme can position the mixed signal source with the near-field signal source and the far-field signal source, does not need parameter matching, and has the advantages of small calculated amount, short operation time and wide application range; in addition, the scheme can correct the amplitude response and phase response errors of the array, eliminate the phase ambiguity, effectively improve the positioning precision when the amplitude phase response errors exist in the array, and increase the positioning accuracy of a signal source.
Example two
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following describes embodiments of the present invention in further detail with reference to a uniform linear array (i.e., M5) composed of 2M + 1-11 array elements.
Referring to fig. 4, a composition diagram of an embodiment of a uniform linear array model provided by the present invention is shown.
In the embodiment of fig. 4, the uniform linear array comprises 11 equidistant array elements 2M +1, and two of the array elements are provided as the required correction array elements (the correction array elements of the embodiment of fig. 4 will be referred to as 5 and-5 array elements, preferably correction array elements).
Referring to fig. 5, a flowchart of the steps of a hybrid signal source positioning method according to another embodiment of the present invention is shown.
Specifically, based on the array model provided in fig. 4, the present embodiment estimates the two-dimensional electron angle estimation valueAnd when the corrected amplitude-phase response diagonal matrix is obtained, the mixed signal source positioning method mainly comprises the following steps:
step S501: and (5) initializing. Initializing an iteration counter i to 0, and initializing an array amplitude-phase response diagonal matrix0＝I11。
Step S502: and calculating an array covariance matrix and performing feature decomposition. According to the received data X (n) of the array, calculating a covariance matrix R ═ E { X (n) X of the whole arrayH(n) }; performing eigenvalue decomposition on the covariance matrix R to obtain corresponding signal subspace estimationSum noise subspace estimation
Step S503: the received data is corrected. In particular, the array response diagonal matrix obtained by last iteration estimation is appliediCorrecting received data X (n)
Step S504: a special cumulant matrix is constructed. Specifically, based on the corrected reception dataConstructing special cumulant matricesAnd (5) m is more than or equal to 5, p is more than or equal to 5, the sequence numbers of the array elements in the cumulant matrix are symmetrical, namely, the cumulant when the array elements are m-n and p-q is solved. Specifically, a fourth-order cumulant matrix may be preferably employed.
Step S505: estimating a first dimension electron angle ωk. Specifically, the special cumulant matrix C is subjected to eigenvalue decomposition to obtain corresponding signal subspace estimationSelecting signal subspace estimatesThe first 10 lines ofAnd the last 10 linesConstructing matrix vectorsWherein#Representing a pseudo-inverse of a matrix; solving for the vector ΨPThe characteristic value is taken as 1/2 of the angle of the characteristic value to obtain the one-dimensional electron angle omega of the incident signalk(K is not less than 1 and not more than K)
Step S506: and constructing a MUSIC spectrum. Specifically, estimated K incident source parameters are usedSubstituting direction vectorEstimated according to step S502Noise subspaceConstructing K MUSIC spectra:
step S507: estimating a second dimension electron angle by spectral peak searchSpecifically, the peak of the MUSIC spectrum in equation (66) is chosen according to equation (33), i.e., PMUSICTo estimate the electron angle with each first dimensionCorresponding another dimension electronic angle
Step S508: an estimate of the array amplitude phase response is calculated. First, a matrix of current iteration counts i is calculated according to equation (40)Wherein, the estimated signal subspace of step S502; determining a matrix WiThe feature vector v corresponding to the maximum feature value ofi(ii) a Then, the vector v can be takeniObtaining an array amplitude response estimateTaking the vector viPhase derived array phase response estimate
Step S509: the phase ambiguity is removed by using a correction array element. Specifically, the fuzzy phase of the array phase response estimate is calculated using two correction array elements, array element 5 and array element-5 in fig. 4:
computing an array phase response estimate after disambiguation-5. ltoreq. m.ltoreq.5; further obtaining the array amplitude-phase response diagonal matrix after the elimination of the ambiguityi+1Estimation of (2):
step S510: and judging whether the iterative algorithm converges.
Let the feature vector matrixComputing
If Pi-1-PiIf rho is greater than a preset positive minimum value, the iteration counter i is i +1, and the step S503 is skipped to for iterative operation; if P isi-1-PiRho is less than or equal to, the iterative operation is ended, and the current estimation is obtained I.e. as an iteratorAs a result, step S511 is performed.
Step S511: and judging the type of the incident signal. After obtaining the iterative calculation result, further judging whether the incident signal is a far-field incident source or a near-field incident source. By setting a positive minimum value p if the estimated value of the second dimension electron angle of the current signal source kThe kth signal source is a far-field signal source; otherwise, the kth signal source is a near field signal source.
Step S512: and outputting a positioning result. And according to the signal estimation value obtained in the previous step, estimating the direction of arrival and the incident distance parameter of the incident signal. Specifically, if the kth signal source is a near-field incident source, its arrival direction isIncident distance ofIf the k-th signal source is a far-field incident source, its arrival direction is
The mixed signal source positioning method provided by the embodiment can effectively estimate the type and the positioning parameter value of each incident signal source through an array model consisting of a small number of array elements, and the calculated amount is small; and the two correction array elements are used for correcting the amplitude phase response error of the array, so that the accuracy of a positioning result can be further improved.
Corresponding to the mixed signal source positioning methods provided by the two embodiments, the embodiment of the invention further provides a mixed signal source positioning system.
EXAMPLE III
Referring to fig. 6, it is a schematic structural diagram of an embodiment of the hybrid signal source positioning system provided in the present invention.
The mixed signal source positioning system provided by the embodiment comprises:
the mixed signal source parameter estimation module 100 is configured to construct a fourth-order cumulant matrix according to the received data of the uniform linear array model, estimate the two-dimensional electron angles of the mixed signal source of the array model one by one based on the fourth-order cumulant matrix, obtain a first-dimensional electron angle ω and a second-dimensional electron angle, and obtain a first-dimensional electron angle ω and a second-dimensional electron angle
An array amplitude-phase response estimation module 200 for estimating the first dimension electron angle and the second dimension electron angle according to the first dimension electron angleCarrying out characteristic decomposition on the covariance matrix R of the received data of the array model, and estimating the amplitude-phase response of the array model, wherein the amplitude-phase response comprises an amplitude response g and a phase response β;
the array fuzzy phase elimination module 300 is configured to eliminate a fuzzy phase in the amplitude-phase response by using two correction array elements, and estimate an amplitude-phase response diagonal matrix;
the mixed signal source parameter estimation module 100 is further configured to correct the received data of the uniform linear array by using the amplitude-phase response matrix, and re-estimate the two-dimensional electronic angle by using the corrected data;
an iteration convergence judging module 400, which sequentially performs iteration, and judges whether the iteration is stopped according to an iteration convergence condition; if the iteration is converged, outputting an array amplitude-phase response diagonal matrix and a convergence value of a two-dimensional electronic angle of the mixed signal source; and otherwise, sending the re-estimated two-dimensional electronic angle to the array amplitude-phase response estimation module for iterative operation.
And a positioning result output module 500, configured to determine the type of the incident signal source in the mixed signal source by using the convergence value of the second-dimensional electronic angle of the final incident signal source, and output a positioning result of the incident signal source according to the type of the incident signal source and the convergence value of the two-dimensional electronic angle of the final incident signal source.
Preferably, in the mixed signal source positioning system, the mixed signal source parameter estimation module 100 includes:
a subspace estimation module 101, configured to calculate a covariance matrix of the entire array according to the received data of the uniform linear array model; performing eigenvalue decomposition on the covariance matrix to obtain corresponding signal subspace estimation and noise subspace estimation;
the array received data correction module 102 is used for correcting the received data of the whole array according to the array amplitude-phase response diagonal matrix; in a specific implementation, during the iterative operation, the array received data correction module 102 is further configured to receive feedback data from the iterative convergence determination module 400, so as to re-estimate the two-dimensional electronic angle.
A fourth-order cumulant matrix constructing module 103, configured to construct a special fourth-order cumulant matrix according to the received data corrected by the uniform linear array model, so that the fourth-order cumulant matrix only includes the first-dimensional electron angle; and carrying out eigenvalue decomposition on the fourth-order cumulant matrix to obtain corresponding fourth-order cumulant signal subspace estimation;
the first-dimension electronic angle calculation module 104 is used for respectively obtaining first-dimension electronic angles corresponding to the multiple incident sources by utilizing the fourth-order cumulant signal subspace estimation and applying an ESPRIT algorithm;
the second-dimension electronic angle calculation module 105 is further configured to construct MUSIC spectra corresponding to the first-dimension electronic angles of the multiple incident sources one to one according to the noise subspace estimation and the estimated first-dimension electronic angles of the multiple incident sources; and performing one-dimensional spectral peak search on the MUSIC spectrum to obtain second-dimensional electronic angles in one-to-one correspondence with the first-dimensional electronic angles.
Further, the array ambiguity phase elimination module 300 includes:
an ambiguity error calculation module 301, configured to select two correction array elements that have undergone phase correction in the uniform linear array model, and calculate an ambiguity error of the first-dimension electronic angle and an ambiguity error of the second-dimension electronic angle respectively;
a fuzzy phase estimation module 302, configured to estimate a fuzzy phase of a phase response of the array model according to the ambiguity error of the first-dimension electronic angle and the ambiguity error of the second-dimension electronic angle;
and the amplitude-phase response updating module 303 is configured to estimate a unique amplitude-phase response of each array element by eliminating the fuzzy phase of the phase response of each array element of the array model, and obtain an amplitude-phase response diagonal matrix after eliminating the fuzzy phase.
Preferably, the positioning result output module 500 includes:
the signal source type determining module 501 is configured to determine that a current incident signal source is a far-field signal source when a convergence estimation value of a second-dimension electron angle of a certain incident signal source in the uniform linear array model is smaller than a preset value; otherwise, the current incident signal source is determined to be the near field signal source.
Further, the positioning result output module 500 further includes:
a positioning result calculation module 502, configured to:
when the kth signal source is a near-field incident source, the output wave direction isIncident distance ofAs a result of the positioning of the current incident signal source;
when the k signal source is a far-field incident source, the wave arrival direction of the k signal source is outputAs a result of the positioning of the current incident signal source;
wherein,a convergence estimate for the first dimension electron angle for the kth signal source;a convergence estimate for a second dimension electron angle for a kth signal source; k is more than or equal to 1 and less than or equal to K, K is the number of incident sources, d is the array element interval, and lambda is the incident signal wavelength.
The working principle of each functional module of the hybrid signal source positioning system provided in the embodiment of fig. 6 is the same as the working principle of each step of the hybrid signal source positioning method provided in the embodiment of fig. 3, and is not described herein again.
The mixed signal source positioning technical scheme provided by the embodiment of the invention is suitable for uniform linear arrays, and the parameter dimension is reduced by constructing a special fourth-order cumulant matrix, so that the calculation complexity of the method is effectively reduced, the positioning operation time is shortened, a near-field and far-field mixed signal source can be positioned at the same time, the incoming wave direction is estimated for a far-field signal source, the incoming wave direction and the incident distance are estimated for a near-field signal source, the amplitude phase response correction of the whole array can be further realized by utilizing two correction array elements, and the signal source positioning problem under the condition that the incident distance of a signal source is uncertain and the array amplitude phase response has errors is solved. The technical scheme provided by the invention has the advantages of moderate calculated amount, short positioning time, no need of parameter matching, and improvement of positioning performance and application range.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

Claims (10)

1. A method for locating a hybrid signal source, comprising:
s1: constructing a fourth-order cumulant matrix according to the received data of the uniform linear array model, and respectively estimating two-dimensional electronic angles of the mixed signal source of the array model one by one on the basis of the fourth-order cumulant matrix to obtain a first-dimensional electronic angle and a second-dimensional electronic angle;
s2: according to the first dimension electron angle and the second dimension electron angle, carrying out characteristic decomposition on a covariance matrix of received data of the array model, and estimating the amplitude-phase response of the array model; the amplitude-phase response comprises an amplitude response and a phase response;
s3: eliminating fuzzy phases in the amplitude-phase response estimation value by utilizing a plurality of correction array elements, and estimating an amplitude-phase response diagonal matrix;
s4: correcting the received data of the uniform linear array by using the amplitude-phase response matrix, reconstructing the fourth-order cumulant matrix, and re-estimating the two-dimensional electronic angle of the mixed signal source based on the fourth-order cumulant matrix;
s5: judging whether the iterative operation is converged; if yes, outputting the array amplitude-phase response diagonal matrix and the convergence value of the two-dimensional electronic angle of the mixed signal source, and executing the step S6; if not, returning to execute the step S2;
s6: and judging the type of an incident signal source in the mixed signal source by using the second-dimension electronic angle convergence value of the mixed signal source, and outputting the positioning result of the incident signal source.
2. The hybrid signal source localization method of claim 1, wherein the steps S1 and S4 respectively comprise:
calculating a covariance matrix of the whole array according to the received data of the uniform linear array model; performing eigenvalue decomposition on the covariance matrix to obtain corresponding signal subspace estimation and noise subspace estimation;
correcting the received data of the whole array according to the array amplitude-phase response diagonal matrix;
constructing a fourth-order cumulant matrix according to the initialized or corrected received data of the uniform linear array model: array element serial numbers in the fourth-order cumulant matrix are symmetrical, so that the matrix only comprises a first-dimension electron angle;
performing eigenvalue decomposition on the fourth-order cumulant matrix to obtain corresponding fourth-order cumulant signal subspace estimation;
respectively obtaining first-dimension electronic angles corresponding to a plurality of incident sources by utilizing the fourth-order cumulant signal subspace estimation and applying an ESPRIT algorithm;
constructing MUSIC spectrums which are in one-to-one correspondence with the first-dimension electron angles of the multiple incident sources according to the noise subspace estimation and the estimated first-dimension electron angles of the multiple incident sources; and performing one-dimensional spectral peak search on the MUSIC spectrum to obtain second-dimensional electronic angles in one-to-one correspondence with the first-dimensional electronic angles.
3. The hybrid signal source localization method according to claim 1, wherein said step S3 comprises:
selecting two correction array elements subjected to phase correction in the uniform linear array model, and respectively calculating the ambiguity error of the first-dimension electronic angle and the ambiguity error of the second-dimension electronic angle;
estimating the fuzzy phase of the phase response of the array model according to the fuzzy error of the first-dimension electronic angle and the fuzzy error of the second-dimension electronic angle;
and estimating the unique amplitude-phase response of each array element by eliminating the fuzzy phase of the phase response of each array element of the array model, and obtaining the amplitude-phase response diagonal matrix after eliminating the fuzzy phase.
4. The hybrid signal source localization method according to claim 1, wherein said step S6 comprises:
when the convergence estimation value of a second-dimension electron angle of a certain incident signal source in the uniform linear array model is smaller than a preset value, judging that the current incident signal source is a far-field signal source; otherwise, the current incident signal source is determined to be the near field signal source.
5. The hybrid signal source localization method according to claim 1, wherein said step S6 comprises:
when the kth signal source is a near-field incident source, the output wave direction isIncident distance ofAs a result of the positioning of the current incident signal source;
when the k signal source is a far-field incident source, the wave arrival direction of the k signal source is outputAs a result of the positioning of the current incident signal source;
wherein,a convergence estimate for the first dimension electron angle for the kth signal source;a convergence estimate for a second dimension electron angle for a kth signal source; k is more than or equal to 1 and less than or equal to K, K is the number of incident sources, d is the array element interval, and lambda is the incident signal wavelength.
6. A hybrid signal source localization system, comprising:
the mixed signal source parameter estimation module is used for constructing a fourth-order cumulant matrix according to the received data of the uniform linear array model, and respectively estimating the two-dimensional electronic angles of the mixed signal source of the array model one by one on the basis of the fourth-order cumulant matrix to obtain a first-dimensional electronic angle and a second-dimensional electronic angle;
the array amplitude-phase response estimation module is used for performing characteristic decomposition on a covariance matrix of received data of the array model according to the first-dimension electronic angle and the second-dimension electronic angle to estimate amplitude-phase response of the array model; the amplitude-phase response comprises an amplitude response and a phase response;
the array fuzzy phase elimination module is used for eliminating fuzzy phases in the amplitude-phase response by utilizing a plurality of correction array elements and estimating an amplitude-phase response diagonal matrix;
the mixed signal source parameter estimation module is further configured to correct the received data of the uniform linear array by using the amplitude-phase response matrix, reconstruct the fourth-order cumulant matrix, and re-estimate the two-dimensional electronic angle of the mixed signal source based on the fourth-order cumulant matrix;
the iteration convergence judging module is used for judging whether the iteration operations sequentially executed by the three modules are converged or not according to the iteration convergence condition; if the iteration is converged, outputting an array amplitude-phase response diagonal matrix and a convergence value of a two-dimensional electronic angle of the mixed signal source; otherwise, sending the re-estimated two-dimensional electronic angle to the array amplitude-phase response estimation module for iterative operation;
and the positioning result output module is used for judging the type of the incident signal source in the mixed signal source by utilizing the convergence value of the second-dimensional electronic angle of the final incident signal source and outputting the positioning result of the incident signal source according to the type of the incident signal source and the convergence value of the two-dimensional electronic angle of the final incident signal source.
7. The hybrid-signal-source localization system of claim 6, wherein the hybrid-signal-source parameter estimation module comprises:
the subspace estimation module is used for calculating a covariance matrix of the whole array according to the received data of the uniform linear array model; performing eigenvalue decomposition on the covariance matrix to obtain corresponding signal subspace estimation and noise subspace estimation;
the array received data correction module is used for correcting the received data of the whole array according to the array amplitude-phase response diagonal matrix;
a fourth order cumulant matrix construction module for constructing a fourth order cumulant matrix according to the initialized or corrected received data of the uniform linear array model: array element serial numbers in the fourth-order cumulant matrix are symmetrical, so that the matrix only comprises a first-dimension electron angle; and carrying out eigenvalue decomposition on the fourth-order cumulant matrix to obtain corresponding fourth-order cumulant signal subspace estimation;
the first-dimension electronic angle calculation module is used for utilizing the fourth-order cumulant signal subspace estimation and applying an ESPRIT algorithm to respectively obtain first-dimension electronic angles corresponding to a plurality of incident sources;
the second-dimension electronic angle calculation module is used for constructing MUSIC spectrums which are in one-to-one correspondence with the first-dimension electronic angles of the plurality of incident sources according to the noise subspace estimation and the estimated first-dimension electronic angles of the plurality of incident sources; and performing one-dimensional spectral peak search on the MUSIC spectrum to obtain second-dimensional electronic angles in one-to-one correspondence with the first-dimensional electronic angles.
8. The hybrid signal source localization system of claim 6, wherein said array ambiguity phase elimination module comprises:
the ambiguity error calculation module is used for selecting two correction array elements which are subjected to phase correction in the uniform linear array model, and calculating the ambiguity error of the first-dimension electronic angle and the ambiguity error of the second-dimension electronic angle respectively;
the fuzzy phase estimation module is used for estimating a fuzzy phase of the phase response of the array model according to the fuzzy error of the first-dimension electronic angle and the fuzzy error of the second-dimension electronic angle;
and the amplitude-phase response updating module is used for estimating the unique amplitude-phase response of each array element by eliminating the fuzzy phase of the phase response of each array element of the array model, and obtaining the amplitude-phase response diagonal matrix after the fuzzy phase is eliminated.
9. The hybrid signal source localization system of claim 6, wherein said localization result output module comprises:
the signal source type judging module is used for judging that the current incident signal source is a far-field signal source when the convergence estimation value of the second-dimension electron angle of a certain incident signal source in the uniform linear array model is smaller than a preset value; otherwise, the current incident signal source is determined to be the near field signal source.
10. The hybrid signal source localization system of claim 6, wherein said localization result output module comprises:
a positioning result calculation module for:
when the kth signal source is a near-field incident source, the output wave direction isIncident distance ofAs a result of the positioning of the current incident signal source;
when the k signal source is a far-field incident source, the wave arrival direction of the k signal source is outputAs a result of the positioning of the current incident signal source;
wherein,a convergence estimate for the first dimension electron angle for the kth signal source;a convergence estimate for a second dimension electron angle for a kth signal source; k is more than or equal to 1 and less than or equal to K, K is the number of incident sources, d is the array element interval, and lambda is the incident signal wavelength.
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