CN110286350A - A kind of perfect match method and device of L-type Sparse Array DOA estimation - Google Patents
A kind of perfect match method and device of L-type Sparse Array DOA estimation Download PDFInfo
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Abstract
The present invention proposes a kind of perfect match method of L-type Sparse Array DOA estimation, comprising: finds out the autocorrelation matrix and cross-correlation matrix of the first submatrix, the second submatrix respectively；Calculate that the first submatrix virtually optimizes the autocorrelation matrix of battle array and the second submatrix virtually optimizes the autocorrelation matrix of battle array；The estimated value of pitch angle is calculated according to the autocorrelation matrix that first submatrix virtually optimizes battle array；The estimated value of the autocorrelation matrix and the pitch angle that virtually optimize battle array according to second submatrix obtains azimuthal blur estimation value；Estimate the power vector of signal, and utilize the vector ambiguity solution, realizes the perfect match at arrival direction estimation and azimuth and pitch angle.The present invention is estimated using the Virtual array of Sparse Array, and compared to traditional algorithm for estimating based on L-type even linear array (ULA), freedom degree has obtained significant increase, and significantly improves the estimation performance of DOA.
Description
Technical Field
The invention belongs to the technical field of wireless communication and radar signal processing, and particularly relates to an accurate pairing method and device for L-shaped sparse array DOA estimation.
Background
Direction of arrival (DOA) estimation is the direction of incidence that an antenna array distinguishes spatial sources in a particular way by receiving the signal. The technology is firstly applied to the military field, and mainly aims at positioning enemy targets and implementing detection and accurate striking. In recent years, the method has been widely used in many fields such as radar, sonar, navigation, earthquake, biomedicine, and radio astronomy.
Among them, two-dimensional DOA estimation plays a crucial role in these fields, because only one-dimensional DOA information is far from sufficient in practical applications, such as: two-dimensional DOA information of an incident signal azimuth angle and a pitch angle is required to be known in the process of data transmission such as mobile communication. The existing two-dimensional DOA estimation method is mostly based on a simplified area array with array element spacing equal to half wavelength, such as an L-shaped array, a double parallel linear array, a cross-shaped array and the like. Among them, L-shaped arrays have gained wide attention and application due to their simple structure, lower cramer limit, and better estimation performance.
The L-shaped array is typically divided into two linear sub-arrays, each located on a respective axis, and estimated values of azimuth and elevation are obtained by one-dimensional DOA estimation of each of the two sub-arrays. This approach avoids two-dimensional spectral peak searching, but creates the problem that the azimuth and pitch angles cannot be correctly paired. For L-shaped arrays, many expert scholars have studied pairing methods for two-dimensional DOA estimation.
On the other hand, aiming at the defects of low degree of freedom, low estimation precision and low resolution of the traditional uniform linear array, related researches on a sparse array are carried out, wherein the researched sparse array mainly refers to a Nested array in [ P.Pal and P.P.Vaidyanathan, New array: A novel approach to array Processing with the Nested array of free, IEEE Trans.Signal Process, 58(8 (2010), 4167. 4181 ], and an interactive array in [ P.Pal, P.P.Vaidyanathan.Copric sampling and the SIC Algorithm. DSP/SPEkshop 2011, Sedona,2011,289 ] and C.Niu et al also combine the sparse array with the L-type array to provide a Nested P.P.526.Y.J.J.N.S. J. N.S. Ser. No. 23 (IEEE-D.J.S. 4. blend-J.S. 4. sub.S. K. K. Because the array structure of the L-shaped sparse array is greatly different from that of the traditional L-shaped array, the related pairing algorithm of the original L-shaped array is not applicable to the L-shaped sparse array. However, at present, the L-type sparse array has few relevant researches, and the research on the L-type sparse array pairing method is less, so that the L-type sparse array pairing method needs to be researched to fully exert the advantages of high degree of freedom, high resolution and the like of the sparse array, so that the research has good development prospect and practical value, and is also a hotspot and difficulty point of the current research.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention aims to provide an accurate pairing method and apparatus for L-type sparse array DOA estimation, which realizes accurate pairing of two-dimensional angles, reduces the system cost of DOA estimation, and significantly improves the estimation performance, the estimation accuracy and the resolution.
In order to achieve the above objects and other related objects, the present invention provides an accurate pairing method for DOA estimation of an L-type sparse array, where the L-type sparse array includes a first subarray having N1 array elements and a second subarray having N2 array elements, the first subarray is located on a z-axis, the second subarray is located on an x-axis, the L-type sparse array receives K uncorrelated far-field narrowband signals, angles between an incident direction of the signal and the z-axis and between the incident direction and the x-axis are phi and β, an angle between a projection of the incident signal in an xoy plane and the x-axis is theta, and data vectors received by the first subarray and the second subarray are x and x1(t) and x2(t); the pairing method comprises the following steps:
respectively solving an autocorrelation matrix and a cross-correlation matrix of the first subarray physical array and the second subarray physical array;
calculating an autocorrelation matrix of the first sub-array virtual optimization array and an autocorrelation matrix of the second sub-array virtual optimization array;
calculating an estimated value of a pitch angle according to the autocorrelation matrix of the first sub-array virtual optimization array;
obtaining a fuzzy estimation value of an azimuth angle according to the autocorrelation matrix of the second sub-array virtual optimization array and the estimation value of the pitch angle;
and estimating the power vector of the signal, and performing ambiguity resolution by using the vector to realize two-dimensional DOA estimation and accurate pairing of the azimuth angle and the pitch angle.
Optionally, the finding the autocorrelation matrix and the cross-correlation matrix of the first sub-array and the second sub-array physical array respectively includes:
calculating the first subarray received data x1(t) at N snapshotsAutocorrelation matrix
Calculating the second subarray received data x2(t) autocorrelation matrix at N snapshots
Calculating the received data x of the first subarray and the second subarray1(t) and x2(t) cross-correlation matrix at N snapshots
Optionally, the calculating the autocorrelation matrix of the first virtual optimized sub-array and the autocorrelation matrix of the second virtual optimized sub-array includes:
to self-correlate the matrixVectorization to obtain a vector z1；
For vector z1Removing redundancy to obtain observation vector
Recording observation vectorsThe middle element is in the vector z1Position vector ξ;
based on observation vectorsConstructing a Hermitian Toeplitz matrixThenVirtually optimizing an autocorrelation matrix of the array for the first sub-array;
to self-correlate the matrixVectorization to obtain a vector z2；
For vector z2Removing redundancy to obtain observation vector
Based on observation vectorsConstructing a Hermitian Toeplitz matrixThenVirtually optimizing the autocorrelation matrix of the array for the second sub-array.
Optionally, the estimation value of the pitch angle is calculated according to an autocorrelation matrix of the first sub-array virtual optimization array;
virtually optimizing the autocorrelation matrix of the first sub-arrayPerforming characteristic decomposition to obtain a signal subspace Us；
Estimation value of pitch angle obtained by utilizing ESPRIT algorithm
Optionally, a fuzzy estimation value of an azimuth angle corresponding to the autocorrelation matrix of the second sub-array virtual optimization array and the estimation value of the pitch angle is obtained;
virtually optimizing the autocorrelation matrix of the array according to the second sub-arrayAnd an estimate of said pitch angleIs given oneObtaining fuzzy estimation values of corresponding k azimuth angles by adopting an ESPRIT algorithm
Optionally, the estimating a power vector of the signal and performing two-dimensional DOA estimation and accurate pairing of an azimuth angle and a pitch angle by using the vector deblurring include:
estimating a direction matrix of a first sub-array
Using estimated value of pitch angle phikEstimating a direction matrix of a first sub-array
Estimating a de-redundancy direction matrix of a first sub-array virtual array
A direction matrix according to the first sub-matrixAnd the position vector ξ is used to obtain the de-redundancy direction matrix of the first sub-matrix virtual array
According to the redundancy removing direction matrix of the first sub-array virtual arrayAnd the observation vectorRemoving redundant direction matrix of first sub-array virtual arrayAnd observation vectorEstimating the power vector of the signal from the noise-disturbed intermediate position element
Estimate based on the pitch angleAnd a fuzzy estimate of said azimuth angleObtaining a fuzzy estimate of the direction matrix of the second sub-array
According to the estimated value of the pitch angleA direction matrix of the first sub-arrayPower vector of the signalA fuzzy estimation of the direction matrix of the second sub-arrayAnd the cross correlation matrixCalculating a correlation metric, determining the value of i by maximizing the correlation metric, and obtaining the correlation metricAre paired
In order to achieve the above objects and other related objects, the present invention further provides an apparatus for accurate matching of DOA estimation for L-type sparse array, where the L-type sparse array includes a first subarray having N1 array elements and a second subarray having N2 array elements, the first subarray is located on the z-axis, the second subarray is located on the x-axis, the L-type sparse array receives K uncorrelated far-field narrowband signals, the incident directions of the signals and the included angles of the z-axis and the x-axis are phi and β, the projection of the incident signals in the xoy plane and the x-axis form an angle theta, and the received data vectors of the first subarray and the second subarray are x and x respectively1(t) and x2(t); the pairing apparatus includes:
the autocorrelation and cross-correlation module is used for respectively solving an autocorrelation matrix and a cross-correlation matrix of the first subarray physical array and the second subarray physical array;
the autocorrelation module is used for calculating an autocorrelation matrix of the first sub-array virtual optimization array and an autocorrelation matrix of the second sub-array virtual optimization array;
the first estimation module is used for calculating an estimation value of a pitch angle according to an autocorrelation matrix of the first sub-array virtual optimization array;
the second estimation module is used for solving a fuzzy estimation value of an azimuth angle according to the autocorrelation matrix of the second sub-array virtual optimization array and the estimation value of the pitch angle;
and the pairing module is used for estimating the power vector of the signal and performing ambiguity resolution by using the vector to realize two-dimensional DOA estimation and accurate pairing of the azimuth angle and the pitch angle.
Optionally, the auto-correlation and cross-correlation module comprises:
a first autocorrelation unit for calculating the first subarray received data x1(t) autocorrelation matrix at N snapshots
A second autocorrelation unit for calculating second subarray received data x2(t) autocorrelation matrix at N snapshots
A cross-correlation unit for calculating the received data x of the first and second sub-arrays1(t) and x2(t) cross-correlation matrix at N snapshots
Optionally, the autocorrelation module includes:
a first vector quantization module for quantizing the autocorrelation matrixVectorized resulting vectorQuantity z1；
A first redundancy removing module for removing the vector z1Removing redundancy to obtain observation vector
A first recording module for recording the observation vectorThe middle element is in the vector z1Position vector ξ;
a first construction module for constructing a vector based on the observation vectorsConstructing a Hermitian Toeplitz matrixThenVirtually optimizing an autocorrelation matrix of the array for the first sub-array;
a second quantization module for quantizing the autocorrelation matrixVectorization to obtain a vector z2；
A second redundancy elimination module for the vector z2Removing redundancy to obtain observation vector
A second construction module for constructing a second vector based on the observation vectorConstructing a Hermitian Toeplitz matrixThenVirtually optimizing the autocorrelation matrix of the array for the second sub-array.
Optionally, the pairing module comprises:
a first estimating unit for estimating a direction matrix of the first sub-array
A second estimating unit for using the estimated value phi of the pitch anglekEstimating a direction matrix of a first sub-array
A third estimation unit for estimating a de-redundancy direction matrix of the first sub-array virtual array
A first direction matrix calculation unit for calculating a direction matrix according to the first sub-matrixAnd said position vector ξ is used to obtain the de-redundancy direction matrix of the first sub-array virtual array
A power vector estimation unit for removing redundant direction matrix according to the first sub-array virtual arrayAnd the observation vectorRemoving redundant direction matrix of first sub-array virtual arrayAnd observation vectorEstimating the power vector of the signal from the noise-disturbed intermediate position element
A fuzzy estimation unit based on the estimated value of the pitch angleAnd a fuzzy estimate of said azimuth angleObtaining a fuzzy estimate of the direction matrix of the second sub-arrayi＝1，...，K；
A pairing unit for estimating the pitch angle based on the estimated valueA direction matrix of the first sub-arrayPower vector of the signalA fuzzy estimation of the direction matrix of the second sub-arrayAnd the cross correlation matrixCalculating a correlation metric, determining the value of i by maximizing the correlation metric, and obtaining the correlation metricAre pairedk＝1，...，K。
As described above, the method and the device for accurate pairing of L-type sparse array DOA estimation of the present invention have the following beneficial effects:
compared with the traditional estimation algorithm based on an L-shaped Uniform Linear Array (ULA), the method disclosed by the invention has the advantages that the degree of freedom is greatly improved, and the DOA estimation performance is obviously improved; not only can two-dimensional DOA information be estimated, but also the power of the signal can be estimated; the accurate pairing of the L-shaped sparse array DOA estimation is realized by utilizing the power vector of the signal, and the pairing success rate is high.
Drawings
To further illustrate the description of the present invention, the following detailed description of the embodiments of the present invention is provided with reference to the accompanying drawings. It is appreciated that these drawings are merely exemplary and are not to be considered limiting of the scope of the invention.
FIG. 1 is a schematic diagram of array setup in an accurate matching method for DOA estimation of an L-type sparse array according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating a relationship between root mean square error of azimuth angle and pitch angle and SNR change in an L-shaped sparse array DOA estimation precise pairing method according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating a relationship between root mean square error of azimuth angle and pitch angle and variation of snapshot number in an accurate L-shaped sparse array DOA estimation pairing method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a relationship between detection probabilities of an azimuth angle and a pitch angle according to an SNR change in an L-shaped sparse array DOA estimation precise pairing method according to an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating a relationship between detection probabilities of an azimuth angle and a pitch angle according to a snapshot number in an L-shaped sparse array DOA estimation precise pairing method according to an embodiment of the present invention;
fig. 6 is a flowchart of an accurate pairing method for L-shaped sparse array DOA estimation according to an embodiment of the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
As shown in fig. 6, a method for accurately pairing L-type sparse array DOA estimation includes the following steps:
step 1: an antenna array is provided.
The L-shaped sparse array is adopted and consists of two identical sparse non-uniform sub-arrays, the sub-arrays can be nested arrays or co-prime arrays, if the sub-arrays are nested arrays, the L-shaped sparse array is the L-shaped nested array, and if the sub-arrays are co-prime arrays, the L-shaped sparse array is the L-shaped co-prime array. For ease of description, an L-shaped nested array is used herein for discussion. If the first subarray is not located on the z-axis, the second subarray is located on the x-axis. Obviously, the two sparse sub-arrays are perpendicular to each other. Similarly, the first sub-array may be located on the x-axis, and the second sub-array may be located on the z-axis. As shown in fig. 1, each subarray has N ═ N1+N2Array element, N1Array element number, N, for each subarray dense ULA2And thinning the array element number of the ULA for each sub-array. λ represents the signal wavelength, and the first and second sub-arrays share an array element at the origin.
Not using dz,iIndicating the position of the ith element of the first sub-array, likewise with dx,iAnd indicating the array element position of the ith array element of the second subarray, wherein i is 1, 2.
Suppose there are K uncorrelated far-field narrow-band signals sk(t) from the direction (theta)k,φk) Incident on the array, where K is 1,2, …, K, θkAnd phikRespectively representing the azimuth and elevation angles of the K-th signal. The noise is independent and equally distributed additive white Gaussian noise and is independent of the signal. Then the received signal vectors of two sub-arrays in the L-shaped nested array can be respectively expressed as:
wherein A is1＝[a1(φ1),a1(φ2),…,a1(φK)]An array flow pattern matrix representing a first sub-array, A2＝[a2(θ1,φ1),a2(θ2,φ2),…,a2(θK,φK)]An array flow pattern matrix representing a second sub-array,representing the steering vector of the first sub-array corresponding to the kth signal,indicating the steering vector, phi, of the second sub-array corresponding to the kth signalkRepresenting the angle between the direction of signal incidence and the z-axis, thetakRepresenting the angle of the projection of the signal in the xoy plane with the x-axis. s (t) ═ s1(t),s2(t),...,sK(t)]TThe vector of signals is represented by a vector of signals,andnoise vectors of the first and second subarrays, respectively, whose elements are independently identically distributed and both obey a complex Gaussian distributionINRepresenting an identity matrix.
Step 2: respectively solving the autocorrelation matrix and the cross-correlation matrix of the first sub-array and the second sub-array:
using x1(t) solving the autocorrelation matrix of the first sub-array as:
wherein,is an autocorrelation matrix of the signal, diagonal elementsDenotes the power of the kth signal, K being 1, …, K. But R is1Is an ideal covariance matrix that is not available, and is actually obtained by T snapshot estimates:
wherein T is the number of fast beats. Similarly, the autocorrelation matrix of the second sub-array may be estimated as:
the cross-correlation matrix of the first and second sub-arrays is:
and step 3: obtaining an autocorrelation matrix and a position vector of the first sub-array virtual optimization array;
vectorization matrixThe vector can be obtained:
wherein, vec (-) is a vectorization operator,is a1(φk) The conjugate of (a) to (b),is the product of Kronecker. ThenThe method can be regarded as an array flow pattern matrix corresponding to the first sub-array virtual optimization array, and p can be regarded as a single snapshot signal vector incident to the virtual optimization array. z is a radical of1The element in (1) is the received data of the first sub-array virtual optimization array, but redundancy exists, therefore, the z-pair is needed1To perform redundancy removing operation to obtain
Wherein,is the observation vector of the first sub-array, gamma-N2(N1+1), vectorExcept that the gamma-th element is 1, the remaining elements are 0,and virtually optimizing the redundancy removing direction matrix of the array for the first sub-array. At the same time need to recordThe middle element is in the vector z1Is recorded as a position vector ξ, then there isIs formed in whichTo representThe mth element of (1), m.
Next, based on the vectorConstructing a Hermitian Toeplitz matrixThe specific structure is as follows:
is constructed byNamely, the autocorrelation matrix of the received signal of the first sub-array virtual optimization array is equivalent to the autocorrelation matrix of the received signal of the Uniform Line Array (ULA) in which the array element position on the z-axis is located at Md (M ═ 1,2, …, γ).
And 4, step 4: calculating an estimated value of the pitch angle according to the autocorrelation matrix of the first sub-array virtual optimization array, and specifically adopting a one-dimensional DOA estimation algorithm to estimate the pitch angle:
the autocorrelation matrix corresponding to the first sub-array in the step 3 is virtualized to be the optimized arrayPerforming characteristic decomposition of
Wherein, ΛsIs a K x K dimensional diagonal matrix comprisingK large eigenvalues of (a); u shapesIs a gamma xK dimensional signal subspace consisting ofExpanding the eigenvectors corresponding to the K large eigenvalues; lambdanIs a (gamma-K) x (gamma-K) dimensional diagonal matrix comprisinggamma-K small eigenvalues of (d); u shapenIs a gamma (gamma-K) -dimensional noise subspace consisting ofThe characteristic vector corresponding to the gamma-K small characteristic values is formed.
Then, based on the signal subspace UsThe pitch angle is estimated by a one-dimensional DOA estimation method, and an ESPRIT algorithm is not adopted for estimation.
Will signal subspace UsThe first gamma-1 line of (1) is marked as Us1Will U issThe last gamma-1 line of (1) is marked as Us2Obtaining the phase matrix of the first sub-matrixWherein (·)+Is the operator of the pseudo-inverse of the matrix. Then the psi is subjected to characteristic decomposition to obtain PVP-1Wherein V is diag (V)1,v2,…,vK) P is formed by a feature vectorTo form a matrix. Finally, the pitch angle phi can be obtainedkEstimated value of (a):
where angle (·) is the phase operator, d is the unit spacing of the array, and λ is the wavelength of the incident signal.
And 5: according to the autocorrelation matrix of the second sub-array virtual optimization array and the fuzzy estimation value of the azimuth angle corresponding to the estimation value of the pitch angle;
similar to step 3, the autocorrelation matrix obtained based on step 2Will be provided withVectorization and redundancy removal to obtain observation vectorBased onConstructing a Hermitian Toeplitz matrixThenNamely the autocorrelation matrix corresponding to the second sub-array virtual optimization array.
Then, in a synchronization step 4, the autocorrelation matrix corresponding to the second sub-matrix is virtually optimizedPerforming characteristic decomposition of
And then, obtaining all fuzzy estimation values of the azimuth angle by adopting a one-dimensional DOA estimation method, and estimating by adopting an ESPRIT algorithm.
Will signal subspace U'sLine γ -1 is denoted as U's1Prepared from U'sLine γ -1 after (U)'s2Obtaining the phase matrix of the first sub-matrixThen carrying out characteristic decomposition on psi 'to obtain psi'-1Wherein V' ═ diag (τ)1,τ2,…,τK). Finally can obtainFuzzy estimate of corresponding k azimuth angles:
step 6: estimating the power vector of the signal, and solving ambiguity by using the vector to realize two-dimensional DOA estimation and accurate pairing of an azimuth angle and a pitch angle:
(6a) estimating a direction matrix of the first sub-array:
using the estimated value of pitch angle in step 4Estimating a direction matrix of the first sub-array as follows
Wherein,is the estimated steering vector of the first sub-array.
(6b) Estimating a redundancy removing direction matrix of the first sub-array virtual array:
combining the direction matrix of the first sub-array in step (6a)Obtaining a first sub-array virtual array direction matrix
Wherein ⊙ represents the calculation of the Khatri-rao product and the vector z1Similarly, vector z1With redundant elements, likewise, direction matricesThere are also redundant row vectors, and then the first sub-array virtual array direction matrix is aligned based on the following constraints according to the position vector ξ of step 3And (3) redundancy removal is carried out:
wherein,is the de-redundancy direction matrix of the first sub-array virtual array, ξ (i) represents the ith element of vector ξ,representation matrixRow i element of (1).
(6c) Estimating the signal power vector:
due to the fact thatAnd vectorExcept the gamma-th element is 1, the other elements are 0, so the first sub-array virtual array in step (6b) removes the redundant direction matrixThe gamma line of (1) and the observation vector of step 3Are all affected by noise and are inaccurate, so need to be removedGet the gamma line element ofRemovingGet the gamma-th element ofThe estimate of the signal power vector is then:
wherein the power vectorIs an estimate of the incident signal power.
(6d) Obtaining a fuzzy estimation value of the second subarray direction matrix:
estimated value based on pitch angle in step 4And fuzzy estimation of azimuth angle in step 5Obtaining a second sub-array direction matrix fuzzy estimation value
Wherein,
(6e) and (3) solving ambiguity by maximizing correlation measurement to realize accurate pairing of two-dimensional angles:
given pitch angle estimateUsing the matrix of step (6a)Power vector of step (6c)Matrix of step (6d)And the cross correlation matrix of step 2The correlation metric is calculated as follows:
wherein ⊙ represents the calculation of Khtri-rao product, | | · | |. luminanceFRepresenting the F-norm of the matrix.
Then the correlation metric η is madeiThe maximum i is the optimal value of i, and the pitch angleThe matched azimuth estimates are:
thus, two-dimensional DOA estimation based on the L-shaped sparse array is completed, and the azimuth angle is realizedAnd a pitch angleThe exact pairing of (a).
For analyzing the algorithm and the document [ J. -F.Gu, P.Wei.Joint SVD of two cross-correlation schemes to an acquisition automatic scheduling in 2-D and interference estimation schemes, IEEE extensions and Wireless processing letters.6(2007)553-556, the present invention is proposed.]JSDD algorithm and document [ C.Niu, Y.Zhang, J.Guo.interleaved double-precision 2-D analysis algorithm L-shaped compared algorithms. IEEE Signal processing letters.23(4) (2016)522-526.]Two sets of simulation experiments are designed for comparison. Among them, the present invention is related to the document [ C.Niu, Y.Zhang, J.Guo.interleaved double-precision 2-D amplification optimization L-shaped processed arrays. IEEE Signal processing letters.23(4) (2016)522-526 ".]All adopt L-shaped nested arrays with array parameters of N1＝N23, document [ J. -F.Gu, P.Wei.Joint SVD of two cross-correlation schemes to achieve automation schemes in 2-D angle estimation schemes IEEE Antennas and WirelessProduction letters.6(2007)553- "556.]The L-type array is adopted, the array parameter is M ═ 6, and obviously, the total number of array elements of the L-type nested array and the L-type array is the same, and there are 11 array elements (the sub-arrays of the two axes share the zero position array element). The number of signals is 2, and the incident directions are (theta)1,φ1) Equal to (55 °,70 °) and (θ)2,φ2) Equal to (60 ° ). Defining the detection probability as: if the deviation between the estimated values of the azimuth angle and the pitch angle and the true value does not exceed the standard value (the experiment is set to be 1.5 degrees), the detection is successful. Otherwise, the detection fails.
The fast beat number of the first group of experiments is 5000, 1000 independent experiments are carried out, the relation of Root Mean Square Error (RMSE) of azimuth angle estimation and pitch angle estimation along with signal-to-noise ratio (SNR) is shown in figure 2, and the relation of detection probability of azimuth angle estimation and pitch angle estimation along with SNR is shown in figure 4.
The signal-to-noise ratio of the other group of experiments is 5dB, 1000 independent experiments are carried out, the relation of Root Mean Square Error (RMSE) of the azimuth angle and the pitch angle along with the change of the snapshot number is shown in figure 3, and the relation of the detection probability of the azimuth angle and the pitch angle along with the change of the snapshot number is shown in figure 5.
As can be seen from the figure, the accurate pairing method based on the L-type sparse array DOA estimation can well improve the two-dimensional DOA estimation performance, reduce the system cost, does not need spectrum search and has low calculation complexity. Meanwhile, the detection probability of the azimuth angle and the pitch angle is high, and the pairing success rate is high.
The embodiment also discloses an accurate pairing device for DOA estimation of the L-type sparse array, the L-type sparse array comprises a first subarray with N1 array elements and a second subarray with N2 array elements, the first subarray is located on a z axis, the second subarray is located on an x axis, the L-type sparse array receives K irrelevant far-field narrow-band signals, included angles between the incident direction of the signals and the z axis and between the incident direction of the signals and the x axis are phi and β respectively, an included angle between the projection of the incident signals in the xoy plane and the x axis is theta, and received data vectors of the first subarray and the second subarray are x and x respectively1(t) and x2(t); the pairing apparatus includes:
the autocorrelation and cross-correlation module is used for respectively solving an autocorrelation matrix and a cross-correlation matrix of the first subarray physical array and the second subarray physical array;
the autocorrelation module is used for calculating an autocorrelation matrix of the first sub-array virtual optimization array and an autocorrelation matrix of the second sub-array virtual optimization array;
the first estimation module is used for calculating an estimation value of a pitch angle according to an autocorrelation matrix of the first sub-array virtual optimization array;
the second estimation module is used for solving a fuzzy estimation value of an azimuth angle according to the autocorrelation matrix of the second sub-array virtual optimization array and the estimation value of the pitch angle;
and the pairing module is used for estimating the power vector of the signal and performing ambiguity resolution by using the vector to realize two-dimensional DOA estimation and accurate pairing of the azimuth angle and the pitch angle.
In some embodiments, the autocorrelation and cross-correlation module comprises:
a first autocorrelation unit for calculating the first subarray received data x1(t) autocorrelation matrix at N snapshots
A second autocorrelation unit for calculating second subarray received data x2(t) autocorrelation matrix at N snapshots
A cross-correlation unit for calculating the received data x of the first and second sub-arrays1(t) and x2(t) cross-correlation matrix at N snapshots
In some embodiments, the autocorrelation module comprises:
a first vector quantization module for quantizing the autocorrelation matrixVectorization to obtain a vector z1；
A first redundancy removing module for removing the vector z1Removing redundancy to obtain observation vector
A first recording module for recording the observation vectorThe middle element is in the vector z1Position vector ξ;
a first construction module for constructing a vector based on the observation vectorsConstructing a Hermitian Toeplitz matrixThenVirtually optimizing an autocorrelation matrix of the array for the first sub-array;
a second quantization module for quantizing the autocorrelation matrixVectorization to obtain a vector z2；
A second redundancy elimination module for the vector z2Removing redundancy to obtain observation vector
A second construction module for constructing a second vector based on the observation vectorConstructing a Hermitian Toeplitz matrixThenVirtually optimizing the autocorrelation matrix of the array for the second sub-array.
In some embodiments, the pairing module comprises:
a first estimating unit for estimating a direction matrix of the first sub-array
A second estimation unit for estimating the pitch angleValue phikEstimating a direction matrix of a first sub-array
A third estimation unit for estimating a de-redundancy direction matrix of the first sub-array virtual array
A first direction matrix calculation unit for calculating a direction matrix according to the first sub-matrixAnd said position vector ξ is used to obtain the de-redundancy direction matrix of the first sub-array virtual array
A power vector estimation unit for removing redundant direction matrix according to the first sub-array virtual arrayAnd the observation vectorRemoving redundant direction matrix of first sub-array virtual arrayAnd observation vectorEstimating the power vector of the signal from the noise-disturbed intermediate position element
A blur estimation unit based onEstimation of pitch angleAnd a fuzzy estimate of said azimuth angleObtaining a fuzzy estimate of the direction matrix of the second sub-array
A pairing unit for estimating the pitch angle based on the estimated valueA direction matrix of the first sub-arrayPower vector of the signalA fuzzy estimation of the direction matrix of the second sub-arrayAnd the cross correlation matrixCalculating a correlation metric, determining the value of i by maximizing the correlation metric, and obtaining the correlation metricAre paired
It should be noted that, because the embodiment of the apparatus portion and the embodiment of the method portion correspond to each other, please refer to the description of the embodiment of the method portion for the content of the embodiment of the apparatus portion, which is not repeated here.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-mentioned division of the functional units and modules is illustrated, and in practical applications, the above-mentioned function distribution may be performed by different functional units and modules according to needs, that is, the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-mentioned functions. Each functional unit and module in the embodiments may be integrated in one processing unit, or each unit may exist alone physically, or two or more units are integrated in one unit, and the integrated unit may be implemented in a form of hardware, or in a form of software functional unit. In addition, specific names of the functional units and modules are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present application. The specific working processes of the units and modules in the system may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the above embodiments, the descriptions of the respective embodiments have respective emphasis, and reference may be made to the related descriptions of other embodiments for parts that are not described or illustrated in a certain embodiment.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
In the embodiments provided in the present invention, it should be understood that the disclosed apparatus/terminal device and method may be implemented in other ways. For example, the above-described embodiments of the apparatus/terminal device are merely illustrative, and for example, the division of the modules or units is only one logical division, and there may be other divisions when actually implemented, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.
Claims (10)
1. An accurate pairing method for DOA estimation of an L-shaped sparse array is characterized in that the L-shaped sparse array comprises a first subarray with N1 array elements and a second subarray with N2 array elements, the first subarray and the second subarray share the array elements at the original points, the first subarray is located on a z axis, the second subarray is located on an x axis, the L-shaped sparse array receives K far-field uncorrelated narrow-band signals, included angles between the incident direction of the signals and the z axis and between the incident direction of the signals and the x axis are phi and β respectively, an included angle between projection of the incident signals in an xoy plane and the x axis is theta, and the first subarray and the second subarray areThe received data vectors of the two sub-arrays are x respectively1(t) and x2(t); the pairing method comprises the following steps:
respectively solving an autocorrelation matrix and a cross-correlation matrix of the first subarray and the second subarray;
calculating an autocorrelation matrix of the first sub-array virtual optimization array and an autocorrelation matrix of the second sub-array virtual optimization array;
calculating an estimated value of a pitch angle according to the autocorrelation matrix of the first sub-array virtual optimization array;
obtaining a fuzzy estimation value of an azimuth angle according to the autocorrelation matrix of the second sub-array virtual optimization array and the estimation value of the pitch angle;
and estimating the power vector of the signal, and performing ambiguity resolution by using the vector to realize two-dimensional DOA estimation and accurate pairing of the azimuth angle and the pitch angle.
2. The method for accurately pairing L-shaped sparse array DOA estimation as claimed in claim 1, wherein the respectively solving of the autocorrelation matrix and the cross-correlation matrix of the first subarray and the second subarray physical array comprises:
calculating the first subarray received data x1(t) autocorrelation matrix at N snapshots
Calculating the second subarray received data x2(t) autocorrelation matrix at N snapshots
Calculating the received data x of the first subarray and the second subarray1(t) and x2(t) cross-correlation matrix at N snapshots
3. The method of claim 2, wherein the calculating the autocorrelation matrix of the first virtual optimized subarray and the autocorrelation matrix of the second virtual optimized subarray comprises:
to self-correlate the matrixVectorization to obtain a vector z1；
For vector z1Removing redundancy to obtain observation vector
Recording observation vectorsThe middle element is in the vector z1Position vector ξ;
based on observation vectorsConstructing a Hermitian Toeplitz matrixThenVirtually optimizing an autocorrelation matrix of the array for the first sub-array;
to self-correlate the matrixVectorization to obtain a vector z2；
For vector z2Removing redundancy to obtain observation vector
Based on observation vectorsConstructing a Hermitian Toeplitz matrixThenVirtually optimizing the autocorrelation matrix of the array for the second sub-array.
4. The method for accurately pairing the DOA estimation of the L-shaped sparse array according to claim 3, wherein the estimation value of the pitch angle is calculated according to the autocorrelation matrix of the first sub-array virtual optimization array;
virtually optimizing the autocorrelation matrix of the first sub-arrayPerforming characteristic decomposition to obtain a signal subspace Us；
Estimation value of pitch angle obtained by utilizing ESPRIT algorithm
5. The method of claim 4, wherein obtaining the ambiguity estimation value of the azimuth angle according to the autocorrelation matrix of the second sub-array virtual optimization array and the estimation value of the pitch angle comprises:
virtually optimizing the autocorrelation matrix of the array according to the second sub-arrayAnd an estimate of said pitch angleIs given oneObtaining fuzzy estimation values of corresponding k azimuth angles by adopting an ESPRIT algorithm
6. The method for accurately pairing L-shaped sparse array DOA estimation as claimed in claim 5, wherein the power vector of the estimated signal is utilized to solve the ambiguity, and the two-dimensional DOA estimation and the accurate pairing of the azimuth angle and the pitch angle are realized, comprising:
estimating a direction matrix of a first sub-array
Using estimated value of pitch angle phikEstimating a direction matrix of a first sub-array
Estimating a de-redundancy direction matrix of a first sub-array virtual array
A direction matrix according to the first sub-matrixAnd the position vector ξ is used to obtain the de-redundancy direction matrix of the first sub-matrix virtual array
According to the redundancy removing direction matrix of the first sub-array virtual arrayAnd the observation vectorRemoving redundant direction matrix of first sub-array virtual arrayAnd observation vectorEstimating the power vector of the signal from the noise-disturbed intermediate position element
Estimate based on the pitch angleAnd a fuzzy estimate of said azimuth angleObtaining a fuzzy estimate of the direction matrix of the second sub-array
According to the estimated value of the pitch angleA direction matrix of the first sub-arrayPower vector of the signalA fuzzy estimation of the direction matrix of the second sub-arrayAnd the cross correlation matrixCalculating a correlation metric, determining the value of i by maximizing the correlation metric, and obtaining the correlation metricAre paired
7. An accurate pairing device for DOA estimation of an L-shaped sparse array is characterized in that the L-shaped sparse array comprises a first subarray with N1 array elements and a second subarray with N2 array elements, the first subarray is located on a z axis, the second subarray is located on an x axis, the L-shaped sparse array receives K irrelevant far-field narrow-band signals, included angles between a signal incidence direction and the z axis and between the z axis and the x axis are phi and β respectively, an included angle between projection of the incident signal in an xoy plane and the x axis is theta, and received data vectors of the first subarray and the second subarray are x and x vectors respectively1(t) and x2(t); the pairing apparatus includes:
the autocorrelation and cross-correlation module is used for respectively solving an autocorrelation matrix and a cross-correlation matrix of the first subarray physical array and the second subarray physical array;
the autocorrelation module is used for calculating an autocorrelation matrix of the first sub-array virtual optimization array and an autocorrelation matrix of the second sub-array virtual optimization array;
the first estimation module is used for calculating an estimation value of a pitch angle according to an autocorrelation matrix of the first sub-array virtual optimization array;
the second estimation module is used for solving a fuzzy estimation value of an azimuth angle according to the autocorrelation matrix of the second sub-array virtual optimization array and the estimation value of the pitch angle;
and the pairing module is used for estimating the power vector of the signal and performing ambiguity resolution by using the vector to realize two-dimensional DOA estimation and accurate pairing of the azimuth angle and the pitch angle.
8. The apparatus for accurate matching of DOA estimation of L-type sparse array according to claim 7, wherein said auto-correlation and cross-correlation module comprises:
a first autocorrelation unit for calculating the first subarray received data x1(t) autocorrelation matrix at N snapshots
A second autocorrelation unit for calculating second subarray received data x2(t) autocorrelation matrix at N snapshots
A cross-correlation unit for calculating the received data x of the first and second sub-arrays1(t) and x2(t) cross-correlation matrix at N snapshots
9. The apparatus for accurate matching of DOA estimation of L-type sparse array according to claim 8, wherein said autocorrelation module comprises:
a first vector quantization module for quantizing the autocorrelation matrixVectorization to obtain a vector z1；
A first redundancy removing module for removing the vector z1Removing redundancy to obtain observation vector
A first recording module for recording the observation vectorThe middle element is in the vector z1Position vector ξ;
a first construction module for constructing a vector based on the observation vectorsConstructing a Hermitian Toeplitz matrixThenVirtually optimizing an autocorrelation matrix of the array for the first sub-array;
a second quantization module for quantizing the autocorrelation matrixVectorization to obtain a vector z2；
A second redundancy elimination module for the vector z2Removing redundancy to obtain observation vector
A second construction module for constructing a second vector based on the observation vectorConstructing a Hermitian Toeplitz matrixThenVirtually optimizing the autocorrelation matrix of the array for the second sub-array.
10. The apparatus for accurate pairing of L-type sparse array DOA estimation according to claim 9, wherein the pairing module comprises:
a first estimating unit for estimating a direction matrix of the first sub-array
A second estimating unit for using the estimated value phi of the pitch anglekEstimating a direction matrix of a first sub-array
A third estimation unit for estimating a de-redundancy direction matrix of the first sub-array virtual array
A first direction matrix calculation unit for calculating a direction matrix according to the first sub-matrixAnd said position vector ξ is used to obtain the de-redundancy direction matrix of the first sub-array virtual array
A power vector estimation unit for removing redundant direction matrix according to the first sub-array virtual arrayAnd the observation vectorRemoving redundant direction matrix of first sub-array virtual arrayAnd observation vectorEstimating the power vector of the signal from the noise-disturbed intermediate position element
A fuzzy estimation unit based on the estimated value of the pitch angleAnd a fuzzy estimate of said azimuth angleObtaining a fuzzy estimate of the direction matrix of the second sub-array
A pairing unit for estimating the pitch angle based on the estimated valueA direction matrix of the first sub-arrayPower vector of the signalA fuzzy estimation of the direction matrix of the second sub-arrayAnd the cross correlation matrixCalculating a correlation metric, determining the value of i by maximizing the correlation metric, and obtaining the correlation metricAre paired
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