CN109633521B - Area array two-dimensional direction of arrival estimation method based on subspace reconstruction - Google Patents
Area array two-dimensional direction of arrival estimation method based on subspace reconstruction Download PDFInfo
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Abstract
The invention discloses a subspace reconstruction-based planar array two-dimensional direction of arrival estimation method, which mainly solves the problems that the prior art is only based on a special array surface, and can not effectively reduce the calculated amount and improve the estimation precision. The method comprises the following implementation steps: 1. the array radar receives the signals to obtain echo data; 2. dividing an area array of the array radar, and obtaining a signal subspace of a partial merging sub-array from echo data; 3. roughly estimating the position of an information source by utilizing a signal subspace of a part of merging submatrices; 4. and constructing a new data matrix by using the covariance matrixes of all array element receiving data, reconstructing a signal subspace, and constructing a spectrum function by using a noise subspace. 5. And performing gradient search on the spectral function in the neighborhood range by taking the roughly estimated position of the information source as a starting point to obtain the accurate position of the information source. The method is based on the area array, can effectively reduce the calculated amount, obtains higher estimation precision at the same time, and can be used for accurately estimating the target parameters.
Description
Technical Field
The invention belongs to the technical field of radars, and further relates to a planar array two-dimensional direction of arrival estimation method which can be used for accurately estimating target parameters.
Background
DOA estimation is an important technology in array signal processing, and is widely applied to the fields of radar detection, communication positioning, modern medicine and the like. When DOA estimation is carried out, because a target is positioned in a three-dimensional space, the azimuth angle and the pitch angle information of the target cannot be provided simultaneously by one-dimensional DOA estimation, and therefore a two-dimensional DOA estimation method needs to be researched. The current effective two-dimensional DOA estimation method designs an algorithm based on special arrays such as an L-shaped array and a cross-shaped array, and the two-dimensional DOA estimation algorithm based on an area array better meets the requirement of signal processing in reality, so that the method has research value.
A paper published by Tankdong, Tang and mountain in China, "two-dimensional DOA estimation algorithm based on propagation operators in an area array" (computer engineering and application, 2017,53(22):35-39) provides a two-dimensional DOA estimation method based on PM, a new data matrix is constructed by utilizing a cross-correlation matrix of sub-area array received data, a rotation invariant relation matrix is obtained by utilizing the PM algorithm for DOA estimation, and the operation amount is effectively reduced. The paper published by Shuangming, Wu Xiaoqiang, Zhang is based on the two-dimensional DOA estimation of the modified ESPRIT algorithm (university of Harbin, 2008,29(4): 407) and 410), and the subarray is merged and solved based on the principle that the ESPRIT algorithm solves the two-dimensional DOA, so that the covariance matrix does not contain redundant data any more, the dimensionality during characteristic value decomposition is effectively reduced, and the calculated amount is reduced. But the disadvantage of the above algorithm is that the estimation accuracy is not ideal.
Jiangzhi, Zhaoxiaofei, Zhang Qin in its published paper "two-dimensional DOA estimation of dimension-reducing Capon in area array" (applied scientific bulletin, 2015,44(6):48-52) proposes a dimension-reducing Capon algorithm suitable for area array, uses one-dimensional global search to realize two-dimensional DOA joint estimation, realizes automatic pairing of two-dimensional angles, improves the precision of parameter estimation, has performance close to that of the two-dimensional Capon algorithm, but has the defects that global search cannot be avoided, the calculated amount is large, and does not meet the requirement of real-time signal processing.
In summary, the existing two-dimensional DOA estimation technology for an area array cannot improve the estimation accuracy while effectively reducing the calculation amount.
Disclosure of Invention
The present invention is directed to overcome the above deficiencies of the prior art, and to provide an area array two-dimensional direction of arrival estimation method based on subspace reconstruction, so as to improve the estimation accuracy while effectively reducing the computation workload.
The technical scheme of the invention is as follows: firstly, a few array elements in an array are utilized to quickly estimate the approximate position of an information source, then a new data matrix reconstruction subspace is constructed by utilizing covariance matrixes of all sub-array received data, and finally gradient search is carried out in a neighborhood range of the roughly estimated position of the information source to obtain the accurate position of the information source, wherein the method comprises the following implementation steps:
(1) generating array radar receiving signals to obtain echo data X (t);
(2) dividing an area array of the array radar to obtain a signal subspace of a partial merging subarray:
2a) dividing an area array of an array radarObtaining the receiving signals of the first three sub-arrays from the echo data X (t) for M sub-arrays: x 1 、X 2 、X 3 And combining the signals two by two to obtain combined signals of the first subarray and the second subarray:
and the combined signal of the third and second subarrays:
2b) respectively constructing a first subarray and a second subarray to combine signal X 12 Of the covariance matrix R 12 And the third and second subarrays combine signal X 32 Of (2) covariance matrix R 32 And performing singular value decomposition on the two covariance matrixes respectively to obtain a signal subspace U of the combined signal of the first subarray and the second subarray S12 And a signal subspace U of the combined signals of the third and second subarrays S32 ：
Wherein, U S1 Signal subspace, U, of the first subarray S2 Signal subspace, U, for the second subarray S3 The signal subspace of the third sub-array;
(3) two signal subspaces U obtained according to 2b) S12 And U S32 Constructing two rotation invariant relationship matrices
And
using the two rotation invariant relation matrices
And
roughly estimating the position of the information source to obtain a roughly estimated pitch angle value
And coarse estimate of azimuth
；
(4) Reconstruction of the subspace:
4a) combining the received signals of the rest subarrays of the array with the received signals of the second subarray in pairs, respectively constructing covariance matrixes of the combined signals, and respectively performing singular value decomposition on the covariance matrixes of the combined signals to obtain a signal subspace U of the combined signals of the rest subarrays of the array and the second subarray Sk2 ：
Wherein, U Sk A signal subspace for the kth sub-array;
4b) signal subspace U of these combined signals Sk2 Signal subspace U projected onto combined signal of first and second subarrays S12 Obtaining a signal subspace U of the combined signals, the combined signals being combined in a first sub-array and a second sub-array S12 Signal subspace at basis:
wherein, U' Sk Is U' Sk2 By U S12 Signal subspace of kth sub-array, U 'when being radix' S2 Is U' Sk2 By U S12 The signal subspace of the second sub-array when the signal subspace is the base;
4c) from 4a) and 4b), a transition matrix is obtained
Wherein [. ]] + Is the pseudo-inverse of the matrix;
4d) according to 4b) and 4c) obtaining a first sub-array and a second sub-arraySignal subspace U of subarray combined signals S12 Signal subspace of the kth sub-array in the base time: u Sk ＝U′ Sk ·V k ；
4e) From 2c) and 4d), the signal subspace after reconstruction is obtained: u shape S ＝[U S1 ,U S2 ,U″ S3 ,U″ S4 ,…,U″ SM ] T Therein [] T Is the transposition of the matrix;
4f) obtaining a noise subspace according to 4 e): u shape N ＝U S ⊥ Therein [] ⊥ Orthogonal complement for matrix;
4g) constructing a spectral function according to the noise subspace:
wherein,
as a steering vector of the array [ ·] H Is a conjugate transpose of the matrix;
(5) and determining the accurate position of the information source by gradient search in a defined range:
5a) defining a search range: i.e. the search range of the azimuth angle is
Search range of pitch angle is
Where σ is the standard deviation of the estimation error for each angle:
θ 3dB the half-power wave beam width of the antenna is shown, snr is a decibel value of a signal-to-noise ratio, N is the number of array elements, and N is the number of fast beats;
5b) coarse azimuthal estimate
And rough estimate of pitch angle
Setting iterative step lengths of an azimuth angle and a pitch angle for the initial position, and performing gradient search on the spectrum function constructed in the step 4g) in a search range, wherein the point with the gradient closest to 0 is the accurate position of the information source.
Compared with the prior art, the invention has the following advantages:
firstly, the rough estimation is firstly used for determining the approximate position of an information source, and only gradient information of a spectrum function is utilized when searching is carried out by taking the rough estimation position as a starting point, so that global searching is avoided, the same estimation performance as that of the existing 2D-MUSIC method is obtained, and higher estimation precision is achieved.
Secondly, the invention greatly reduces the computational complexity by reconstructing the subspace, the construction of the covariance matrix, the decomposition of singular values in the real number domain and the determination of the accurate position of the information source, and the computational complexity is far less than that of the existing 2D-MUSIC method.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram of an array radar area array structure in the present invention;
FIG. 3 is a scatter plot of source location estimation using the present invention;
FIG. 4 is a graph comparing the RMS error with the SNR variation for the present invention and the prior 2D-MUSIC method, the first step of the source position coarse estimation method;
FIG. 5 is a graph comparing the variation of root mean square error with snapshot number in the present invention with the existing 2D-MUSIC method and the first step of the source position rough estimation method;
FIG. 6 is a graph comparing the computational complexity of the present invention and the prior 2D-MUSIC method with the number of array elements.
Detailed Description
The invention is described in further detail below with reference to the figures and examples.
Referring to fig. 1, the specific implementation steps of this example are as follows:
step 1: generating array radar receiving signals to obtain echo data X (t).
The echo data is represented as follows:
X(t)＝AS(t)+N(t)，
wherein, A is a guide vector of the array radar area array, S (t) is a signal model, and N (t) is randomly generated Gaussian white noise.
Step 2: and dividing the area array of the array radar to obtain a signal subspace of a partial merging subarray.
2a) Dividing the area array of the array radar into M sub-arrays, and obtaining the received signals X of the first three sub-arrays from the echo data X (t) as shown in FIG. 2 1 (t)、X 2 (t)、X 3 (t)：
X 1 (t)＝A 1 S(t)+N 1 (t)＝A 2 Φ 12 S(t)+N 1 (t)，
X 2 (t)＝A 2 S(t)+N 2 (t)，
X 3 (t)＝A 3 S(t)+N 3 (t)＝A 2 Φ 32 S(t)+N 3 (t)；
Wherein A is 1 、A 2 、A 3 Array flow patterns of the first, second and third sub-arrays, phi 12 For the first sub-array to be rotationally invariant with respect to the second sub-array, phi 32 For the third sub-array in a rotationally invariant relationship with the second sub-array, N 1 (t) noise, N, of the first subarray 2 (t) noise, N, of the second subarray 3 (t) is the noise of the third sub-array.
2b) Combining the received signals of the three sub-arrays pairwise to obtain a combined signal X of the first sub-array and the second sub-array 12 Combining signal X of the third and second subarrays 32 ：
Wherein,
an array flow pattern for combining signals for the first subarray and the second subarray,
array flow pattern for combining signals for the third subarray with the second subarray, N 12 Combining the noise of the signals for the first and second subarrays, N 32 Combining the noise of the signal for the third subarray and the second subarray;
2c) respectively constructing a first subarray and a second subarray to combine signals X 12 Of the covariance matrix R 12 And the third and second subarrays combine signal X 32 Of the covariance matrix R 32 ：
Wherein R is S As a covariance matrix of the signals, δ 2 Is the variance of the noise, I is the unit matrix [ ·] H Is the conjugate transpose of the matrix.
2d) Respectively carrying out singular value decomposition on the two covariance matrixes to obtain a signal subspace U of a combined signal of the first subarray and the second subarray S12 And a signal subspace U of the combined signals of the third and second subarrays S32 ：
Wherein, U S1 Signal subspace, U, of the first subarray S2 Signal subspace, U, for the second subarray S3 The signal subspace of the third subarray;
and step 3: the source position is roughly estimated.
When roughly estimating the source position, the existing root-finding MUSIC method, ESPRIT method and the like can be used, the defects of the existing root-finding MUSIC method, the ESPRIT method and the like are only suitable for uniform arrays, and the improved ESPRIT method is adopted and is realized as follows:
3a) two signal subspaces U obtained according to 2d) S12 And U S32 Constructing two rotation invariant relationship matrices
And
3a1) defining an upper bisection matrix Γ 1 ＝[I K×K ，0 K×K ]And a lower bisection matrix Γ 2 ＝[0 K×K ,I K×K ]Wherein I is a unit array, 0 is a full zero array, and K is the number of information sources;
3a2) signal subspace U for combining signals according to a first subarray and a second subarray S12 And a signal subspace U of combined signals of the third subarray and the second subarray S32 And 3a1) to obtain an upper bisection matrix F of the subspace of the combined signal of the first subarray and the second subarray, respectively 12 And a lower bisection matrix E 12 The third subarray and the second subarray combine the upper bisection matrix F of the signal subspace 32 And a lower bisection matrix E 32 ：
F 12 ＝Γ 1 U S12 ，E 32 ＝Γ 2 U S32 ，F 32 ＝Γ 1 U S32 ，E 12 ＝Γ 2 U S12 ；
3a3) According to 3a2), obtaining an on-subarray bisection matrix F 'of the combined signal of the first subarray and the second subarray' 12 And submatrix lower bisection matrix E' 12 And the submatrix of the combined signal of the third and second submatrixes is subjected to an on-submatrix bisection matrix F' 32 And submatrix lower bisection matrix E' 32 ：
F′ 12 ＝F 12 (F 12 H F 12 ) -1 F 12 H F 12 ，
E′ 12 ＝E 12 (E 12 H E 12 ) -1 E 12 H E 12 ，
F′ 32 ＝F 32 (F 32 H F 32 ) -1 F 32 H F 12 ，
E′ 32 ＝E 32 (E 32 H E 32 ) -1 E 32 H E 12 ；
3a4) According to 3a3), respectively obtaining a rotation matrix psi of the combined signal of the first sub-array and the second sub-array 12 And a rotation matrix Ψ of the combined signal of the third and second sub-arrays 32 ：
3a5) The rotation matrix Ψ for combining the signals of the first and second sub-arrays 12 Is expressed as Q 12 Based on the rotation matrix psi of the combined signal of the first and second sub-array 12 Obtaining the estimated value of the rotation invariant relation matrix of the first sub-array and the second sub-array
3a6) According to the eigenvector matrix Q 12 And a rotation matrix Ψ of the combined signal of the third and second sub-arrays 32 Obtaining the estimated value of the rotation invariant relation matrix of the third subarray and the second subarray
3b) With two rotation invariant relationship matrices 3a5) and 3a6)
And
roughly estimating the position of the information source to obtain a roughly estimated pitch angle value
Coarse estimate of sum azimuth
Where angle () is the phase angle of the matrix and diag () is the diagonal element of the matrix, [ · C] * Is the conjugate of the matrix.
And 4, step 4: the subspace is reconstructed.
When the signal source position is roughly estimated, due to the fact that the signal subspace of a few sub-arrays of the array radar is only utilized to carry out rapid estimation on the signal source position to provide prior information for gradient search, the signal subspace of the whole radar array face is not fully utilized, the estimation precision is not high, and the signal subspace of the whole radar array face needs to be reconstructed in order to further improve the estimation precision and reduce the calculated amount.
When reconstructing a signal subspace, the existing EMD method, singular value decomposition method and the like can be used, the defects of the EMD method, the singular value decomposition method and the like are that the calculated amount is large, and the projection method is adopted in the embodiment and is realized as follows:
4a) combining the received signals of the rest subarrays of the array with the received signals of the second subarray pairwise respectively, constructing covariance matrixes of the combined signals respectively, and performing singular value decomposition on the covariance matrixes of the combined signals respectively to obtain a signal subspace U of the combined signals of the rest subarrays of the array and the second subarray Sk2 ：
Wherein, U Sk A signal subspace for the kth sub-array;
4b) signal subspace U of these combined signals Sk2 Signal subspace U projected onto combined signal of first and second subarrays S12 Obtaining a signal subspace U of the combined signals, the combined signals being combined in a first sub-array and a second sub-array S12 Signal subspace at basis:
wherein, U' Sk Is U' Sk2 By U S12 Signal subspace of kth sub-array, U 'when being radix' S2 Is U' Sk2 By U S12 The signal subspace of the second sub-array when the signal subspace is the base;
4c) from 4a) and 4b), a transition matrix is obtained
Wherein [. ]] + Is the pseudo-inverse of the matrix;
4d) obtaining a signal subspace U) of the combined signal of the first sub-array and the second sub-array according to 4b) and 4c) S12 Signal subspace of the kth sub-array at the basis: u Sk ＝U′ Sk ·V k ；
4e) From 2d) and 4d), the signal subspace after reconstruction is obtained:
U S ＝[U S1 ,U S2 ,U″ S3 ,U″ S4 ,…,U″ SM ] T ，
wherein [. ]] T Is the transposition of the matrix;
4f) obtaining a noise subspace according to 4 e): u shape N ＝U S ⊥ Therein [] ⊥ Is the orthogonal complement of the matrix;
4g) the spectral function is constructed from the noise subspace as follows:
wherein,
as a steering vector of the array [ ·] H Is a conjugate transpose of the matrix;
and 5: and performing gradient search in the defined range to determine the accurate position of the information source.
5a) Defining a search range:
according to the characteristic that the estimation error of the improved ESPRIT method obeys the combined zero-mean Gaussian distribution, calculating the standard deviation sigma of each angular estimation error:
wherein, theta 3dB The half-power wave beam width of the antenna is defined, snr is a decibel value of a signal-to-noise ratio, N is the number of array elements, and N is a fast beat number, namely the number of sampling points of signals received by the array radar;
according to the characteristic that the confidence interval reflects the probability that the true value of the parameter falls in the neighborhood of the measurement result, the probability that the roughly estimated information source position is in the neighborhood of the true position 3 sigma of the information source is 99.74 percent, so that the search range for defining the azimuth angle is
Search range of pitch angle is
5b) Coarse azimuthal estimate
And rough estimate of pitch angle
Setting the search step length of an azimuth angle and a pitch angle for the initial position, performing gradient search on the spectrum function constructed in the step 4g) in the search range, wherein the point with the gradient closest to 0 is the accurate position of the information source.
The invention and the effects are further described in combination with simulation experiments.
1. Simulation conditions
The simulation adopts the array radar area array structure shown in fig. 2, the distance between adjacent array elements is half wavelength, each sub-array comprises 16 array elements, and the total number of the sub-arrays comprises 16 sub-arrays.
2. Emulated content
assuming that there are 3 narrowband sources incident on the array from the far field, the source positions are (20, 30), (30, 40), (40, 40), respectively. The search step size when performing the gradient search is 0.01 °, the fast beat number is 128, the signal-to-noise ratio is 2dB, and the source position is estimated by performing the monte carlo experiment 1000 times by using the present invention, and the result is shown in fig. 3, where fig. 3(a) is a dispersion plot of the estimated direction of arrival at the source position (20 °,30 °), fig. 3(b) is a dispersion plot of the estimated direction of arrival at the source position (30 °,40 °), and fig. 3(c) is a dispersion plot of the estimated direction of arrival at the source position (40 ° ). As can be seen from fig. 3, the estimates of the 3 source positions are substantially maintained near their true values, and the fluctuation is small, which shows that the present invention can implement two-dimensional direction-of-arrival estimation of the source positions.
assuming that there are 3 narrowband sources incident on the array from the far field, the source positions are (20, 30), (30, 40), (40, 40), respectively. The invention and the existing 2D-MUSIC method respectively carry out 1000 search Monte Carlo experiments with the step length of 0.01 degrees and the fast beat number of 128, and compare the root mean square error of the method of the invention and the existing 2D-MUSIC method and the information source position rough estimation method under the conditions of different signal-to-noise ratios. The results are shown in fig. 4, where the signal to noise ratio in fig. 4 is from-5 dB to 5 dB. As can be seen from FIG. 4, as the signal-to-noise ratio increases, the root mean square error decreases, and the precision of the final result obtained by the method after the fine search of the information source position is greatly improved relative to the rough estimation result, which approaches the estimation performance of the existing 2D-MUSIC method.
Simulation 3, performance analysis under different snapshot number conditions:
assuming that there are 3 narrowband sources incident on the array from the far field, the source positions are (20, 30), (30, 40), (40, 40), respectively. The invention and the existing 2D-MUSIC method are respectively used for carrying out Monte Carlo experiments of 1000 searches with the step length of 0.01 degrees and the signal-to-noise ratio of 2dB, and the root mean square error of the method of the invention under different fast beat number conditions is compared with the root mean square error of the existing 2D-MUSIC method and the information source position rough estimation method. The result is shown in fig. 5, where the number of beats in fig. 5 is from 64 to 512. As can be seen from FIG. 5, as the fast beat number increases, the root mean square error decreases, and the accuracy of the final result after the fine search of the information source position is greatly improved relative to the coarse estimation result, which is basically equivalent to the estimation performance of the existing 2D-MUSIC method.
Simulation 4, computational complexity analysis:
assume that the number of sources is 3. The existing 2D-MUSIC method defines the azimuth dimension in the first search range: theta e [ -90 DEG, 90 DEG]The pitch dimension:
the first search step size is set as:
the second search range is a range of +/-2 degrees of the source position obtained by the first search, and the second search step length is set as follows:
the required search times of the existing 2D-MUSIC method are: n is g 121800; the search step length of the present invention is set to acc equal to 0.01 °, then the maximum number of searches required by the present invention is: n is a radical of an alkyl radical l 810. FIG. 6 is a graph comparing the computational complexity of the present invention and the prior 2D-MUSIC method with the number of array elements. It can be seen from fig. 6 that the method effectively reduces the computational complexity.
Claims (3)
1. A method for estimating the two-dimensional direction of arrival of an area array based on subspace reconstruction is characterized by comprising the following steps:
(1) generating array radar receiving signals to obtain echo data X (t);
(2) dividing an area array of the array radar to obtain a signal subspace of a partial merging subarray:
2a) dividing an area array of the array radar into M sub-arrays, and obtaining receiving signals of the first three sub-arrays according to echo data X (t): x 1 、X 2 、X 3 And combining the signals two by two to obtain combined signals of the first subarray and the second subarray:
and the combined signal of the third and second subarrays:
2b) respectively constructing a first subarray and a second subarray to combine signal X 12 Of (2) covariance matrix R 12 And combining the signal X with the third and second subarrays 32 Of the covariance matrix R 32 And performing singular value decomposition on the two covariance matrixes respectively to obtain a signal subspace U of the combined signal of the first subarray and the second subarray S12 And a signal subspace U of the combined signals of the third and second subarrays S32 ：
Wherein, U S1 Signal subspace, U, of the first subarray S2 Signal subspace, U, for the second subarray S3 The signal subspace of the third sub-array;
(3) two signal subspaces U obtained according to 2b) S12 And U S32 Constructing two rotation invariant relationship matrices
And
using the two rotation invariant relation matrices
And
roughly estimating the position of the information source to obtain a roughly estimated pitch angle value
Coarse estimate of sum azimuth
(4) Reconstruction of the subspace:
4a) combining the received signals of the rest subarrays of the array with the received signals of the second subarray in pairs, respectively constructing covariance matrixes of the combined signals, and respectively performing singular value decomposition on the covariance matrixes of the combined signals to obtain a signal subspace U of the combined signals of the rest subarrays of the array and the second subarray Sk2 ：
Wherein, U Sk A signal subspace of the kth sub-array;
4b) signal subspace U of these combined signals Sk2 Signal subspace U projected onto combined signals of the first and second subarrays S12 Obtaining a signal subspace U of the combined signals, the combined signals being combined in a first sub-array and a second sub-array S12 Signal subspace at basis:
wherein, U' Sk Is U' Sk2 By U S12 Signal subspace of kth sub-array, U 'when being radix' S2 Is U' Sk2 By U S12 The signal subspace of the second sub-array when the signal subspace is the base;
4c) from 4a) and 4b), a transition matrix V is obtained k ＝U′ S2 + U S2 Therein [] + Is the pseudo-inverse of the matrix;
4d) obtaining a signal subspace U) of the combined signal of the first sub-array and the second sub-array according to 4b) and 4c) S12 Signal subspace of the kth sub-array at the basis: u Sk ＝U′ Sk ·V k ；
4e) From 2b) and 4d), the signal subspace after reconstruction is obtained: u shape S ＝[U S1 ,U S2 ,U″ S3 ,U″ S4 ,…,U″ SM ] T Therein [. C] T Is a transposition of the matrix;
4f) obtaining a noise subspace according to 4 e): u shape N ＝U S ⊥ Therein [] ⊥ Is the orthogonal complement of the matrix;
4g) constructing a spectral function according to the noise subspace:
wherein,
is a steering vector of the array [ ·] H Is a conjugate transpose of the matrix;
(5) performing gradient search in a defined range to determine the accurate position of an information source:
5a) defining a search range: i.e. the search range of the azimuth angle is
Search range of pitch angle is
Where σ is the standard deviation of the estimation error for each angle:
θ 3dB the half-power wave beam width of the antenna is shown, snr is a decibel value of a signal-to-noise ratio, N is the number of array elements, and N is the number of fast beats;
5b) coarse azimuthal estimate
And rough estimate of pitch angle
Setting search step lengths of an azimuth angle and a pitch angle for the initial position, and performing gradient search on the spectrum function constructed in the step 4g) in a search range, wherein the point with the gradient closest to 0 is the accurate position of the information source.
2. The method of claim 1, wherein step (3) is performed by two signal subspaces U S12 And U S32 Constructing two rotation invariant relationship matrices
And
the implementation is as follows:
3a) defining an upper bisection matrix Γ 1 ＝[I K×K ，0 K×K ]And a lower bisection matrix F 2 ＝[0 K×K ,I K×K ]Wherein I is a unit array, 0 is a full zero array, and K is the number of information sources;
3b) signal subspace U for combining signals according to a first subarray and a second subarray S12 And a signal subspace U of combined signals of the third subarray and the second subarray S32 And 3a) defining the upper bisection matrix F for combining signal subspaces of the first subarray and the second subarray respectively 12 And a lower bisection matrix E 12 The third subarray and the second subarray combine the upper bisection matrix F of the signal subspace 32 And a lower bisection matrix E 32 ：
F 12 ＝Γ 1 U S12 ，E 32 ＝Γ 2 U S32 ，F 32 ＝Γ 1 U S32 ，E 12 ＝Γ 2 U S12 ；
3c) Obtaining a pair matrix F 'on the subarrays of the combined signals of the first subarray and the second subarray according to 3 b)' 12 And submatrix lower bisection matrix E' 12 And the submatrix of the combined signal of the third and second submatrixes is subjected to an on-submatrix bisection matrix F' 32 And submatrix lower bisection matrix E' 32 ：
F′ 12 ＝F 12 (F 12 H F 12 ) -1 F 12 H F 12 ，E′ 12 ＝E 12 (E 12 H E 12 ) -1 E 12 H E 12 ，
F′ 32 ＝F 32 (F 32 H F 32 ) -1 F 32 H F 12 ，E′ 32 ＝E 32 (E 32 H E 32 ) -1 E 32 H E 12 ；
3d) According to 3c), respectively obtaining a rotation matrix psi of the combined signal of the first sub-array and the second sub-array 12 And the rotation moment of the combined signal of the third subarray and the second subarrayMatrix psi 32 ：
Ψ 12 ＝(F′ 12 H F′ 12 ) -1 F′ 12 H E′ 12 ，Ψ 32 ＝(F′ 32 H F′ 32 ) -1 F′ 32 H E′ 32 ；
3e) The rotation matrix Ψ for combining the signals of the first and second sub-arrays 12 Is denoted as Q 12 Based on the rotation matrix psi of the combined signal of the first and second sub-array 12 Obtaining the estimated value of the rotation invariant relation matrix of the first sub-array and the second sub-array
3f) According to the eigenvector matrix Q 12 And a rotation matrix Ψ of the combined signal of the third and second sub-arrays 32 Obtaining the estimated value of the rotation invariant relation matrix of the third sub-array and the second sub-array
3. The method of claim 2, wherein step (3) uses two rotation invariant relationship matrices
And
coarsening source positionEstimating to obtain a rough estimated value of the pitch angle
Coarse estimate of sum azimuth
The implementation is as follows:
with two rotation invariant relationship matrices 3e) and 3f)
And
roughly estimating the position of the information source to obtain a roughly estimated pitch angle value of the information source
And coarse estimate of azimuth
Where angle (-) is the phase angle of the matrix and diag (-) is the diagonal element of the matrix, [. ]] * Is the conjugate of the matrix.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101426862B1 (en) * | 2013-03-19 | 2014-08-07 | 국방과학연구소 | 3 Dimension Array Antenna System and Altitude Angle Estimation Method thereof |
| CN104101868A (en) * | 2014-06-30 | 2014-10-15 | 西安电子科技大学 | Jamming subspace reconstruction-based radar multi-false target jamming suppression method |
| CN104678350A (en) * | 2015-03-10 | 2015-06-03 | 重庆邮电大学 | TLS-ESPRTT algorithm-based 2D DOA estimation in large scale MIMO system |
| CN104698433A (en) * | 2015-03-16 | 2015-06-10 | 电子科技大学 | Single-snapshot data-based coherent signal DOA (direction of arrival) estimating method |
-
2019
- 2019-01-25 CN CN201910075086.7A patent/CN109633521B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101426862B1 (en) * | 2013-03-19 | 2014-08-07 | 국방과학연구소 | 3 Dimension Array Antenna System and Altitude Angle Estimation Method thereof |
| CN104101868A (en) * | 2014-06-30 | 2014-10-15 | 西安电子科技大学 | Jamming subspace reconstruction-based radar multi-false target jamming suppression method |
| CN104678350A (en) * | 2015-03-10 | 2015-06-03 | 重庆邮电大学 | TLS-ESPRTT algorithm-based 2D DOA estimation in large scale MIMO system |
| CN104698433A (en) * | 2015-03-16 | 2015-06-10 | 电子科技大学 | Single-snapshot data-based coherent signal DOA (direction of arrival) estimating method |
Non-Patent Citations (2)
| Title |
|---|
| Low Complexity Method for Wideband DOA Estimation Based on Sparse Representation Using Rotational Signal Subspace;Yonghong Zhao et al.;《2017 IEEE Radar Conference》;20170512;第0460-0463页 * |
| 面阵中基于传播算子的二维DOA估计算法;田正东 等;《计算机工程与应用》;20161221;第35-39页 * |
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