CN106844886B - Target direction of arrival acquisition method based on principal component analysis - Google Patents

Target direction of arrival acquisition method based on principal component analysis Download PDF

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CN106844886B
CN106844886B CN201611245361.8A CN201611245361A CN106844886B CN 106844886 B CN106844886 B CN 106844886B CN 201611245361 A CN201611245361 A CN 201611245361A CN 106844886 B CN106844886 B CN 106844886B
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CN106844886A (en
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王彤
夏月明
王娟
吴建新
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Xidian University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves

Abstract

The invention discloses a method for acquiring a target direction of arrival based on principal component analysis, which mainly comprises the following steps: determining that a radar comprises N array elements, determining a radar space spectrum region, and then performing spectrum division on the radar space spectrum region at equal intervals epsilon to obtain M space spectrum intervals, wherein the M space spectrum intervals comprise T target signals; respectively calculating a base vector matrix of M space spectrum intervals and a base coefficient vector matrix of the M space spectrum intervals; determining the received echo data of radar as X, and calculating the sampling covariance matrix estimation of the radar echo data
Figure DDA0001196958630000011
(ii) a Sampling covariance matrix estimation for radar echo data
Figure DDA0001196958630000012
Performing characteristic decomposition, and sequentially calculating sampling covariance matrix estimation of radar echo data
Figure DDA0001196958630000013
Noise subspace matrix of
Figure DDA0001196958630000014
M spatial frequency spectrum intervals respectively transform a matrix F and a spectrum function value corresponding to each frequency point in the M spatial frequency spectrum intervals; and then calculating to obtain the respective arrival directions of the T target signals in the M space spectrum intervals.

Description

Target direction of arrival acquisition method based on principal component analysis
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a target direction of arrival acquisition method based on Principal Component Analysis (PCA), namely a target direction of arrival acquisition method based on Principal Component Analysis (PCA), which is suitable for determining the direction of arrival of a target.
Background
The DOA estimation of the direction of arrival of the target has important significance in array signal processing, and the MUSIC algorithm is widely applied due to the high resolution capability of the MUSIC algorithm; however, the implementation of the conventional spectrum search MUSIC algorithm requires one-dimensional or multi-dimensional search in the whole angle range, the amount of calculation increases with the number of search points and the number of array elements, and the feature decomposition of the covariance matrix also requires a large amount of calculation.
A series of modified algorithms were subsequently proposed to reduce the computational complexity of the covariance matrix eigendecomposition and spectral search processes, including root-MUSIC, compressed MUSIC; however, the computation amount of these algorithms increases faster with the increase of the number of array elements, and the root-MUSIC algorithm is not numerically stable with a large number of array elements.
Disclosure of Invention
The invention aims to provide a target direction of arrival acquisition method based on principal component analysis, aiming at solving the problem that the traditional MUSIC algorithm has large calculation amount in a spectrum search stage, particularly under the condition of large array element number.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
A target direction of arrival acquisition method based on principal component analysis comprises the following steps:
step 1, determining that a radar comprises N array elements, and determining a radar space spectrum area, wherein the radar space spectrum area is the whole space spectrum area which can be detected by the radar; then, carrying out frequency spectrum division on the radar space frequency spectrum region at equal intervals epsilon to obtain M space frequency spectrum intervals, wherein the M space frequency spectrum intervals comprise T target signals; wherein epsilon is 2/M, and M represents the total number of spectrum intervals contained after the whole space spectrum region which can be detected by the radar is divided at equal intervals; n, T and epsilon are integers greater than 0;
step 2, respectively calculating to obtain M space spectrum interval basis vector matrixes and M space spectrum interval basis coefficient vector matrixes;
step 3, determining the echo data received by the radar as X, and then calculating to obtain the sampling covariance matrix estimation of the radar echo data
Figure BDA0001196958610000021
Sampling covariance matrix estimation for radar echo data
Figure BDA0001196958610000022
Performing characteristic decomposition, and calculating to obtain sampling covariance matrix estimation of radar echo data
Figure BDA0001196958610000023
Noise subspace matrix of
Figure BDA0001196958610000024
And 4, estimating by using M space spectrum interval basis vector matrixes and sampling covariance matrix of radar echo data
Figure BDA0001196958610000025
Noise subspace matrix of
Figure BDA0001196958610000026
Calculating to obtain M spatial frequency spectrum interval respective transformation matrixes F;
step 5, calculating to obtain a spectrum function value corresponding to each frequency point in the M space spectrum intervals according to the respective transformation matrix F of the M space spectrum intervals and the basis coefficient vector matrix of the M space spectrum intervals;
step 6, searching a peak point with the maximum spectrum function value in the spectrum function values corresponding to each frequency point in M space spectrum intervals, wherein the number of the peak points with the maximum spectrum function value is T', the frequency corresponding to the peak point with the maximum tth spectrum function value is used as the direction of arrival of the tth target signal, namely the frequency corresponding to the peak point with the maximum tth spectrum function value is the angle sine value of the tth target signal;
let T 'take 1 to T' respectively, and then get the direction of arrival of the 1 st target signal to the direction of arrival of the T th target signal, i.e. the respective directions of arrival of the T target signals in the M spatial frequency spectrum intervals; the number of peak points with the maximum spectrum function value is equal to and corresponds to the number of target signals contained in the M space spectrum intervals.
The invention has the following advantages:
the invention carries out principal component decomposition on the guide vector, expresses the principal component decomposition into a linear combination of a plurality of base vectors, reduces the computational complexity by realizing frequency spectrum search under low dimensionality and improves the real-time processing capability; in addition, compared with the traditional MUSIC algorithm and the root-MUSIC algorithm, the target direction of arrival estimation performance obtained by using the method of the invention is not deteriorated; in addition, the method can reduce the algorithm of MUSIC calculation complexity, and aims at the problem of high calculation amount of the traditional MUSIC algorithm under the condition of large array element number, the method decomposes the guide vector in the determined frequency spectrum area into a group of linear combinations of base vectors by utilizing the low-rank characteristic of the guide vector matrix, and executes the frequency spectrum search of the MUSIC algorithm in a low-dimensional space, thereby reducing the calculation complexity and improving the real-time processing capability.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a general flow chart of a principal component analysis-based target direction of arrival acquisition method of the present invention;
FIG. 2a is a graph of approximate error versus angle for steering vectors for different subspace dimensions obtained using the method of the present invention;
FIG. 2b is a graph of approximate error of steering vectors with different subspace dimensions as a function of the number of elements of the radar antenna array, obtained by using the method of the present invention;
FIG. 3 is a graph of the variation of the target signal angle RMSE with subspace dimension estimated by the method of the present invention;
FIG. 4 is a graph comparing the variation of target signal angle RMSE with SNR and target signal split angle estimated by various algorithms;
FIG. 5 is a graph illustrating a comparison of the estimated RMSE as a function of the separation angle of two target signals using various algorithms.
Detailed Description
Referring to fig. 1, it is a flowchart of a target direction of arrival obtaining method based on principal component analysis according to the present invention; the target direction of arrival obtaining method based on principal component analysis comprises the following steps:
step 1, determining that a radar comprises N array elements, and determining that a radar space frequency spectrum region is [ -1,1], wherein the radar space frequency spectrum region is the whole space frequency spectrum region which can be detected by the radar; then, carrying out frequency spectrum division on the radar space frequency spectrum region at equal intervals epsilon to obtain M space frequency spectrum intervals, wherein the M space frequency spectrum intervals comprise T target signals; wherein epsilon is 2/M, and M represents the total number of spectrum intervals contained after the whole space spectrum region which can be detected by the radar is divided at equal intervals; in the embodiment, the total number of frequency spectrum intervals contained in the whole space frequency spectrum region which can be detected by the radar after equal-interval division is performed is equal to the number of array elements contained in the radar; n, T and ε are integers greater than 0, respectively.
Wherein, the obtaining process of the radar space frequency spectrum region of [ -1,1] is as follows: firstly, the space pointing range of the radar beam is determined to be [ -90 degrees and 90 degrees ], and then the radar space frequency spectrum region is determined to be [ sin (-90 degrees) and sin (90 degrees ], namely [ -1 and 1 ].
And 2, respectively calculating the basis vector matrixes of the M space spectrum intervals and the basis coefficient vector matrixes of the M space spectrum intervals.
Specifically, a least square method is used for respectively calculating base vector matrixes corresponding to the M space spectrum intervals; the specific implementation substeps are as follows:
2.1 initialization: let M represent the mth space spectrum interval, where M belongs to {1,2, …, M }, and M represents the total number of spectrum intervals contained after the whole space spectrum region capable of being detected by the radar is divided at equal intervals; the mth space frequency spectrum interval contains a plurality of frequency points, K of which are selected,respectively recording the spatial frequency of the k frequency point in the m spatial frequency spectrum interval as fmk，fmk∈[-1+(m-1)ε,-1+mε]Recording the guide vector corresponding to the spatial frequency of the kth frequency point in the mth spatial frequency spectrum interval as a (f)mk)，
Figure BDA0001196958610000041
K belongs to {1,2, …, K }, wherein K represents the total number of frequency points selected from a plurality of frequency points contained in the mth spatial frequency spectrum interval, e represents an exponential function, and superscript T represents transposition; the initial values of m and k are 1, respectively.
2.2 obtaining the low-dimensional approximation of the guide vector corresponding to the spatial frequency of the k frequency point in the m spatial frequency spectrum interval by using the least square method
Figure BDA0001196958610000042
Namely, it is
Figure BDA0001196958610000043
And then calculating to obtain a cost function of the kth frequency point in the mth space spectrum interval
Figure BDA0001196958610000044
Is the approximate error of the steering vector corresponding to the spatial frequency of the k frequency point in the m spatial frequency spectrum interval, gmkIs a base coefficient vector, g, corresponding to the k frequency point in the m spatial frequency spectrum intervalmk＝[g1mk,…,gjmk,…,gJmk]T，gjmkThe number of the coefficients is J corresponding to the kth frequency point in the mth space spectrum interval, J belongs to {1,2, …, J }, and J is the dimension of the guide vector subspace; t ismA base vector matrix corresponding to the mth spatial spectrum interval,
Figure BDA0001196958610000046
representing two-norm operation, and superscript T representing transposition; the dimension J of the guide vector subspace is determined through an experimental simulation result; when J is>3, the error is considered to be within the acceptable range, so the value of J is takenThe range is as follows: j. the design is a square>3。
2.3 calculating to obtain the base vector matrix estimation corresponding to the mth space spectrum interval
Figure BDA0001196958610000045
Determining a steering vector matrix of K frequency points in the mth space frequency spectrum interval as Am，
Am＝[a(fm1),a(fm2),…,a(fmk),…,a(fmK)]A guide vector matrix A of K frequency points in the mth space frequency spectrum intervalmSingular value decomposition, Am＝UmΛmVmRespectively obtaining singular vectors corresponding to the N 'singular values and the N' singular values; u shapemIs a U-shaped singular matrix formed by singular vectors corresponding to N' singular values which are sequentially arranged from large to small, VmIs a V-shaped singular matrix formed by singular vectors corresponding to N' singular values which are sequentially arranged from large to small, and the inverted V-shaped singular matrix ismThe method comprises the steps that a diagonal matrix of K frequency points in an mth spatial frequency spectrum interval is obtained, and the diagonal matrix of the K frequency points in the mth spatial frequency spectrum interval is N' singular values which are sequentially arranged from large to small; u shapem＝]UmJ'|Um(N'-J')]，UmJ'Is a matrix formed by singular vectors corresponding to the first J ' large singular values in the N ' singular values arranged from large to small, and U is a matrix formed by singular vectors corresponding to the first J ' large singular valuesm(N'-J')The matrix U is formed by singular vectors corresponding to the residual N ' -J ' singular values in the N ' singular values after the N ' singular values are arranged from large to small in sequence, and then the matrix U is formed by the singular vectors corresponding to the previous J ' singular values in the N ' singular values after the N ' singular values are arranged from large to small in sequencemJ'As a basis vector matrix estimate for the mth spatial spectral interval
Figure BDA0001196958610000051
The number of singular values is equal to the number of array elements contained in the radar.
2.4 calculating to obtain a base coefficient vector g corresponding to the kth frequency point in the mth space spectrum intervalmkIs a calculation expression of
Figure BDA0001196958610000052
The superscript H denotes the conjugate transpose,
Figure BDA0001196958610000053
for the basis vector matrix estimate corresponding to the mth spatial spectrum interval, the inverse operation is denoted by the superscript-1.
2.5 adding 1 to k, repeating the substeps 2.2 to 2.4 in sequence until obtaining the base coefficient vector g corresponding to the 1 st frequency point in the m-th space spectrum intervalm1Is a calculation expression of
Figure BDA0001196958610000054
The base coefficient vector g corresponding to the Kth frequency point in the interval from the mth space frequency spectrummKIs a calculation expression of
Figure BDA0001196958610000055
And is used as a base coefficient vector of K frequency points in the mth space frequency spectrum interval
Figure BDA0001196958610000056
2.6 adding 1 to m, repeating substeps 2.2 to 2.5 in sequence until the base vector matrix estimation corresponding to the 1 st space spectrum interval is obtained
Figure BDA0001196958610000057
Base vector matrix estimation corresponding to Mth space spectrum interval
Figure BDA0001196958610000058
And the base coefficient vector of K frequency points in the 1 st space frequency spectrum interval
Figure BDA0001196958610000059
Vector of basis coefficients of K frequency points in space spectrum interval from M
Figure BDA00011969586100000510
And are respectively marked as a base vector matrix of the M space spectrum intervals and a base coefficient vector matrix of the M space spectrum intervals.
Step 3, determining that the echo data received by the radar is X, recording the kth ' sample data in the echo data received by the radar as X (K '), wherein the kth ' sample data X (K ') in the echo data received by the radar is an Nx 1-dimensional column vector, and K ' belongs to {1,2,3, …, K ' }, and K ' is the number of sample points contained in the echo data X received by the radar; then, the sampling covariance matrix estimation of the radar echo data is obtained through calculation
Figure BDA00011969586100000511
Figure BDA00011969586100000512
The superscript H denotes the conjugate transpose operation.
Sampling covariance matrix estimation for radar echo data
Figure BDA00011969586100000513
Performing characteristic decomposition to respectively obtain characteristic vectors corresponding to the N 'characteristic values and the N' characteristic values; arranging N characteristic values in the order from big to small, and respectively arranging the first N characteristic valuessSampling covariance matrix estimation using large eigenvalues as radar echo data
Figure BDA0001196958610000061
Is diagonal matrix of
Figure BDA0001196958610000062
Will be N beforesFeature vectors corresponding to large feature values respectively are used as sampling covariance matrix estimation of radar echo data
Figure BDA0001196958610000063
Of a signal subspace matrix
Figure BDA0001196958610000064
Mix N "-NsSampling covariance matrix estimation using eigenvalues as radar echo data
Figure BDA0001196958610000065
Noise subspace diagonal matrix of
Figure BDA0001196958610000066
Mix N "-NsFeature vectors corresponding to the feature values are used as sampling covariance matrix estimation of radar echo data
Figure BDA0001196958610000067
Noise subspace matrix of
Figure BDA0001196958610000068
Namely sampling covariance matrix estimation of radar echo data
Figure BDA0001196958610000069
After the characteristic decomposition, the following conditions are satisfied:
Figure BDA00011969586100000610
→ represents the sampled covariance matrix estimate of the radar echo data
Figure BDA00011969586100000611
Carrying out eigenvalue decomposition; the total number of target signals contained in the M space spectrum intervals is equal to the number of large eigenvalues selected after the N characteristic values are arranged in the descending order.
And 4, estimating by using M space spectrum interval basis vector matrixes and sampling covariance matrix of radar echo data
Figure BDA00011969586100000612
Noise subspace matrix of
Figure BDA00011969586100000613
Calculating to obtain respective transformation matrix F of M space spectrum intervals, wherein the transformation matrix of the mth space spectrum interval is Fm，
Figure BDA00011969586100000614
Figure BDA00011969586100000615
A basis vector matrix estimate corresponding to the mth spatial spectrum interval,
Figure BDA00011969586100000616
sampling covariance matrix estimation for radar echo data
Figure BDA00011969586100000617
The noise subspace matrix of (a); m belongs to {1,2, …, M }, the superscript H represents the conjugate transpose operation, and M represents the total number of spectrum intervals contained after the whole space spectrum region which can be detected by the radar is divided at equal intervals.
Step 5, according to the respective transformation matrix F of the M space spectrum intervals and the base coefficient vector matrix of the M space spectrum intervals, calculating to obtain a spectrum function value corresponding to each frequency point in the M space spectrum intervals, wherein the spectrum function value corresponding to the k-th frequency point in the M space spectrum interval is F (F)mk)，
Figure BDA00011969586100000618
F (-) represents a spectral function,
Figure BDA00011969586100000619
the representation represents a two-norm operation,
Figure BDA00011969586100000620
a base coefficient vector g corresponding to the k frequency point in the m spatial frequency spectrum intervalmkThe M belongs to {1,2, …, M }, and M represents the total number of spectrum intervals contained after the whole space spectrum region which can be detected by the radar is divided at equal intervals; k belongs to {1,2, …, K }, wherein K represents the total number of selected frequency points in a plurality of frequency points contained in the mth spatial frequency spectrum interval.
And (3) setting m to 1, and setting K to 1 to K respectively to obtain spectral function values corresponding to K frequency points in the mth spatial frequency spectrum interval respectively.
And then, taking 1 to M from M respectively, and further obtaining a spectrum function value corresponding to each frequency point in M space spectrum intervals.
And 6, searching a peak point with the maximum spectrum function value in the spectrum function values corresponding to each frequency point in the M space spectrum intervals, wherein the number of the peak points with the maximum spectrum function value is T', the frequency corresponding to the peak point with the maximum tth spectrum function value is used as the direction of arrival of the tth target signal, namely the frequency corresponding to the peak point with the maximum tth spectrum function value is the angle sine value of the tth target signal.
Let T 'take 1 to T' respectively, and then get the direction of arrival of the 1 st target signal to the direction of arrival of the T th target signal, i.e. the respective directions of arrival of the T target signals in the M spatial frequency spectrum intervals; the number of peak points with the maximum spectrum function value is equal to and corresponds to the number of target signals contained in the M space spectrum intervals.
The effect of the present invention is further verified and explained by the following simulation experiment.
Description of simulation experiment data
In simulation, a radar array element number N is equal to 32, three information sources are arranged in the whole frequency band, the angles are respectively-20-1 and 1, the SNR of a single information source is equal to 10dB, and the subspace dimension J is equal to 4; in addition, in the simulation experiment of the RMSE estimated by the angle of the target signal changing along with the separation angle of the target signal, two information sources are provided, wherein the angle of one information source is fixed at-1, the angle of the other information source changes along with the separation angle of the target signal, and other parameters are not changed
(II) simulation results and analysis
The simulation results of the present invention are shown in fig. 2a, fig. 2b, fig. 3, fig. 4 and fig. 5, fig. 2a is a graph of the approximate error of the steering vector with angle change under different subspace dimensions obtained by using the method of the present invention; FIG. 2b is a graph of approximate error of steering vectors with different subspace dimensions as a function of the number of elements of the radar antenna array, obtained by using the method of the present invention; FIG. 3 is a graph of the variation of the target signal angle RMSE with subspace dimension estimated by the method of the present invention; FIG. 4 is a graph comparing the variation of target signal angle RMSE with SNR and target signal split angle estimated by various algorithms; FIG. 5 is a graph illustrating a comparison of the estimated RMSE as a function of the separation angle of two target signals using various algorithms.
Fig. 2a and 2b show the approximate error of the steering vector under different subspace dimensions as a function of angle and array element number, and the result shows that the error decreases with the increase of the subspace dimension, but the error is basically unchanged when the array element number increases, and when the subspace dimension is greater than 3, the error is considered to be in an acceptable range; the method of the present invention can be seen from fig. 3 that at low dimensions, the RMSE decreases with increasing dimension, and at dimensions greater than 3, the RMSE tends to stabilize, so in later simulation experiments, a subspace dimension of 4 is generally chosen, and the performance loss is considered to be within an acceptable range. As can be seen from fig. 4 and 5, RMSE decreases with increasing SNR and target signal angular separation.
The simulation results show that the method can obtain almost the same performance as the traditional MUSIC algorithm in all SNR and separation angles, and the performance is slightly worse than that of the root-MUSIC algorithm, but the method has lower calculation amount compared with the other two algorithms, especially under the condition of large array element number.
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the method.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention; thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (5)

1. A target direction of arrival acquisition method based on principal component analysis is characterized by comprising the following steps:
step 1, determining that a radar comprises N array elements, and determining a radar space spectrum area, wherein the radar space spectrum area is the whole space spectrum area which can be detected by the radar; then, carrying out frequency spectrum division on the radar space frequency spectrum region at equal intervals epsilon to obtain M space frequency spectrum intervals, wherein the M space frequency spectrum intervals comprise T target signals; wherein epsilon is 2/M, and M represents the total number of spectrum intervals contained after the whole space spectrum region which can be detected by the radar is divided at equal intervals; n, T and epsilon are integers greater than 0;
step 2, respectively calculating to obtain M space spectrum interval basis vector matrixes and M space spectrum interval basis coefficient vector matrixes;
the substep of step 2 is:
2.1 initialization: let M represent the mth space spectrum interval, where M belongs to {1,2, …, M }, and M represents the total number of spectrum intervals contained after the whole space spectrum region capable of being detected by the radar is divided at equal intervals; the mth space spectrum interval contains a plurality of frequency points, K frequency points are selected, and the space frequency of the kth frequency point in the mth space spectrum interval is respectively recorded as fmk，fmk∈[-1+(m-1)ε,-1+mε]Recording the guide vector corresponding to the spatial frequency of the kth frequency point in the mth spatial frequency spectrum interval as a (f)mk)，
Figure FDA0002300134030000011
K belongs to {1,2, …, K }, wherein K represents the total number of frequency points selected from a plurality of frequency points contained in the mth spatial frequency spectrum interval, e represents an exponential function, and superscript T represents transposition; the initial values of m and k are respectively 1;
2.2 obtaining the low-dimensional approximation of the guide vector corresponding to the spatial frequency of the k frequency point in the m spatial frequency spectrum interval by using the least square method
Figure FDA0002300134030000012
Namely, it is
Figure FDA0002300134030000013
And then calculating to obtain a cost function of the kth frequency point in the mth space spectrum interval
Figure FDA0002300134030000014
Is the approximate error of the steering vector corresponding to the spatial frequency of the k frequency point in the m spatial frequency spectrum interval, gmkIs a base coefficient vector, g, corresponding to the k frequency point in the m spatial frequency spectrum intervalmk＝[g1mk,…,gjmk,…,gJmk]T，gjmkIs the jth base coefficient corresponding to the kth frequency point in the mth space frequency spectrum interval, J belongs to {1,2, …, J }, J is the dimension of the director quantum space, J>3；TmA base vector matrix, T, corresponding to the mth spatial spectral intervalm＝[tm1,...,tmj,...,tmJ]，tmjA jth base vector in a base vector matrix corresponding to the mth space spectrum interval;
Figure FDA0002300134030000021
representing two-norm operation, and superscript T representing transposition;
2.3 calculating to obtain the base vector matrix estimation corresponding to the mth space spectrum interval
Figure FDA0002300134030000022
Determining a steering vector matrix of K frequency points in the mth space frequency spectrum interval as Am，
Am＝[a(fm1),a(fm2),…,a(fmk),…,a(fmK)]A guide vector matrix A of K frequency points in the mth space frequency spectrum intervalmSingular value decomposition, Am＝UmΛmVmRespectively obtaining singular vectors corresponding to the N 'singular values and the N' singular values; u shapemIs a U-shaped singular matrix formed by singular vectors corresponding to N' singular values which are sequentially arranged from large to small, VmIs a V-shaped singular matrix formed by singular vectors corresponding to N' singular values which are sequentially arranged from large to small, and the inverted V-shaped singular matrix ismThe method comprises the steps that a diagonal matrix of K frequency points in an mth spatial frequency spectrum interval is obtained, and the diagonal matrix of the K frequency points in the mth spatial frequency spectrum interval is N' singular values which are sequentially arranged from large to small; u shapem＝[UmJ'|Um(N'-J')]，UmJ'Is a matrix formed by singular vectors corresponding to the first J ' large singular values in the N ' singular values arranged from large to small, and U is a matrix formed by singular vectors corresponding to the first J ' large singular valuesm(N'-J')The singular vectors corresponding to the remaining N '-J' singular values in the N 'singular values after the N' singular values are arranged from large to smallMeasuring the matrix formed by the vectors, and then forming a matrix U by singular vectors corresponding to the first J 'large singular values in the N' singular values which are arranged from large to smallmJ'As a basis vector matrix estimate for the mth spatial spectral interval
Figure FDA0002300134030000023
The number of singular values is equal to the number of array elements contained in the radar;
2.4 calculating to obtain a base coefficient vector g corresponding to the kth frequency point in the mth space spectrum intervalmkIs a calculation expression of
Figure FDA0002300134030000024
Figure FDA0002300134030000025
The superscript H denotes the conjugate transpose,
Figure FDA0002300134030000026
for the base vector matrix estimation corresponding to the mth space spectrum interval, superscript-1 represents the inversion operation;
2.5 adding 1 to k, repeating the substeps 2.2 to 2.4 in sequence until obtaining the base coefficient vector g corresponding to the 1 st frequency point in the m-th space spectrum intervalm1Is a calculation expression of
Figure FDA0002300134030000027
The base coefficient vector g corresponding to the Kth frequency point in the interval from the mth space frequency spectrummKIs a calculation expression of
Figure FDA0002300134030000028
And is used as a base coefficient vector of K frequency points in the mth space frequency spectrum interval
Figure FDA0002300134030000029
2.6 adding 1 to m, repeating substeps 2.2 to 2.5 in sequence until the base vector matrix estimation corresponding to the 1 st space spectrum interval is obtained
Figure FDA00023001340300000210
Base vector matrix estimation corresponding to Mth space spectrum interval
Figure FDA00023001340300000211
And the base coefficient vector of K frequency points in the 1 st space frequency spectrum interval
Figure FDA00023001340300000212
Vector of basis coefficients of K frequency points in space spectrum interval from M
Figure FDA00023001340300000213
Respectively recording the vector matrixes as basis vector matrixes of M space spectrum intervals and basis coefficient vector matrixes of M space spectrum intervals;
step 3, determining the echo data received by the radar as X, and then calculating to obtain the sampling covariance matrix estimation of the radar echo data
Figure FDA0002300134030000031
Sampling covariance matrix estimation for radar echo data
Figure FDA0002300134030000032
Performing characteristic decomposition, and calculating to obtain sampling covariance matrix estimation of radar echo data
Figure FDA0002300134030000033
Noise subspace matrix of
Figure FDA0002300134030000034
And 4, estimating by using M space spectrum interval basis vector matrixes and sampling covariance matrix of radar echo data
Figure FDA0002300134030000035
Noise subspace moment ofMatrix of
Figure FDA0002300134030000036
Calculating to obtain M spatial frequency spectrum interval respective transformation matrixes F;
step 5, calculating to obtain a spectrum function value corresponding to each frequency point in the M space spectrum intervals according to the respective transformation matrix F of the M space spectrum intervals and the basis coefficient vector matrix of the M space spectrum intervals;
step 6, searching a peak point with the maximum spectrum function value in the spectrum function values corresponding to each frequency point in M space spectrum intervals, wherein the number of the peak points with the maximum spectrum function value is T', the frequency corresponding to the peak point with the maximum tth spectrum function value is used as the direction of arrival of the tth target signal, namely the frequency corresponding to the peak point with the maximum tth spectrum function value is the angle sine value of the tth target signal;
let T 'take 1 to T' respectively, and then get the direction of arrival of the 1 st target signal to the direction of arrival of the T th target signal, i.e. the respective directions of arrival of the T target signals in the M spatial frequency spectrum intervals; the number of peak points with the maximum spectrum function value is equal to and corresponds to the number of target signals contained in the M space spectrum intervals.
2. The method for obtaining the target direction of arrival based on principal component analysis according to claim 1, wherein in step 1, the radar spatial frequency spectrum region is [ -1,1], and the obtaining process for determining the radar spatial frequency spectrum region as [ -1,1] is: firstly, the space pointing range of the radar beam is determined to be [ -90 degrees and 90 degrees ], and then the radar space frequency spectrum region is determined to be [ sin (-90 degrees) and sin (90 degrees ], namely [ -1 and 1 ].
3. The principal component analysis-based target direction of arrival acquisition method of claim 1, wherein in step 3, the sampled covariance matrix estimation of radar echo data
Figure FDA0002300134030000037
The expression is as follows:
Figure FDA0002300134030000038
x (K ') is the kth sampling data in the echo data received by the radar, the kth sampling data X (K') in the echo data received by the radar is an Nx 1-dimensional column vector, K 'belongs to {1,2,3, …, K' } is the number of sampling points contained in the echo data X received by the radar, and the superscript H represents the conjugate transpose operation;
sampling covariance matrix estimation of the radar echo data
Figure FDA0002300134030000039
Noise subspace matrix of
Figure FDA00023001340300000310
The obtaining process comprises the following steps:
sampling covariance matrix estimation for radar echo data
Figure FDA00023001340300000311
Performing characteristic decomposition to respectively obtain characteristic vectors corresponding to the N 'characteristic values and the N' characteristic values; arranging N characteristic values in the order from big to small, and respectively arranging the first N characteristic valuessSampling covariance matrix estimation using large eigenvalues as radar echo data
Figure FDA0002300134030000041
Is diagonal matrix of
Figure FDA0002300134030000042
Will be N beforesFeature vectors corresponding to large feature values respectively are used as sampling covariance matrix estimation of radar echo data
Figure FDA0002300134030000043
Of a signal subspace matrix
Figure FDA0002300134030000044
Mix N "-NsSampling covariance matrix estimation using eigenvalues as radar echo data
Figure FDA0002300134030000045
Noise subspace diagonal matrix of
Figure FDA0002300134030000046
Mix N "-NsFeature vectors corresponding to the feature values are used as sampling covariance matrix estimation of radar echo data
Figure FDA0002300134030000047
Noise subspace matrix of
Figure FDA0002300134030000048
Namely sampling covariance matrix estimation of radar echo data
Figure FDA0002300134030000049
After the characteristic decomposition, the following conditions are satisfied:
Figure FDA00023001340300000410
→ represents the sampled covariance matrix estimate of the radar echo data
Figure FDA00023001340300000411
Carrying out eigenvalue decomposition; the total number of target signals contained in the M space spectrum intervals is equal to the number of large eigenvalues selected after the N characteristic values are arranged in the descending order.
4. The method according to claim 3, wherein in step 4, the M spatial spectrum intervals are respectively transformed into a matrix F, and the transform matrix of the M spatial spectrum interval is denoted as Fm，
Figure FDA00023001340300000412
Figure FDA00023001340300000413
A basis vector matrix estimate corresponding to the mth spatial spectrum interval,
Figure FDA00023001340300000414
sampling covariance matrix estimation for radar echo data
Figure FDA00023001340300000415
The noise subspace matrix of (a); m belongs to {1,2, …, M }, the superscript H represents the conjugate transpose operation, and M represents the total number of spectrum intervals contained after the whole space spectrum region which can be detected by the radar is divided at equal intervals.
5. The method according to claim 2 or 3, wherein in step 5, the obtaining process of the spectral function value corresponding to each frequency point in the M spatial spectrum intervals is as follows:
firstly, calculating a spectrum function value F (F) corresponding to the k frequency point in the m spatial spectrum intervalmk)，
Figure FDA00023001340300000416
F (-) represents a spectral function,
Figure FDA00023001340300000417
the representation represents a two-norm operation,
Figure FDA00023001340300000418
a base coefficient vector g corresponding to the k frequency point in the m spatial frequency spectrum intervalmkThe M belongs to {1,2, …, M }, and M represents the total number of spectrum intervals contained after the whole space spectrum region which can be detected by the radar is divided at equal intervals; k belongs to {1,2, …, K }, wherein K represents the total number of selected frequency points in a plurality of frequency points contained in the mth spatial frequency spectrum interval;
then, setting m to 1, and setting K to 1 to K respectively to obtain spectral function values corresponding to K frequency points in the mth spatial frequency spectrum interval respectively;
and finally, taking 1 to M from M respectively to obtain a spectrum function value corresponding to each frequency point in M space spectrum intervals.
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