CN112666513A - Improved MUSIC direction of arrival estimation method - Google Patents
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Abstract
The invention discloses an improved MUSIC direction of arrival estimation method, which comprises the following steps: constructing a DOA estimation model of the far-field signal; calculating a covariance matrix of the array observation signals, and performing characteristic decomposition on the covariance matrix; presetting the number of signal sources, and solving a noise subspace; performing spatial spectrum estimation by applying an MUSIC algorithm, and estimating an arrival angle by searching a peak; for a group of observed signals, the arrival angle of the signals is estimated for multiple times, and then the DOA finally estimated is obtained through an averaging processing mode. The method can estimate the number of the signal sources, can avoid the adverse effect of inaccurate estimation of the number of the signal sources on DOA estimation by adopting other technologies to estimate the number of the signal sources, and improves the estimation precision of the incoming wave direction of the signal.
Description
Technical Field
The invention belongs to the technical field of signal processing, relates to the technical field of radar and communication countermeasure reconnaissance, and particularly relates to an improved MUSIC direction of arrival estimation method, which is used for estimating the direction of incoming waves of narrow-band signal sources such as radar signals and communication signals in a complex electromagnetic environment.
Background
In electronic warfare, a passive detection system aiming at signal reconnaissance performs reconnaissance by intercepting electromagnetic signals radiated by electronic equipment of an enemy, has the advantages of long acting distance, good concealment, strong anti-electronic interference capability and the like, and plays an important role in modern electronic warfare. The estimation of the Direction of radiation source signals, also called Direction of Arrival (DOA), is an important link in the activities of implementing Direction-finding positioning and performing comprehensive reconnaissance. The direction of arrival estimation of the passive detection system is to obtain the information of the incident angle of the target by receiving the target radiation electromagnetic wave, and the detection system does not radiate the electromagnetic wave, so the passive detection system has good concealment, difficult exposure and strong anti-interference capability, and is widely applied to electronic warfare.
DOA estimation develops rapidly in almost thirty years, beam forming, maximum likelihood estimation, subspace class and the like are the most common methods in DOA estimation, and abundant research results are obtained in the aspects of Gaussian/non-Gaussian noise, color noise, non-uniform noise, broadband signals, coherent signals, array element coupling, operation complexity and the like. Compared with beam forming and maximum likelihood estimation, the subspace method has higher resolution and moderate computational complexity, and becomes a mainstream method in related fields such as DOA estimation. Among them, the Multiple Signal Classification (MUSIC) method has a milestone meaning in the development history of high-resolution direction finding technology, realizes array super-resolution direction finding in the true sense, and is one of the methods used by researchers most, on the basis of which, the researchers have made various beneficial improvements.
Generally, before estimating the incoming wave direction of a signal, the number of signal sources needs to be known first. In an electronic reconnaissance environment, due to the non-cooperative countermeasure characteristic of the two parties, the number of signal sources needs to be estimated by adopting another technology, and then the direction-finding algorithm is applied to estimate the DOA. If the number of the estimated signals is not consistent with the actual number, the number of the spectral peaks obtained by a plurality of super-resolution algorithms is inconsistent with the actual number of the spectral peaks, so that the DOA estimation is wrong, and the estimation of the number of the signal sources has important influence on the direction finding effect; however, the estimation of the number of signal sources is also a technical difficulty in the field of array signal processing, and it is very difficult to achieve accurate estimation of the number of signal sources under complicated electromagnetic environment conditions such as low signal-to-noise ratio.
Disclosure of Invention
Aiming at the problem that the MUSIC method needs to estimate the number of signal sources in advance through other technologies in DOA estimation, the invention aims to provide an improved MUSIC direction-of-arrival estimation method.
In order to achieve the purpose, the invention adopts the following technical scheme:
an improved MUSIC direction of arrival estimation method comprises the following steps:
s1, constructing a far-field signal DOA estimation model
Set with K far-field signals from the direction theta1,θ2,…,θKIncident on an array consisting of M sensors, and observing signals of the array at the time t are X (t) and are expressed as
Wherein X (t) ═ X1(t),X2(t),…,XM(t)]TFor array observation signal vectors, T represents transposition;
a(θk) Is an array direction vector;
A(θ)＝[a(θ1),a(θ2),…,a(θK)]a steering vector matrix formed by the direction vectors;
θ＝[θ1,θ2,…,θK]Tis the parameter vector of the incoming wave angle of the signal;
S(t)＝[s1(t),s2(t),…,sK(t)]Tis an incident signal vector;
k is the number of signals;
N(t)＝[n1(t),n2(t),…,nM(t)]Tfor additive noise vectors, sample point T is 1,2, …, T1，T1Counting the number of signal sampling points;
s2, calculating the covariance matrix R of the array observation signals X (t) in the step S1, and performing feature decomposition on the covariance matrix
A covariance matrix of the array observation signal x (t) is calculated, expressed as:
R＝E[XXH]＝AE[SSH]AH+E[NNH]＝ARSAH+RN (2)
wherein R isSAnd RNRespectively a signal covariance matrix and a noise covariance matrix, wherein H represents conjugate transposition; since the signal and the noise are independent of each other, the data covariance matrix is decomposed into two parts, AR, related to the signal and the noiseSAHIs a signal portion; for spatially perfect white noise, and the noise power is σ2Then, there are:
R＝ARSAH+RN＝ARSAH+σ2I (3)
and (3) performing characteristic decomposition on the covariance matrix R, namely:
R＝ARSAH+RN＝Q∑QH (4)
wherein, matrix Q is the eigenvector matrix, diagonal matrix sigma is formed by the eigenvalue, namely:
in the equation (5), the characteristic values satisfy the following relationship:
λ1≥λ2≥…≥λK>λK+1≈…≈λM≈σ2
the steering vector matrix A is a Van der Monte matrix, provided that the target signal direction θi≠θp(i ≠ p), wherein i and p respectively represent the serial numbers of the signals, and K characteristic values corresponding to different target signals are total;
corresponding to the characteristic value lambdaiI is 1,2, …, M, and its feature vector is ei,i＝1,2,…,M；
S3, presetting the number of signal sources, and obtaining the noise subspace
Setting the number of signal sources as
The range of variation is
Wherein M is the number of antenna elements of the array antenna;
in setting the number of signal sources
On the basis of (1), a noise subspace is obtained, the expression of which is
Wherein λ ispAnd epRespectively carrying out characteristic value decomposition on the covariance matrix R to obtain a pth characteristic value and a characteristic vector;
s4, theoretically, under the condition that the signal sources are independent and have no noise, the signal subspace ESAnd noise subspace EN′Orthogonal, it is known that the steering vector in the signal subspace is also orthogonal to the noise subspace, i.e.
aH(θ)EN′＝0 (7)
Wherein the steering vector matrix
aH(θ)＝[exp(-j2πfτ1k),exp(-j2πfτ2k),…,exp(-j2πfτMk)]H，
The time delay of the kth signal reaching the mth array element relative to the 1 st array element, M is 1,2, …, M, K is 1,2, …, K;
c is the speed of light;
d is the interval between adjacent array elements;
s5, in practice, the vector a is guided by the presence of noiseH(theta) and noise subspace EN′And cannot be completely orthogonal, so DOA is realized by taking the maximum value of the spatial spectrum, and the calculation formula of the spatial spectrum estimation by applying the MUSIC algorithm is
Changing theta from-90 degrees to 90 degrees according to a certain step length by the above formula, and estimating an arrival angle by searching a peak;
s6, due to
Thus, the settings are different
Different arrival angle estimation results are obtained according to the formula (8) in the step S5;
sequentially taking values from 1 to M-1 to obtain M-1 kinds of arrival angle estimation results, which are expressed as
The number of angles of (a) represents the number of estimated signal sources, the angle value represents the incoming wave direction of the signal source, and the setting is based on
The number of the judged signal sources is
Angle of arrival of signal of
S7, mixing
Form a row vector, denoted ne＝[n1,n2,…,nM-1]Counting the number of the signal sources which appear most from the vector as the final estimated number of the signal sources
The number appearing in the vector
The serial number positions are marked, and the serial numbers are
The number of occurrences is given as num; to obtain
Then, will correspond to the number
The arrival angles of the signals form a row vector represented as
Vector formed by num group signal arrival angles
Averaging to obtain the final signal arrival angle estimation value expressed as
Obtaining the number of the signal sources estimated finally
And the final estimated angle of arrival
Further, in step S1, the far-field signals are mutually independent narrow-band stationary signals, and satisfy the mean value E { S (t) ═ 0} and the covariance matrix
Wherein
Is the power of the kth signal; the superimposed noise in the array observation signal vector is additive white Gaussian noise and is independent from the signal; the number of far-field signals is less than the number of array elements and the number of sampling points, i.e. K<min(M,T1) (ii) a The signals are propagated in an ideal space, and the array sensor has omnidirectional consistency.
Further, in the above step S7, the above step may be performed
Forming a column vector, counting the most appeared numbers from the column vector as the number of the signal sources to be finally estimated
Furthermore, the number K of the signal sources is at most half of the number of the antenna elements, i.e. the number K of the signal sources is equal to the number of the antenna elements
Indicating a rounding down.
Due to the adoption of the technical scheme, the invention has the following advantages:
according to the improved MUSIC direction-of-arrival estimation method, the number of signal sources is estimated without additionally adopting other technologies, the number of the signal sources can be automatically estimated, and the function of the MUSIC direction-finding method is expanded; for a group of observation signals, the arrival angle of the signal is estimated for multiple times, and then the finally estimated DOA is obtained through a mean value solving processing mode, so that the problem that the information source number is difficult to estimate in the incoming wave direction estimation by applying the MUSIC algorithm can be solved, the adverse effect on the DOA estimation caused by inaccurate information source number estimation is avoided, the estimation precision of the incoming wave direction of the signal is improved, and the method has good popularization and application values.
Drawings
Fig. 1 shows the spatial spectrum estimation result when the SNR is-5 dB and the number of signal sources is 3;
fig. 2 shows the spatial spectrum estimation result when the SNR is 10dB and the number of signal sources is 1;
fig. 3 shows the spatial spectrum estimation result when the SNR is 10dB and the number of signal sources is 4.
Detailed Description
The technical solution of the present invention will be further described in detail with reference to the accompanying drawings and examples.
The experimental verification of the improved MUSIC direction of arrival estimation method is carried out under the simulation conditions of DELL9020MT type personal computer, Intel (R) core (TM) i7-4770 CPU @3.40GHz and 64-bit Windows operating system, and MATLAB R2010a is adopted as simulation software.
The radiation source signal is taken as
T1Is a signalThe noise is complex Gaussian white noise, and the input signal-to-noise ratio (SNR) is defined as
Wherein
And
representing the variance of the signal and noise, respectively.
Example one
The input signal-to-noise ratio SNR is-5 dB, and the number of signal sampling points is T1The number of signals is 3, the arrival angles of the signals are-45 degrees, 30 degrees and 60 degrees respectively, and the number of array elements is M-8.
An improved MUSIC direction of arrival estimation method comprises the following specific steps:
s1, constructing a far-field signal DOA estimation model
Set with 3 far-field signals from the direction theta1,θ2,θ3Incident on an array of 8 sensors, and the observed signal of the array at time t is X (t) and is expressed as
Wherein X (t) ═ X1(t),X2(t),…,XM(t)]TFor array observation signal vectors, T represents transposition;
a(θk) Is an array direction vector;
A(θ)＝[a(θ1),a(θ2),a(θ3)]a steering vector matrix formed by the direction vectors;
θ＝[θ1,θ2,θ3]Tis the parameter vector of the incoming wave angle of the signal;
S(t)＝[s1(t),s2(t),s3(t)]Tis an incident signal vector;
k is the number of signals, and K is 3;
N(t)＝[n1(t),n2(t),…,nM(t)]Tfor additive noise vectors, sample point T is 1,2, …, T1，T1Number of signal samples, T1＝1024；
S2, calculating the covariance matrix R of the array observation signals X (t) in the step S1, and performing feature decomposition on the covariance matrix
A covariance matrix of the array observation signal x (t) is calculated, expressed as:
R＝E[XXH]＝AE[SSH]AH+E[NNH]＝ARSAH+RN (2)
wherein R isSAnd RNRespectively a signal covariance matrix and a noise covariance matrix, wherein H represents conjugate transposition; since the signal and the noise are independent of each other, the data covariance matrix is decomposed into two parts, AR, related to the signal and the noiseSAHIs a signal portion; for spatially perfect white noise, and the noise power is σ2Then, there are:
R＝ARSAH+RN＝ARSAH+σ2I (3)
and (3) performing characteristic decomposition on the covariance matrix R, namely:
R＝ARSAH+RN＝Q∑QH (4)
wherein, matrix Q is the eigenvector matrix, diagonal matrix sigma is formed by the eigenvalue, namely:
in the equation (5), the characteristic values satisfy the following relationship:
λ1≥λ2≥λ3>λ4≈…≈λM≈σ2
the steering vector matrix A is a Van der Monte matrix, and K is 3 eigenvalues corresponding to different target signals;
corresponds to specialEigenvalue λiI is 1,2, …, M, and its feature vector is ei,i＝1,2,…,M；
S3, presetting the number of signal sources, and obtaining the noise subspace
Setting the number of signal sources as
Respectively taking the values of 1,2 and … 7;
in setting the number of signal sources
On the basis of (1), a noise subspace is obtained, the expression of which is
Wherein λ ispAnd epRespectively carrying out characteristic value decomposition on the covariance matrix R to obtain a pth characteristic value and a characteristic vector;
s4, theoretically, under the condition that the signal sources are independent and have no noise, the signal subspace ESAnd noise subspace EN′Orthogonal, it is known that the steering vector in the signal subspace is also orthogonal to the noise subspace, i.e.
aH(θ)EN′＝0 (7)
Wherein the steering vector matrix
aH(θ)＝[exp(-j2πfτ1k),exp(-j2πfτ2k),…,exp(-j2πfτMk)]H，
The time delay of the kth signal reaching the mth array element relative to the 1 st array element, M is 1,2, …, M, K is 1,2, …, K;
c is the speed of light;
d is the interval between adjacent array elements;
s5 factIn the interim, the steering vector a is present due to the presence of noiseH(theta) and noise subspace EN′And cannot be completely orthogonal, so DOA is realized by taking the maximum value of the spatial spectrum, and the calculation formula of the spatial spectrum estimation by applying the MUSIC algorithm is
Changing theta from-90 degrees to 90 degrees according to a certain step length by the above formula, and estimating an arrival angle by searching a peak to obtain MUSIC spectral functions shown as (a) to (g) in figure 1 respectively;
s6, with the array element number M being 8, 7 arrival angle estimation results are obtained, which are expressed as
DOA1＝[-48.9°,31.3°,61.5°]That is, the arrival angles are-48.9 deg., 31.3 deg., 61.5 deg., respectively, and the estimated number of signal sources is n1＝3；
DOA2＝[-45.5°,29.8°,61.2°]That is, the arrival angles are-45.5 deg., 29.8 deg., 61.2 deg., respectively, and the estimated number of signal sources is n2＝3；
DOA3＝[-45.2°,30.0°，60.2°]That is, the arrival angles are-48.9 deg., 31.3 deg., 61.5 deg., respectively, and the estimated number of signal sources is n3＝3；
DOA4＝[-45.0°,29.8°,59.6°]That is, the arrival angles are-45.0 degrees, 29.8 degrees and 59.6 degrees, respectively, and the estimated number of signal sources is n4＝3；
DOA5＝[-45.2°,30.0°,60.0°]That is, the arrival angles are-45.5 deg., 29.8 deg., 61.2 deg., respectively, and the estimated number of signal sources is n5＝3；
DOA6＝[-45.6°,30.1°,60.1°]That is, the arrival angles are-45.6 degrees, 30.1 degrees and 60.1 degrees, respectively, and the estimated number of signal sources is n6＝3；
DOA7＝[-45.5°,9.7°,29.6°,60.9°]That is, the arrival angles are-45.5 °,9.7 °,29.6 °, and 60.9 °, respectively, and the estimated number of signal sources is n7＝4；
S7, mixing
Form a row vector, denoted ne＝[3,3,3,3,3,3,4]Counting the number of the signal sources which appear most from the vector as the final estimated number of the signal sources
It is obvious that
The number of times num of occurrence is 6; the DOA estimation results with the number of signal sources of 3 (namely 3 spectral peaks) are respectively the 1 st, 2 nd, 3 rd, 4 th, 5 th and 6 th groups
Vector formed by the arrival angles of the 6 groups of signals
Averaging to obtain the final signal arrival angle estimation value expressed as
Example two
As shown in fig. 2, the input signal-to-noise ratio SNR is 10dB, and the number of signal samples is T11024, the number of signals is 1, the arrival angle of the signals is-60 degrees, and the number of array elements is M-8.
An improved MUSIC direction of arrival estimation method comprises the following specific steps:
s1, constructing a far-field signal DOA estimation model
Set with 1 far-field signal from direction theta1Incident on an array of 8 sensors, and the observed signal of the array at time t is X (t) and is expressed as
Wherein X (t) ═ X1(t),X2(t),…,XM(t)]TFor array observation signal vectors, T represents transposition;
a(θk) Is an array direction vector;
A(θ)＝[a(θ1)]a steering vector matrix formed by the direction vectors;
θ＝[θ1]Tis the parameter vector of the incoming wave angle of the signal;
S(t)＝[s1(t)]Tis an incident signal vector;
k is the number of signals, and K is 1;
N(t)＝[n1(t),n2(t),…,nM(t)]Tfor additive noise vectors, sample point T is 1,2, …, T1，T1Number of signal samples, T1＝1024；
S2, calculating the covariance matrix R of the array observation signals X (t) in the step S1, and performing feature decomposition on the covariance matrix
A covariance matrix of the array observation signal x (t) is calculated, expressed as:
R＝E[XXH]＝AE[SSH]AH+E[NNH]＝ARSAH+RN (2)
wherein R isSAnd RNRespectively a signal covariance matrix and a noise covariance matrix, wherein H represents conjugate transposition; since the signal and the noise are independent of each other, the data covariance matrix is decomposed into two parts, AR, related to the signal and the noiseSAHIs a signal portion; for spatially perfect white noise, and the noise power is σ2Then, there are:
R＝ARSAH+RN＝ARSAH+σ2I (3)
and (3) performing characteristic decomposition on the covariance matrix R, namely:
R＝ARSAH+RN＝Q∑QH (4)
wherein, matrix Q is the eigenvector matrix, diagonal matrix sigma is formed by the eigenvalue, namely:
in the equation (5), the characteristic values satisfy the following relationship:
λ1>λ2≈…≈λM≈σ2
the steering vector matrix A is a Van der Monte matrix, and K is 1 in total and corresponds to different characteristic values of the target signals;
corresponding to the characteristic value lambdaiI is 1,2, …, M, and its feature vector is ei,i＝1,2,…,M；
S3, presetting the number of signal sources, and obtaining the noise subspace
Setting the number of signal sources as
Respectively taking the values of 1,2 and … 7;
in setting the number of signal sources
On the basis of (1), a noise subspace is obtained, the expression of which is
Wherein λ ispAnd epThe p-th one after characteristic value decomposition is respectively carried out on the covariance matrix REigenvalues and eigenvectors;
s4, theoretically, under the condition that the signal sources are independent and have no noise, the signal subspace ESAnd noise subspace EN′Orthogonal, it is known that the steering vector in the signal subspace is also orthogonal to the noise subspace, i.e.
aH(θ)EN′＝0 (7)
Wherein the steering vector matrix
aH(θ)＝[exp(-j2πfτ1k),exp(-j2πfτ2k),…,exp(-j2πfτMk)]H，
The time delay of the kth signal reaching the mth array element relative to the 1 st array element, wherein M is 1,2, …, and M, k is 1;
c is the speed of light;
d is the interval between adjacent array elements;
s5, in practice, the vector a is guided by the presence of noiseH(theta) and noise subspace EN′And cannot be completely orthogonal, so DOA is realized by taking the maximum value of the spatial spectrum, and the calculation formula of the spatial spectrum estimation by applying the MUSIC algorithm is
From the above formula, changing theta from-90 degrees to 90 degrees according to a certain step length, estimating an arrival angle by searching a peak, and respectively obtaining MUSIC spectral functions as shown in (a) to (g) of FIG. 2;
s6, with the array element number M being 8, 7 arrival angle estimation results are obtained, which are expressed as
DOA1＝[-59.9°]I.e. the angle of arrival is-59.9 deg., the estimated signal sourceThe number is n1＝1；
DOA2＝[-60.0°,-27.5°,-3.8°]I.e. angles of arrival of-60.0 deg. -27.5 deg. -3.8 deg., respectively, the estimated number of signal sources is n2＝3；
DOA3＝[-60.0°,44.5°]That is, the arrival angles are-60.0 DEG and 44.5 DEG, respectively, and the estimated number of signal sources is n3＝2；
DOA4＝[-59.9°]I.e. the angle of arrival is-59.9 deg., the estimated number of signal sources is n4＝1；
DOA5＝[-60.0°]I.e. the angle of arrival is-60.0 deg., the estimated number of signal sources is n5＝1；
DOA6＝[-60.1°,-31.1°,-11.4°,20.2°,53.9°]I.e. angles of arrival of-60.1 deg. -31.1 deg. -11.4 deg., 20.2 deg., 53.9 deg., respectively, the estimated number of signal sources being n6＝5；
DOA7＝[-59.8°,-7.1°,17.2°,35.7°,56.8°]I.e. the angles of arrival are-59.8 deg. -7.1 deg., 17.2 deg., 35.7 deg., 56.8 deg., respectively, and the estimated number of signal sources is n7＝5；
S7, mixing
Form a row vector, denoted ne＝[1,3,2,1,1,5,5]Counting the number of the signal sources which appear most from the vector as the final estimated number of the signal sources
It is obvious that
The number of times num of occurrence is 3; the DOA estimation results with the number of signal sources of 1 (namely 1 spectral peak) are respectively the 1 st, 4 th and 5 th groups
Vector formed by the angle of arrival of the 3 groups of signals
Averaging to obtain the final signal arrival angle estimation value expressed as
Since the actual number of signal sources is 1 and the incoming wave angle is-60 °, comparing the estimation result with the actual result, it can be found that the arrival direction estimation method of the present invention can realize accurate estimation of the number of signal sources and realize estimation of the arrival angle of the signal with very small error.
EXAMPLE III
The input signal-to-noise ratio SNR is 10dB, and the number of signal sampling points is T1The number of signals is 4, the arrival angles of the signals are respectively-60 degrees, 15 degrees, 30 degrees and 45 degrees, and the number of array elements is 8.
An improved MUSIC direction of arrival estimation method comprises the following specific steps:
s1, constructing a far-field signal DOA estimation model
4 far-field signals are set from the direction theta1,θ2,θ3,θ4Incident on an array of 8 sensors, and the observed signal of the array at time t is X (t) and is expressed as
Wherein X (t) ═ X1(t),X2(t),…,XM(t)]TFor array observation signal vectors, T represents transposition;
a(θk) Is an array direction vector;
A(θ)＝[a(θ1),a(θ2),a(θ3),a(θ4)]a steering vector matrix formed by the direction vectors;
θ＝[θ1,θ2,θ3,θ4]Tis the parameter vector of the incoming wave angle of the signal;
S(t)＝[s1(t),s2(t),s3(t),s4(t)]Tis an incident signal vector;
k is the number of signals, and K is 4;
N(t)＝[n1(t),n2(t),…,nM(t)]Tfor additive noise vectors, sample point T is 1,2, …, T1，T1Number of signal samples, T1＝1024；
S2, calculating the covariance matrix R of the array observation signals X (t) in the step S1, and performing feature decomposition on the covariance matrix
A covariance matrix of the array observation signal x (t) is calculated, expressed as:
R＝E[XXH]＝AE[SSH]AH+E[NNH]＝ARSAH+RN (2)
wherein R isSAnd RNRespectively a signal covariance matrix and a noise covariance matrix, wherein H represents conjugate transposition; since the signal and the noise are independent of each other, the data covariance matrix is decomposed into two parts, AR, related to the signal and the noiseSAHIs a signal portion; for spatially perfect white noise, and the noise power is σ2Then, there are:
R＝ARSAH+RN＝ARSAH+σ2I (3)
and (3) performing characteristic decomposition on the covariance matrix R, namely:
R＝ARSAH+RN＝Q∑QH (4)
wherein, matrix Q is the eigenvector matrix, diagonal matrix sigma is formed by the eigenvalue, namely:
in the equation (5), the characteristic values satisfy the following relationship:
λ1≥λ2≥…≥λ4>λ5≈…≈λM≈σ2
the steering vector matrix A is a Van der Monte matrix, and K is 4 eigenvalues corresponding to different target signals;
corresponding to the characteristic value lambdaiI is 1,2, …, M, and its feature vector is ei,i＝1,2,…,M；
S3, presetting the number of signal sources, and obtaining the noise subspace
Setting the number of signal sources as
Respectively taking the values of 1,2 and … 7;
in setting the number of signal sources
On the basis of (1), a noise subspace is obtained, the expression of which is
Wherein λ ispAnd epRespectively carrying out characteristic value decomposition on the covariance matrix R to obtain a pth characteristic value and a characteristic vector;
s4, theoretically, under the condition that the signal sources are independent and have no noise, the signal subspace ESAnd noise subspace EN′Orthogonal, it is known that the steering vector in the signal subspace is also orthogonal to the noise subspace, i.e.
aH(θ)EN′＝0 (7)
Wherein the steering vector matrix
aH(θ)＝[exp(-j2πfτ1k),exp(-j2πfτ2k),…,exp(-j2πfτMk)]H，
The time delay of the kth signal reaching the mth array element relative to the 1 st array element, M is 1,2, …, M, K is 1,2, …, K;
c is the speed of light;
d is the interval between adjacent array elements;
s5, in practice, the vector a is guided by the presence of noiseH(theta) and noise subspace EN′And cannot be completely orthogonal, so DOA is realized by taking the maximum value of the spatial spectrum, and the calculation formula of the spatial spectrum estimation by applying the MUSIC algorithm is
From the above formula, changing theta from-90 degrees to 90 degrees according to a certain step length, estimating an arrival angle by searching a peak, and obtaining MUSIC spectral functions shown as (a) to (g) in FIG. 3 respectively;
s6, since the number of array elements is M ═ 8, 7 arrival angle estimation results are obtained, and are expressed as
DOA1＝[38.3°]I.e. the angle of arrival is 38.3 deg., the estimated number of signal sources is n1＝1；
DOA2＝[-60.9°,38.4°]That is, the arrival angles are-60.9 DEG and 38.4 DEG, respectively, and the estimated number of signal sources is n2＝2；
DOA3＝[-61.4°,17.4°,37.2°]That is, the arrival angles are-61.4 deg., 17.4 deg., 37.2 deg., respectively, and the estimated number of signal sources is n3＝3；
DOA4＝[-60.0°,15.0°,29.9°,45.0°]That is, the arrival angles are-60.0 degrees, 15.0 degrees, 29.9 degrees and 45.0 degrees, respectively, and the estimated number of signal sources is n4＝4；
DOA5＝[-60.0°,15.0°,30.0°,45.0°]That is, the arrival angles are-60.0 degrees, 15.0 degrees, 30.0 degrees and 45.0 degrees, respectively, and the estimated number of signal sources is n5＝4；
DOA6＝[-60.0°,15.0°,29.9°,44.9°]That is, the arrival angles are-60.0 °,15.0 °,29.9 °, and 44.9 °, respectively, and the estimated number of signal sources is n6＝4；
DOA7＝[-60.0°,-14.4°,14.9°,29.8°,44.8°]I.e. the angles of arrival are-60.0 deg. -14.4 deg., 14.9 deg., 29.8 deg., 44.8 deg., respectively, and the estimated number of signal sources is n7＝5；
S7, mixing
Form a row vector, denoted ne＝[1,2,3,4,4,4,5]Counting the number of the signal sources which appear most from the vector as the final estimated number of the signal sources
It is obvious that
The number of times num of occurrence is 3; the DOA estimation results with 4 signal sources (namely 4 spectrum peaks) are respectively set as 4 th, 5 th and 6 th
Vector formed by the angle of arrival of the 3 groups of signals
Averaging to obtain the final signal arrival angle estimation value expressed as
The actual number of the signal sources is determined to be 4, the incoming wave angles of the signal sources are-60 degrees, 15 degrees, 30 degrees and 45 degrees respectively, and the estimation result and the actual result are compared, so that the arrival direction estimation method can realize accurate estimation of the number of the signal sources and realize estimation of the arrival angle of the signal with small error.
In the above embodiments, step S4 provides a steering vector matrix of uniform linear arrays; the technical scheme of the invention is also suitable for uniform circular arrays.
The above description is only a preferred embodiment of the present invention, and not intended to limit the present invention, and all equivalent changes and modifications made within the scope of the claims of the present invention should fall within the protection scope of the present invention.
Claims (4)
1. An improved MUSIC direction of arrival estimation method is characterized in that: which comprises the following steps:
s1, constructing a far-field signal DOA estimation model
Set with K far-field signals from the direction theta1,θ2,…,θKIncident on an array consisting of M sensors, and observing signals of the array at the time t are X (t) and are expressed as
Wherein X (t) ═ X1(t),X2(t),…,XM(t)]TFor array observation signal vectors, T represents transposition;
a(θk) Is an array direction vector;
A(θ)＝[a(θ1),a(θ2),…,a(θK)]a steering vector matrix formed by the direction vectors;
θ＝[θ1,θ2,…,θK]Tis the parameter vector of the incoming wave angle of the signal;
S(t)＝[s1(t),s2(t),…,sK(t)]Tis an incident signal vector;
k is the number of signals;
N(t)＝[n1(t),n2(t),…,nM(t)]Tfor additive noise vectors, sample point T is 1,2, …, T1，T1Counting the number of signal sampling points;
s2, calculating a covariance matrix R of the array observation signals X (t) in the step S1, and performing feature decomposition on the covariance matrix;
s3, presetting the number of signal sources, and obtaining the noise subspace
Setting the number of signal sources as
The range of variation is
Wherein M is the number of antenna elements of the array antenna;
in setting the number of signal sources
On the basis of (1), a noise subspace is obtained, the expression of which is
Wherein λ ispAnd epRespectively carrying out characteristic value decomposition on the covariance matrix R to obtain a pth characteristic value and a characteristic vector;
s4, theoretically, under the condition that the signal sources are independent and have no noise, the signal subspace ESAnd noise subspace EN′Orthogonal, it is known that the steering vector in the signal subspace is also orthogonal to the noise subspace, i.e.
aH(θ)EN′＝0 (7)
Wherein the steering vector matrix
aH(θ)＝[exp(-j2πfτ1k),exp(-j2πfτ2k),…,exp(-j2πfτMk)]H，
The time delay of the kth signal reaching the mth array element relative to the 1 st array element, M is 1,2, …, M, K is 1,2, …, K;
c is the speed of light;
d is the interval between adjacent array elements;
s5, in practice, the vector a is guided by the presence of noiseH(theta) and noise subspace EN′And cannot be completely orthogonal, so DOA is realized by taking the maximum value of the spatial spectrum, and the calculation formula of the spatial spectrum estimation by applying the MUSIC algorithm is
Changing theta from-90 degrees to 90 degrees according to a certain step length by the above formula, and estimating an arrival angle by searching a peak;
s6, setting different
Different arrival angle estimation results are obtained according to the formula (8) in the step S5;
sequentially taking values from 1 to M-1 to obtain M-1 kinds of arrival angle estimation results, which are expressed as
The number of angles of (a) represents the number of estimated signal sources, the angle value represents the incoming wave direction of the signal source, and the setting is based on
The number of the judged signal sources is
Angle of arrival of signal of
S7, mixing
Form a row vector, denoted ne＝[n1,n2,…,nM-1]Counting the number of the signal sources which appear most from the vector as the final estimated number of the signal sources
The number appearing in the vector
The serial number positions are marked, and the serial numbers are
The number of occurrences is given as num; to obtain
Then, will correspond to the number
The arrival angles of the signals form a row vector represented as
Vector formed by num group signal arrival angles
Averaging to obtain the final signal arrival angle estimation value expressed as
Obtaining the number of the signal sources estimated finally
And the final estimated angle of arrival
2. The improved MUSIC direction of arrival estimation method of claim 1, wherein: in step S1, the far-field signals are mutually independent narrow-band stationary signals, and satisfy the mean value E { S (t) ═ 0} and the covariance matrix
Wherein
Is the power of the kth signal; the superimposed noise in the array observation signal vector is additive white Gaussian noise and is independent from the signal; the number of far-field signals is less than the number of array elements and the number of sampling points, i.e. K<min(M,T1) (ii) a The signals are propagated in an ideal space, and the array sensor has omnidirectional consistency.
3. The improved MUSIC direction of arrival estimation method of claim 1, wherein: in step S2, a covariance matrix of the array observation signal x (t) is calculated, which is expressed as:
R＝E[XXH]＝AE[SSH]AH+E[NNH]＝ARSAH+RN (2)
wherein R isSAnd RNAre respectively a signalCovariance matrix and noise covariance matrix, H represents conjugate transpose; since the signal and the noise are independent of each other, the data covariance matrix is decomposed into two parts, AR, related to the signal and the noiseSAHIs a signal portion; for spatially perfect white noise, and the noise power is σ2Then, there are:
R＝ARSAH+RN＝ARSAH+σ2I (3)
and (3) performing characteristic decomposition on the covariance matrix R, namely:
R＝ARSAH+RN＝Q∑QH (4)
wherein, matrix Q is the eigenvector matrix, diagonal matrix sigma is formed by the eigenvalue, namely:
in the equation (5), the characteristic values satisfy the following relationship:
λ1≥λ2≥…≥λK>λK+1≈…≈λM≈σ2
the steering vector matrix A is a Van der Monte matrix, provided that the target signal direction θi≠θp(i ≠ p), wherein i and p respectively represent the serial numbers of the signals, and K characteristic values corresponding to different target signals are total;
corresponding to the characteristic value lambdaiI is 1,2, …, M, and its feature vector is ei,i＝1,2,…,M。
4. The improved MUSIC direction of arrival estimation method of claim 1, wherein: the number K of signal sources is at most half of the number of antenna elements, i.e.
Indicating a rounding down.
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