CN114460531A - Uniform linear array MUSIC spatial spectrum estimation method - Google Patents

Uniform linear array MUSIC spatial spectrum estimation method Download PDF

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CN114460531A
CN114460531A CN202011245176.5A CN202011245176A CN114460531A CN 114460531 A CN114460531 A CN 114460531A CN 202011245176 A CN202011245176 A CN 202011245176A CN 114460531 A CN114460531 A CN 114460531A
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matrix
subspace
signal
vector
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张柏华
汤加跃
刘俊秀
王令欢
邓一鹗
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Xi'an Kaiyang Microelectronic Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • 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
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
    • 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
    • G01S3/04—Details
    • G01S3/10—Means for reducing or compensating for quadrantal, site, or like errors

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Abstract

The invention provides a uniform linear array MUSIC spatial spectrum estimation method, which is applied to target angle measurement of radar communication and navigation, and comprises the following steps: acquiring a covariance matrix of array received signals; performing Topriz preprocessing on the covariance matrix; performing characteristic decomposition on the matrix subjected to Topriz pretreatment; estimating the number of information sources by using the characteristic value after the characteristic decomposition; constructing an error correction matrix by using the steering vectors of the array received signals; and constructing a spectrum estimation formula by using the approximate orthogonality of the guide vector in the signal subspace and the noise subspace and the error correction matrix, and performing optimization search. When various non-ideal factors exist simultaneously, the method can still stably and accurately estimate the direction of arrival of the echo signal.

Description

Uniform linear array MUSIC spatial spectrum estimation method
Technical Field
The invention belongs to the field of signal processing, and particularly relates to a uniform array MUSIC spatial spectrum estimation method.
Background
Direction of Arrival (DOA) estimation is an important research Direction for array signal processing, and is gradually developed on the basis of a beam forming technology, a null technology and a time domain spectrum estimation technology. The spatial sampling of the spatial information source is completed through antenna units at different spatial positions, and then the high-precision and high-resolution azimuth estimation of the spatial information source is realized through the analysis and processing of snapshot data. Since the orientation information in the airspace corresponds to the spectral information in the time domain, the DOA estimate is also commonly referred to as a Spatial Spectrum (Spatial Spectrum) estimate.
In conventional array direction finding, the angular resolution of the target depends on the physical aperture size of the array, i.e. is subject to Rayleigh limit (Rayleigh Limitation). In practical applications, the physical aperture of the array is always limited by practical conditions and cannot be infinitely increased, which makes it difficult to obtain a high precision target direction using conventional processing methods. The high-resolution DOA estimation technology breaks through the Rayleigh limit constraint, and can greatly improve the angle estimation precision, the angle resolution and other related parameter estimation precision of spatial signals in system processing bandwidth, so that the method has a very wide application prospect in the fields of radar, communication, sonar and the like. In particular, it has recently become a key technology in the hotspot field, such as array radar passive detection, smart antenna Spatial Division Multiple Access (SDMA) vehicle-mounted millimeter wave radar, and the like.
The multiple signal classification (MUSIC) algorithm was proposed by r.o.schmidt doctor, et al, in 1979, and the proposed algorithm initiated a new era of spatial spectrum estimation algorithm, promoted the rise and development of feature structure class algorithm, and became an algorithm with spatial spectrum estimation notability. The MUSIC algorithm can obtain high angle measurement precision under ideal conditions. However, in practical application, various non-ideal factors often exist: array errors, unknown clutter, different noise, channel inconsistency, array cross-coupling, signal source coherence, and the like. In recent years, many researchers have proposed some solutions around the non-ideal factors in practice, but often the single non-ideal factor is not good or even fails when multiple non-ideal factors exist.
Disclosure of Invention
In view of the above, the present invention provides a method for estimating a uniform array MUSIC spatial spectrum, which is used to solve the deficiencies of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
the embodiment of the invention provides a method for estimating a uniform array MUSIC spatial spectrum, which comprises the following steps:
acquiring a covariance matrix of array received signals;
performing Topriz preprocessing on the covariance matrix;
performing characteristic decomposition on the matrix subjected to Topriz pretreatment;
estimating the number of information sources by using the characteristic value after the characteristic decomposition;
constructing an error correction matrix by using the steering vectors of the array received signals;
and constructing a spectrum estimation formula by using the approximate orthogonality of the guide vector in the signal subspace and the noise subspace and the error correction matrix, and performing optimization search.
Further, the specific process of obtaining the covariance matrix of the array received signals is as follows:
the N narrow-band far-field signals received by the M arrays are:
X(t)＝A(θ)s(t)+N(t) (1)
wherein X (t) is M × 1 dimension snapshot data vector of array, N (t) is M × 1 dimension noise data vector of array, S (t) is N × 1 dimension vector of space signal, A is M × N dimension flow pattern matrix (guide vector matrix) of space array
A＝[a1(ω),a2(ω),…,aN(ω)] (2)
Wherein the guide vector
Figure BDA0002769735680000021
Wherein,
Figure BDA0002769735680000031
c is the speed of light, lambda is the wavelength, tau is the wave path difference, for a uniform linear array, the wave path difference of adjacent array elements is
Figure BDA0002769735680000032
Wherein d is the array element spacing, and theta is the signal incidence angle.
At this time, the covariance matrix of the array data can be obtained as
R＝E[XXH]＝AE[SSH]AH+σ2I＝ARSAH+σ2I (5)
Wherein R isSBeing a covariance matrix of the signal, ARSAHAs signal part, σ2Variance of noise, σ2I is the noise portion.
Further, the specific process of performing Topriz preprocessing on the covariance matrix is as follows:
the NxN array covariance matrix R is
Figure BDA0002769735680000033
Matrix R after Topritz preprocessingTIs composed of
Figure BDA0002769735680000034
The following relationships apply: rTElement on diagonal: rt is an integer of1,1＝rt2,2＝rti,i＝rtN,N；RTElement above diagonal: rt is an integer of1,2＝rt2,3＝rti,i+1＝rtN-1,N；RTElements below the diagonal: rt is an integer of2,1＝rt3,2＝rti+1,i＝rtN,N-1And so on; all RTThe elements with the same size on the matrix diagonal are obtained by averaging the corresponding elements of the array covariance matrix R, that is:
Figure BDA0002769735680000035
and so on.
Further, the specific process of performing characteristic decomposition on the matrix after the Topriz preprocessing comprises the following steps:
matrix R after pretreatment of TopritzTIs subjected to characteristic decomposition of
Figure BDA0002769735680000041
Wherein, USIs a subspace spanned by the eigenvectors corresponding to the large eigenvalues, i.e. the signal subspace, and UNIs a subspace spanned by the feature vectors corresponding to the small feature values, namely a noise subspace;
ideally, the signal subspace and the noise subspace in the data space are orthogonal to each other, i.e. the steering vector in the signal subspace is also orthogonal to the noise subspace
aH(θ)UN＝0 (9)。
Further, the specific process of constructing the error correction matrix by using the steering vector of the array received signal comprises the following steps:
assuming that the signal steering vector in the ideal case is a (θ), the error correction matrix T consists of two parts:
T＝T1+T2 (10)
wherein, T1 and T2 are respectively calculated by the following formulas:
Figure BDA0002769735680000042
Figure BDA0002769735680000043
further, a spectrum estimation formula is constructed by using the approximate orthogonality of the steering vector in the signal subspace and the noise subspace and the error correction matrix, and the specific process of optimizing and searching is as follows:
the spectral calculation formula constructed is as follows:
Figure BDA0002769735680000044
where det () denotes a determinant.
And setting a proper threshold, searching in a preset angle range, and determining that the angle has the target when the angle passes the threshold.
The invention provides a robust MUSIC spatial spectrum estimation method suitable for a uniform linear array, which can still obtain stable and accurate target angle estimation under the condition of simultaneously having various non-ideal factors. The method is particularly suitable for engineering implementation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a method for estimating a spatial spectrum of a uniform array MUSIC according to an embodiment of the present invention;
FIG. 2 is the spectral estimation result of the classical MUSIC algorithm;
fig. 3 is a spectrum estimation result of the uniform array MUSIC spatial spectrum estimation method provided by the present application.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic flowchart illustrating a method for estimating a uniform array MUSIC spatial spectrum according to an embodiment of the present invention. The method is applied to target angle measurement of radar communication and navigation. The method comprises the following steps:
s101, acquiring a covariance matrix of array received signals.
The main method steps for forming the covariance matrix by the array received signals are as follows:
assume that the N narrow-band far-field signals received by the M arrays are:
X(t)＝A(θ)s(t)+N(t) (1)
wherein X (t) is M × 1 dimension snapshot data vector of array, N (t) is M × 1 dimension noise data vector of array, S (t) is N × 1 dimension vector of space signal, A is M × N dimension flow pattern matrix (guide vector matrix) of space array
A＝[a1(ω),a2(ω),…,aN(ω)] (2)
Wherein the guide vector
Figure BDA0002769735680000061
Wherein,
Figure BDA0002769735680000062
c is the speed of light, lambda is the wavelength, tau is the wave path difference, for a uniform linear array, the wave path difference of adjacent array elements is
Figure BDA0002769735680000063
Wherein d is the array element spacing, and theta is the signal incidence angle.
At this time, the covariance matrix of the array data can be obtained as
R＝E[XXH]＝AE[SSH]AH+σ2I＝ARSAH+σ2I (5)
Wherein R isSBeing a covariance matrix of the signal, ARSAHAs signal part, σ2Variance of noise, σ2I is the noise portion.
S102, Topriz preprocessing is carried out on the covariance matrix.
The main method steps for preprocessing the covariance matrix of the array data by Toeplitz pre (Toeplitz) are as follows:
assume that the array covariance matrix R of NxN obtained in S101 is
Figure BDA0002769735680000064
Matrix R after Toeplitz pretreatmentTIs composed of
Figure BDA0002769735680000065
The following relationships apply: rTElement on diagonal: rt is an integer of1,1＝rt2,2＝rti,i＝rtN,N；RTElement above diagonal: rt is an integer of1,2＝rt2,3＝rti,i+1＝rtN-1,N；RTElements below the diagonal: rt is an integer of2,1＝rt3,2＝rti+1,i＝rtN,N-1And so on. All RTThe elements with the same size on the matrix diagonal are obtained by averaging the corresponding elements of the array covariance matrix R, that is:
Figure BDA0002769735680000071
and so on.
S103, performing characteristic decomposition on the matrix subjected to Topritz preprocessing.
Matrix R after pretreatment of ToeplitzTThe main method steps for performing characteristic decomposition are as follows:
matrix R after pretreatment of TopritzTIs subjected to characteristic decomposition of
Figure BDA0002769735680000072
Wherein, USIs a subspace spanned by the eigenvectors corresponding to the large eigenvalues, i.e. the signal subspace, and UNIs a subspace spanned by the feature vectors corresponding to the small feature values, i.e. the noise subspace.
Ideally, the signal subspace and the noise subspace in the data space are orthogonal to each other, i.e. the steering vector in the signal subspace is also orthogonal to the noise subspace
aH(θ)UN＝0 (9)
And S104, estimating the number of the information sources by using the characteristic values after the characteristic decomposition.
And sequencing the characteristic values from large to small, and setting a threshold so as to determine the number of the information sources.
And S105, constructing an error correction matrix by using the guide vectors of the array received signals.
An error correction matrix T is constructed using the steering vectors. The method comprises the following steps:
assuming that the signal steering vector in the ideal case is a (θ), T consists of two parts:
T＝T1+T2 (10)
wherein, T1 and T2 are respectively calculated by the following formulas:
Figure BDA0002769735680000073
Figure BDA0002769735680000081
and S106, constructing a spectrum estimation formula by using the approximate orthogonality of the guide vector and the noise subspace in the signal subspace and the error correction matrix, and performing optimization search.
And (4) constructing a spectrum estimation formula by using the approximate orthogonality of the guide vector in the signal subspace and the noise subspace and the error correction matrix T obtained in the step S105, and performing optimization search. The method mainly comprises the following steps:
the spectral calculation formula constructed is as follows:
Figure BDA0002769735680000082
where det () denotes a determinant.
An appropriate threshold is set, a search is performed over the range of angles of interest (e.g., -90 °,90 °), and the angle is considered to have a target when the threshold is exceeded.
The following simulations compare the estimated performance of the classical MUSIC algorithm and the proposed method in the presence of various errors.
Simulation conditions are as follows: the ground clutter noise ratio is 15dB, the array element number is 8, the two coherent targets are respectively positioned at-5 degrees and 5 degrees, and the amplitude phase error: -1dB, -10 °,10 °) randomly distributed; array element cross coupling degree of freedom: 2, mutual coupling coefficient: c1 ═ 0.1+0.1 × i.
Fig. 2 and fig. 3 show the spectrum estimation results of the classical MUSIC algorithm and the method of the present invention, respectively, and it can be seen from the graphs that the classical MUSIC algorithm has failed when there are many non-ideal factors, but the method of the present invention can still obtain stable and accurate angle estimation.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think of the changes or substitutions within the technical scope of the present invention, and shall cover the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (6)

1. A method for estimating a uniform array MUSIC spatial spectrum is characterized by comprising the following steps:
acquiring a covariance matrix of array received signals;
performing Topriz preprocessing on the covariance matrix;
performing characteristic decomposition on the matrix subjected to Topriz pretreatment;
estimating the number of information sources by using the characteristic value after the characteristic decomposition;
constructing an error correction matrix by using the steering vectors of the array received signals;
and constructing a spectrum estimation formula by using the approximate orthogonality of the guide vector in the signal subspace and the noise subspace and the error correction matrix, and performing optimization search.
2. The method of claim 1, wherein the obtaining the covariance matrix of the array received signals comprises:
the N narrow-band far-field signals received by the M arrays are:
X(t)＝A(θ)s(t)+N(t) (1)
wherein X (t) is M × 1 dimension snapshot data vector of array, N (t) is M × 1 dimension noise data vector of array, S (t) is N × 1 dimension vector of space signal, A is M × N dimension flow pattern matrix (guide vector matrix) of space array
A＝[a1(ω),a2(ω),…,aN(ω)] (2)
Wherein the guide vector
Figure FDA0002769735670000011
Wherein,
Figure FDA0002769735670000012
c is the speed of light, lambda is the wavelength, tau is the wave path difference, for a uniform linear array, the wave path difference of adjacent array elements is
Figure FDA0002769735670000013
Wherein d is the array element spacing, and theta is the signal incidence angle.
At this time, the covariance matrix of the array data can be obtained as
R＝E[XXH]＝AE[SSH]AH+σ2I＝ARSAH+σ2I (5)
Wherein R isSBeing a covariance matrix of the signal, ARSAHAs signal part, σ2Variance of noise, σ2I is the noise portion.
3. The method according to claim 1, wherein the Topritz preprocessing of the covariance matrix comprises:
the NxN array covariance matrix R is
Figure FDA0002769735670000021
Matrix R after Topritz preprocessingTIs composed of
Figure FDA0002769735670000022
The following relationships apply: rTElement on diagonal: rt is an integer of1,1＝rt2,2＝rti,i＝rtN,N；RTElements above the diagonal: rt is an integer of1,2＝rt2,3＝rti,i+1＝rtN-1,N；RTElements below the diagonal: rt is an integer of2,1＝rt3,2＝rti+1,i＝rtN,N-1And so on; all RTThe elements with the same size on the matrix diagonal are obtained by averaging the corresponding elements of the array covariance matrix R, that is:
Figure FDA0002769735670000023
and so on.
4. The method according to claim 1, wherein the characteristic decomposition of the Topritz-preprocessed matrix comprises the following specific steps:
matrix R after pretreatment of TopritzTIs subjected to characteristic decomposition of
Figure FDA0002769735670000024
Wherein, USIs a feature vector sheet corresponding to a large feature valueA subspace of, i.e., a signal subspace, and UNIs a subspace spanned by the feature vectors corresponding to the small feature values, namely a noise subspace;
ideally, the signal subspace and the noise subspace in the data space are orthogonal to each other, i.e. the steering vector in the signal subspace is also orthogonal to the noise subspace
aH(θ)UN＝0 (9)。
5. The method of claim 1, wherein constructing the error correction matrix using the steering vectors of the array received signals comprises:
assuming that the signal steering vector in the ideal case is a (θ), the error correction matrix T consists of two parts:
T＝T1+T2 (10)
wherein, T1 and T2 are respectively calculated by the following formulas:
Figure FDA0002769735670000031
Figure FDA0002769735670000032
。
6. the method of claim 1, wherein the spectral estimation formula is constructed by using the approximate orthogonality of the steering vector in the signal subspace and the noise subspace and the error correction matrix, and the optimization search is performed by:
the constructed spectrum calculation formula is as follows:
Figure FDA0002769735670000033
where det () denotes a determinant.
And setting a proper threshold, searching in a preset angle range, and determining that the angle has the target when the angle passes the threshold.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117331027A (en) * 2023-09-27 2024-01-02 青岛哈尔滨工程大学创新发展中心 Sound source number estimation method and system based on subspace matching measurement
CN117970227A (en) * 2024-02-04 2024-05-03 哈尔滨工程大学 Amplitude-phase error and angle parameter joint estimation method and system based on coherent distribution source under strong impulse noise

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117331027A (en) * 2023-09-27 2024-01-02 青岛哈尔滨工程大学创新发展中心 Sound source number estimation method and system based on subspace matching measurement
CN117331027B (en) * 2023-09-27 2024-06-04 青岛哈尔滨工程大学创新发展中心 Sound source number estimation method and system based on subspace matching measurement
CN117970227A (en) * 2024-02-04 2024-05-03 哈尔滨工程大学 Amplitude-phase error and angle parameter joint estimation method and system based on coherent distribution source under strong impulse noise

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