CN113253194B - Broadband arrival angle and polarization combined measurement method based on sparse representation - Google Patents

Broadband arrival angle and polarization combined measurement method based on sparse representation Download PDF

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CN113253194B
CN113253194B CN202110429111.4A CN202110429111A CN113253194B CN 113253194 B CN113253194 B CN 113253194B CN 202110429111 A CN202110429111 A CN 202110429111A CN 113253194 B CN113253194 B CN 113253194B
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沈志博
王浩丞
朱全江
傅劲松
唐勇
刘俊
王星斗
曲焕全
霍东红
韩海周
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CETC 29 Research Institute
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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
    • 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

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Abstract

The invention discloses a sparse representation-based combined measurement method for wide-band arrival angle and polarization, which comprises the following steps of: s1, carrying out Fourier transform on vector data received by an antenna array of a direction-finding system to obtain a frequency domain model, and respectively measuring the central frequency of each signal; s2, calculating the polarization angle of each signal by using the output response of an orthogonal dual-polarized antenna in the antenna array; s3, uniformly and discretely dividing a space angle aiming at the kth signal in the space, and constructing a spatial domain redundant dictionary to obtain a sparse representation model of the space signal; s4, carrying out sparse reconstruction on vector data received by the antenna array on a redundant dictionary to obtain a sparse vector, and calculating the arrival angle of a signal through the position of a non-zero coefficient; s5, repeating the steps S3 and S4 to obtain the arrival angles of all signals. The invention provides a two-dimensional arrival angle and polarization combined measurement method in a wide frequency band, which can simultaneously obtain the center frequency, the two-dimensional arrival angle and the polarization parameters.

Description

Broadband arrival angle and polarization combined measurement method based on sparse representation
Technical Field
The invention relates to the technical field of array signal processing, in particular to a broadband arrival angle and polarization combined measurement method based on sparse representation.
Background
The existing array direction finding algorithm is mainly represented by a Multiple Signal Classification (MUSIC) method, and the basic principle is as follows:
for K far-field signals in space incident on the array, the array received data at time t x (t) is:
Figure BDA0003030705560000011
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000012
respectively representing the center frequency, pitch angle, azimuth angle, polarization auxiliary angle and polarization phase difference of the kth signal,
Figure BDA0003030705560000013
Figure BDA0003030705560000014
s (t) is a signal vector, and n (t) is a noise vector.
The covariance matrix of the array received data is:
Figure BDA0003030705560000015
for covariance matrix RxxPerforming eigenvalue decomposition, wherein the eigenvalue ΛsThe signal subspace spanned by the corresponding eigenvectors is UsCharacteristic value ΛnThe noise subspace spanned by the corresponding feature vectors is UnAnd U issAnd UnThe two-dimensional MUSIC spectral peak search calculation formula is
Figure BDA0003030705560000016
In the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000017
for the guide vector, a space spectrum is obtained by multi-dimensional parameter joint search
Figure BDA0003030705560000018
The spectral peak is maximum. Because the MUSIC algorithm needs to determine the position of a spectral peak through a multi-dimensional search process, the operation complexity is higher, the higher the required direction-finding precision is, the wider the frequency band is, the more dense the division of a spectral peak search grid is, the more obvious the parameter calculation efficiency is reduced, and the requirement of direction-finding real-time direction finding cannot be met.
The existing measurement method based on sparse representation utilizes the sparsity of a signal incoming wave direction on a space domain to establish a multi-dimensional redundant dictionary, and then a sparse coefficient is obtained through signal sparse reconstruction, wherein the redundant dictionary is constructed as follows:
Figure BDA0003030705560000021
the constructed redundant dictionary is irrelevant to the actual information source DOA, and the dimensionality is in direct proportion to the measurement precision and the resolution. The signals can be sparsely represented by using the redundant dictionary, and a sparse representation model of the signals is obtained as follows:
x(t)＝Dz(t)+n(t) (5)
in the formula, z (t) is a sparse vector, only K groups of non-zero coefficients exist in z (t), and parameter measurement of K space signals is obtained by sparsely solving the positions of the non-zero coefficients. The method needs to establish a multi-dimensional joint redundant dictionary, the higher the required direction-finding precision is, the wider the frequency band is, the length of the dictionary is increased rapidly, the calculated amount of sparse solution is huge, and the requirement of real-time processing of a direction-finding system is difficult to meet.
Disclosure of Invention
In order to solve the problem of high complexity of the joint measurement operation of the multi-dimensional parameters (such as center frequency, two-dimensional arrival angle and polarization) of the signals, the invention provides a sparse representation-based wide-band arrival angle and polarization joint measurement method, which can avoid a multi-dimensional joint search process, optimize the operation complexity of the multi-dimensional parameters, has higher calculation efficiency and can improve the real-time processing performance of a direction-finding system.
The technical scheme adopted by the invention is as follows:
a broadband angle of arrival and polarization joint measurement method based on sparse representation comprises the following steps:
s1, carrying out Fourier transform on vector data received by an antenna array of a direction-finding system to obtain a frequency domain model x (f)k) And respectively measuring the center frequency f of each signalk(ii) a Wherein K is 1,2, K is the number of signals;
s2, calculating the polarization auxiliary angle gamma of each signal by using the output response of the orthogonal dual-polarized antenna in the antenna arraykAnd a polarization phase angle ηk；
S3, aiming at the kth signal in the space, uniformly and discretely dividing the space angle to construct a spatial domain redundant dictionary
Figure BDA0003030705560000031
Obtaining a sparse representation model of a spatial signal
Figure BDA00030307055600000312
Wherein
Figure BDA0003030705560000032
Is the pitch angle of the signal, theta is the azimuth angle of the signal;
s4, vector data received by the antenna array is stored in a redundant dictionary
Figure BDA0003030705560000033
Performing sparse reconstruction to obtain sparse vector
Figure BDA00030307055600000313
And calculating the arrival angle of the signal, namely the pitch angle, through the position of a non-zero coefficient
Figure BDA00030307055600000311
And an azimuth angle θ;
s5, repeating the steps S3 and S4 to obtain the arrival angles of all K signals.
Furthermore, the antenna array adopts a polarization sensitive vector cross-shaped linear array, an orthogonal dual-polarized antenna is arranged at the original point of the array, the phase centers are overlapped, other array elements are arranged in a multi-polarization mode, and the distance between the array elements is d.
Furthermore, considering K completely polarized far-field narrow-band signals in space to be incident on the antenna array, and the pitch angle
Figure BDA0003030705560000034
Defined as the angle between the incident signal and the positive direction of the z-axis, the azimuth angle thetakThe epsilon (-pi/2, pi/2) is defined as the included angle of the incident signal in the yoz plane and the positive direction of the x axis, and the polarization domain guide vector of the kth signal and the direction of the y axis is expressed as:
Figure BDA0003030705560000035
in the formula, the polarization auxiliary angle gammakE [0, π/2), polarization phase angle ηkE is [ -pi, pi), e is a natural constant, and j is an imaginary unit;
the polarization domain steering vector in the x-axis direction is represented as:
Figure BDA0003030705560000036
further, according to the antenna array structure, the space domain steering vectors in the x and y axis directions are respectively expressed as:
Figure BDA0003030705560000037
Figure BDA0003030705560000038
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000039
and
Figure BDA00030307055600000310
representing the spatial phase factor at the m-th array element,
Figure BDA0003030705560000041
representing the direction cosine of the incident signal along the x-axis,
Figure BDA0003030705560000042
the cosine of the direction of an incident signal along the y-axis direction is shown, d is the array element distance, lambda is the wavelength of the incident signal, and M is the number of array elements.
Further, the steering vector of the polarization sensitive vector cross linear array is a Kronecker product of the polarization domain steering vector and the space domain steering vector, and the steering vector of the whole antenna array is expressed as:
Figure BDA0003030705560000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000044
representing the Kronecker product.
Further, in step S1, the frequency domain model x (f)k) Expressed as:
Figure BDA0003030705560000045
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000046
a steering vector, s (f), representing the k-th signalk) Representing a central frequency of fkSignal vector of (d), n (f)k) Representing the noise vector and a the vector array flow pattern.
Further, in step S2, if the output response of the orthogonal dual-polarized antenna is represented as:
e＝heh+vev(10)
in the formula, ehAnd evIs a direction unit vector, h and v are complex coefficients after polarization decomposition, the polarization auxiliary angle and the polarization phase angle of the signal are respectively:
Figure BDA0003030705560000047
further, in step S3, the spatial domain redundant dictionary is constructed as:
Figure BDA0003030705560000048
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000049
equally spaced division by any potential angle of arrival, NSThe number of grids is divided for the angle of arrival,
Figure BDA00030307055600000410
representing the ith potential angle of arrival of the kth signal;
sparse representation is carried out on the signals by utilizing a space domain redundant dictionary to obtain a sparse representation model:
Figure BDA00030307055600000411
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000056
in the form of a sparse vector, the vector is,
Figure BDA0003030705560000057
is a noise vector.
Further, in step S4, the sparse vector is applied
Figure BDA0003030705560000058
The solution problem of non-zero coefficients of (a) is converted into a convex optimization problem:
Figure BDA0003030705560000051
in the formula, z represents a sparse vector to be solved, D represents a redundant dictionary, and epsilon represents a sparse reconstruction error; the above formula represents the reconstruction error | | | | Dz-x | | | non-woven phosphor2Under the condition of less than epsilon, the 1-norm of z is minimized; the angle of arrival of the signal is obtained by solving for the position of the non-zero coefficient in z.
Further, if necessary, a highly accurate polarization auxiliary angle γ is obtainedkAnd then, uniformly and discretely dividing the polarization angle on the obtained signal arrival angle to construct a polarization domain redundancy dictionary:
Figure BDA0003030705560000052
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000053
equally spaced at any potential polarization angle, NSThe grid number is divided for the polarization angle,
Figure BDA0003030705560000054
indicating an angle of arrival of
Figure BDA0003030705560000055
The ith potential polarization angle of the kth signal; the polarization auxiliary angle gamma can be obtained by utilizing the above formula to carry out polarization domain sparse reconstruction on the signalkAccurate measurement of.
The invention has the beneficial effects that:
the invention provides a novel method for the combined measurement of the two-dimensional arrival angle and the polarization in the wide frequency band, and the measurement of the center frequency, the two-dimensional arrival angle and the polarization parameter can be obtained simultaneously. The method utilizes the multi-polarization vector array to decompose the multi-dimensional parameter joint measurement of the signals into frequency domain, space domain and polarization domain independent processing, and avoids the multi-dimensional joint search process, thereby greatly improving the parameter calculation efficiency.
Drawings
FIG. 1 is a polarization sensitive vector cross-bar model of the present invention;
FIG. 2 is a block diagram showing the components of embodiment 2 of the present invention;
FIG. 3 is a block flow diagram of a joint measurement method of the present invention;
FIG. 4 frequency measurement results of the present invention;
FIG. 5 polarization measurements of the present invention;
FIG. 6 is a diagram of the angle of arrival measurement root mean square error of the present invention;
FIG. 7 is a comparison result of operation time of the present invention and a conventional multi-dimensional joint search method.
Detailed Description
In order to more clearly understand the technical features, objects, and effects of the present invention, specific embodiments of the present invention will now be described. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
In this embodiment, an antenna array of the direction finding system adopts a polarization sensitive vector cross-shaped array, as shown in fig. 1. An orthogonal dual-polarized antenna is arranged at the origin of the array, the phase centers are overlapped, other array elements are arranged in a multi-polarization mode, and the distance between the array elements is d. Consider K fully polarized far-field narrow-band signals in space incident on the antenna array, where fkThe center frequency of the kth (K ═ 1, 2.. K) signal, the pitch angle
Figure BDA0003030705560000061
Defined as the angle between the incident signal and the positive direction of the z-axis, the azimuth angle thetakE (-pi/2, pi/2) is defined as the angle between the incident signal in the yoz plane and the positive direction of the x axis, and the polarization domain steering vector of the k signal and the direction of the y axis is expressed as:
Figure BDA0003030705560000062
in the formula, gammakE [0, π/2) represents the polarization assist angle, ηkE [ - π, π) represents the polarization phase angle, e is a natural constant, and j is an imaginary unit.
The polarization domain steering vector in the x-axis direction is represented as:
Figure BDA0003030705560000063
and respectively representing the space domain guide vectors in the x and y axis directions as follows according to the antenna array structure:
Figure BDA0003030705560000071
Figure BDA0003030705560000072
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000073
and
Figure BDA0003030705560000074
representing the spatial phase factor at the m-th array element,
Figure BDA0003030705560000075
representing the direction cosine of the incident signal along the x-axis,
Figure BDA0003030705560000076
the direction cosine of an incident signal along the y-axis direction is shown, d is the array element interval, lambda is the wavelength of the incident signal, and M is the array element number.
And the guide vector of the polarization sensitive vector cross linear array is a Kronecker product of the polarization domain guide vector and the airspace guide vector, and the guide vector of the whole antenna array is expressed as follows:
Figure BDA0003030705560000077
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000078
representing the Kronecker product.
Transforming the data received by the multi-polarization vector array to a frequency domain to obtain a frequency domain model:
Figure BDA0003030705560000079
in the formula (I), the compound is shown in the specification,
Figure BDA00030307055600000710
a steering vector, s (f), representing the k-th signalk) Representing a central frequency of fkSignal vector of (d), n (f)k) Representing the noise vector and a the vector array flow pattern.
Because the space electromagnetic signal may be polarized in any way after reaching the antenna array, the orthogonal dual-polarized antenna at the original point position of the polarization sensitive vector cross-shaped array can be used for acquiring the polarization information of the space electromagnetic signal. The output response of the orthogonal dual-polarized antenna for receiving the electromagnetic wave with any polarization can be expressed as:
e＝heh+vev (12)
in the formula, ehAnd evIs a direction unit vector, h and v are complex coefficients after polarization decomposition, the polarization auxiliary angle and the polarization phase angle of the signal are respectively:
Figure BDA00030307055600000711
the output response of the received signal through the orthogonal dual-polarized antenna allows the polarization assist angle and phase angle of the signal to be calculated according to the above equations. Because the signal satisfies the space domain sparsity, a redundant dictionary can be established in the space domain to carry out sparse representation on the signal. According to the theory of electromagnetic field, any polarized electromagnetic wave can be formed byA plurality of fixed polarization electromagnetic waves are synthesized. Because the antenna array is a polarization sensitive vector cross linear array, the array flow pattern of the polarization mode of incoming wave signals can be synthesized through different polarization responses of the array. For the k signal in space (center frequency f)kWith an auxiliary angle of polarization of gammakPolarization phase angle of ηk) Uniformly and discretely dividing the space angle to construct a spatial domain redundant dictionary:
Figure BDA0003030705560000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000082
equally spaced division by any potential angle of arrival, NSThe number of grids is divided for the angle of arrival,
Figure BDA0003030705560000083
representing the ith potential angle of arrival of the kth signal.
The constructed space domain redundant dictionary is irrelevant to the actual information source DOA, and the dimensionality is in direct proportion to the measurement precision and the resolution. The signals can be sparsely represented by utilizing a spatial domain redundant dictionary to obtain a spatial domain sparse representation model:
Figure BDA0003030705560000084
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000086
is a sparse vector, the position of the non-zero coefficient of which corresponds to the actual angle of arrival of the spatial signal,
Figure BDA0003030705560000087
is a noise vector. According to the sparse reconstruction theory, the solution is obtained
Figure BDA0003030705560000088
ZhongfeiThe angle of the signal can be obtained by the position of the zero coefficient, and the solution of the non-zero coefficient can be converted into a convex optimization problem:
Figure BDA0003030705560000085
s.t.||Dz-x||2<ε (17)
in the formula, z represents a sparse vector to be solved, D represents a redundant dictionary, and epsilon represents a sparse reconstruction error. The above formula represents the reconstruction error | | | | Dz-x | | | non-woven phosphor2And a condition less than epsilon, such that the 1-norm of z is minimized. The angle of arrival of the signal can be obtained by solving the position of the non-zero coefficient in z.
In addition, the formula (13) utilizes the orthogonal dual-polarized antenna to obtain the rough measurement of the polarization angle of the signal, and because the polarization parameters in the electronic reconnaissance mainly take part in the sorting and identification of the signal as one-dimensional characteristics, the result of the rough measurement of the polarization can generally meet the requirements. If high-precision polarization angle measurement (mainly polarization auxiliary angle) needs to be obtained, the polarization angle can be uniformly and discretely divided on the obtained signal arrival angle, and a polarization domain redundancy dictionary is constructed:
Figure BDA0003030705560000091
in the formula (I), the compound is shown in the specification,
Figure BDA0003030705560000092
equally spaced at any potential angle of polarization, NSThe number of grids is divided for the polarization angle,
Figure BDA0003030705560000093
indicating an angle of arrival of
Figure BDA0003030705560000094
The ith potential polarization angle of the kth signal. And (3) carrying out polarization domain sparse reconstruction on the signals by using the above formula, so as to obtain accurate measurement of the polarization auxiliary angle.
As shown in fig. 3, the sparse representation-based wide-band angle-of-arrival and polarization joint measurement method of the present embodiment includes the following steps:
s1, carrying out Fourier transform on vector data received by an antenna array of a direction-finding system to obtain a frequency domain model x (f)k) And respectively measuring the center frequency f of each signalk(ii) a Wherein K is 1,2, K is the number of signals;
s2, calculating the polarization auxiliary angle gamma of each signal according to the formula (13) by using the output response of the orthogonal dual-polarized antenna in the antenna arraykAnd a polarization phase angle ηk；
S3, aiming at the kth signal in the space, uniformly and discretely dividing the space angle, and constructing a spatial domain redundant dictionary according to the formula (14)
Figure BDA0003030705560000095
Obtaining a sparse representation model of a spatial signal
Figure BDA00030307055600000910
Wherein
Figure BDA0003030705560000096
Is the pitch angle of the signal, theta is the azimuth angle of the signal;
s4, vector data received by the antenna array is stored in a redundant dictionary
Figure BDA0003030705560000097
Performing sparse reconstruction to obtain sparse vector
Figure BDA0003030705560000099
And calculating the arrival angle of the signal, namely the pitch angle, through the position of a non-zero coefficient
Figure BDA0003030705560000098
And an azimuth angle θ;
s5, repeating the steps S3 and S4 to obtain the arrival angles of all K signals.
Preferably, the polarization assist angle γ is obtained with high precision if necessarykThen, the polarization angle is uniformly and discretely divided on the obtained signal arrival angle, a polarization domain redundant dictionary is constructed according to the formula (18), and the polarization domain sparse reconstruction is performed on the signal, so that the polarization auxiliary angle gamma can be obtainedkAccurate measurement of.
The sparse representation-based wide-band arrival angle and polarization combined measurement method can realize fractal dimension measurement and independent processing of the center frequency, the two-dimensional arrival angle and the polarization parameter, and reduce the computation of multi-dimensional parameter measurement of signals.
Example 2
This example is based on example 1:
in this embodiment, by using a radiation source test in a microwave darkroom, the combined measurement method of the angle of arrival and polarization of a plurality of radiation source signals based on the sparse representation, which is provided in embodiment 1, is used to measure the angle of arrival and the polarization of a plurality of radiation source signals. Wherein, the radiation source signal conditions are set as follows:
1) erecting 3 radiation source antennas in a microwave darkroom, installing a direction-finding system on a turntable, and measuring the spatial angle of the radiation source
Figure BDA0003030705560000102
Set up as (-15 °, -20 °), (5 °,15 °), (30 °, -5 °), respectively, wherein the antenna polarization angle of radiation source 1 can be changed from 0 ° -90 ° linear polarization by controlling the polarization synthesis source, radiation source 2 is vertically polarized, and radiation source 3 is horizontally polarized;
2) setting the frequencies of the radiation sources 1,2 and 3 to be 3.3GHz, 5.6GHz and 9.5GHz respectively, the repetition frequency to be 1000 mus, the pulse width to be 10 mus, pulse signals, and the radiation source signals are overlapped on the time domain.
The specific steps for measuring the angle of arrival and polarization of a signal using the measurement method proposed in embodiment 1 are as follows:
1) the antenna array is shown in fig. 1, the number of array elements on the array x and the array y is 7, wherein the origin position is an orthogonal dual-polarized antenna with overlapped phase centers;
2) as shown in fig. 2, the radio frequency signal received by the antenna array is down-converted to an intermediate frequency signal by a switch component, a frequency conversion component (i.e., a down-conversion module in fig. 2), and the like, and then the intermediate frequency signal is subjected to parallel sampling processing by a multi-channel digital acquisition processor, and the sampled data is transmitted to a signal processor for storage and processing;
3) carrying out frequency measurement on the received data and obtaining array frequency domain output data;
4) calculating the polarization mode of each signal according to the formula (13) through the output response of the orthogonal dual-polarized antenna;
5) constructing a spatial domain redundant dictionary for each signal according to equation (14)
Figure BDA0003030705560000101
Obtaining a sparse representation model of the signal;
6) obtaining a signal arrival angle measuring result on a space domain redundant dictionary through sparse reconstruction according to the formulas (16) and (17);
7) constructing a polarization domain redundant dictionary for each signal according to equation (18)
Figure BDA0003030705560000111
And obtaining a polarization measurement result through sparse reconstruction.
Comparing the method with the traditional multidimensional joint search method, the angle search range is-45 degrees to 45 degrees, the stepping interval is 0.5 degrees, the polarization angle search range is 0 degree to 90 degrees, the stepping interval is adjusted to respectively take 10 degrees, 7 degrees, 5 degrees, 3 degrees, 1 degree and 0.5 degree, and the multidimensional joint search method and the angle and polarization measurement time of the method are respectively counted (counted according to the total time result of continuous 100 times of angle and polarization measurement). And (3) singly opening the radiation source 1, controlling the frequency output of a signal source to respectively count the root mean square errors of the measurement of the pitch angle and the azimuth angle from 2GHz to 12GHz (counting according to the processing result of 1000 pulse data).
As shown in fig. 4, the present invention enables accurate measurement of the frequency of all 3 radiation sources. The results of fig. 5 show that the present invention can correctly measure the polarization angles of 3 radiation sources. As shown in fig. 6, the method of the present invention can accurately measure the two-dimensional arrival angle of each frequency band signal in the wide frequency band, the maximum root mean square error of the pitching and azimuth measurement in the full frequency band is not more than 0.5 °, wherein the maximum root mean square error of the pitching and azimuth measurement in the C, X band is not more than 0.2 °.
As shown in fig. 7, the present invention adopts a mode of independent processing in a dimension division, which improves the measurement efficiency, and the calculation amount is basically unchanged under the condition of reducing the search interval of the polarization angle. In contrast, if a multi-dimensional joint search mode is directly adopted, the calculation amount is obviously increased, and the requirement of direction finding in real time cannot be met, so that the direction finding processing instantaneity of the method is verified to be obviously superior to that of the multi-dimensional joint search method.
The verification shows that the multi-dimensional parameter joint measurement of the signals is decomposed into frequency domain, space domain and polarization domain independent processing by adopting the multi-polarization vector array, so that the multi-dimensional joint search process is avoided, the operand is reduced, and two-dimensional high-precision direction finding and polarization measurement can be realized.
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A broadband angle of arrival and polarization joint measurement method based on sparse representation is characterized by comprising the following steps:
s1, carrying out Fourier transform on vector data received by an antenna array of a direction-finding system to obtain a frequency domain model x (f)k) And respectively measuring the center frequency f of each signalk(ii) a Wherein K is 1,2, K is the number of signals;
s2, calculating the polarization auxiliary angle gamma of each signal by using the output response of the orthogonal dual-polarized antenna in the antenna arraykAnd a polarization phase angle ηk；
S3, aiming at the kth signal in the space, the space angle is homogenizedDiscrete division and construction of spatial domain redundant dictionary
Figure FDA0003670953790000011
Obtaining a sparse representation model of a spatial signal
Figure FDA0003670953790000012
Wherein
Figure FDA0003670953790000013
Is the pitch angle of the signal, theta is the azimuth angle of the signal;
s4, vector data received by the antenna array is stored in a redundant dictionary
Figure FDA0003670953790000014
Performing sparse reconstruction to obtain sparse vector
Figure FDA0003670953790000015
And calculating the arrival angle of the signal, namely the pitch angle, through the position of a non-zero coefficient
Figure FDA0003670953790000016
And an azimuth angle θ;
s5, repeating the steps S3 and S4 to obtain the arrival angles of all K signals;
the antenna array adopts a polarization sensitive vector cross-shaped linear array, an orthogonal dual-polarized antenna is arranged at the original point of the array, the phase centers are overlapped, the rest array elements are arranged in a multi-polarization mode, and the array element interval is d;
considering K completely polarized far-field narrow-band signals in space to be incident on the antenna array and the pitch angle
Figure FDA0003670953790000017
Defined as the angle between the incident signal and the positive direction of the z-axis, the azimuth angle thetakE (-pi/2, pi/2) is defined as the angle between the incident signal in the yoz plane and the positive direction of the x axis, and the polarization domain steering vector of the k signal and the direction of the y axis is expressed as:
Figure FDA0003670953790000018
in the formula, the polarization auxiliary angle gammakE [0, π/2), polarization phase angle ηkE is a natural constant, and j is an imaginary number unit;
the polarization domain steering vector in the x-axis direction is represented as:
Figure FDA0003670953790000019
according to the antenna array structure, the space domain steering vectors in the x and y axis directions are respectively expressed as:
Figure FDA0003670953790000021
Figure FDA0003670953790000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003670953790000023
and
Figure FDA0003670953790000024
representing the spatial phase factor at the m-th array element,
Figure FDA0003670953790000025
representing the direction cosine of the incident signal along the x-axis,
Figure FDA0003670953790000026
expressing the direction cosine of an incident signal along the y-axis direction, wherein d is the array element interval, lambda is the wavelength of the incident signal, and M is the number of array elements;
and the guide vector of the polarization sensitive vector cross linear array is a Kronecker product of the polarization domain guide vector and the airspace guide vector, and the guide vector of the whole antenna array is expressed as follows:
Figure FDA0003670953790000027
in the formula (I), the compound is shown in the specification,
Figure FDA0003670953790000028
represents the Kronecker product;
in step S1, frequency domain model x (f)k) Expressed as:
Figure FDA0003670953790000029
in the formula (I), the compound is shown in the specification,
Figure FDA00036709537900000210
a steering vector, s (f), representing the k-th signalk) Representing a central frequency of fkSignal vector of (d), n (f)k) Representing a noise vector, and A representing a vector array flow pattern;
in step S3, the constructed spatial domain redundant dictionary is expressed as:
Figure FDA00036709537900000211
in the formula (I), the compound is shown in the specification,
Figure FDA00036709537900000212
equally spaced division by any potential angle of arrival, NSThe number of grids is divided for the angle of arrival,
Figure FDA00036709537900000213
representing the ith potential angle of arrival of the kth signal;
performing sparse representation on the signals by using a spatial domain redundant dictionary to obtain a sparse representation model:
Figure FDA00036709537900000214
in the formula (I), the compound is shown in the specification,
Figure FDA00036709537900000215
in the form of a sparse vector, the vector is,
Figure FDA00036709537900000216
is a noise vector;
if it is desired to obtain a high precision polarization auxiliary angle gammakAnd then, uniformly and discretely dividing the polarization angle on the obtained signal arrival angle to construct a polarization domain redundancy dictionary:
Figure FDA0003670953790000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003670953790000032
equally spaced at any potential angle of polarization, NSThe number of grids is divided for the polarization angle,
Figure FDA0003670953790000033
indicating an angle of arrival of
Figure FDA0003670953790000034
The ith potential polarization angle of the kth signal is obtained by utilizing the above formula to carry out polarization domain sparse reconstruction on the signalkThe accurate measurement of (2).
2. The sparse-representation-based combined measurement method for wide-band angle of arrival and polarization of claim 1, wherein in step S2, if the output response of the orthogonal dual-polarized antenna is represented as:
e＝heh+vev (10)
in the formula, ehAnd evIs a direction unit vector, h and v are complex coefficients after polarization decomposition, the polarization auxiliary angle and the polarization phase angle of the signal are respectively:
Figure FDA0003670953790000035
3. the method for joint measurement of wide-band angle of arrival and polarization based on sparse representation as claimed in claim 1, wherein in step S4, sparse vector is applied
Figure FDA0003670953790000036
The solution problem of non-zero coefficients of (a) is converted into a convex optimization problem:
Figure FDA0003670953790000037
s.t.||Dz-x||2<ε
in the formula, z represents a sparse vector to be solved, D represents a redundant dictionary, and epsilon represents a sparse reconstruction error; the above formula represents the reconstruction error | | | | Dz-x | | | non-woven phosphor2The 1-norm of z is minimized under the condition of being less than epsilon; the angle of arrival of the signal is obtained by solving for the position of the non-zero coefficients in z.
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