CN109188346B - Single snapshot DOA estimation method for large-scale uniform cylindrical array - Google Patents

Single snapshot DOA estimation method for large-scale uniform cylindrical array Download PDF

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CN109188346B
CN109188346B CN201811006677.0A CN201811006677A CN109188346B CN 109188346 B CN109188346 B CN 109188346B CN 201811006677 A CN201811006677 A CN 201811006677A CN 109188346 B CN109188346 B CN 109188346B
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苏涛
***
吴凯
张杏
陈艳利
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Xidian University
Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute 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
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Abstract

The invention discloses a large-scale uniform cylindrical array single snapshot DOA estimation method, which mainly solves the problems of high computation amount and high hardware realization difficulty in the prior art. The implementation scheme is as follows: setting corresponding parameters according to the model of the uniform cylindrical array to obtain a steering matrix A; arranging single snapshot signals received by the array into a matrix form X; performing FFT transformation, incoherent accumulation and maximum value detection on X rows in sequence to obtain a pitch angle rough estimation value
Figure DDA0001784123240000011
Introducing a pitch phase compensation variable eta el To is aligned with
Figure DDA0001784123240000012
The adjacent interval is searched and matched to obtain a fine pitch angle estimated value
Figure DDA0001784123240000013
Matching and transforming the X to obtain a virtual circular array signal y UCA Then carrying out cyclic convolution and maximum value detection to obtain a coarse estimation value of the azimuth angle
Figure DDA0001784123240000014
Introducing an azimuth phase compensation variable eta az To, for
Figure DDA0001784123240000015
The adjacent interval is searched and matched to obtain the fine azimuth angle estimated value
Figure DDA0001784123240000016
The method can greatly reduce the operation amount on the premise of ensuring the estimation precision, and can be used for target detection, target tracking or signal extraction.

Description

Single snapshot DOA estimation method for large-scale uniform cylindrical array
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a DOA (direction of arrival) estimation method which can be used for target detection, target tracking or signal extraction.
Background
The array signal processing is to arrange a plurality of sensors at different positions in space to form a sensor array, and to receive and process a space signal field by using the array so as to extract signals received by the array and characteristic information thereof, and simultaneously suppress interference and noise or uninteresting information.
Direction of arrival (DOA) estimation is one of the main research contents in array signal processing, is one of the important tasks in many fields such as radar, communication and sonar, and is the research focus from now on. The traditional DOA estimation algorithm comprises MUSIC, ESPRIT and related derivative algorithms, but the algorithms are limited by the operation amount and cannot be directly applied to a large-scale array, so that the DOA estimation algorithm based on conventional beam forming has advantages, and the disadvantage of low angular resolution is made up to a certain extent due to the factor of large array scale.
Most of the current DOA estimation algorithms are discussed in terms of uniform line arrays because the uniform line arrays satisfy the van der mond matrix form, thereby facilitating mathematical processing. However, the uniform linear array has the characteristics of only providing unambiguous azimuth information within the range of 180 degrees, and the array normal direction has high resolution and poor axial direction. In view of the above disadvantages, special structural arrays, including rectangular area arrays, uniform circular arrays, conformal arrays, etc., need to be studied.
Currently, for the DOA estimation method of the uniform cylindrical array, all uniform circular arrays forming the uniform cylindrical array are mapped into a virtual linear array mainly based on a phase mode transformation method, and then subsequent related algorithms such as UCA-RB-MUSIC, UCA-Root-MUSIC or UCA-ESPRIT are applied. Aiming at the situation of large-scale uniform cylindrical arrays, the operation precision needs to be ensured by the number of phase modes, but the increase of the number of the phase modes can cause great increase of the operation amount; the subsequent correlation algorithm needs matrix eigenvalue decomposition, polynomial root solving and the like, and the computation amount is huge; in addition, the subsequent correlation algorithm generally needs multi-beat accumulation, which further increases the computation amount.
Disclosure of Invention
The invention aims to provide a large-scale uniform cylindrical array single snapshot DOA estimation method aiming at the problems in the prior art, so as to greatly reduce the calculation amount on the premise of ensuring the estimation precision.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
(1) Setting corresponding parameters according to the model of the uniform cylindrical array to obtain a uniform cylindrical array guide vector a forming the uniform cylindrical array UCA And the steering vector a of the uniform linear array ULA And according to the uniform circular array steering vector a UCA And the guide vector a of the uniform linear array ULA Obtaining a guide matrix A of a uniform cylindrical array;
(2) Arranging the single snapshot signals received by the uniform cylindrical array into a matrix according to the steering matrix A of the arrayForm(s) of
Figure BDA0001784123220000021
Each element is respectively corresponding to an array element with corresponding number, wherein x mn The receiving signal of the mth array element of the nth circle of uniform circular array is represented, M represents the number of the array elements contained in each uniform circular array, and N represents the number of the array elements contained in each uniform circular array;
(3) Estimating the pitch angle of the signal source relative to the uniform cylindrical array according to the signal snapshot matrix X
Figure BDA0001784123220000029
(3a) Splitting the uniform cylindrical array into uniform linear arrays, namely performing FFT (fast Fourier transform) on each row of X independently, and performing incoherent accumulation on FFT conversion results of each row to obtain an incoherent accumulation result vector s el ；
(3b) For non-coherent accumulation result vector s el Maximum value detection is carried out, and the pitch angle of the signal source relative to the uniform cylindrical array is calculated
Figure BDA0001784123220000022
Is roughly estimated value of
Figure BDA0001784123220000023
(3c) Introducing a pitch phase compensation variable eta el For coarse estimation of pitch angle
Figure BDA0001784123220000024
Searching and matching correlation are carried out in the adjacent range of the pitch angle and the pitch angle is calculated
Figure BDA0001784123220000025
Fine estimated value of
Figure BDA0001784123220000026
(4) Fine estimation value according to signal snapshot matrix X and pitch angle
Figure BDA0001784123220000027
Estimating the azimuth angle θ of the signal source relative to the uniform cylindrical array:
a) Fine estimate from pitch angle
Figure BDA0001784123220000028
Synthesizing the uniform cylindrical array into a uniform circular array, namely obtaining a virtual circular array signal y by matching and transforming X UCA ；
(4b) For virtual circular array signal y UCA Performing cyclic convolution and maximum detection, and calculating the coarse estimate of the azimuth angle theta of the signal source relative to the uniform cylindrical array
Figure BDA0001784123220000031
(4c) Introducing an azimuth phase compensation variable eta az Coarse estimate of azimuth angle
Figure BDA0001784123220000032
Is searched and matched for correlation, and calculates a fine estimate of the azimuth angle theta
Figure BDA0001784123220000033
The invention has the beneficial effects that:
(1) Compared with the existing algorithm, the method greatly reduces the operation amount on the premise of ensuring the estimation precision.
Most of the existing signal processing algorithms for the structure containing the uniform circular array map the uniform circular array into a virtual linear array based on a phase mode transformation method, and then subsequent related algorithms such as UCA-RB-MUSIC, UCA-Root-MUSIC or UCA-ESPRIT are applied. In this process, the complexity of the algorithm such as eigenvalue decomposition is O (M) 3 ) And M is the number of the mapped phase modes, and in order to ensure the operation accuracy, the number of the phase modes is usually equivalent to the number of array elements of a uniform circular array, so that an algorithm based on eigenvalue decomposition is almost not realizable for a large-scale array.
The invention is based on the conventional beam forming algorithmThe operation amount of rough estimation is reduced through FFT and cyclic convolution, phase compensation and adjacent interval search and matching correlation are introduced, and estimation accuracy is improved. The arithmetic complexity of the algorithm provided by the invention is O (Mlog) 2 M + GM), wherein M represents the number of array elements of a uniform linear array or a uniform circular array, G represents the number of division of search intervals, and G < M is common for larger-scale arrays, and the operand can be simplified to O (Mlog) 2 M) magnitude, much smaller than existing algorithms.
(2) The algorithm has simple structure and is easy to program or realize on a hardware structure.
In the existing processing method, the UCA-RB-MUSIC, UCA-Root-MUSIC or UCA-ESPRIT algorithm is included, operations such as characteristic value decomposition, polynomial solution and the like need to be carried out, and the common signal processing device does not generally include such operation packages or libraries. The required operations of the invention are mainly FFT and search algorithms, and can be realized by the quick programming of an operation package or a library in a common signal processing device.
(3) According to the practical situation, the balance between the operation speed and the estimation precision can be realized by setting the dividing number of the pitching or azimuth searching intervals.
When the optimal pitching or azimuth phase compensation variable is searched, the number of the partitions of the pitching or azimuth search interval needs to be set, the more the number of the partitions is, the higher the estimation accuracy is, but the slower the operation speed is, otherwise, the less the number of the partitions is, the faster the operation speed is, but the lower the estimation accuracy is, so that a user can balance the operation speed and the estimation accuracy according to the actual situation.
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FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic diagram of a uniform cylindrical array model in accordance with the present invention;
FIG. 3 is a schematic diagram of a uniform circular array model in the present invention;
FIG. 4 is a schematic diagram of the real part of a matrix X of single snapshot signals received by the emulation array of the present invention;
FIG. 5 is a simulated incoherent integration result vector s of the present invention el A schematic diagram of (a);
FIG. 6 shows the final output z of the simulated uniform linear array of the present invention ULA Compensation variable eta of phase with pitching el Schematic diagram of the variation curve of (1);
FIG. 7 is a diagram of a simulated cyclic convolution norm vector s according to the present invention az A schematic diagram of (a);
FIG. 8 is a graph of the simulation uniform circular array matching output modulus z of the present invention UCA Compensation variable eta of phase with azimuth az Schematic diagram of the variation curve of (2).
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.
Referring to fig. 1, the implementation of the present invention is as follows:
step 1, calculating a steering matrix A of the uniform cylindrical array.
(1a) Setting corresponding parameters according to the model of the uniform cylindrical array to obtain a uniform cylindrical array guide vector a forming the uniform cylindrical array UCA And the guide vector a of the uniform linear array ULA ：
Referring to fig. 2 and 3, the uniform cylindrical array can be regarded as being composed of a plurality of uniformly spaced linear arrays or a plurality of uniformly spaced circular arrays, and the model of the uniform cylindrical array comprises: the working wavelength lambda of the array, the number M of the array elements of the uniform circular array, the array element spacing d of the uniform circular array, the number N of the array elements of the uniform linear array, the array element spacing h of the uniform linear array, and the pitch angle of the signal source relative to the uniform cylindrical array
Figure BDA0001784123220000051
An azimuth angle theta of the signal source relative to the uniform cylindrical array;
among the above parameters, the parameters to be set by the present invention include λ, M, d, N and h, where d is required to satisfy the condition
Figure BDA0001784123220000052
h needs to satisfy the condition
Figure BDA0001784123220000053
Among the above parameters, the parameters to be estimated according to the present invention include
Figure BDA0001784123220000054
And theta, wherein
Figure BDA0001784123220000055
The method is defined as the radial included angle of the signal source direction between the cylindrical plane projection and the reference direction, namely the number 0 array element, and the value range is [0,2 pi ]; theta is defined as the included angle between the signal source direction and the positive direction of the cylindrical axis, and the value range is [0, pi]；
Obtaining the guide vector a of the uniform circular array according to the model parameters of the uniform circular array UCA Expressed as follows:
Figure BDA0001784123220000056
where j is the unit of an imaginary number,
Figure BDA0001784123220000057
obtaining a guide vector a of the uniform linear array according to the model parameters of the uniform cylindrical array ULA Expressed as follows:
Figure BDA0001784123220000058
wherein
Figure BDA0001784123220000059
(1b) Steering vector a according to a uniform circular array UCA And the guide vector a of the uniform linear array ULA To obtain a uniform cylindrical arraySteering matrix a:
Figure BDA00017841232200000510
wherein
Figure BDA0001784123220000061
Representing Kronecker multiplication and T representing rank.
And 2, arranging the single snapshot signals received by the array into a matrix form X.
Arranging the single snapshot signals received by the uniform cylindrical array into a matrix form according to a guide matrix A of the array
Figure BDA0001784123220000062
Each element in X corresponds to the array element with corresponding number in A, wherein X mn And the received signal of the mth array element of the nth circle of uniform circular array is shown.
Step 3, estimating the pitch angle of the signal source relative to the uniform cylindrical array
Figure BDA0001784123220000063
(3a) Splitting the uniform cylindrical array into uniform linear arrays, namely, independently performing FFT (fast Fourier transform) on each row of X, and performing incoherent accumulation on FFT conversion results of each row to obtain an incoherent accumulation result vector s el Is specifically shown as s el (= Σ | XF |), where
Figure BDA0001784123220000064
Is FFT transformation matrix, Σ = [1 ]] 1×N Is a column sum vector, and p and q are variables indicating the row coordinates and the column coordinates of the matrix, respectively;
(3b) For the non-coherent accumulation result vector s el Maximum value detection is carried out, and the pitch angle of the signal source relative to the uniform cylindrical array is calculated
Figure BDA0001784123220000065
Is roughly estimated value of
Figure BDA0001784123220000066
Let q be el For non-coherent accumulation result vector s el Position of the maximum value element of (1), q el Is {0, 1.., N-1}, based on the incoherent accumulation result vector s el Position q of the maximum value element of (1) el Calculating the pitch angle
Figure BDA0001784123220000067
Is roughly estimated value of
Figure BDA0001784123220000068
When in use
Figure BDA0001784123220000069
When the temperature of the water is higher than the set temperature,
Figure BDA00017841232200000610
when in use
Figure BDA00017841232200000611
When the temperature of the water is higher than the set temperature,
Figure BDA00017841232200000612
(3c) Introducing a pitch phase compensation variable eta el For rough estimation of pitch angle
Figure BDA00017841232200000613
Is searched and matched and correlated, and the pitch angle is calculated
Figure BDA00017841232200000614
Fine estimated value of
Figure BDA00017841232200000615
Setting the number G of divisions of a pitch search space el Defining a pitch phase compensation variable η el Eta is then el Has a value space of
Figure BDA0001784123220000071
Defining a uniform linear array matching coefficient vector as
Figure BDA0001784123220000072
Setting the uniform linear array to match the output vector as
Figure BDA0001784123220000073
Wherein denotes conjugation;
let the final output of the uniform linear array be z ULA ＝||y ULA || 1 Search for z ULA Maximum value-derived pitch phase compensation variable
Figure BDA0001784123220000074
And will be
Figure BDA0001784123220000075
Defined as an optimal pitch phase compensation variable, where | · | | | non calculation 1 Representing 1 norm of the vector;
compensating variables according to optimal pitch phase
Figure BDA0001784123220000076
And a vector s of incoherent accumulation results el Maximum value element position q el Calculating the pitch angle
Figure BDA0001784123220000077
Fine estimated value of
Figure BDA0001784123220000078
When the temperature is higher than the set temperature
Figure BDA0001784123220000079
When the temperature of the water is higher than the set temperature,
Figure BDA00017841232200000710
when in use
Figure BDA00017841232200000711
When the temperature of the water is higher than the set temperature,
Figure BDA00017841232200000712
and 4, estimating the azimuth angle theta of the signal source relative to the uniform cylindrical array.
(4a) Fine estimate from pitch angle
Figure BDA00017841232200000713
Synthesizing the uniform cylindrical array into a uniform circular array, namely, obtaining a virtual circular array signal y by matching and transforming the signal snapshot matrix X UCA Is specifically shown as
Figure BDA00017841232200000714
Wherein
Figure BDA00017841232200000715
Is the optimal matching coefficient vector of the uniform linear array,
Figure BDA00017841232200000716
for the optimal pitch phase compensation variable, the conjugate is represented;
(4b) For virtual circular array signal y UCA Performing cyclic convolution and maximum detection, and calculating the coarse estimate of the azimuth angle theta of the signal source relative to the uniform cylindrical array
Figure BDA00017841232200000717
Defining uniform circular array initial matching coefficient vector
Figure BDA00017841232200000718
Wherein
Figure BDA00017841232200000719
Is the pitch angle of the signal source relative to the uniform cylindrical array
Figure BDA00017841232200000720
A fine estimate of (d);
setting the modulus vector of the circular convolution result as s az ＝|h UCA_0 ⊙y UCA I, where |, represents a cyclic convolution and | represents a modulus value;
let q az Is a modulus vector s of the result of the cyclic convolution az Position of the maximum value element of (b), q az The value space of (a) is {0, 1.., M-1};
according to the module value vector s of the cyclic convolution result az Position q of the maximum value element of (1) az Calculating a coarse estimate of the azimuth angle θ as
Figure BDA0001784123220000081
(4c) Introducing an azimuth phase compensation variable eta az Coarse estimate of azimuth angle
Figure BDA0001784123220000082
Is searched and matched for correlation, and calculates a fine estimate of the azimuth angle theta
Figure BDA0001784123220000083
The division number of the azimuth search interval is set as G az Defining an azimuth phase compensation variable η az Then η az Has a value space of
Figure BDA0001784123220000084
Defining a uniform circular array matching coefficient vector as
Figure BDA0001784123220000085
Setting the result of uniform circular array matching output modulus as
Figure BDA0001784123220000086
Search for z UCA Obtaining maximum azimuth phase compensation variable
Figure BDA0001784123220000087
And will be
Figure BDA0001784123220000088
Defining an optimal azimuth phase compensation variable, wherein H represents a conjugate rotation rank;
compensating variables according to optimal azimuth phase
Figure BDA0001784123220000089
And the modulus vector s of the result of the cyclic convolution az Position q of the maximum value element of (2) az Calculating a fine estimate of the azimuth angle θ as
Figure BDA00017841232200000810
The effects of the present invention are further demonstrated by the following Matlab simulation test.
Simulation conditions:
the simulation directly gives the relevant parameter parameters of the array, and specifically comprises the following steps: the working wavelength lambda =1M, the number of array elements of the uniform circular array M =128, the array element spacing d of the uniform circular array =0.45M, the number of array elements of the uniform linear array N =64, and the array element spacing h of the uniform linear array =0.5M. The preset parameters to be estimated are as follows: pitch angle of signal source relative to uniform cylindrical array
Figure BDA00017841232200000811
The azimuth angle θ =70 ° of the signal source with respect to the uniform cylindrical array.
The additional parameters are: the signal-to-noise ratio SNR of the received signal of each array element =20dB.
When DOA estimation is carried out, the number G of the pitching search interval division is set el =100, number of azimuth search interval divisions G az ＝100。
The error threshold for the angle estimate is set to 0.1 °.
(II) simulation content and result:
simulation 1, constructing a single snapshot signal matrix X received by the array according to the method of the present invention by using the simulation parameters, and recording the real part of the matrix X, wherein the result is shown in FIG. 4. The phase relationship of the signals of the individual elements can be observed from fig. 4.
Simulation 2, calculating to obtain incoherent accumulation result vector s according to the method of the invention by using the simulation parameters el As in fig. 5. From FIG. 5, a vector s can be derived el Is 5806, the position of the maximum is 6.
Using a vector s el The maximum value position of the pitch angle is further calculated to obtain the pitch angle
Figure BDA0001784123220000091
Is roughly estimated value of
Figure BDA0001784123220000092
And calculates a coarse estimation error of pitch angle as
Figure BDA0001784123220000093
Therefore, the rough estimation error of the pitch angle is larger than the error threshold value and does not meet the precision requirement of angle estimation.
Simulation 3, calculating and drawing uniform linear array and finally outputting z according to the method of the invention by using the simulation parameters ULA Compensation variable eta of phase with pitching el As shown in fig. 6. From FIG. 6, it can be seen that when eta is el Has a value of 0.0432,z ULA Taking the maximum value 8203, i.e. the optimum pitch phase compensation variable
Figure BDA0001784123220000094
By using
Figure BDA0001784123220000095
Further calculating to obtain a pitch angle
Figure BDA0001784123220000096
Fine estimation of
Figure BDA0001784123220000097
And calculating a fine estimation error of pitch angle of
Figure BDA0001784123220000098
Therefore, the fine pitch angle estimation error is smaller than the error threshold value, and the accuracy requirement of angle estimation is met.
Simulation 4, calculating to obtain a module value vector s of a circular convolution result according to the method of the invention by using the simulation parameters az And combining the vectors s az The individual elements of (a) are plotted point by point in position, as shown in figure 7. From FIG. 7, the vector s can be derived az The maximum value is 8009 and the maximum position is 25.
Using a vector s az Further calculating to obtain a coarse estimation value of the azimuth angle theta
Figure BDA0001784123220000101
And calculating a coarse estimate error of the azimuth angle of
Figure BDA0001784123220000102
It can be seen that the coarse estimation error of the azimuth is greater than the error threshold, and the accuracy requirement of the angle estimation is not met.
Simulation 5, calculating and drawing uniform circular array matching output module value z according to the method of the invention by using the simulation parameters UCA Compensation variable eta of phase with azimuth az As shown in fig. 8. From FIG. 8, it can be seen that when η az When the value of (b) is-0.00589, z UCA Taking the maximum value 8201, i.e. the optimum azimuth phase compensation variable
Figure BDA0001784123220000103
By using
Figure BDA0001784123220000104
Further calculating to obtain a fine estimated value of the azimuth angle theta
Figure BDA0001784123220000105
And calculating a fine estimate error of the azimuth angle as
Figure BDA0001784123220000106
It can be seen that the fine estimation error of the azimuth is less than the errorAnd the difference threshold value meets the precision requirement of angle estimation.
Those of ordinary skill in the art will understand that: all or part of the steps for realizing the method embodiments can be completed by hardware related to program instructions, the program can be stored in a computer readable storage medium, and the program executes the steps comprising the method embodiments when executed; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
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 conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within 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 (8)

1. The single-snapshot DOA estimation method of the large-scale uniform cylindrical array is characterized by comprising the following steps of:
(1) Setting corresponding parameters according to the model of the uniform cylindrical array to obtain a uniform cylindrical array guide vector a forming the uniform cylindrical array UCA And the steering vector a of the uniform linear array ULA And according to a uniform circular array, steering the vector a UCA And the steering vector a of the uniform linear array ULA Obtaining a guide matrix A of a uniform cylindrical array;
(2) Arranging the single snapshot signals received by the uniform cylindrical array into a matrix form X = [ X ] according to a guide matrix A of the array mn ] m∈[0,M-1],n∈[0,N-1] Each element corresponding to a correspondingly numbered array element, wherein x mn The receiving signal of the mth array element of the nth circle of uniform circular array is represented, M represents the number of the array elements contained in each uniform circular array, and N represents the number of the array elements contained in each uniform linear array;
(3) Estimating the pitch angle of the signal source relative to the uniform cylindrical array according to the signal snapshot matrix X
Figure FDA0003879641760000011
(3a) Splitting the uniform cylindrical array into uniform linear arrays, namely performing FFT (fast Fourier transform) on each row of X independently, and performing incoherent accumulation on FFT conversion results of each row to obtain an incoherent accumulation result vector s el ；
(3b) For non-coherent accumulation result vector s el Maximum value detection is carried out, and the pitch angle of the signal source relative to the uniform cylindrical array is calculated
Figure FDA0003879641760000012
Is roughly estimated value of
Figure FDA0003879641760000013
(3c) Introducing a pitch phase compensation variable eta el For coarse estimation of pitch angle
Figure FDA0003879641760000014
Is searched and matched and correlated, and the pitch angle is calculated
Figure FDA0003879641760000015
Fine estimated value of
Figure FDA0003879641760000016
(4) Fine estimation value according to signal snapshot matrix X and pitch angle
Figure FDA0003879641760000017
Estimating the azimuth angle θ of the signal source relative to the uniform cylindrical array:
(4a) Fine estimate from pitch angle
Figure FDA0003879641760000018
Synthesizing the uniform cylindrical arrays into a uniform circular array, namely, obtaining a virtual circular array signal y by matching and transforming X UCA ；
(4b) For virtual circular array signal y UCA Performing cyclic convolution and maximum detection, and calculating the coarse estimate of the azimuth angle theta of the signal source relative to the uniform cylindrical array
Figure FDA0003879641760000021
The implementation is as follows:
defining uniform circular array initial matching coefficient vector
Figure FDA0003879641760000022
Wherein
Figure FDA0003879641760000023
Is the pitch angle of the signal source relative to the uniform cylindrical array
Figure FDA0003879641760000024
A fine estimation value of the amount of the,
Figure FDA0003879641760000025
Figure FDA0003879641760000026
lambda is the working wavelength of the array, M is the number of the array elements of the uniform circular array, d is the array element spacing of the uniform circular array, and the requirements are met
Figure FDA0003879641760000027
Setting the modulus vector of the cyclic convolution result as s az ＝|h UCA_0 ⊙y UCA L, where y UCA Is a virtual circular array signal, | represents a circular convolution, | - | represents a modulus value;
let q az Is a modulus vector s of the result of the cyclic convolution az Position of the maximum value element of (1), q az The value space of (1) is {0, 1., M-1}, wherein M is the number of array elements of a uniform circular array;
according to the module value vector s of the circular convolution result az Position q of the maximum value element of (2) az Calculating a coarse estimate of the azimuth angle θ as
Figure FDA0003879641760000028
(4c) Introducing an azimuth phase compensation variable eta az Coarse estimate of azimuth angle
Figure FDA0003879641760000029
Is searched and matched for correlation, and calculates a fine estimate of the azimuth angle theta
Figure FDA00038796417600000210
The implementation is as follows:
the division number of the azimuth search interval is set as G az Defining an azimuth phase compensation variable η az Then η az Is taken as a value space of
Figure FDA00038796417600000211
Wherein M is the number of array elements of the uniform circular array;
defining a uniform circular array matching coefficient vector as
Figure FDA00038796417600000212
Wherein
Figure FDA00038796417600000213
Is the pitch angle of the signal source relative to the uniform cylindrical array
Figure FDA00038796417600000214
Fine estimate of (q), q az Is a modulus vector s of the result of the cyclic convolution az The position of the element of the maximum value of (c),
Figure FDA0003879641760000031
lambda is the working wavelength of the array, d is the array element spacing of the uniform circular array, and the requirement is met
Figure FDA0003879641760000032
Setting the result of uniform circular array matching output module value as
Figure FDA0003879641760000033
Search for z UCA Maximum value-derived azimuth phase compensation variable
Figure FDA0003879641760000034
And will be
Figure FDA0003879641760000035
Defined as an optimum azimuthal phase compensation variable, where y UCA Is a virtual circular array signal, H represents the conjugate transfer rank, | · | represents the modulus;
compensating variables according to optimal azimuth phase
Figure FDA0003879641760000036
And the modulus vector s of the result of the cyclic convolution az Position q of the maximum value element of (2) az Calculating a fine estimate of the azimuth angle θ as
Figure FDA0003879641760000037
2. The method of claim 1, wherein (1) the uniform circular array steering vector a of the uniform circular array is UCA Expressed as follows:
Figure FDA0003879641760000038
wherein
Figure FDA0003879641760000039
Lambda is the working wavelength of the array, M is the number of the array elements of the uniform circular array, d is the array element spacing of the uniform circular array, and the requirements are met
Figure FDA00038796417600000310
3. The method of claim 1 wherein the steering vectors a of the uniform linear arrays of the uniform cylindrical array in (1) are ULA Expressed as follows:
Figure FDA00038796417600000311
wherein
Figure FDA00038796417600000312
Lambda is the working wavelength of the array, N is the number of the array elements of the uniform linear array, and h is the array element spacing of the uniform linear array, so that the requirements of
Figure FDA00038796417600000313
4. The method of claim 1, wherein the steering matrix a of the uniform cylindrical array in (1) is represented as follows:
Figure FDA0003879641760000041
wherein
Figure FDA0003879641760000042
Representing Kronecker multiplication and T representing rank.
5. The method of claim 1, wherein the vector s of non-coherent accumulation results in (3 a) el Expressed as follows:
s el ＝Σ|XF|，
where X is the signal snapshot matrix,
Figure FDA0003879641760000043
is FFT transform matrix, N is the number of array elements of uniform linear array, sigma = [1 =] 1×N Is a column sum vector.
6. The method according to claim 1, characterized in that said (3 b), which is carried out as follows:
let q el For non-coherent accumulation result vector s el Position of the maximum value element of (b), q el The value space of (1) is {0, 1., N-1}, wherein N is the number of array elements of the uniform linear array;
from the incoherent accumulation result vector s el Position q of the maximum value element of (1) el Calculating the pitch angle
Figure FDA0003879641760000044
Is roughly estimated value of
Figure FDA0003879641760000045
When in use
Figure FDA0003879641760000046
When the temperature of the water is higher than the set temperature,
Figure FDA0003879641760000047
when in use
Figure FDA0003879641760000048
When the temperature of the water is higher than the set temperature,
Figure FDA0003879641760000049
wherein
Figure FDA00038796417600000410
Lambda is the working wavelength of the array, h is the array element spacing of the uniform linear array, and the requirement is met
Figure FDA00038796417600000411
7. The method according to claim 1, wherein said (3 c), is implemented as follows:
setting division number G of pitching search interval el Defining a pitch phase compensation variable η el Eta is then el Has a value space of
Figure FDA0003879641760000051
Wherein N is the number of array elements of the uniform linear array;
defining a uniform linear array matching coefficient vector as
Figure FDA0003879641760000052
Wherein q is el For non-coherent accumulation of the result vector s el The position of the maximum value element of (b);
setting the uniform linear array to match the output vector as
Figure FDA0003879641760000053
Wherein X is a signal snapshot matrix, representing a conjugate;
let the final output of the uniform linear array be z ULA ＝||y ULA || 1 Search for z ULA Maximum value-derived pitch phase compensation variable
Figure FDA0003879641760000054
And will be
Figure FDA0003879641760000055
Defined as an optimal pitch phase compensation variable, where | · | | | non calculation 1 Representing 1 norm of the vector;
compensating variables according to optimal pitch phase
Figure FDA0003879641760000056
And a vector s of incoherent accumulation results el Maximum value element position q el Calculating the pitch angle
Figure FDA0003879641760000057
Fine estimation ofEvaluating value
Figure FDA0003879641760000058
When in use
Figure FDA0003879641760000059
When the temperature of the water is higher than the set temperature,
Figure FDA00038796417600000510
when in use
Figure FDA00038796417600000511
When the utility model is used, the water is discharged,
Figure FDA00038796417600000512
wherein
Figure FDA00038796417600000513
Lambda is the working wavelength of the array, h is the array element spacing of the uniform linear array, and the requirements are met
Figure FDA00038796417600000514
8. The method according to claim 1, wherein the virtual circular array signal y in (4 a) UCA Expressed as follows:
Figure FDA0003879641760000061
where X is a signal snapshot matrix, denotes a conjugate,
Figure FDA0003879641760000062
is the optimal matching coefficient vector of the uniform linear array, N is the number of array elements of the uniform linear array, q el For non-coherent accumulation of the result vector s el The position of the element of the maximum value of (c),
Figure FDA0003879641760000063
the variable is compensated for the optimal pitch phase.
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