CN109901146B - Hemispherical array and differential angle decoupling method based on spiral distribution - Google Patents
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Abstract
The invention discloses a semispherical array and differential angle decoupling method based on spiral distribution, which comprises the following steps: firstly, distributing N array elements on a hemispherical surface with the radius of R according to a spiral distribution arrangement mode; then redefining the azimuth angle of the signal coming from a certain direction
And a pitch angle theta to obtain a redefined slow vector r; then, the azimuth deviation is obtained
And four beams with the pitching direction deviation of +/-Delta theta, respectively obtaining a sum beam, an azimuth direction difference beam and a pitching direction difference beam for the four beams, and then obtaining an azimuth direction difference sum ratio and a pitching direction difference sum ratio; then setting an azimuth observation window
And a pitch viewing window theta win So as to obtain the angle identifying curves of the uncoupled azimuth direction and the uncoupled elevation direction in the observation window. The method reduces the pre-stored data quantity, has smaller angle measurement error per se and high angle measurement speed, and ensures the requirements of speed and precision of angle measurement of the radar array.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a hemispherical array and differential angle decoupling method, which is suitable for a hemispherical radar array in spiral distribution, and solves the problem that the data volume required to be prestored is huge due to the azimuth direction and elevation direction coupling existing in the process of measuring the sum and differential angles.
Background
Early radar array, main wired array and area array etc. because the array distribution is more regular, antenna element's directional unanimity, consequently it is easier to carry out theoretical analysis, and the shortcoming is that the receiving visual angle of array is limited, and hemispherical distributed's radar visual angle has advantages such as directive property is good, interference clutter suppression ability is strong, detection distance is far away and wide beam visual angle, but hemispherical array's antenna element directional nonconformity leads to hemispherical array theoretical analysis more difficult.
The sum and difference angle measurement technology has an early origin and obvious advantages, can measure the angle information of a target in a pulse, and has great application in engineering practice along with the research of a radar algorithm and the great improvement of the precision of the sum and difference angle measurement, particularly the sum and difference angle measurement technology of a linear array, which is developed to date and has a double-beam pointing method, a direct weighting method, a symmetrical negation method and the like. The main problem of area array sum and difference angle measurement exists in the information coupling of azimuth and elevation, the main solving method comprises two methods of coordinate system transformation, guide vector transformation and the like, when the method is applied to a hemispherical array, because the directions of all antenna units are inconsistent in the hemispherical array based on directional array elements, the theoretical analysis is difficult; meanwhile, azimuth information and elevation information are coupled, and a decoupling method of an area array is not completely applicable, so that a sum-difference angle measurement technology based on a hemispherical array has difficulty.
Disclosure of Invention
In order to solve the problems, the invention discloses a sum and difference angle measurement decoupling method based on a hemispherical array, which redefines the azimuth angle and the pitch angle of a coordinate system on the basis of the hemispherical array in spiral distribution, respectively synthesizes four beams, respectively obtains the difference and the ratio of the pitch direction and the pitch direction of an expected direction, approximately considers that the difference and the ratio of the azimuth direction are irrelevant to the pitch angle and the difference and the ratio of the pitch direction are irrelevant to the azimuth angle within a certain small angle range of the expected direction, and thus achieves the purpose of decoupling the azimuth direction and the pitch direction.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a sum and difference angle decoupling method based on a hemispherical array comprises the following steps:
step 1: distributing N array elements on a hemispherical surface with the radius of R according to a spiral distribution arrangement mode;
step 2: redefining the azimuth angle of a signal arriving from a certain direction
And a pitch angle theta to obtain a redefined slow vector r;
and 3, step 3: assuming a target beam with a desired direction of
On the basis of step 1 and step 2, the respective synthetic beam directions are respectively
And
four beams, denoted P respectively 1 、P 2 、P 3 And P 4 (ii) a Wherein Δ θ and
angular deviations in azimuth and pitch directions, respectively;
and 4, step 4: separately calculating sum beam P sum Elevation difference beam P ele Azimuth difference beam P azi Differential pitch and ratio r ele Sum of azimuth differences r azi ；
And 5: set up the azimuth observation window
And a pitch viewing window theta win Respectively taking an azimuth viewInspection window
And a pitch viewing window theta win Inner pitch sum ratio r ele Sum of azimuth differences r azi And angle identifying curves of the azimuth direction and the pitching direction are obtained, so that the decoupling purpose is achieved.
Compared with the prior art, the invention has the following advantages:
(1) The method effectively solves the problem of coupling of the azimuth direction and the pitch direction, thereby effectively reducing the data volume of the angle identification curve required to be stored by the sum and difference angle measurement algorithm, reducing the engineering implementation complexity of the angle measurement algorithm and reducing the data volume;
(2) The method obtains the angle identification curve on the basis of approximation, reduces the data volume, does not increase errors obviously, and improves the comprehensive performance of the algorithm.
Drawings
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 schematic flow chart of a hemispherical array and differential angle decoupling method based on spiral distribution;
FIG. 2 is a graph of the array element coordinate of the mth array element in the hemispherical array;
FIG. 3 is a slow vector definition diagram in a rectangular coordinate system;
FIG. 4 is a spiral distribution diagram of a hemispherical array for simulation experiments;
FIG. 5 is a beam pattern for the pointing (0, 0) direction of the simulation experiment;
FIG. 6 shows a beam P of a simulation experiment 1 、P 2 、P 3 、P 4 A drawing;
FIG. 7 is a view in the X-Y dimension of FIG. 6;
FIG. 8 is an enlarged view of a portion of FIG. 7;
FIG. 9 is a sum beam diagram of a simulation experiment;
FIG. 10 is an azimuth difference beam pattern of a simulation experiment;
FIG. 11 is a view of elevation difference beams from a simulation experiment;
FIG. 12 is a plot of the azimuthal difference sum ratio within the observation window for a simulation experiment;
FIG. 13 is an X-Z view of the azimuthal difference sum ratio within the observation window of a simulation experiment;
FIG. 14 is a graph of the fitting results of the azimuthal curves in the observation window of the simulation experiment;
FIG. 15 is a plot of the sum of the pitching differences within the observation window of a simulation experiment;
FIG. 16 is a Y-Z dimensional view of the sum of the pitching differences within the observation window of the simulation experiment;
FIG. 17 is a graph of the results of fitting the azimuthal curves in the observation window for the simulation experiment;
FIG. 18 is a plot of SNR versus azimuthal estimation error for a simulation experiment;
FIG. 19 is a plot of SNR versus pitch estimation error for a simulation experiment;
FIG. 20 is a slow vector definition plot in the conventional array coordinate system for comparative experiments;
FIG. 21 is an original view of four beam patterns in a conventional coordinate system of a comparative experiment;
FIG. 22 is an X-Y view of FIG. 21;
FIG. 23 is an original view of the azimuthal difference and ratio within the observation window of the comparative experiment;
FIG. 24 is an X-Z view of FIG. 23;
FIG. 25 is an original view of the sum of the pitching differences within the observation window of a comparative experiment;
fig. 26 is a Y-Z view of fig. 25.
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 of a hemispherical array based on spiral distribution and a differential angle decoupling method according to an embodiment of the present invention.
As shown in fig. 1, the hemispherical array based on spiral distribution and the differential angle decoupling method provided in the embodiment of the present invention include the following steps:
step 1: distributing N array elements on a hemispherical surface with the radius of R according to a spiral distribution arrangement mode;
n array elements are distributed on the hemispherical spherical surface, and the whole hemisphere is collectively called a radar array, namely the radar array comprises the N array elements.
Sub-step 1a, n array elements, where the position of the m-th array element in the coordinate system as shown in fig. 2 is denoted as point p m Remember q m Is a point p m A projection point on a plane XOY, wherein
∠ZOp m ＝θ m Then, according to the definition of the helical distribution:
θ m ＝arccos(h m )，
wherein m is more than or equal to 1 and less than or equal to N;
substep 1b, as can be obtained from substep 1a, the XYZ coordinate of the m-th array element in the rectangular coordinate system as shown in the figure is:
z m ＝R sinθ m
and a substep 1c, according to the array element coordinates of the m-th array element obtained in the substep 1b, distributing the N array elements on a hemisphere with a radius of R according to a spiral.
Step 2: redefining the azimuth angle of a signal arriving in a certain direction
And a pitch angle θ, thereby obtaining a redefined slow vector r; the method specifically comprises the following substeps:
substep 2a, assume an incoming signal as in FIG. 3
Q is a projection point of a p point on a plane XOZ, black solid dots in the figure are array elements, and the angle qOZ = theta is defined,
and a substep 2b, obtaining a slow vector as follows according to the definition of the slow vector:
and step 3: assuming a target beam with a desired direction of
On the basis of step 1 and step 2, the synthesized beam is respectively pointed to
And
four beams, respectively denoted as P 1 、P 2 、P 3 And P 4 (ii) a Wherein, Δ θ and
angular deviations in azimuth and pitch directions, respectively;
the method specifically comprises the following substeps:
substep 3a of obtaining the pointing direction according to the definition of hemispherical array beam forming
The beam of (a) is:
wherein the content of the first and second substances,
and theta is as defined in figure 3,
angle of target azimuth, θ 0 Is the angle of a target pitch angle, N is the total number of array elements in the radar array, H represents the conjugate transpose,
denotes Heander Meng Deji, L i Is the spatial position of the ith array element in the radar array, and L i ＝[x i y i z i ] T I is more than or equal to 1 and less than or equal to N, r is a slow vector,
for spatial orientation of the ith array element
Weighted value of, and
j is an imaginary factor, λ is the wavelength of the incoming signal,
is the ith array element directional diagram function, and
p can be obtained according to the above definition 1 、P 2 、P 3 And P 4 Respectively as follows:
and 4, step 4: computing sum beam P sum Elevation difference beam P ele Azimuth difference beam P azi Differential pitch and ratio r ele Sum-azimuth ratio r azi ；
The method specifically comprises the following substeps:
substep 4a of obtaining a sum beam P based on the definition of the sum beam sum The calculation formula of (c) is:
P sum ＝P 1 +P 2 +P 3 +P 4 ；
substep 4b, obtaining the elevation difference beam P according to the definition of the elevation difference beam ele The calculation formula of (2) is as follows:
P ele ＝P 1 +P 2 -P 3 -P 4 ；
substep 4c, according to the definition of the azimuth difference beam, obtaining the azimuth difference beam P azi The calculation formula of (2) is as follows:
P azi ＝P 1 -P 2 +P 3 -P 4 ；
substep 4d, obtaining the pitching difference sum ratio r according to the definition of the pitching difference sum ratio ele The calculation formula of (c) is:
substep 4e, obtaining the azimuth difference sum ratio r according to the definition of the azimuth difference sum ratio azi The calculation formula of (2) is as follows:
thereby obtaining a sum beam P sum Elevation difference beam P ele Azimuth difference beam P azi Differential pitch and ratio r ele Sum of azimuth differences r azi 。
And 5: set up the direction observation window
And a pitch viewing window theta win Respectively taking the azimuth viewing window
And a pitch viewing window theta win Inner pitch sum ratio r ele Sum-azimuth ratio r azi And angle identifying curves of the azimuth direction and the pitching direction are obtained, so that the decoupling purpose is achieved.
Specifically, the azimuth observation window is arranged at 1-2 degrees
And a pitch viewing window theta win . The sum of the differences in pitch direction r obtained in the step 4 ele Sum of azimuth differences r azi In fact one about θ and
by setting a small range of azimuthal viewing windows
And a pitch viewing window theta win Approximately, the sum of the pitching differences r is considered ele And azimuth angle
Independently, the sum of the azimuthal differences r azi Independent of the pitch angle theta, thereby achieving the purpose of decoupling. Then the angle curve of the azimuth direction is the azimuth direction difference and the ratio curve in theta o The elevation angle curve of the section is the elevation difference and the specific surface
The slice of (6).
The effect of the method provided by the embodiment of the invention is verified through a simulation experiment as follows:
1. simulation experiment environment and data:
the experimental environment is as follows: inter (R) Core (TM) i5-6500 CPU@3.20HGz,64 bits Windows operating system and MATLAB 2016b simulation software.
Experimental parameters: the total number N of array elements of the radar array is 200, and the azimuth angle
The value range of the pitch angle theta is-90 degrees, and the target direction is
Is (0 deg. ), a pitching declination angle delta theta =1 deg., an azimuth declination angle
Elevation direction observation window theta win =1 °, squarePosition observation window
2. Simulation experiment results:
the spiral distribution of the hemispherical array obtained from step 1 is shown in fig. 4;
the beam pointing to the target azimuth (0 ° ) obtained according to step 3 is shown in fig. 5;
beam P 1 、P 2 、P 3 And P 4 As shown in fig. 6, fig. 7 is an X-Y dimensional view of fig. 6, and fig. 8 is a partially enlarged view of fig. 7. As can be seen in fig. 8, the four beams are directed at (-1 ° ), (-1 °,1 °), (1 °, -1 °) and (1 ° ), respectively.
As can be seen in fig. 9, the sum beam is directed (0 ° ). As can be seen from fig. 10 and 11, the azimuth difference beam and the elevation difference beam have a peak and a trough respectively beside the (0 ° ) point, except that the peak and the trough beside the azimuth difference beam (0 ° ) are
In this dimension, the peaks and troughs next to the elevation difference beam (0 ° ) are in the dimension θ.
From fig. 12 and 13, it can be seen that the azimuthal difference sum ratio in the viewing window is only related to the azimuth angle
In this regard, regardless of the pitch angle θ, the present invention recognizes that the azimuthal difference and ratio approximate the azimuth angle within the observation window
Is a linear relation, the curve obtained by fitting the linear relation is shown in figure 14, as can be seen from figure 14, the fitting effect is good, and the expression of the fitting straight line is
From fig. 15 and 16, it can be seen that the sum of the difference in pitch in the observation windowRatio is related only to pitch angle θ, to azimuth angle
Regardless, in the observation window, the invention considers that the pitch difference sum ratio approximation and the pitch angle theta are in a linear relation, the curve obtained by fitting the linear relation is shown in figure 17, as can be seen from figure 17, the fitting effect is good, and the expression of the fitting straight line is r ele ＝-0.1175θ。
On the basis of the angle profile shown in fig. 14 and 17, the sum and difference angle measurement and error analysis are performed to obtain an error-SNR curve as shown in fig. 18 and 19.
As can be seen from fig. 18 and 19, on the basis of the angle identification curves obtained in fig. 14 and 17, the sum and difference angles are measured by using the array with hemispherical spiral distribution, the obtained error is about 0.07, the error is in a relatively small range, and the influence of the SNR on the error is not large, which is mainly caused by the accumulation of signals before the sum beam and the difference beam are ratioed.
As shown in fig. 18 and 19, the size of the azimuth observation window and the pitch observation window are set to be 2 ° respectively, because the azimuth observation window and the pitch observation window are already decoupled, and therefore the pre-stored straight line data is 180 straight lines; however, if there is no decoupling, the amount of data to be prestored is about thousands of planes, and each plane is assumed to be composed of several hundreds of straight lines, and the straight lines to be stored is about 10 5 And (3) strips.
3. And (3) comparing the experimental results:
the conventional array coordinate system is defined as shown in FIG. 20, where p is the space-electromagnetic wave vector, q is the projection of p on XOY plane, where
Angle ZOp = θ. Then the slow vector is:
assuming that the spherical radius R =10 λ and the angle of pointing of the center beam is (10 ° ), beams pointing in four directions of (11 °,9 °), (9 °,11 °), (9 ° ) and (11 °,11 °) are synthesized, respectively, as shown in fig. 21 and 22:
FIG. 21 is an original view of four beam patterns in a conventional coordinate system, and FIG. 22 is an X-Y view of FIG. 21; it can be seen that: only two beams in elevation are shown. This is because the beams are relatively wide in azimuth but have small differences in pointing angles, so that the two beams in azimuth are coincident, and therefore only the two beams in elevation can be seen in the figure. In summary, it can be concluded that: in a conventional coordinate system, four beam patterns distributed spirally are completely asymmetric in elevation.
Assumed azimuth observation window
Elevation direction observation window theta win The calculated azimuth difference sum ratio and the calculated pitch difference sum ratio in the observation window are shown in fig. 23 to 26. FIG. 23 is an original view of the azimuthal difference sum ratio within the viewing window, FIG. 24 is an X-Z view of FIG. 23, FIG. 25 is an original view of the pitch difference sum ratio within the viewing window, and FIG. 26 is a Y-Z view of FIG. 25. As can be seen from the figure, the azimuth difference sum ratio and the pitch difference sum ratio are not only related to the azimuth angle, but also related to the pitch angle, so that under the conventional coordinate system, the azimuth direction and the pitch direction of the spirally distributed hemispherical array are coupled, and the angle is measured, the pre-stored data will be much.
As can be seen from the results of the simulation experiment and the comparison experiment, the method effectively solves the problem of the coupling of the azimuth direction and the pitch direction existing in the process of the spiral distribution of the hemispherical array and the angle difference measurement in a partial range on the basis of the redefinition and approximation of coordinates, greatly reduces the data quantity required to be prestored in the angle difference measurement, and ensures that the error of the angle difference measurement is in a smaller range.
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 (6)
1. A semispherical array and differential angle decoupling method based on spiral distribution is characterized by comprising the following steps:
step 1: distributing N array elements on a hemispherical surface with the radius of R according to a spiral distribution arrangement mode;
step 2: redefining the azimuth angle of a signal arriving from a certain direction
And a pitch angle theta to obtain a redefined slow vector r;
and step 3: assuming a target beam with a desired direction of
On the basis of step 1 and step 2, the synthesized beam is respectively pointed to
And
four beams, respectively denoted as P 1 、P 2 、P 3 And P 4 (ii) a Wherein, Δ θ and
angular deviations in azimuth and pitch directions, respectively;
and 4, step 4: computing sum beam P sum Elevation difference beam P ele Azimuth difference beam P azi Differential pitch and ratio r ele Sum of azimuth differences r azi ；
And 5: set up the direction observation window
And a pitch viewing window theta win Respectively taking the azimuth direction observation window
And a pitch viewing window theta win Inner pitch sum ratio r ele Sum of azimuth differences r azi And angle identifying curves of the azimuth direction and the pitching direction are obtained, so that the decoupling purpose is achieved.
2. The hemispherical array and differential angle decoupling method based on spiral distribution as claimed in claim 1, wherein in step 1, the N array elements are distributed on a hemispherical surface with a radius R according to the arrangement of spiral distribution, which includes the following sub-steps:
sub-step 1a, N array elements, where the position of the m-th array element in the coordinate system is denoted as point p m Remember q m Is a point p m A projection point on a plane XOY, wherein
Then, according to the definition of the helical distribution, we get:
Substep 1b, according to substep 1a, the XYZ coordinate of the m-th array element in the rectangular coordinate system is:
z m ＝Rsinθ m
and a substep 1c, according to the array element coordinates of the m-th array element obtained in the substep 1b, distributing the N array elements on a hemisphere with a radius of R according to a spiral.
3. The hemispherical array and differential angle decoupling method based on spiral distribution as claimed in claim 1, wherein in step 2, the step of obtaining the redefined slow vector r comprises the following sub-steps:
substep 2a, assuming an incoming signal
q is the projection point of the point p on the plane XOZ, defines ≈ qOZ = theta,
and a substep 2b, obtaining a slow vector as follows according to the definition of the slow vector:
4. according to claim 1The hemispherical array based on spiral distribution and the differential angle decoupling method are characterized in that in step 3, four beams P 1 、P 2 、P 3 And P 4 The calculation algorithm of (2) comprises the following substeps:
substep 3a, deriving the pointing direction according to the definition of hemispherical array beamforming
The beam of (a) is:
wherein the content of the first and second substances,
angle of target azimuth, θ 0 Is the angle of a target pitch angle, N is the total number of array elements in the radar array, H represents conjugate transposition,
denotes Heander Meng Deji, L i Is the spatial position of the ith array element in the radar array, and L i ＝[x i y i z i ] T I is more than or equal to 1 and less than or equal to N, r is a slow vector,
for spatial orientation of the ith array element
Weighted value of, and
j is an imaginary factor, λ is the wavelength of the incoming signal,
is the ith array element directionA graph function, and
substep 3b, according to substep 3a, obtaining the orientation
Directional beam P 1 Comprises the following steps:
substep 3c, according to substep 3a, obtaining the orientation
Directional beam P 2 Comprises the following steps:
substep 3d, according to substep 3a, obtaining the orientation
Directional beam P 3 Comprises the following steps:
substep 3e, according to substep 3a, obtaining the orientation
Directional beam P 4 Comprises the following steps:
5. the method according to claim 1, wherein the calculating in step 4 comprises the following sub-steps:
substep 4a of obtaining a sum beam P based on the definition of the sum beam sum The calculation formula of (2) is as follows:
P sum ＝P 1 +P 2 +P 3 +P 4 ；
wherein, P 1 Is directed to
A directional beam; p 2 Is directed to
A directional beam; p 3 Is directed to
A directional beam; p 4 Is directed to
A directional beam;
substep 4b, obtaining the elevation difference beam P according to the definition of the elevation difference beam ele The calculation formula of (2) is as follows:
P ele ＝P 1 +P 2 -P 3 -P 4 ；
substep 4c, according to the definition of the azimuth difference beam, obtaining the azimuth difference beam P azi The calculation formula of (2) is as follows:
P azi ＝P 1 -P 2 +P 3 -P 4 ；
substep 4d, obtaining the pitching difference sum ratio r according to the definition of the pitching difference sum ratio ele The calculation formula of (2) is as follows:
a substep 4e of obtaining a sum of azimuth differences r according to the definition of the sum of azimuth differences r azi The calculation formula of (2) is as follows:
6. the method for decoupling hemispherical array and differential angle based on spiral distribution according to claim 1, wherein in step 5, the obtaining of the angle identifying curves of azimuth and elevation specifically comprises the following sub-steps:
substep 5a, setting an azimuth observation window of 1-2 DEG
And a pitch viewing window theta win Viewing in the azimuth viewing window
And a pitch viewing window theta win Azimuthal difference within range and ratio r azi And the sum of the pitching differences r ele ；
Substep 5b, consider the sum of the pitching differences r ele And azimuth angle
Independently, the sum of the azimuthal differences r azi Independent of the pitch angle theta, obtaining azimuth angle curve and pitch angle curve respectively, namely the azimuth angle curve is azimuth difference and ratio curve surface at theta o The elevation angle curve of the section is the elevation difference and the specific surface
The slice of (6).
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