CN113311403A - Radar far-field target positioning method based on time reversal technology - Google Patents

Radar far-field target positioning method based on time reversal technology Download PDF

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CN113311403A
CN113311403A CN202110568891.0A CN202110568891A CN113311403A CN 113311403 A CN113311403 A CN 113311403A CN 202110568891 A CN202110568891 A CN 202110568891A CN 113311403 A CN113311403 A CN 113311403A
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array antenna
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CN113311403B (en
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赵勋旺
柳灿
张玉
林中朝
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Xidian University
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The invention provides a radar far-field target positioning method based on a time reversal technology, and aims to solve the problems that selective focusing positioning of multiple targets cannot be realized under a multipath effect and the angular resolution is low in the prior art. The method comprises the following implementation steps: generating a transmission matrix; generating a time reversal operator by using the transmission matrix; acquiring inversion excitation of the array antenna; calculating a directional diagram of the array antenna; an angle of the radar target relative to the antenna array is determined. The method can more accurately obtain the orientations of a plurality of radar far-field targets and has higher angular resolution when positioning the targets, thereby realizing the function of positioning the radar far-field targets by the array antenna.

Description

Radar far-field target positioning method based on time reversal technology
Technical Field
The invention belongs to the technical field of radars, and further relates to a radar far-field target positioning method based on a time reversal technology in the technical field of radar target positioning. The invention utilizes time reversal technology to determine the azimuth of radar far-field targets and realize the selective focusing of a plurality of targets.
Background
The principle of radar far-field target positioning is to utilize the linearity of electromagnetic wave transmitted in a uniform medium, the directivity of a radar antenna and a radar echo signal of a target to realize the measurement of the target azimuth. However, in an actual object detection process, due to the inhomogeneity and complexity of the propagation background medium, the signal may arrive at the receiving array along different paths, which is called multipath effect. Multipath effects are a common phenomenon in radar and radio communications, and multipath scattering is simply considered clutter noise in the design of most radar systems, thereby adversely affecting the resolution of the radar system and the accuracy with which objects are located. In a radar detection system, high resolution of a target is an important performance parameter required by a radar system, good adaptability and stability in a complex multipath scattering environment are also important targets pursued by the radar system, and how to accurately position a far-field target without changing an actual radar system is one of difficulties in radar signal processing.
The university of sienna electronics technology discloses a radar target positioning method in the patent document "radar target positioning method based on multipath utilization" (application No. 201710983123.5, application publication No. CN 107918115 a) applied by the university of sienna electronics technology. The method comprises the following steps: 1) generating a transmitting signal to obtain echo data; 2) processing echo data to obtain arrival time of different paths; 3) establishing a radar target geometric positioning model; 4) bringing the obtained arrival time of different paths into the established geometric positioning model; 5) initializing an initial search point; 6) inputting the geometric positioning model and the initial search point into a search function lsqnolin, and searching by using the search function lsqnolin to obtain an accurate target position; 7) and expanding the target position obtained by searching to a three-dimensional space to realize the positioning of the target. The method has the disadvantages that the accurate target position needs to be obtained by searching with the help of a search function, the calculation amount in the searching process is large, the requirement on hardware is high, the method does not solve the problem of selective focusing and positioning of each target under the condition that a plurality of targets exist, and the method is not suitable for a multi-target positioning system of the radar in the actual target detection process.
A paper "expanding Multipath from Airborne Platforms for orientation of Arrival Estimation" (20093 rd European Conference on Antennas and Propagation (2009):3131-3135.) published by Marija M.Nikolic et al discloses a method for Direction of Arrival Estimation using Multipath signals from Airborne Platforms. The method includes the steps that an antenna array is installed on an airborne platform, an objective function is built through received multipath signals, unknown parameters of the objective function are estimated through a maximum likelihood estimation method, accordingly, an estimated value of the DOA is obtained, and the estimation accuracy of the DOA is measured through calculating the Claritrol bound. The method has the disadvantages that when the minimum value of the objective function is solved, the number of linear equation sets to be solved is large, the calculation process is complex, the calculated amount is large, and when a plurality of targets exist, the method is low in angular resolution and cannot realize accurate positioning of the targets.
Disclosure of Invention
The invention aims to provide a radar far-field target positioning method based on a time reversal technology aiming at the defects of the prior art, and is used for solving the problems that the prior art cannot realize selective focusing positioning of a plurality of targets under the multipath effect and has low angular resolution.
The idea of achieving the purpose of the invention is that a time reversal operator is constructed by utilizing a transmission matrix generated by a radar echo signal, the time reversal operator is subjected to characteristic value decomposition, a characteristic vector corresponding to a main characteristic value contains azimuth information of a corresponding target, and the characteristic vector corresponding to the main characteristic value is used as a group of inversion excitation of an array antenna to achieve selective focusing positioning of a single target in a plurality of targets.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) generating a transmission matrix:
(1a) each unit in the array antenna converts a received echo signal of a radar far-field target into a frequency domain signal through Fourier transformation, wherein the Fourier transformation is realized by the following formula:
Figure BDA0003081876290000021
wherein S ism(ω) represents the frequency domain echo signal corresponding to the mth unit in the array antenna, ω represents the frequency of the frequency domain echo signal, t1Representing the initial time of reception of the time-domain echo signal, t2Representing the end time, s, of the reception of the time-domain echo signalm(t) represents the time domain echo signal received by the mth unit in the array antenna within the time t;
(1b) discretizing each frequency domain signal along the frequency axis of the frequency domain signal to obtain the amplitude corresponding to each frequency point in the discrete frequency domain signal of each antenna unit, and forming the amplitudes of all the frequency points into a transmission matrix;
(2) the time reversal operator is generated using the transmission matrix as follows:
T(ω)＝K(ω)KH(ω)
wherein T (omega) represents a time reversal operator, K (omega) represents a transmission matrix, and H represents a conjugate transpose operation;
(3) obtaining inversion excitation of the array antenna:
(3a) using T (omega) ═ V Λ V-1The formula is used for carrying out eigenvalue decomposition on the time reversal operator T (omega), wherein Λ represents a diagonal matrix containing M nonnegative real eigenvalues, M represents the total number of antenna units in the array antenna, V represents an eigenvector matrix corresponding to Λ, and-1 represents matrix inversion operation;
(3b) sorting the M non-negative real eigenvalues from large to small, taking the significant large eigenvalue of all eigenvalues of which the numerical value is larger than the numerical value of the minimum eigenvalue by at least one order of magnitude as a main eigenvalue, and taking the eigenvector corresponding to each main eigenvalue as a group of inversion excitations of the array antenna;
(4) calculating a directional diagram of the array antenna:
calculating the directional diagram of the array antenna of the inversion excitation corresponding to the main eigenvalue according to the following formula:
Figure BDA0003081876290000031
wherein the content of the first and second substances,
Figure BDA0003081876290000032
the directional diagram of the array antenna of inversion excitation corresponding to the ith main eigenvalue is represented, theta represents the pitch angle of the array antenna, and the range of the pitch angle is [ -90 DEG, and 90 DEG]，
Figure BDA0003081876290000033
The azimuth angle of the array antenna is represented and ranges from 0 degrees to 360 degrees]Sigma (-) represents summation operation, M represents serial number of antenna unit in array antenna, and the value range is [1, 2 ], …, M]，
Figure BDA0003081876290000034
Representing the amplitude of the inverted excitation corresponding to the mth antenna element in the array antenna, e(·)Denotes an exponential operation with a natural constant e as the base, j denotes an imaginary unit, k denotes a propagation constant in free space with a value of 2 pi/lambda, pi denotes a circumferential ratio, lambda denotes the wavelength of the operating frequency of the array antenna, xm，ymAnd zmRepresents the corresponding coordinate value of the mth antenna unit in the rectangular space coordinate system, cos (-) represents the cosine-taking operation, sin (-) represents the sine-taking operation,
Figure BDA0003081876290000035
factors representing the antenna elements in relation to their geometry and structure;
(5) determining the angle of the radar target relative to the antenna array:
and taking the angle corresponding to the maximum value in the directional diagrams of all the array antennas corresponding to the main characteristic value as the angle of the radar far-field target relative to the antenna array.
Compared with the prior art, the invention has the following advantages:
firstly, when the direction of a radar far-field target relative to an array antenna is calculated, a time reversal operator is constructed by using a transmission matrix generated by a radar echo signal, the time reversal operator is subjected to characteristic decomposition, and a characteristic vector which is obtained by decomposition and contains radar target angle information and corresponds to each main characteristic value is used as a group of inversion excitation of the array antenna, so that the selective focusing positioning of a single target in a plurality of targets can be realized, the problem that the selective focusing positioning of the plurality of targets cannot be realized under the multipath effect in the prior art is solved, and the method has the advantage of more accurately obtaining the directions of the plurality of radar far-field targets.
Secondly, in the process of generating the transmission matrix, only the received echo signal of the radar far-field target is needed, and other information about the target is not needed, so that the requirement on hardware is reduced, the process is simple, the operand is small, the implementation is easy, the positioning of other targets cannot be influenced in the process of positioning a single target corresponding to the main eigenvalue, the problem of low target angular resolution under the condition of multiple targets in the prior art is solved, and the method has the advantage of higher angular resolution when positioning multiple targets.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a distribution diagram of feature values after feature decomposition of a time reversal operator in a simulation experiment according to the present invention;
fig. 3 is a directional diagram of an array antenna corresponding to different main eigenvalues in a simulation experiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The implementation steps of the present invention are further described with reference to fig. 1.
Step 1, generating a transmission matrix.
Each unit in the array antenna converts the received echo signal of the radar far-field target into a frequency domain signal through Fourier transform.
The Fourier transform is realized by the following formula:
Figure BDA0003081876290000051
wherein S ism(ω) represents the frequency domain echo signal corresponding to the mth unit in the array antenna, ω represents the frequency of the frequency domain echo signal, t1Representing the initial time of reception of the time-domain echo signal, t2Representing the end time, s, of the reception of the time-domain echo signalmAnd (t) represents a time domain echo signal received by the mth unit in the array antenna within the time t.
In the embodiment of the invention, the form of the array antenna is assumed to be a uniform linear array, 8 antenna units are provided, all the antenna units are ideal omnidirectional antennas, and the center frequency f of the array antenna is01.2GHz, an array spacing d λ/2, 3 radar far-field targets, each at an angle θ with respect to the antenna array1＝-15°，θ20 ° and θ3The echo signals of 3 targets are all narrow-band far-field signals and are all incoherent single-tone signals with the frequencies f1＝1GHz，f21.3GHz and f3The SNR is 10dB for SNR1, 5dB for SNR2, and 0dB for SNR3, respectively at 1.5 GHz. 8 antenna units respectively receive radar far-field time domain echo signals s1(t),s2(t),s3(t)…,s8(t)。
Discretizing each frequency domain signal along the frequency axis of the frequency domain signal to obtain the amplitude corresponding to each frequency point in the discrete frequency domain signal of each antenna unit, and forming the amplitudes of all the frequency points into a transmission matrix.
The expression of the transmission matrix K (ω) in the embodiment of the present invention is as follows:
Figure BDA0003081876290000052
and 2, generating a time reversal operator through the transmission matrix by using the following formula.
T(ω)＝K(ω)KH(ω)
Where T (ω) represents a time reversal operator, K (ω) represents a transmission matrix, and H represents a conjugate transpose operation.
The specific expression of the time reversal operator in the embodiment of the invention is as follows:
Figure BDA0003081876290000061
and 3, acquiring inversion excitation of the array antenna.
Using T (omega) ═ V Λ V-1And (3) carrying out eigenvalue decomposition on the time inversion operator T (omega), wherein Λ represents a diagonal matrix containing M nonnegative real eigenvalues, M represents the total number of antenna units in the array antenna, V represents an eigenvector matrix corresponding to Λ, and-1 represents matrix inversion operation.
The specific method for performing characteristic decomposition on the time reversal operator T (omega) in the embodiment of the invention is as follows:
assume that a matrix V exists such that T (ω) V ═ V Λ, where Λ is a diagonal matrix and V is an orthogonal matrix:
Figure BDA0003081876290000062
Figure BDA0003081876290000063
wherein λ is1，λ2，…，λ8The value of the characteristic is represented by a value,
Figure BDA0003081876290000064
and representing the feature vector corresponding to the feature value.
From the equation T (ω) V ═ V Λ, one can derive
Figure BDA0003081876290000065
Solved to obtain lambdamAnd
Figure BDA0003081876290000066
the value of (A) is solved for 8 times to obtain the corresponding of the non-negative real eigenvalue diagonal matrix Lambda and the diagonal matrix LambdaThe eigenvector matrix V:
Figure BDA0003081876290000067
Figure BDA0003081876290000068
and sequencing the M non-negative real eigenvalues from large to small, taking the significant large eigenvalue as a main eigenvalue, and taking the eigenvector corresponding to each main eigenvalue as a group of inversion excitations of the array antenna.
The significant large eigenvalue refers to all eigenvalues whose value is at least one order of magnitude greater than the value of the smallest eigenvalue among the M ranked eigenvalues from large to small.
In the embodiment of the invention, three significant characteristic values lambda are used1，λ2And λ3As the main eigenvalue, corresponding to 3 far-field targets, the eigenvector corresponding to 3 main eigenvalues
Figure BDA0003081876290000071
And
Figure BDA0003081876290000072
the single target is selectively focused and positioned in 3 targets by calculating an array antenna directional diagram of one group of excitation to obtain the azimuth of one target.
And 4, calculating the directional diagram of the array antenna of the inversion excitation corresponding to the main eigenvalue according to the following formula.
Figure BDA0003081876290000073
Wherein the content of the first and second substances,
Figure BDA0003081876290000074
the directional diagram of the array antenna of inversion excitation corresponding to the ith main eigenvalue is represented, theta represents the pitch angle of the array antenna, and the range of the pitch angle is [ -90 DEG, and 90 DEG]，
Figure BDA0003081876290000075
The azimuth angle of the array antenna is represented and ranges from 0 degrees to 360 degrees]Sigma (-) represents summation operation, M represents serial number of antenna unit in array antenna, and the value range is [1, 2 ], …, M]，
Figure BDA0003081876290000076
Representing the amplitude of the inverted excitation corresponding to the mth antenna element in the array antenna, e(·)Denotes an exponential operation with a natural constant e as the base, j denotes an imaginary unit, k denotes a propagation constant in free space with a value of 2 pi/lambda, pi denotes a circumferential ratio, lambda denotes the wavelength of the operating frequency of the array antenna, xm，ymAnd zmRepresents the corresponding coordinate value of the mth antenna unit in the rectangular space coordinate system, cos (-) represents the cosine-taking operation, sin (-) represents the sine-taking operation,
Figure BDA0003081876290000077
representing factors of the antenna element that are related to the geometry and structure of the antenna element.
In the embodiment of the invention, a uniform linear array is adopted, and in the array model, the azimuth angle of the array antenna is not considered
Figure BDA0003081876290000078
And the antenna elements are ideally omni-directional antennas, i.e.
Figure BDA0003081876290000079
The formula of the array antenna directional diagram can be simplified as follows:
Figure BDA00030818762900000710
wherein f isi(θ) And d represents the distance between the antenna units in the array antenna.
And 5, determining the angle of the radar target relative to the antenna array.
And taking the angle corresponding to the maximum value in the directional diagrams of all the array antennas corresponding to the main characteristic value as the angle of the radar far-field target relative to the antenna array.
In the embodiment of the invention, the angle corresponding to the maximum value in the 3 array antenna directional diagrams is taken as the angle of the 3 targets relative to the array antenna.
The technical effects of the invention are further explained by combining simulation experiments as follows:
1. simulation experiment conditions are as follows:
the hardware platform of the simulation experiment of the invention is as follows: the processor is Intel Core i7, the main frequency is 3.6GHz, and the memory is 8 GB.
The software platform of the simulation experiment of the invention is as follows: MATLAB.
2. Simulation content and result analysis thereof:
the simulation array antenna adopted in the simulation of the invention is in the form of a uniform linear array, has 8 antenna units which are all ideal omnidirectional antennas, and has the central frequency f of the array antenna01.2GHz, an array spacing d λ/2, 3 radar far-field targets, each at an angle θ with respect to the antenna array1＝-15°，θ20 ° and θ3The echo signals of 3 targets are all narrow-band far-field signals and are all incoherent single-tone signals with the frequencies f1＝1GHz，f21.3GHz and f3The SNR is 10dB for SNR1, 5dB for SNR2, and 0dB for SNR3, respectively at 1.5 GHz.
The simulation experiment of the invention is to simulate the array antenna and the radar far-field target constructed by simulation by adopting the method of the invention, and the result is shown in fig. 2 and fig. 3. Fig. 2 is a distribution diagram of characteristic values after characteristic decomposition by a time reversal operator, and fig. 3 is a directional diagram of an array antenna corresponding to different main characteristic values.
In fig. 2, the horizontal axis represents the number of eigenvalues, and the vertical axis represents the amplitude of the eigenvalues. The curve in fig. 2 is a curve that is drawn by constructing a time reversal operator by using a transmission matrix generated by an echo signal, performing feature decomposition on the time reversal operator, and sequencing 8 obtained feature values according to 8 amplitudes from large to small. It can be seen from fig. 3 that there are 3 significant large eigenvalues among the 8 eigenvalues, and the 3 significant large eigenvalues are taken as main eigenvalues to represent 3 far-field targets. Obviously, the simulation result of the invention is consistent with the number of radar far-field targets constructed by simulation.
In fig. 3, the horizontal axis represents the pitch angle θ of the array antenna, and the vertical axis represents the pattern f of the array antennai(θ) amplitude. The curve in fig. 3 is a set of inversion excitations using eigenvectors corresponding to the 3 main eigenvalues obtained in fig. 2 as array antennas, and the directional diagram f of the array antenna corresponding to different main eigenvalues is calculatedi(theta) a curve of variation with pitch angle theta. The solid line in fig. 3 indicates the directional pattern of the array antenna corresponding to main characteristic value 1, the dotted line indicates the directional pattern of the array antenna corresponding to main characteristic value 2, and the cross line indicates the directional pattern of the array antenna corresponding to main characteristic value 3. As can be seen from fig. 3, the array antenna pattern f corresponding to the main eigenvalue 11The maximum point of (theta) is at theta1Array antenna directional diagram f corresponding to-15-degree direction and main characteristic value 22The maximum point of (theta) is at theta2Array antenna directional diagram f corresponding to main characteristic value 3 in 0 degree direction3The maximum point of (theta) is at theta3The angles of the three targets with respect to the array antenna can be determined to be in the directions of-15 °, 0 ° and 30 °, respectively. It can be seen that the simulation result of the invention is consistent with the angle set by the radar far-field target constructed by simulation.
The above simulation experiments show that: according to the method, a time reversal operator is constructed by using a transmission matrix generated by a radar echo signal, characteristic decomposition is carried out on the time reversal operator, a characteristic vector which is obtained by decomposition and contains radar target angle information and corresponds to each main characteristic value is used as a group of inversion excitation of an array antenna, selective focusing positioning of a single target in a plurality of targets can be achieved, the problem that selective focusing positioning of the plurality of targets cannot be achieved when the prior art is applied to a multipath effect is solved, positioning of other targets cannot be affected in the process of positioning the single target corresponding to the main characteristic value, and the problem that in the prior art, under the condition that multiple targets exist, the target angle resolution is low is solved. The method is a very effective method for positioning radar far-field targets.

Claims (3)

1. A radar far-field target positioning method based on a time reversal technology is characterized in that a time reversal operator is generated by using a transmission matrix, eigenvalue decomposition is carried out by using the time reversal operator, the number of main eigenvalues is used as the number of targets, and selective positioning of the corresponding targets is realized by using eigenvectors corresponding to the main eigenvalues as inversion excitation of an array antenna; the method comprises the following steps:
(1) generating a transmission matrix:
(1a) each unit in the array antenna converts a received echo signal of a radar far-field target into a frequency domain signal through Fourier transform;
(1b) discretizing each frequency domain signal along the frequency axis of the frequency domain signal to obtain the amplitude corresponding to each frequency point in the discrete frequency domain signal of each antenna unit, and forming the amplitudes of all the frequency points into a transmission matrix;
(2) the time reversal operator is generated using the transmission matrix as follows:
T(ω)＝K(ω)KH(ω)
wherein T (omega) represents a time reversal operator, K (omega) represents a transmission matrix, and H represents a conjugate transpose operation;
(3) obtaining inversion excitation of the array antenna:
(3a) using T (omega) ═ V Λ V-1The formula is used for carrying out eigenvalue decomposition on the time reversal operator T (omega), wherein Λ represents a diagonal matrix containing M nonnegative real eigenvalues, M represents the total number of antenna units in the array antenna, V represents an eigenvector matrix corresponding to Λ, and-1 represents matrix inversion operation;
(3b) sequencing the M non-negative real eigenvalues from large to small, taking the significant large eigenvalue as a main eigenvalue, and taking the eigenvector corresponding to each main eigenvalue as a group of inversion excitation of the array antenna;
(4) calculating a directional diagram of the array antenna:
calculating the directional diagram of the array antenna of the inversion excitation corresponding to the main eigenvalue according to the following formula:
Figure FDA0003081876280000011
wherein the content of the first and second substances,
Figure FDA0003081876280000012
the directional diagram of the array antenna of inversion excitation corresponding to the ith main eigenvalue is represented, theta represents the pitch angle of the array antenna, and the range of the pitch angle is [ -90 DEG, and 90 DEG]，
Figure FDA0003081876280000013
The azimuth angle of the array antenna is represented and ranges from 0 degrees to 360 degrees]Sigma (-) represents summation operation, M represents serial number of antenna unit in array antenna, and the value range is [1, 2 ], …, M]，
Figure FDA0003081876280000021
Representing the amplitude of the inverted excitation corresponding to the mth antenna element in the array antenna, e(·)Denotes an exponential operation with a natural constant e as the base, j denotes an imaginary unit, k denotes a propagation constant in free space with a value of 2 pi/lambda, pi denotes a circumferential ratio, lambda denotes the wavelength of the operating frequency of the array antenna, xm，ymAnd zmRepresents the corresponding coordinate value of the mth antenna unit in the rectangular space coordinate system, cos (-) represents the cosine-taking operation, sin (-) represents the sine-taking operation,
Figure FDA0003081876280000022
factors representing the antenna elements in relation to their geometry and structure;
(5) determining the angle of the radar target relative to the antenna array:
and taking the angle corresponding to the maximum value in the directional diagrams of all the array antennas corresponding to the main characteristic value as the angle of the radar far-field target relative to the antenna array.
2. The time reversal technique-based radar far-field target locating method according to claim 1, wherein the fourier transform in step (1a) is implemented by the following formula:
Figure FDA0003081876280000023
wherein S ism(ω) represents the frequency domain echo signal corresponding to the mth unit in the array antenna, ω represents the frequency of the frequency domain echo signal, t1Representing the initial time of reception of the time-domain echo signal, t2Representing the end time, s, of the reception of the time-domain echo signalmAnd (t) represents a time domain echo signal received by the mth unit in the array antenna within the time t.
3. The time-reversal technique-based radar far-field target positioning method according to claim 1, wherein the significant large eigenvalue in step (3b) refers to all eigenvalues whose values are at least one order of magnitude larger than the value of the minimum eigenvalue among the M eigenvalues sorted from large to small.
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