CN116577749A - Scanning radar super-resolution method under unknown broadening of antenna pattern - Google Patents

Scanning radar super-resolution method under unknown broadening of antenna pattern Download PDF

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Publication number
CN116577749A
CN116577749A CN202310427532.2A CN202310427532A CN116577749A CN 116577749 A CN116577749 A CN 116577749A CN 202310427532 A CN202310427532 A CN 202310427532A CN 116577749 A CN116577749 A CN 116577749A
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representing
broadening
target
antenna pattern
azimuth
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杨水锋
杨建宇
庹兴宇
黄钰林
赵献
张寅�
张永超
杨海光
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University of Electronic Science and Technology of China
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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
    • G01S7/411—Identification of targets based on measurements of radar reflectivity
    • 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
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • 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
    • G01S7/40—Means for monitoring or calibrating
    • 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

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  • Engineering & Computer Science (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a scanning radar super-resolution method under unknown broadening of an antenna pattern, which comprises the steps of firstly constructing azimuth echo into convolution of a target scattering coefficient and the antenna pattern through echo modeling, then introducing a broadening correction matrix into an echo convolution model for representing errors of an antenna pattern function, and finally updating the broadening correction matrix and the target scattering coefficient by adopting an alternating iteration strategy until convergence, traversing all distance units in the echo, and outputting an azimuth super-resolution imaging result. According to the method, the broadening correction error matrix is introduced into the azimuth echo convolution model, and the target and the error matrix are continuously updated in an alternate iteration mode, so that stable imaging under an error condition is realized.

Description

Scanning radar super-resolution method under unknown broadening of antenna pattern
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to a scanning radar super-resolution method under unknown broadening of an antenna pattern.
Background
The super-resolution technology of scanning radar uses signal processing means to break through the inherent limitation of antenna aperture and obtain azimuth resolution better than real wave beam. The technology has important research significance and application value in applications such as sea surface searching, earth observation and the like.
The super-resolution technology mainly utilizes the convolution relation between the scattering coefficient of the target and the antenna function, and adopts deconvolution to realize super-resolution imaging. Literature "Huang Y, zha Y, wang Y, et al Forward looking radar imaging by truncated singular value decomposition and its application for adverse weather aircraft sorting. Sensors,2015, 15 (6): 14397-14414 propose a truncated singular value decomposition super-resolution method, which realizes the improvement of azimuth resolution. Document "Zhang Q, zhang, huang Y, et al spark with fast MM superresolution algorithm for radar forward-locking imaging.IEEE Access,2019,7:105247-105257 on the basis of a convolution model, a rapid MM sparse super-resolution imaging method is provided, and higher resolution improvement is obtained. Literature "yardbi T, li J, stoica P, et al source localization and sensing: A nonparametric iterative adaptive approach based on weighted least squares ieee Transactions on Aerospace and Electronic Systems,2010, 46 (1): the mathematical similarity of a convolution model and an array processing model is utilized, an iterative self-adaptive super-resolution method is provided, and the parameter-free iterative self-adaptive super-resolution imaging is obtained.
However, in practical application, due to motion errors such as pitch, yaw, roll, etc. of the radar platform, there is an unknown beam broadening error of the radar actual antenna pattern compared with the ideal measured antenna pattern. The super-resolution imaging performance of the existing super-resolution method is drastically reduced or even disabled.
Disclosure of Invention
In order to solve the technical problems, the invention provides a scanning radar super-resolution method under unknown broadening of an antenna pattern, wherein a broadening correction error matrix is introduced into a azimuth echo convolution model, and a target and the error matrix are continuously updated in an alternate iteration mode, so that stable imaging under an error condition is realized.
The invention adopts the technical scheme that: a scanning radar super-resolution method under unknown broadening of an antenna pattern comprises the following specific steps:
modeling an azimuth convolution model;
the scanning radar radiates the chirped LFM signal at a set fixed pulse repetition frequency PRF while the observation area is probed with the antenna scan. Based on the scanning imaging process, the echo signals in one distance unit of the observation area are constructed as the convolution of an antenna function and a target scattering coefficient, and the additive Gaussian white noise is considered, the azimuth signal model is expressed as follows:
y＝Hx+n (1)
wherein ,representing the received echo vector with dimensions Nx1, -, for example>The i (i is more than or equal to 1 and less than or equal to N) element of the echo vector; />Representing a target scattering coefficient vector with dimensions N x 1, x (θi) The i (i is more than or equal to 1 and less than or equal to N) element of the target scattering coefficient vector; />Noise vectors satisfying a Gaussian distribution are represented with dimensions N1, < >>I (i is more than or equal to 1 and is less than or equal to N) element of the noise vector; t represents the transpose operation of the vector, N represents the azimuth sampling point number, [ theta ] 1 ,θ 2 ,…,θ N ]Azimuth sampling representing an imaging scene; h represents an antenna pattern matrix consisting of antenna pattern samples, with dimensions n×n, expressed as follows:
wherein ,representing the antenna pattern sample vector, < >>Representing sampled values of the antenna pattern. N represents the azimuth sampling point number, and +.>Omega denotes the imaging region, omega denotes the scanning speed, PRF denotes the pulse repetition frequency.
Step two, correcting a convolution model;
introducing a broadening correction error matrix in consideration of the condition that the antenna directional diagram has unknown broadening errors of the beam, and correcting a convolution model in the formula (1) as follows:
y＝(H+E)x+n (3)
where E represents a widening correction error matrix of dimension n×n.
Step three, constructing an objective function;
based on the sparsity of the target, on the basis of least squares, an objective function J (x, E) is constructed as follows:
wherein ,representing data fidelity item->Representing the square of the vector 2 norm; alpha x 1 Representing the target constraint term, alpha represents a parameter for adjusting the strength of the target constraint term, |·|| 1 Representing the vector L1 norm; />Representing the constraint term of the broadening correction error matrix, beta representing a parameter for adjusting the intensity of the constraint term of the broadening correction error matrix,/and%>Representing the square of the matrix Frobenius norm.
Step four, solving the E problem;
and solving an objective function by adopting an alternate iteration strategy.
First, the variable x is fixed, and the objective function is converted into:
obtaining an updated expression of the variable E by adopting a derivative strategy:
wherein the superscript H denotes a conjugate transpose operation.
Step five, solving the problem x;
fixed variable E, letThe objective function is translated into:
the problem of the formula (7) contains an unpredictable L1 norm constraint term, and is solved by adopting an iterative re-weighting method, wherein the specific updating steps are as follows:
forj＝1,2,…,J
W j ＝diag(|x j-1 | -1 )
end (8)
wherein the subscript J denotes the iteration order, J denotes the number of iterations required to solve the problem convergence in equation (7), x 0 Representing initialized target scattering coefficient, x j Represents the scattering coefficient, W, of the target after j iterations j Representing the weighting matrix after j iterations, diag (·) represents the diagonal matrix.
Step six, obtaining an imaging result;
updating the target scattering coefficient to x=x J And step four, repeating the step five until the target scattering coefficient and the error matrix reach convergence, outputting the result of the distance unit, traversing all the distance units in the echo, and obtaining the azimuth super-resolution imaging result of the whole observation area.
The invention has the beneficial effects that: according to the method, firstly, azimuth echoes are constructed into convolution of target scattering coefficients and antenna patterns through echo modeling, then, a widening correction matrix is introduced into an echo convolution model and used for representing errors of antenna pattern functions, finally, the widening correction matrix and the target scattering coefficients are updated by adopting an alternate iteration strategy until convergence, all distance units in the echoes are traversed, and an azimuth super-resolution imaging result is output. According to the method, the broadening correction error matrix is introduced into the azimuth echo convolution model, and the target and the error matrix are continuously updated in an alternate iteration mode, so that stable imaging under an error condition is realized.
Drawings
Fig. 1 is a flowchart of a scanning radar super-resolution method under unknown broadening of an antenna pattern according to the present invention.
Fig. 2 is a schematic diagram of a real aperture scanning radar in an embodiment of the invention.
Fig. 3 is a graph of an ideal antenna pattern function and an antenna pattern function in the presence of a splay error in an embodiment of the present invention.
Fig. 4 is a diagram of simulation results in an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the drawings and examples.
As shown in fig. 1, the method for super-resolution scanning radar under unknown broadening of an antenna pattern according to the present invention comprises the following specific steps:
modeling an azimuth convolution model;
as shown in fig. 2, a real aperture radar scanning model is used in this embodiment, and specific system parameters of the radar system are shown in table 1. The scanning radar radiates a chirped (LFM) signal at a set fixed pulse repetition frequency prf=2000 Hz.
TABLE 1
Simulation parameters Numerical value
Carrier frequency 10.75GHz
Time width 2us
Bandwidth of a communication device 40MHz
Antenna beam width 2.5°
Pulse repetition frequency 2000Hz
Scanning speed 60°/s
Scanning range ±10°
Initial slant distance 3km
Platform speed 30m/s
The simulated scanning detection area in this embodiment is set to Ω= -10 ° to 10 °, the antenna beam width is 2.5 °, and the scanning speed is 60 °/s.
The radar transmit chirp is expressed as:
where τ represents distance dimension time; carrier frequency f c =10.75 GHz; pulse time width T of transmitted signal p =2us; k represents the frequency modulation frequency, anSignal bandwidth b=40Μ hz, rect (·) represents a rectangular window function.
And performing distance dimension matching filtering and scaling processing on the demodulated original echo in a frequency domain, wherein an echo expression can be converted into:
wherein t represents azimuth dimension time; sigma represents the target scattering backward coefficient; h (t) represents an antenna pattern modulation function; sinc (·) denotes the impulse compression response function; r is R 0 The initial slant distance between the radar and the target is represented as R 0 ＝3km；Representing the distance history, v=30m/s is the platform movement speed, θ 0 The azimuth angle is represented, and the value interval is the scanning range omega= -10 degrees in table 1; c=3×10 8 Represents the propagation speed of electromagnetic waves, lambda represents the wavelength of the transmitted signal; n (τ, t) represents additive gaussian white noise.
After pulse compression and motion compensation processing, the echo may be converted into the following form:
y＝Hx+n (11)
wherein ,representing the received echo vector with dimensions Nx1, -, for example>The i (i is more than or equal to 1 and less than or equal to N) element of the echo vector; />Representing a target scattering coefficient vector, having dimensions N x 1,the i (i is more than or equal to 1 and less than or equal to N) element of the target scattering coefficient vector; />Noise vectors satisfying a Gaussian distribution are represented with dimensions N1, < >>I (i is more than or equal to 1 and is less than or equal to N) element of the noise vector; t represents the transpose operation of the vector, N represents the azimuth sampling point number, [ theta ] 1 ,θ 2 ,…,θ N ]Azimuth sampling representing an imaging scene; h represents an antenna pattern matrix consisting of antenna pattern samples, with dimensions n×n, expressed as follows:
wherein ,representing antenna pattern samples, +.>Sample value representing antenna pattern, N represents azimuth sample point number, and +.>Ω= -10 ° to 10 ° represents the imaging region, ω=60°/s represents the scanning speed, and prf=2000 Hz represents the pulse repetition frequency.
Step two, correcting a convolution model;
in this embodiment, considering that there is a widening error in the antenna directivity diagram, a widening correction error matrix is introduced, and the convolution model in the equation (11) is corrected as:
y＝(H+E)x+n (13)
where E represents a widening correction error matrix of dimension n×n.
Step three, constructing an objective function;
based on the sparsity of the target, on the basis of least squares, an objective function is constructed as follows:
wherein ,representing data fidelity item->Representing the square of the vector 2 norm; alpha x 1 Representing the target constraint term, alpha represents a parameter for adjusting the strength of the target constraint term, |·|| 1 Representing the vector L1 norm; />Representing the constraint term of the broadening correction error matrix, beta representing a parameter for adjusting the intensity of the constraint term of the broadening correction error matrix,/and%>Representing the square of the matrix Frobenius norm. Alpha, beta are both set to 1 in the simulation of this embodiment.
Step four, solving the E problem;
in this embodiment, an alternate iterative strategy is used to solve the objective function.
First, the variable x is fixed, and the objective function is converted into:
by adopting the derivative strategy, the updated expression of the variable E can be obtained:
wherein the superscript H denotes a conjugate transpose operation.
Step five, solving the problem x;
fixed variable E, letThe objective function is translated into:
the problem of equation (17) contains an unpredictable L1 norm constraint term, so an iterative re-weighting method is adopted to solve, and the specific updating steps are as follows:
for j＝1,2,…,J
W j ＝diag(|x j-1 | -1 )
end (18)
wherein the subscript J denotes the iteration order, J denotes the number of iterations required to solve the problem convergence in equation (17), x 0 Representing initialized target scattering coefficient, x j Represents the scattering coefficient, W, of the target after j iterations j Representing the weighting matrix after j iterations, diag (·) represents the diagonal matrix.
Step six, obtaining an imaging result;
updating the target scattering coefficient to x=x J Then repeating the fourth step and the fifth step until the target scattering coefficient and the error matrix reach convergence, namely
Where k represents the outer loop iteration order, j represents the inner loop iteration order, and η represents the convergence threshold.
And traversing all distance units in the echo, and finally outputting a direction super-resolution imaging result.
The simulation parameters of this example are shown in table 1. Fig. 3 shows an ideal antenna pattern function and an antenna pattern function in the presence of a splay error. Fig. 4 is a graph of simulation results in the embodiment of the present invention, where fig. 4 (a) shows the original distribution of the target, fig. 4 (b) shows the original echo, fig. 4 (c) shows the reconstruction result of the conventional sparse method, and fig. 4 (d) shows the reconstruction result of the method of the present invention. As can be seen from fig. 4, when the antenna directional diagram has a stretching error, the reconstruction result generates a larger error in the conventional sparse method, and when the antenna directional diagram has a stretching error, the method provided by the invention still realizes the effective reconstruction of the target.
In summary, the method introduces a broadening correction error matrix in the azimuth echo convolution model, and continuously updates the target and the error matrix in an alternate iteration mode, so that steady imaging under an error condition is realized.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Various modifications and variations of the present invention will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (1)

1. A scanning radar super-resolution method under unknown broadening of an antenna pattern comprises the following specific steps:
modeling an azimuth convolution model;
scanning a radar to radiate a linear frequency modulation LFM signal at a set fixed pulse repetition frequency PRF, and simultaneously scanning and detecting an observation area by using an antenna; based on the scanning imaging process, the echo signals in one distance unit of the observation area are constructed as the convolution of an antenna function and a target scattering coefficient, and the additive Gaussian white noise is considered, the azimuth signal model is expressed as follows:
y＝Hx+n (1)
wherein ,representing the received echo vector with dimensions Nx1, -, for example>The i (i is more than or equal to 1 and less than or equal to N) element of the echo vector; />Representing a target scattering coefficient vector with dimensions Nx1, ">The i (i is more than or equal to 1 and less than or equal to N) element of the target scattering coefficient vector; />Noise vectors satisfying a Gaussian distribution are represented with dimensions N1, < >>I (i is more than or equal to 1 and is less than or equal to N) element of the noise vector; t represents the transpose operation of the vector, N represents the azimuth sampling point number, [ theta ] 1 ,θ 2 ,…,θ N ]Azimuth sampling representing an imaging scene; h represents an antenna pattern matrix formed by antenna pattern sampling, and the dimension isN×n, the expression is as follows:
wherein ,representing the antenna pattern sample vector, < >>Sample values representing antenna patterns; n represents the azimuth sampling point number, and +.>Omega denotes the imaging region, omega denotes the scanning speed, PRF denotes the pulse repetition frequency;
step two, correcting a convolution model;
introducing a broadening correction error matrix in consideration of the condition that the antenna directional diagram has unknown broadening errors of the beam, and correcting a convolution model in the formula (1) as follows:
y＝(H+E)x+n (3)
wherein E represents a widening correction error matrix with dimension of N multiplied by N;
step three, constructing an objective function;
based on the sparsity of the target, on the basis of least squares, an objective function J (x, E) is constructed as follows:
wherein ,representing data fidelity item->Representation directionSquaring the 2 norms of the quantity; alpha x 1 Representing the target constraint term, alpha represents a parameter for adjusting the strength of the target constraint term, |·|| 1 Representing the vector L1 norm; />Representing the constraint term of the broadening correction error matrix, beta representing a parameter for adjusting the intensity of the constraint term of the broadening correction error matrix,/and%>Representing the square of the matrix Frobenius norm;
step four, solving the E problem;
solving an objective function by adopting an alternate iteration strategy;
first, the variable x is fixed, and the objective function is converted into:
obtaining an updated expression of the variable E by adopting a derivative strategy:
wherein, the superscript H represents conjugate transpose operation;
step five, solving the problem x;
fixed variable E, letThe objective function is translated into:
the problem of the formula (7) contains an unpredictable L1 norm constraint term, and is solved by adopting an iterative re-weighting method, wherein the specific updating steps are as follows:
forj＝1,2,…,J
W j ＝diag(|x j-1 | -1 )
end (8)
wherein the subscript J denotes the iteration order, J denotes the number of iterations required to solve the problem convergence in equation (7), x 0 Representing initialized target scattering coefficient, x j Represents the scattering coefficient, W, of the target after j iterations j Representing a weighting matrix after j iterations, diag (°) representing a diagonal matrix;
step six, obtaining an imaging result;
updating the target scattering coefficient to x=x J And step four, repeating the step five until the target scattering coefficient and the error matrix reach convergence, outputting the result of the distance unit, traversing all the distance units in the echo, and obtaining the azimuth super-resolution imaging result of the whole observation area.
CN202310427532.2A 2023-04-20 2023-04-20 Scanning radar super-resolution method under unknown broadening of antenna pattern Pending CN116577749A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116908845A (en) * 2023-09-12 2023-10-20 厦门大学 MIMO radar super-resolution imaging method, MIMO radar and storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116908845A (en) * 2023-09-12 2023-10-20 厦门大学 MIMO radar super-resolution imaging method, MIMO radar and storage medium
CN116908845B (en) * 2023-09-12 2024-01-16 厦门大学 MIMO radar super-resolution imaging method, MIMO radar and storage medium

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