CN110888133A - V frequency modulation signal ISAR sparse imaging method under low signal-to-noise ratio condition - Google Patents

V frequency modulation signal ISAR sparse imaging method under low signal-to-noise ratio condition Download PDF

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CN110888133A
CN110888133A CN201911155781.0A CN201911155781A CN110888133A CN 110888133 A CN110888133 A CN 110888133A CN 201911155781 A CN201911155781 A CN 201911155781A CN 110888133 A CN110888133 A CN 110888133A
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frequency modulation
signal
sparse
target
reconstruction
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潘小义
陈吉源
谢前朋
赵锋
冯德军
艾小锋
顾赵宇
肖顺平
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National University of Defense Technology
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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
    • 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
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G01S13/9064—Inverse SAR [ISAR]
    • 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
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9021—SAR image post-processing techniques
    • G01S13/9029—SAR image post-processing techniques specially adapted for moving target detection within a single SAR image or within multiple SAR images taken at the same time

Abstract

The invention discloses an ISAR sparse imaging method for V frequency modulation signals under the condition of low signal-to-noise ratio, which comprises the following steps: firstly, carrying out pulse compression processing on a sparse V frequency modulation echo signal; and secondly, adopting improved weighted compressed sensing reconstruction to obtain a target image. The beneficial effects of the invention mainly comprise: firstly, the V frequency modulation signal can improve the detection distance and the resolution, eliminate the distance and speed ambiguity and improve the two-dimensional resolution. Secondly, a V frequency modulation signal sparse echo model is solved, a target ISAR image can be reconstructed through a small amount of measurement data, and the method can be more suitable for the multifunctional multi-task application requirement under modern radar resource scheduling. Thirdly, the target image can be accurately reconstructed through an improved weighted compressive sensing method under the condition of low signal-to-noise ratio, and the imaging capacity under the conditions of noise and the like is improved.

Description

V frequency modulation signal ISAR sparse imaging method under low signal-to-noise ratio condition
[ technical field ] A method for producing a semiconductor device
The invention discloses a V frequency modulation signal ISAR sparse imaging method under the condition of low signal-to-noise ratio, belongs to the technical field of radar detection, and further relates to a sparse V frequency modulation signal ISAR imaging method, in particular to an improved weighted compressive sensing V frequency modulation signal ISAR sparse imaging method, which can obtain a better radar target imaging effect under the condition of low signal-to-noise ratio.
[ background of the invention ]
The Inverse Synthetic Aperture Radar (ISAR) imaging technology plays an important role in the aspects of radar detection, identification, classification and the like of moving targets, and is widely applied to the field of microwave detection of aerospace targets (such as artificial satellites, space debris and the like). In radar imaging, a pulse compression technology and a large-time-width-bandwidth product signal are adopted to improve the detection distance and the imaging resolution, and compared with a distance and speed two-dimensional fuzzy effect caused by a linear frequency modulation signal knife edge type fuzzy function, the V frequency modulation signal is similar to a pin type fuzzy function, so that the fuzzy can be effectively eliminated, and the target distance-speed two-dimensional resolution capability is improved. In addition, radar target high-resolution imaging often requires support of long-time observation data, which may be difficult for non-cooperative targets; and radar time resources often need to satisfy multifunctional and multitask, such as scanning, tracking, imaging and the like, so that echo data obtained in observation time available for imaging is sparse in a slow azimuth time domain.
The ISAR target two-dimensional image only contains a small number of scattering points, the number of the scattering points is generally far smaller than the number of sampling points, and the signal sparse condition required by compressed sensing reconstruction is met. The echo of a modern radar target is often disturbed by more serious noise, clutter and other non-ideal signals, and how to obtain a high-resolution imaging result in a low signal-to-noise ratio environment still needs to be solved. At present, compressed sensing-based ISAR signal sparse imaging methods such as linear frequency modulation and step frequency are researched, but the ISAR sparse imaging method for V frequency modulation signals needs to be researched urgently under the condition of low signal-to-noise ratio.
[ summary of the invention ]
The technical problem to be solved by the invention is as follows: aiming at the condition of low signal-to-noise ratio, an improved weighted compressive sensing method is provided for ISAR sparse imaging of V frequency modulation signals.
The invention discloses an ISAR sparse imaging method of V frequency modulation signals under the condition of low signal-to-noise ratio, which adopts the following technical scheme:
firstly, carrying out pulse compression processing on sparse V frequency modulation echo signals
After the V frequency modulation signal is scattered by a target, the echo signal at the radar receiver is as follows:
Figure BDA0002284761210000021
wherein I represents the total scattering point number of the target, sigmaiRepresents the scattering intensity of the ith scattering point, TpWhich represents the duration of the pulse or pulses,
Figure BDA0002284761210000022
c represents the electromagnetic wave propagation velocity, exp is an exponential function, j is a unit imaginary number,
Figure BDA0002284761210000023
indicating fast time, tmRepresenting slow time, t representing total time, RiDenotes the distance from the i-th scattering point to the radar, gamma denotes the modulation frequency, f0Representing the carrier frequency.
And (3) obtaining a one-dimensional range profile by adopting a mature two-channel line-relief frequency modulation pulse compression technology, namely performing difference frequency processing and Fourier transform (FFT) on the two channels and a reference signal respectively, and synthesizing the one-dimensional range profiles obtained by the two channels to obtain the one-dimensional range profile of the target. The one-dimensional image of one of the range units selected after motion compensation can be represented as:
Figure BDA0002284761210000024
wherein f isdi＝2xiω/λ denotes the Doppler frequency, x, of the scattering point iiIs the lateral coordinate value of scattering point i, ω represents the target rotational angular velocity, λ represents the signal wavelength, and n represents the noise，tm＝[1:M]TΔ t represents the slow time t in equation onemCorresponding discrete time series, M ═ TaWhere,/Δ t represents the number of pulses, Δ t 1/PRF represents the time interval, and PRF represents the pulse repetition frequency, [. cndot.]TRepresenting a transpose; here, the frequency resolution is defined as Δ fdDiscrete Doppler sequence is fd＝[1:M]TΔfd- (PRF/2), a dictionary can thus be obtained as follows:
Figure BDA0002284761210000031
wherein
Figure BDA0002284761210000032
Due to the sparse azimuth slow time domain, the P-th pulse train in the nth range unit has Z, assuming that P pulse train data are collectedpSample points, which can be expressed as: sp,n＝[sn(Mp+1)sn(Mp+2)…sn(Mp+Zp)]Then the nth range bin echo vector can be expressed as:
Figure BDA0002284761210000033
wherein s is1，n,s2，n,…,sP，nTo represent
Figure BDA0002284761210000034
Of data length Z1,,Z2,…,ZPThus the vector form of the sparse echo is represented as:
Figure BDA0002284761210000035
wherein the content of the first and second substances,
Figure BDA0002284761210000036
represents a partially-aware dictionary, [ theta ]n]M×1Representing the nth range cell reconstruction data.
Second, adopting improved weighted compressed sensing reconstruction to obtain target image
In low signal-to-noise ratio, the signal can be weighted1The norm reconstruction model obtains the result, i.e. solves the following optimal problem
min(||wθ||1)s.t.||s-Ψθ||2≦ epsilon (formula four)
Wherein w represents a weighting coefficient vector, and an improved weighting rule and a corresponding iterative algorithm are provided for obtaining a better reconstruction effect.
(1) By weighting1Norm reconstruction solving formula four:
Figure BDA0002284761210000037
the results were calculated using a Maltab toolkit, outer ALgorithms for L1(YALL1), where μl>0 is a penalty factor, wlIs the weighting vector of current iteration for one time, and the result theta obtained by two times of calculationl，θl+1。
(2) Suppose klDenotes thetalNumber k of support setsl:＝|supp(θl) I, make hl＝θl-θl-1H is to belThe absolute values of the elements are arranged in descending order,
Figure BDA0002284761210000041
let N be the null space of Ψ, defining the unit in the null space1Norm-obtainable BETA1＝{h∈M|h∈N,||h||1Let i (k) denote the set of all index sets not greater than k, i.e. 1
Figure BDA0002284761210000042
Let T be0To solve the support set of θ, it can be obtained by solving the following optimal problem
Figure BDA0002284761210000043
The ratio coefficient of the best problem of one equation five is defined,
Figure BDA0002284761210000044
it is obvious that
Figure BDA0002284761210000045
And satisfy
Figure BDA0002284761210000046
ξ therein1<1 is a very small positive number, and
Figure BDA0002284761210000047
in summary, the element w of the weight vector can be updated by the following formula
Figure BDA0002284761210000048
Wherein 0<ξ2Less than or equal to 1. And (3) returning the obtained updated weight to the substep (1) for reconstruction to obtain theta, and if the exit condition is not met, continuing updating the iteration until the optimal solution is met or the maximum iteration number is reached.
The beneficial effects of the invention mainly comprise:
firstly, the V frequency modulation signal can improve the detection distance and the resolution, eliminate the distance and speed ambiguity and improve the two-dimensional resolution.
Secondly, a V frequency modulation signal sparse echo model is solved, a target ISAR image can be reconstructed through a small amount of measurement data, and the method can be more suitable for the multifunctional multi-task application requirement under modern radar resource scheduling.
Thirdly, the target image can be accurately reconstructed through an improved weighted compressive sensing method under the condition of low signal-to-noise ratio, and the imaging capacity under the conditions of noise and the like is improved.
[ description of the drawings ]
Figure 1 is an imaging flow chart and a weighted reconstruction algorithm flow chart.
FIG. 2 is a model of civil aircraft target scattering points for ISAR imaging;
FIG. 3 is a schematic diagram of a target sparse echo signal;
FIG. 4 is a diagram of a target after motion compensation of a high-resolution one-dimensional range profile;
fig. 5 is a schematic diagram of target ISAR reconstruction imaging.
[ detailed description ] embodiments
The invention will be further described with reference to the accompanying drawings.
The invention discloses an ISAR sparse imaging method of V frequency modulation signals under the condition of low signal-to-noise ratio, which comprises the following steps:
firstly, carrying out pulse compression processing on sparse V frequency modulation echo signals
After the V frequency modulation signal is scattered by a target, the echo signal at the radar receiver is as follows:
Figure BDA0002284761210000051
wherein I represents the total scattering point number of the target, sigmaiRepresents the scattering intensity of the ith scattering point, TpWhich represents the duration of the pulse or pulses,
Figure BDA0002284761210000052
c represents the electromagnetic wave propagation velocity, exp is an exponential function, j is a unit imaginary number,
Figure BDA0002284761210000053
indicating fast time, tmRepresenting slow time, t representing total time, RiDenotes the distance from the i-th scattering point to the radar, gamma denotes the modulation frequency, f0Representing the carrier frequency.
And (3) obtaining a one-dimensional range profile by adopting a mature two-channel line-relief frequency modulation pulse compression technology, namely performing difference frequency processing and Fourier transform (FFT) on the two channels and a reference signal respectively, and synthesizing the one-dimensional range profiles obtained by the two channels to obtain the one-dimensional range profile of the target. The one-dimensional image of one of the range units selected after motion compensation can be represented as:
Figure BDA0002284761210000061
wherein f isdi＝2xiPowder of omega/lambda expressionDoppler frequency, x, of point iiIs the lateral coordinate value of scattering point i, ω represents the target rotation angular velocity, λ represents the signal wavelength, n represents the noise, tm＝[1:M]TΔ t represents the slow time t in equation onemCorresponding discrete time series, M ═ TaWhere,/Δ t represents the number of pulses, Δ t 1/PRF represents the time interval, and PRF represents the pulse repetition frequency, [. cndot.]TRepresenting a transpose; here, the frequency resolution is defined as Δ fdDiscrete Doppler sequence is fd＝[1:M]TΔfd- (PRF/2), a dictionary can thus be obtained as follows:
Figure BDA0002284761210000062
wherein
Figure BDA0002284761210000063
Due to the sparse azimuth slow time domain, the P-th pulse train in the nth range unit has Z, assuming that P pulse train data are collectedpSample points, which can be expressed as: sp,n＝[sn(Mp+1)sn(Mp+2)…sn(Mp+Zp)]Then the nth range bin echo vector can be expressed as:
Figure BDA0002284761210000064
wherein s is1,n,s2,n,…,sP,nTo represent
Figure BDA0002284761210000065
Of data length Z1,,Z2,…,ZPThus the vector form of the sparse echo is represented as:
Figure BDA0002284761210000066
wherein the content of the first and second substances,
Figure BDA0002284761210000067
represents a partially-aware dictionary, [ theta ]n]M×1Representing the nth range cell reconstruction data.
Second, adopting improved weighted compressed sensing reconstruction to obtain target image
In low signal-to-noise ratio, the signal can be weighted1The norm reconstruction model obtains the result, i.e. solves the following optimal problem
min(||wθ||1)s.t.||s-Ψθ||2≦ epsilon (formula four)
Wherein w represents a weighting coefficient vector, and an improved weighting rule and a corresponding iterative algorithm are provided for obtaining a better reconstruction effect.
(1) By weighting1Norm reconstruction solving formula four:
Figure BDA0002284761210000068
the results were calculated using a Maltab toolkit, outer ALgorithms for L1(YALL1), where μl>0 is a penalty factor, wlIs the weighting vector of current iteration for one time, and the result theta obtained by two times of calculationl，θl+1。
(2) Suppose klDenotes thetalNumber k of support setsl:＝|supp(θl) I, make hl＝θl-θl-1H is to belThe absolute values of the elements are arranged in descending order,
Figure BDA0002284761210000071
let N be the null space of Ψ, defining the unit in the null space1Norm-obtainable BETA1＝{h∈M|h∈N,||h||1Let i (k) denote the set of all index sets not greater than k, i.e. 1
Figure BDA0002284761210000072
Let T be0To solve the support set of θ, it can be obtained by solving the following optimal problem
Figure BDA0002284761210000073
The ratio coefficient of the best problem of one equation five is defined,
Figure BDA0002284761210000074
it is obvious that
Figure BDA0002284761210000075
And satisfy
Figure BDA0002284761210000076
ξ therein1<1 is a very small positive number, and
Figure BDA0002284761210000077
in summary, the element w of the weight vector can be updated by the following formula
Figure BDA0002284761210000078
Wherein 0<ξ2Less than or equal to 1. Returning the obtained updated weight value to the substep (1) for reconstruction to obtain theta, and if the weight value does not meet the exit bar
Detailed description of the preferred embodiments
The simulation experiment of the invention is compiled on Matlab 2016a, and the execution environment is Windows 10; the target shown in fig. 2 is a civil jacque 42 aircraft model consisting of 330 scattering points, the distance between the radar and the target being 500 KM. The radar center frequency is 10GHz, the bandwidth of a transmitted V frequency modulation signal is 300MHz, the pulse repetition frequency is 1KHz, the pulse width is 100us, 128 pulses are completely received in simulation, and the target is assumed to have no translation and the rotating speed is 0.05 prad/s.
The method comprises the following specific steps:
firstly, transmitting a V frequency modulation signal, and obtaining an echo signal which is shown in figure 3 and has missing discontinuity in an azimuth slow time domain by a receiver after the signal is scattered by a target shown in figure 2.
And secondly, performing dual-channel line-removing frequency modulation pulse compression processing on the V frequency modulation signal echo, and obtaining a one-dimensional distance image shown in figure 4 after motion compensation.
And thirdly, obtaining a final ISAR imaging result under the condition of low signal-to-noise ratio through an improved weighted compressive sensing reconstruction algorithm. Firstly, obtaining a reconstructed signal of each distance unit by adopting a YALL1 solver, then updating the weighting coefficient according to a formula seven, and returning to the previous step for solving until a reconstructed image which meets the conditions and is shown in FIG. 5 is obtained.

Claims (1)

1. A V frequency modulation signal ISAR sparse imaging method under the condition of low signal-to-noise ratio is characterized in that: the method comprises the following steps:
firstly, carrying out pulse compression processing on sparse V frequency modulation echo signals
Processing the target echo by adopting a mature two-channel line-relief frequency modulation pulse compression technology to obtain a one-dimensional range profile: the two channels respectively perform difference frequency processing and Fourier transform with a reference signal, and then the one-dimensional range images obtained by the two channels are synthesized to obtain a one-dimensional range image of a target; after motion compensation, a one-dimensional image of one of the range units is selected, and after vectorization, the one-dimensional image can be expressed as:
Figure FDA0002284761200000011
wherein I represents the total scattering point number of the target, sigmaiRepresents the scattering intensity of the ith scattering point, TpRepresenting the pulse duration, exp is an exponential function, j is an imaginary number of units, fdi＝2xiω/λ denotes the Doppler frequency, x, of the scattering point iiIs the lateral coordinate value of scattering point i, ω represents the target rotation angular velocity, λ represents the signal wavelength, n represents the noise, tm＝[1:M]TΔ t represents the slow time t in equation onemCorresponding discrete time series, M ═ TaWhere,/Δ t represents the number of pulses, Δ t 1/PRF represents the time interval, and PRF represents the pulse repetition frequency, [. cndot.]TRepresenting a transpose; here, the frequency resolution is defined as Δ fdDiscrete Doppler sequence is fd＝[1:M]TΔfd- (PRF/2), a dictionary can thus be obtained as follows:
Figure FDA0002284761200000012
wherein
Figure FDA0002284761200000013
0≤m≤M；
Due to the sparse azimuth slow time domain, the P-th pulse train in the nth range unit has Z, assuming that P pulse train data are collectedpSample points, which can be expressed as: sp,n＝[sn(Mp+1) sn(Mp+2)…sn(Mp+Zp)]Then the nth range bin echo vector can be expressed as:
Figure FDA0002284761200000021
wherein s is1,n,s2,n,…,sP,nTo represent
Figure FDA0002284761200000022
Of data length Z1,,Z2,…,ZPThus the vector form of the sparse echo is represented as:
Figure FDA0002284761200000023
wherein the content of the first and second substances,
Figure FDA0002284761200000024
represents a partially-aware dictionary, [ theta ]n]M×1Representing nth range cell reconstruction data;
second, adopting improved weighted compressed sensing reconstruction to obtain target image
In low signal-to-noise ratio, the signal can be weighted1The norm reconstruction model obtains the result, i.e. solves the following optimal problem
min(||wθ||1)s.t.||s-Ψθ||2≦ epsilon (formula four)
Wherein w represents a weighting coefficient vector, and an improved weighting rule and a corresponding iterative algorithm are provided for obtaining a better reconstruction effect;
(1) by weighting1Norm reconstruction solving formula four:
Figure FDA0002284761200000025
the results were calculated using a Maltab toolkit, outer ALgorithms for L1 solver, where μl>0 is a penalty factor, wlIs the weighting vector of current iteration for one time, and the result theta obtained by two times of calculationl，θl+1；
(2) Suppose klDenotes thetalNumber k of support setsl:＝|supp(θl) I, make hl＝θl-θl-1H is to belThe absolute values of the elements are arranged in descending order,
Figure FDA0002284761200000026
let N be the null space of Ψ, and define a norm of 1 unit in the null space to obtain BETA1＝{h∈M|h∈N,||h||1Let i (k) denote the set of all index sets not greater than k, i.e. 1
Figure FDA0002284761200000027
Let T be0To solve the support set of θ, it can be obtained by solving the following optimal problem
Figure FDA0002284761200000028
The ratio coefficient of the best problem of one equation five is defined,
Figure FDA0002284761200000031
it is obvious that
Figure FDA0002284761200000032
And satisfy
Figure FDA0002284761200000033
ξ therein1<1 isA very small positive number, otherwise thetal＝α1θl-1，α1>1，θ0>0, in summary, the element w of the weight vector can be updated by the following formula
Figure FDA0002284761200000034
Wherein 0<ξ2Less than or equal to 1; and (3) returning the obtained updated weight to the substep (1) for reconstruction to obtain theta, and if the exit condition is not met, continuing updating the iteration until the optimal solution is met or the maximum iteration number is reached.
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