CN107271996B - Airborne CSSAR (compact spherical synthetic aperture radar) ground moving target imaging method - Google Patents

Airborne CSSAR (compact spherical synthetic aperture radar) ground moving target imaging method Download PDF

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CN107271996B
CN107271996B CN201710413062.9A CN201710413062A CN107271996B CN 107271996 B CN107271996 B CN 107271996B CN 201710413062 A CN201710413062 A CN 201710413062A CN 107271996 B CN107271996 B CN 107271996B
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李永康
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Northwestern Polytechnical 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
    • 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
    • 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
    • G01S13/9088—Circular SAR [CSAR, C-SAR]

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Abstract

The invention provides an airborne CSSAR ground moving target imaging method, and relates to the field of radar signal processing. The method comprises the steps that an airborne CSSAR receives an echo signal of a ground moving target, distance Fourier transform and direction Fourier transform are carried out, distance matching filtering and a distance migration correction filter are constructed in a two-dimensional frequency domain to carry out distance migration correction, then distance Fourier inverse transform and direction compression are carried out, a direction compression filter bank is constructed and direction compression is carried out, the peak power of a target signal after direction compression is calculated, the distance migration correction filter is updated by the frequency modulation rate of the direction compression filter enabling the target peak power after direction compression to be maximum, and the direction compression filter is used for carrying out direction compression on the target signal after distance migration correction. The range migration correction method has high accuracy and can be used for a system with high range resolution.

Description

Airborne CSSAR (compact spherical synthetic aperture radar) ground moving target imaging method
Technical Field
The invention relates to the field of radar signal processing, in particular to a synthetic aperture radar ground moving target imaging method.
Background
An airborne Circular track Synthetic aperture radar (CSSAR) is a new type of airborne SAR developed in recent years, and has the characteristics of wide coverage range and periodic revisit, so that the CSSAR is suitable for air-to-ground wide-area reconnaissance and time-sensitive target (such as ground moving target) monitoring.
Since the onboard CSSAR is a new onboard SAR that has appeared in recent years, there is little research on imaging of ground moving objects under the onboard CSSAR. The document "group moving target imaging for single channel aircraft CSSAR" (Electronics Letters,2014,50:24) firstly proposes a Ground moving target imaging method suitable for airborne single channel CSSAR, but the method is only suitable for systems with lower distance resolution. When the system range resolution is high, the method cannot correct range migration of the target correctly, and therefore high-quality imaging of the target cannot be achieved.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a ground moving target imaging method which can be used for an airborne CSSAR system with high range resolution. The improved imaging method is provided for solving the problem that the existing airborne single-channel CSSAR ground moving target imaging method cannot correct the range migration of the target when the system range resolution is high.
Aiming at the problem that the existing imaging method cannot correct the range migration of the target correctly when the system range resolution is higher, the invention improves the method and provides an iterative processing flow to realize the accurate correction of the range migration of the target. The technical scheme adopted for solving the technical problems comprises the following steps:
step 1, an airborne CSSAR receives echo signals of a ground moving target, distance Fourier transform and direction Fourier transform are respectively carried out on the received echo signals of the target, the target signals are transformed to a two-dimensional frequency domain, and two-dimensional frequency domain target signals are obtained;
step 2, constructing a distance matching filter in the two-dimensional frequency domain, and multiplying the two-dimensional frequency domain target signal in the step 1 by the distance matching filter to perform distance direction matching filtering to realize distance compression;
step 3, constructing a range migration correction filter H in a two-dimensional frequency domainrcmc(l) The detailed steps are as follows:
a) matching the distance direction of the step 2 with the filtered target signal Src(fr,fa) Is shown as
Figure BDA0001312966310000021
Wherein, Wa(. is an azimuth frequency envelope, Wr(. is a distance frequency envelope, faIs the base band azimuth frequency and satisfies-PRF/2 ≤ faPRF is less than or equal to PRF/2, PRF is pulse repetition frequency of radar, frIs the range frequency, M is the Doppler ambiguity number, tacFor the moment when the radar beam center crosses the target, RcIs tacDistance of the radar to the target at time, l1And l2Respectively, the first and second order coefficients of the target distance equation, c is the speed of light, fcA carrier frequency for the radar transmit signal;
b) according to an expression of the target signal after the distance matching filtering, namely formula (1), constructing the following distance migration correction filter:
Figure BDA0001312966310000022
wherein l is a range migration correction factor;
step 4, the two-dimensional frequency domain target signal after the distance compression in the step 2 and H are combinedrcmc(l) Multiplying, performing range migration correction, performing range-to-Fourier inverse transformation on the range migration corrected target signal, and converting the range migration corrected target signal from a two-dimensional frequency domain to a range-Doppler domain to obtain a range-Doppler domain target signal;
step 5, constructing an azimuth compression filter bank, performing azimuth compression on the range-Doppler domain target signal in the step 4 by using each azimuth compression filter in the azimuth compression filter bank, and calculating the peak power of the target signal after azimuth compression, wherein the detailed steps are as follows:
a) step 4, the range-Doppler domain target signal srcmc(tr,fa) Is shown as
Figure BDA0001312966310000023
Wherein, trFor a fast time of distance, pr(. is a distance-compressed impulse response function;
b) according to the target signal expression after the range migration correction, namely formula (3), the ith filter H in the azimuth compression filter bankac,i(Ka,i) The structure is as follows:
Figure BDA0001312966310000024
in the formula (4), the reaction mixture is,
Figure BDA0001312966310000031
Figure BDA0001312966310000032
wherein, Ka,iAdjusting the azimuth frequency of the ith filter, L being the number of required filters, Ka,minAnd Ka,maxRespectively, the minimum possible value and the maximum possible value of the azimuth frequency modulation of the ground moving object of interest, TaIn order to target the synthetic aperture time,
Figure BDA0001312966310000033
represents rounding up;
will srcmc(tr,fa) And Hac,i(Ka,i) Multiplying, and performing azimuth inverse Fourier transform to obtain the target signal s after azimuth compression of the ith filterac,i(tr,ta) Comprises the following steps:
Figure BDA0001312966310000036
wherein the inverse azimuth fourier transform is performed;
c) target peak power P after azimuth compression of ith filteriCalculated using the following formula:
Figure BDA0001312966310000034
wherein the content of the first and second substances,
Figure BDA0001312966310000035
indicates acquisition with trAnd taAs a binary function of an argument sac,i(tr,ta) The maximum value of (c), represents the absolute value;
step 6, target peak power P after azimuth compression from step 5iTo select the maximum value PqAnd a corresponding azimuth compression filter Hac,q(Ka,q)；
Step 7, judging whether l is equal to lambda Ka,q/4, where λ is the wavelength of the radar emission signal, Ka,qIs an azimuth compression filter Hac,q(Ka,q) If yes, step 8 is executed, otherwise, let l ═ λ Ka,q/4, update Hrcmc(l) Then returns toStep 4;
step 8, with Hac,q(Ka,q) And (4) carrying out azimuth compression on the range-Doppler domain target signal in the step (4) to finish the imaging of the target.
The method has the advantages that the range migration correction is carried out in the form of iterative processing, the range migration correction filter is updated by using the frequency modulation rate of the azimuth compression filter which enables the target peak power to be maximum after azimuth compression, and the residual range migration caused by azimuth frequency modulation error can be remarkably reduced. The range migration correction method has higher accuracy and can be used for a system with high range resolution.
Drawings
FIG. 1 is a schematic flow diagram of the present invention.
FIG. 2 is an airborne CSSAR observation geometry, where raRadius of radar movement track, ω is angular velocity of radar, h is radar height, vxAnd vySpeed of the target along the x-axis and y-axis, r, respectively0And theta0The distance from the target to the origin of coordinates at time zero and the azimuth angle of the target.
Fig. 3 is a graph of distance compression results.
Fig. 4 is a graph of a simulation result of range migration correction, in which fig. 4(a) is a result of range migration correction of a method of document "group moving targeting algorithm for single channel air CSSAR" (Electronics Letters,2014,50:24), and fig. 4(b) is a result of range migration correction of the present invention.
Fig. 5 is a diagram of the result of an object imaging simulation, in which fig. 5(a) is an azimuth cross-sectional view, and fig. 5(b) is a distance cross-sectional view, in which IRW is an Impulse Response Width (Impulse Response Width).
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a schematic flow chart of the present invention, which comprises the following specific steps:
step 1, an airborne CSSAR receives echo signals of a ground moving target, distance Fourier transform and direction Fourier transform are respectively carried out on the received echo signals of the target, the target signals are transformed to a two-dimensional frequency domain, and two-dimensional frequency domain target signals are obtained;
FIG. 2 is a geometric view of an airborne single-channel CSSAR observation, and the motion trail of a radar platform is a radius raThe angular velocity of the radar platform is omega, the flying height is h, and the radar beam is always perpendicular to the velocity direction and points to the outer side of the motion trail. Suppose that the target moves linearly at a constant speed and has a velocity v along the x-axis and the y-axis respectivelyxAnd vyAt taTime (t) 0aAzimuth slow time), the coordinate of the radar is (r)a0, h) the coordinates of the target are (r)0cosθ0,r0sinθ00), wherein r0Is taDistance of target to origin of coordinates at time 0, θ0Is taThe azimuth of the target at time 0.
According to FIG. 2, the target distance equation can be expressed as
Figure BDA0001312966310000041
In the formula (9), the reaction mixture is,
Figure BDA0001312966310000051
wherein, tacFor the moment when the radar beam center crosses the target, RcIs ta＝tacDistance of the radar to the target at the moment rcIs ta＝tacDistance of time target to origin of coordinates, thetacIs ta＝tacAzimuth of the time of day, l1And l2The first order coefficient and the second order coefficient of the target distance equation are respectively.
Assuming that the signal transmitted by the radar is a chirp signal, the demodulated target echo signal can be represented as:
Figure BDA0001312966310000052
wherein，trFor a fast time of distance, wr(. is) the distance envelope, c is the speed of light, wa(. is an azimuth envelope, f)cCarrier frequency, K, for radar-transmitted signalsrThe frequency of the radar emission signal is adjusted. For simplicity of presentation, the constant amplitude term of the target echo signal is ignored.
Two-dimensional Fourier transform is carried out on the target echo signal, and a stationary phase principle is utilized to obtain a target signal of a two-dimensional frequency domain:
Figure BDA0001312966310000053
in the formula (12), the reaction mixture is,
Figure BDA0001312966310000054
wherein f isrFor range frequency, PRF is the pulse repetition frequency, faIs the base band azimuth frequency and satisfies-PRF/2 ≤ fa≤PRF/2，Wa(. is an azimuth frequency envelope, Wr(fr) M is the doppler ambiguity number for the range frequency envelope. For simplicity of expression, the constant phase and amplitude terms in equation (12) are ignored.
Due to fc＞＞frIs approximately 1/(f)c+fr)≈1/fc-fr/fc 2It is true that, as a result,
Figure BDA0001312966310000055
can be further expressed as:
Figure BDA0001312966310000061
therefore, the target echo signal of the two-dimensional frequency domain can be represented as:
Figure BDA0001312966310000062
step 2, constructing a distance matching filter in the two-dimensional frequency domain, and multiplying the two-dimensional frequency domain target signal in the step 1 by the distance matching filter to perform distance direction matching filtering to realize distance compression;
the distance compression can be realized by matching and filtering at two-dimensional frequency to compensate the quadratic term of the distance frequency in the phase of the target signal. The distance-matched filter may be configured as a two-dimensional frequency domain representation of the target signal
Figure BDA0001312966310000063
The target echo signal S (f) of the two-dimensional frequency domain of the formula (15)r,fa) And Hrc(fr) Multiplying to obtain a target signal after distance direction matching filtering:
Figure BDA0001312966310000064
step 3, constructing a range migration correction filter H in a two-dimensional frequency domainrcmc(l)；
In order to correct the range migration of the target, the coupling direction of the range frequency and the azimuth frequency in the phase of the target signal needs to be compensated, and the following range migration correction filter is constructed according to the expression of the target signal after range matching filtering, namely the formula (1):
Figure BDA0001312966310000065
wherein l is a range migration correction factor.
Step 4, the two-dimensional frequency domain target signal after the distance compression in the step 2 and H are combinedrcmc(l) Multiplying, performing range migration correction, performing range-to-Fourier inverse transformation on the range migration corrected target signal, and converting the range migration corrected target signal from a two-dimensional frequency domain to a range-Doppler domain to obtain a range-Doppler domain target signal;
will Src(fr,fa) And Hrcmc(l) Multiplication can result in:
Figure BDA0001312966310000071
to Src(fr,fa) Performing range inverse Fourier transform to obtain a range-Doppler domain target signal after range migration correction:
Figure BDA0001312966310000072
wherein p isr(. cndot.) is a distance-compressed impulse response function.
As can be seen from equation (3), there is also a residual range migration. When the system range resolution is high, e.g. above 0.5m, the residual range migration is likely to be larger than half a range resolution unit and thus not negligible. To this end, an iterative process flow of step 7 is proposed to reduce the residual range migration.
Step 5, constructing an azimuth compression filter bank, performing azimuth compression on the range-Doppler domain target signal in the step 4 by using each azimuth compression filter in the azimuth compression filter bank, and calculating the peak power of the target signal after azimuth compression, wherein the detailed steps are as follows:
a) in order to perform azimuth compression on a target, a quadratic term of azimuth frequency in a target signal phase needs to be compensated, and the azimuth compression is performed by using an azimuth compression filter bank considering that the azimuth frequency modulation rate of the target is unknown. According to the target signal expression after the range migration correction, the ith filter H in the azimuth compression filter bankac,i(Ka,i) The structure is as follows:
Figure BDA0001312966310000073
in the formula (4), the reaction mixture is,
Figure BDA0001312966310000074
Figure BDA0001312966310000075
wherein, Ka,iAdjusting the azimuth frequency of the ith filter, L being the number of required filters, Ka,minAnd Ka,maxRespectively, the minimum possible value and the maximum possible value of the azimuth frequency modulation of the ground moving object of interest, TaIn order to target the synthetic aperture time,
Figure BDA0001312966310000081
represents rounding up;
will srcmc(tr,fa) And Hac,i(Ka,i) Multiplying, and performing azimuth inverse Fourier transform to obtain the target signal s after azimuth compression of the ith filterac,i(tr,ta) Comprises the following steps:
Figure BDA0001312966310000085
wherein
Figure BDA0001312966310000086
Indicating that an azimuth Fourier inverse transformation is performed;
b) since different azimuth compression filters in the filter bank use different azimuth modulation frequencies, these filters have different compression effects on the target. The azimuth compression filter that maximizes the target peak power after azimuth compression is the filter with the best azimuth compression effect, that is, the filter that is finally used to compress the target azimuth. Target peak power P after azimuth compression of ith filteriCalculated using the following formula:
Figure BDA0001312966310000082
wherein the content of the first and second substances,
Figure BDA0001312966310000083
indicates acquisition with trAnd taAs a binary function of an argument sac,i(tr,ta) The maximum value of (c), represents modulo;
step 6, target peak power P after azimuth compression from step 5iTo select the maximum value PqAnd a corresponding azimuth compression filter Hac,q(Ka,q)；
Performing the following mathematical operation to determine the index q of the azimuth compression filter that maximizes the target peak power:
Figure BDA0001312966310000084
the azimuth compression filter that maximizes the target peak power is Hac，q(Ka,q)。
Step 7, judging whether l is equal to lambda Ka,q/4, where λ is the wavelength of the radar emission signal, Ka,qIs an azimuth compression filter Hac,q(Ka,q) If yes, step 8 is executed, otherwise, let l ═ λ Ka,q/4, update Hrcmc(l) Then returning to the step 4;
step 8, with Hac，q(Ka,q) And (4) carrying out azimuth compression on the range-Doppler domain target signal in the step (4) to finish the imaging of the target.
H is to beac，q(Ka,q) And srcmc(tr,fa) Multiplication can obtain
Figure BDA0001312966310000091
To sac,q(tr,fa) And performing azimuth Fourier inverse transformation to obtain an imaged target signal:
Figure BDA0001312966310000092
the effect of the invention is further illustrated by the following simulation experiment:
(1) distance migration correction simulation
The parameters of the airborne single-channel CSSAR system are shown in table 1, and the target parameters are as follows: v. ofx＝30m/s，vy＝26m/s，r0＝23.81km，θ 00. Fig. 3 is a target track after distance compression, and it can be seen that a significant distance migration exists in the target. Fig. 4(a) shows the result of correcting the range migration by the method of the document "group moving target imaging for single channel air cssar" (Electronics Letters,2014,50:24), and there is a more obvious range migration, which indicates that the method cannot completely correct the range migration of the target. Fig. 4(b) shows the result of the range migration correction of the present invention, in which the trajectory of the target is perpendicular to the range axis, i.e., the range migration of the target is well corrected, which indicates that the present invention can correct the range migration of the target correctly.
TABLE 1 airborne CSSAR System parameters
Radar platform velocity 150m/s
Radius of flight 3km
Radar platform height 12km
Carrier frequency 10GHz
Bandwidth of transmitted signal 150MHz
Sampling frequency 180MHz
Pulse repetition frequency 1000Hz
Azimuth beam width 2°
Scene center angle of incidence 60°
(2) Target imaging simulation
The parameter settings in this simulation are the same as those in simulation 1, and the simulation results are shown in fig. 5. Fig. 5(a) shows an azimuth cross-sectional view of the target after imaging, and indicates the broadening of the azimuth Impulse Response Width (IRW) of the target. Fig. 5(b) shows a range profile of the imaged object, and identifies the range IRW spread of the object. As can be seen from fig. 5, the range IRW of the target is less than 2%, and the range IRW is zero, which indicates that the target imaging quality of the present invention is high.

Claims (1)

1. An airborne CSSAR ground moving target imaging method is characterized by comprising the following steps:
step 1, an airborne CSSAR receives echo signals of a ground moving target, distance Fourier transform and direction Fourier transform are respectively carried out on the received echo signals of the target, the target signals are transformed to a two-dimensional frequency domain, and two-dimensional frequency domain target signals are obtained;
step 2, constructing a distance matching filter in the two-dimensional frequency domain, and multiplying the two-dimensional frequency domain target signal in the step 1 by the distance matching filter to perform distance direction matching filtering to realize distance compression;
step 3, constructing a range migration correction filter H in a two-dimensional frequency domainrcmc(l) The detailed steps are as follows:
a) matching the distance direction of the step 2 with the filtered target signal Src(fr,fa) Is shown as
Figure FDA0002193821140000011
Wherein, Wa(. is an azimuth frequency envelope, Wr(. is a distance frequency envelope, faIs the base band azimuth frequency and satisfies-PRF/2 ≤ faPRF is less than or equal to PRF/2, PRF is pulse repetition frequency of radar, frIs the range frequency, M is the Doppler ambiguity number, tacFor the moment when the radar beam center crosses the target, RcIs tacDistance of the radar to the target at time, l1And l2Respectively, the first and second order coefficients of the target distance equation, c is the speed of light, fcA carrier frequency for the radar transmit signal;
b) according to an expression of the target signal after the distance matching filtering, namely formula (1), constructing the following distance migration correction filter:
Figure FDA0002193821140000012
wherein l is a range migration correction factor;
step 4, the two-dimensional frequency domain target signal after the distance compression in the step 2 and H are combinedrcmc(l) Multiplying, performing range migration correction, performing range-to-Fourier inverse transformation on the range migration corrected target signal, and converting the range migration corrected target signal from a two-dimensional frequency domain to a range-Doppler domain to obtain a range-Doppler domain target signal;
step 5, constructing an azimuth compression filter bank, performing azimuth compression on the range-Doppler domain target signal in the step 4 by using each azimuth compression filter in the azimuth compression filter bank, and calculating the peak power of the target signal after azimuth compression, wherein the detailed steps are as follows:
a) step 4, the range-Doppler domain target signal srcmc(tr,fa) Is shown as
Figure FDA0002193821140000021
Wherein, trFor a fast time of distance, pr(. is a distance-compressed impulse response function;
b) according to the target signal expression after the range migration correction, namely formula (3), the ith filter H in the azimuth compression filter bankac,i(Ka,i) The structure is as follows:
Figure FDA0002193821140000022
in the formula (4), the reaction mixture is,
Figure FDA0002193821140000023
Figure FDA0002193821140000024
wherein, Ka,iAdjusting the azimuth frequency of the ith filter, L being the number of required filters, Ka,minAnd Ka,maxRespectively, the minimum possible value and the maximum possible value of the azimuth frequency modulation of the ground moving object of interest, TaIn order to target the synthetic aperture time,
Figure FDA0002193821140000025
represents rounding up;
will srcmc(tr,fa) And Hac,i(Ka,i) Multiplying, and performing azimuth inverse Fourier transform to obtain the target signal s after azimuth compression of the ith filterac,i(tr,ta) Comprises the following steps:
Figure FDA0002193821140000026
wherein
Figure FDA0002193821140000027
To representPerforming azimuth Fourier inverse transformation;
c) target peak power P after azimuth compression of ith filteriCalculated using the following formula:
Figure FDA0002193821140000028
wherein the content of the first and second substances,
Figure FDA0002193821140000029
indicates acquisition with trAnd taAs a binary function of an argument sac,i(tr,ta) Maximum value of, taFor azimuth slow time, | · | represents modulo;
step 6, target peak power P after azimuth compression from step 5iTo select the maximum value PqAnd a corresponding azimuth compression filter Hac,q(Ka,q)；
Step 7, judging whether l is equal to lambda Ka,q/4, where λ is the wavelength of the radar emission signal, Ka,qIs an azimuth compression filter Hac,q(Ka,q) If yes, step 8 is executed, otherwise, let l ═ λ Ka,q/4, update Hrcmc(l) Then returning to the step 4;
step 8, with Hac,q(Ka,q) And (4) carrying out azimuth compression on the range-Doppler domain target signal in the step (4) to finish the imaging of the target.
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