CN111413696A - Improved wave number domain imaging algorithm of squint frequency modulation continuous wave SAR - Google Patents
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Abstract
The invention relates to an improved wave number domain imaging algorithm of a squint frequency modulation continuous wave Synthetic Aperture Radar (binary Synthetic Aperture Radar-SAR), which comprises the following steps: constructing a slope distance expression in a squint mode; carrying out frequency modulation removal processing on the echo signal of the frequency modulation continuous wave SAR corresponding to the slope distance; removing Residual Video Phase (RVP) terms from the de-modulated signal; transforming the signal subjected to RVP removal into a two-dimensional frequency domain; performing phase compensation of fixed slope distance on the two-dimensional frequency spectrum of the echo; carrying out Taylor series expansion on the two-dimensional frequency spectrum subjected to the fixed-slant-distance phase compensation processing with respect to distance-direction frequency, and reserving the two-dimensional frequency spectrum to a cubic term; phase compensation is carried out according to the two-dimensional frequency spectrum based on Taylor series expansion, and distance migration correction, residual distance compression and compensation of high-order coupling phases are completed; and transforming the compensated signal to a two-dimensional time domain to obtain a focused image. The method improves the imaging resolution of the frequency-modulated continuous wave SAR in the squint mode to a certain extent, and simultaneously improves the operation efficiency of the algorithm.
Description
Technical Field
The invention relates to the field of radar signal processing, in particular to an improved squint frequency modulation continuous wave SAR wave number domain imaging algorithm based on Taylor series decomposition.
Background
Synthetic Aperture Radar (Synthetic Aperture Radar-SAR) is a high resolution imaging Radar, and has great significance in many military applications. The frequency modulation continuous wave SAR is a synthetic aperture radar of a novel system formed by combining a frequency modulation continuous wave technology and a synthetic aperture radar technology, and has the characteristics of small volume, light weight, high resolution and the like. Compared with the traditional pulse SAR, the peak power of the frequency-modulated continuous wave SAR is relatively low, and the frequency-modulated continuous wave SAR has the characteristics of low interception rate and strong anti-interference capability. SAR typically operates in a front side view mode, i.e., the transmit beam is directed perpendicular to the direction of motion of the platform. Squint SAR imaging started in the 80 s, and large-oblique-angle SAR imaging with out-of-area detection capability plays an important role in resource exploration, border reconnaissance, battlefield, accurate combat application and the like. The transmitting beam of the squint SAR and the moving direction of the platform have a certain angle, and the angle can influence the resolution of SAR imaging to a great extent, thereby increasing the difficulty of SAR signal processing. Therefore, the method has important practical significance for the research of the strabismus SAR imaging algorithm.
The main imaging algorithms of the frequency modulation continuous wave SAR include a range Doppler algorithm, a frequency scaling algorithm and a wave number domain algorithm. The first two algorithms are generally used for side-looking SAR imaging, and the wavenumber domain algorithm is suitable for SAR with large squint angle and long synthetic aperture. The literature has proposed a signal processing method for squint frequency modulated continuous wave SAR. For example, Robert Wang et al studied squint mode wave number domain algorithms, which further discuss their application in frequency modulated continuous wave SAR data processing. The Wangzhou and Duzhonghong research the wave number domain imaging algorithm of the frequency modulation continuous wave SAR in the bunching mode, and well solve the problem of distance walking caused by the motion of a platform which is specific to the continuous wave SAR in the bunching mode in a sweep frequency period. Emiliano Casalini researches a refocusing technology of a moving target based on a wave number domain algorithm, namely refocusing the moving target in an SAR image generated by an original wave number domain algorithm. The algorithm processing in the above documents is performed by performing Stolt transformation on the distance and orientation coupling terms in a two-dimensional frequency domain, the Stolt transformation process is interpolation operation, additional errors are caused by interpolation, and meanwhile, the operation efficiency is greatly reduced.
Based on the above problems, overcoming the defects of the existing methods is a problem to be solved urgently in the technical field.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a processing method based on two-dimensional frequency spectrum Taylor series expansion, and provides an improved wave number domain algorithm of a squint frequency modulation continuous wave SAR, which avoids interpolation and improves the operation efficiency.
In order to achieve the purpose, the technical scheme of the invention is as follows:
an improved wavenumber domain imaging algorithm for squint-modulated continuous wave SAR, comprising:
constructing a slope distance expression of a frequency-modulated continuous wave SAR in a squint mode;
carrying out frequency modulation removal processing on the echo signal of the frequency modulation continuous wave SAR corresponding to the slope distance expression;
removing RVP terms from the signals after frequency modulation;
transforming the signal subjected to RVP removal to a two-dimensional frequency domain to obtain a two-dimensional frequency spectrum of the signal;
performing fixed slope phase compensation processing on the two-dimensional frequency spectrum to obtain a processed two-dimensional frequency spectrum;
carrying out Taylor series expansion on the two-dimensional frequency spectrum subjected to the fixed-slant-distance phase compensation processing with respect to distance-direction frequency, and reserving the two-dimensional frequency spectrum to a cubic term;
performing phase compensation according to a two-dimensional frequency spectrum based on Taylor series expansion, and completing distance migration correction, residual distance compression and compensation of high-order coupling phase in a two-dimensional frequency domain;
and performing azimuth compression in a two-dimensional frequency domain, and finally converting the compressed signal into a two-dimensional time domain to obtain a focused image.
Preferably, in the step of constructing the pitch expression of the frequency modulated continuous wave SAR in the squint mode, the pitch expression is as follows:
where v is the velocity of the platform, taTime variables, x, for the distance and azimuth directions, respectively0＝R0tanθsquIs the position of the zero Doppler time of the point target, R0Is the nearest slope of the point target, θsquIs the squint angle of the frequency modulated continuous wave SAR.
Preferably, the frequency-modulated continuous wave SAR echo signal corresponding to the slant range expression is subjected to frequency-detuning processing, which specifically includes:
the expression of the echo signal of the squint frequency modulation continuous wave SAR is as follows:
where γ is the chirp rate of the transmitted signal, c is the speed of light, λ is the wavelength, and j is the imaginary unit.
The expression of the de-tuned reference signal is as follows:
wherein ,RrefFor reference runout for dechirp, j is an imaginary unit.
And multiplying the conjugate of the echo signal and the reference signal to obtain a signal expression after frequency modulation removal as follows:
preferably, the removing step of Residual Video Phase (RVP) is performed on the de-modulated signal:
RVP is caused by the dechirp operation, which affects the imaging resolution, so to remove it, the compensation function for removing RVP is as follows:
the signal expression after RVP removal is:
preferably, in the step of transforming the signal after RVP removal into a two-dimensional frequency domain to obtain a two-dimensional spectrum of the signal, the two-dimensional spectrum is represented as follows:
wherein ,frIs the range frequency, fdIs the frequency of the doppler frequency and is,
the phase of the two-dimensional spectrum.
The phase of the two-dimensional spectrum is expressed as follows:
wherein ,fcIs the carrier frequency.
According to the phase structure, the first term is a distance and azimuth coupling term which is similar to the two-dimensional spectrum phase of the pulse SAR; the second term and the third term are respectively a distance direction offset and an azimuth direction offset which are introduced by the frequency-removing operation; the fourth term is a distance walking term, caused by the change of the slant distance within the pulse duration; the last term is the azimuthal phase term caused by strabismus.
Preferably, in the step of performing fixed slope phase compensation processing on the two-dimensional frequency spectrum to obtain the processed two-dimensional frequency spectrum, an expression of a corresponding fixed slope phase compensation function is as follows:
wherein ,RcThe reference slant distance of focusing treatment is generally taken as the center slant distance of the surveying and mapping belt;
is the phase of the compensation function.
Two-dimensional frequency spectrum S after fixed slope distance phase compensation processing1(fr,fd) The phase of (A) is:
preferably, the phase of the two-dimensional frequency spectrum after the fixed slope distance phase compensation processing is performed
And carrying out Taylor-series expansion on the distance to the frequency, and reserving the distance to a cubic term, wherein the Taylor-series expansion specifically comprises the following steps:
the range-azimuth coupling phase is:
to pair
At frTaylor expansion is performed at 0:
wherein 
Bringing the Taylor expansion of the range-azimuth coupled phase back to the phase expression
To obtain a new two-dimensional spectrum phase expression, in particularThe following were used:
wherein the first term and the last term are related to the Doppler frequency only and are azimuth modulation terms; the second term is aboutrThe first order term of (a) is a range migration term; the third term relates to frThe square term of (d), corresponding to distance compression; the fourth term is the high order coupling term for distance and azimuth.
Preferably, the step of performing phase compensation according to the two-dimensional spectrum based on the Taylor series expansion to complete the distance migration correction, the residual distance compression and the compensation of the high-order coupling phase specifically includes:
and in the two-dimensional frequency domain, performing range migration correction, wherein the corresponding range migration correction function is as follows:
in the two-dimensional frequency domain, residual distance compression is performed, and the corresponding distance compression function is specifically as follows:
and performing high-order coupling phase compensation in a two-dimensional frequency domain, wherein the corresponding high-order coupling phase compensation function is as follows:
two-dimensional frequency spectrum S of the frequency-modulated continuous wave SAR echo1(fr,fd) And the phase compensation function HRCM(fr,fd)、HRC(fr,fd) and HG(fr,fd) And multiplying to complete the distance migration correction, the residual distance compression and the compensation of the high-order coupling phase.
Preferably, the azimuth compression is performed in a two-dimensional frequency domain, and finally the compressed signal is transformed to a two-dimensional time domain to obtain a focused image, which specifically includes:
and completing azimuth compression in a two-dimensional frequency domain, wherein the corresponding azimuth compression function is as follows:
and transforming the azimuth compressed signal to a two-dimensional time domain to obtain a focused image.
After the scheme is adopted, the invention has the beneficial effects that:
(1) based on the squint mode, the method solves the problem that the imaging resolution is influenced by a large squint angle, and improves the imaging resolution;
(2) the method solves the problems that the traditional wave number domain algorithm introduces extra interpolation error by using Stolt transform, expands and reserves the distance and azimuth coupling terms to cubic terms through a Taylor polynomial, and compensates the cubic terms in a two-dimensional frequency domain;
(3) the processing steps of the method are based on Fourier transform and dot multiplication, the efficiency is high, and the method is suitable for engineering realization;
(4) the method processes the data based on the Taylor-series expansion, improves the operation efficiency and has timeliness.
The present invention is described in further detail with reference to the accompanying drawings and embodiments, but the improved wavenumber domain imaging algorithm of the squint frequency modulated continuous wave SAR of the present invention is not limited to the embodiments.
Drawings
FIG. 1 is a flow chart of an imaging algorithm of the present invention;
FIG. 2 is a graph of the imaging effect of the present invention: (a) the algorithm images a point target elevation map; (b) a point target elevation map obtained by imaging through a traditional algorithm; (c) comparing the impulse responses in the distance direction; (d) and comparing the pulse impulse responses in the azimuth direction.
Detailed Description
The technical solutions in the embodiments of the present invention will be described and discussed in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, the improved wave number domain imaging algorithm of the squint frequency modulated continuous wave SAR of the present invention comprises the following steps:
s101, constructing a slope distance expression of the frequency-modulated continuous wave SAR in the squint mode.
Specifically, in the squint mode, the instantaneous slope distance expression of the target and the radar is as follows:
where v is the platform velocity, taTime variables, x, for the distance and azimuth directions, respectively0＝R0tanθsquIs the position of the zero Doppler time of the point target, R0Is the nearest slope of the point target, θsquIs the squint angle of the frequency modulated continuous wave SAR.
And S102, performing frequency modulation removal processing on the echo signal of the frequency modulated continuous wave SAR corresponding to the slant range expression.
Specifically, the echo signal expression of the frequency modulated continuous wave SAR in the squint mode is as follows:
where γ is the chirp rate of the transmitted signal, c is the speed of light, λ is the wavelength, and j is the imaginary unit.
The expression of the de-frequency modulated reference signal is:
wherein ,RrefFor reference runout for dechirp, j is an imaginary unit.
And multiplying the conjugate of the echo signal and the reference signal, wherein the signal after frequency modulation is removed has the expression:
and S103, removing Residual Video Phase (RVP) of the de-frequency modulated signal.
The RVP is caused by the dechirp operation, which affects the imaging resolution, so the RVP is removed by the following compensation function:
the signal expression after RVP removal is:
and S104, transforming the signal subjected to RVP removal to a two-dimensional frequency domain to obtain a two-dimensional frequency spectrum of the signal.
Specifically, the first step is to perform distance-to-time frequency substitution:
wherein ,frIs the frequency variation of the distance direction.
The echo signal is converted into a distance frequency domain after time-frequency substitution, and the specific expression is as follows:
wherein ,fcIs the carrier frequency.
Secondly, using the principle of resident phase to carry out azimuth FT on the signals of the distance frequency domain to obtain a two-dimensional spectrum expression as follows:
wherein ,fdIs the frequency of the doppler frequency and is,
the phase of the two-dimensional spectrum.
The phase of the two-dimensional spectrum is expressed as follows:
according to the phase structure, the first term is a distance and azimuth coupling term which is similar to the two-dimensional spectrum phase of the pulse SAR; the second term and the third term are respectively a distance direction offset and an azimuth direction offset which are introduced by the frequency-removing operation; the fourth term is a distance walking term, caused by the change of the slant distance within the pulse duration; the last term is the azimuthal phase term caused by strabismus.
And S105, performing fixed slope distance phase compensation processing on the two-dimensional frequency spectrum to obtain a processed two-dimensional frequency spectrum.
The corresponding fixed-slope phase compensation function is expressed as follows:
wherein ,RcThe reference slant distance of focusing treatment is generally taken as the center slant distance of the surveying and mapping belt;
is the phase of the compensation function.
Two-dimensional frequency spectrum S after fixed slope distance phase compensation processing1(fr,fd) The phase expression of (d) is:
s106, the phase of the two-dimensional frequency spectrum after the fixed slope distance phase compensation processing is carried out
A Taylor-series expansion is performed on the distance to frequency and retained up to a cubic term.
Specifically, the term of the two-dimensional spectrum phase after the fixed slope phase compensation processing in step S105 with respect to the range-azimuth coupling is as follows:
to pair
At frTaylor expansion is performed at 0:
wherein ,
bringing the Taylor expansion of the range-azimuth coupled phase term back to the phase expression
In the above, a new phase expression of the two-dimensional spectrum is obtained, specifically as follows:
wherein the first term and the last term are related to the Doppler frequency only and are azimuth modulation terms; the second term is aboutrThe first order term of (a) is a range migration term; the third term relates to frThe square term of (d), corresponding to distance compression; the fourth term is the high order coupling term for distance and azimuth.
S107, phase compensation is carried out according to the two-dimensional frequency spectrum based on the Taylor series expansion, and distance migration correction, residual distance compression and compensation of high-order coupling phases are completed in a two-dimensional frequency domain, and the method specifically comprises the following steps:
(1) and in the two-dimensional frequency domain, performing range migration correction, wherein the corresponding range migration correction function is as follows:
(2) in the two-dimensional frequency domain, residual distance compression is performed, and the corresponding distance compression function is specifically as follows:
(3) and performing high-order coupling phase compensation in a two-dimensional frequency domain, wherein the corresponding high-order coupling phase compensation function is as follows:
two-dimensional frequency spectrum S of the frequency-modulated continuous wave SAR echo1(fr,fd) And the phase compensation function HRCM(fr,fd)、HRC(fr,fd) and HG(fr,fd) And multiplying to complete the distance migration correction, the residual distance compression and the compensation of the high-order coupling phase.
And S108, performing azimuth compression on the two-dimensional frequency domain, and finally converting the compressed signal into a two-dimensional time domain to obtain a focused image.
Specifically, the azimuth compression is completed in the two-dimensional frequency domain, and the corresponding azimuth compression function is specifically as follows:
and transforming the azimuth compressed signal to a two-dimensional time domain to obtain a focused image.
The method of the present invention will be explained below by means of simulation experiments.
The simulation parameters are shown in table 1.
TABLE 1 improved wave number domain algorithm simulation parameters
The method comprises the steps of imaging a single-point target in a scene area by respectively adopting an improved wave number domain algorithm based on Taylor series expansion and a traditional wave number domain algorithm based on Stolt interpolation, wherein a simulation result IS shown in fig. 2, (a) the figure IS a high line graph obtained by imaging by the algorithm, the main side lobe IS clear and has better symmetry and IS close to an ideal point target, (b) the figure IS a high line graph obtained by imaging by the traditional algorithm, the main side lobe IS also coupled and has poorer symmetry, and distortion begins to appear, (c) the figure IS a distance direction impulse response comparison of two algorithms, and as can be seen from the figure, the main lobe of the algorithm IS narrower, the first side lobe IS reduced, the imaging performance of the distance direction IS improved compared with that of the traditional algorithm, (d) the figure IS a comparison of the azimuth impulse responses of the two algorithms, the main lobe IS slightly narrower and has better symmetry, but the first side lobe IS increased, the resolution of the algorithm IS higher than that of the traditional algorithm, in order to further show that the sidelobe performance of the algorithm IS slightly narrower, the algorithm, the imaging performance of the Integral algorithm IS improved by using a decimal point comparison table (PSI) and the imaging performance of the Integral algorithm, and the imaging performance of the Integral algorithm (PS) IS improved by using a decimal point comparison table (S) and the imaging performance of the Integral index (3) of the imaging target area, wherein the imaging target area of the imaging area, the imaging area of the imaging area, the imaging area of the imaging area, the.
TABLE 2 Main lobe Width, Peak to sidelobe ratio and Integrated sidelobe ratio
Although there is an approximation in the taylor series expansion-based method, no interpolation operation is performed, and the interpolation operation may greatly reduce the operation efficiency. The imaging time of the traditional wave number domain algorithm on a computer simulation platform is about 69.784s, and the imaging time of the algorithm is about 5.090 s. The latter imaging time was 64.694s faster than the former, indicating that the algorithm herein is more computationally efficient.
The above is just one preferred implementation of the present invention. However, the present invention is not limited to the above embodiments, and any equivalent changes and modifications made according to the present invention, which do not exceed the scope of the present invention, are included in the protection scope of the present invention.
Claims (9)
1. An improved wavenumber domain imaging algorithm for squint-modulated continuous wave SAR, comprising:
step S1: constructing a slope distance expression of a frequency-modulated continuous wave SAR in a squint mode;
step S2: carrying out frequency modulation removal processing on the echo signal of the frequency modulation continuous wave SAR corresponding to the slope distance expression;
step S3: RVP item removal is carried out on the signals after frequency modulation removal;
step S4: transforming the signal subjected to RVP item removal to a two-dimensional frequency domain to obtain a two-dimensional frequency spectrum of the signal;
step S5: performing fixed slope phase compensation processing on the two-dimensional frequency spectrum to obtain a processed two-dimensional frequency spectrum;
step S6: carrying out Taylor series expansion on the two-dimensional frequency spectrum subjected to the fixed-slant-distance phase compensation processing with respect to distance-direction frequency, and reserving the two-dimensional frequency spectrum to a cubic term;
step S7: performing phase compensation according to a two-dimensional frequency spectrum based on Taylor series expansion, and completing distance migration correction, residual distance compression and compensation of high-order coupling phase in a two-dimensional frequency domain;
step S8: and performing azimuth compression in a two-dimensional frequency domain, and finally converting the compressed signal into a two-dimensional time domain to obtain a focused image.
2. The improved wavenumber domain imaging algorithm for squint chirp SAR of claim 1, wherein in step S1, said skew expression is as follows:
where v is the platform velocity, taTime variables, x, for the distance and azimuth directions, respectively0＝R0tanθsquIs the position of the zero Doppler time of the point target, R0Is the nearest slope of the point target, θsquIs the squint angle of the frequency modulated continuous wave SAR.
3. The improved wavenumber domain imaging algorithm of the squint-frequency-modulated continuous wave SAR of claim 2, wherein the step S2 specifically comprises:
the expression of the echo signal of the squint frequency modulation continuous wave SAR is as follows:
where γ is the chirp rate of the transmitted signal, c is the speed of light, λ is the wavelength, and j is the imaginary unit.
The expression of the de-frequency modulated reference signal is:
wherein ,RrefIs the reference slope distance of the de-frequency modulation processing;
and multiplying the conjugate of the echo signal and the reference signal to obtain a signal expression after frequency modulation removal, wherein the signal expression is as follows:
4. the improved wavenumber domain imaging algorithm of the squint-frequency-modulated continuous wave SAR of claim 3, wherein the step S3 specifically comprises:
the compensation function for RVP removal is as follows:
the signal expression after RVP removal is:
5. the improved wavenumber domain imaging algorithm for squint-frequency-modulated continuous wave SAR of claim 4, wherein in step S4, said two-dimensional frequency spectrum is represented as follows:
wherein ,frIs the range frequency, fdIs the Doppler frequency, fcIs the carrier frequency and is,
is the phase of the two-dimensional spectrum;
in the phase expression of the two-dimensional frequency spectrum, a first item is a distance and azimuth coupling item and is similar to the two-dimensional frequency spectrum phase of the pulse SAR; the second term and the third term are respectively a distance direction offset and an azimuth direction offset which are introduced by the frequency-removing operation; the fourth term is a distance walking term, caused by the change of the slope distance in the pulse duration; the last term is the azimuthal phase term caused by strabismus.
6. The improved wavenumber domain imaging algorithm for squint chirp SAR of claim 5, wherein in step S5, the expression of the corresponding phase compensation function is as follows:
wherein ,RcThe reference slant distance of focusing treatment is generally taken as the center slant distance of the surveying and mapping belt;
is the phase of the compensation function.
Two-dimensional frequency spectrum S after fixed slope distance phase compensation processing1(fr,fd) The phase expression of (d) is:
7. the improved wavenumber domain imaging algorithm of the squint-frequency-modulated continuous wave SAR of claim 6, wherein in the step S6, the method specifically comprises:
the range-azimuth coupling phase is:
to pair
At frIs developed by Taylor series at the position of 0
wherein ,
substituting the Taylor expansion of the distance azimuth coupling phase into the phase expression of the two-dimensional frequency spectrum after the fixed-slant-distance phase compensation processing
Obtaining a new phase expression, which comprises the following steps:
wherein the first term and the last term are related to the Doppler frequency only and are azimuth modulation terms; the second term is aboutrThe first order term of (a) is a range migration term; the third term relates to frThe square term of (d), corresponding to distance compression; the fourth term is the high order coupling term for distance and azimuth.
8. The improved wavenumber domain imaging algorithm of the squint-frequency-modulated continuous wave SAR of claim 7, wherein the step S7 specifically comprises:
and in a two-dimensional frequency domain, performing range migration correction, wherein the corresponding range migration correction function expression is as follows:
in the two-dimensional frequency domain, residual distance compression is performed, and the corresponding distance compression function is specifically as follows:
and performing high-order coupling phase compensation in a two-dimensional frequency domain, wherein the corresponding high-order coupling phase compensation function is as follows:
two-dimensional frequency spectrum S of the frequency-modulated continuous wave SAR echo1(fr,fd) And the phase compensation function HRCM(fr,fd)、HRC(fr,fd) and HG(fr,fd) And multiplying to complete the range migration correction, the residual range compression and the compensation of the high-order coupling phase of the range azimuth.
9. The improved wavenumber domain imaging algorithm for squint chirp SAR of claim 8, wherein said step S8 comprises:
and completing azimuth compression in a two-dimensional frequency domain, wherein the corresponding azimuth compression function is as follows:
and transforming the azimuth compressed signal to a two-dimensional time domain to obtain a focused image.
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