CN115291212A - Space variable nonlinear track expansion mapping high-resolution imaging method - Google Patents
Space variable nonlinear track expansion mapping high-resolution imaging method Download PDFInfo
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Abstract
The invention discloses a space variable nonlinear track extended mapping high-resolution imaging method, which mainly solves the problems that in the prior art, frequency modulation continuous wave imaging cannot be realized under a curved track, space variation is serious under the condition of a large width, and imaging quality is low. The realization scheme is that Taylor expansion of echo signals is obtained; constructing a two-dimensional rotation correction function to orthogonalize a two-dimensional wave number spectrum of the signal; constructing an acceleration consistent compensation function to restore a signal two-dimensional wave number spectrum; compensating the signals by using an acceleration consistent compensation function; resampling the acceleration compensation signal by adopting a wavenumber domain azimuth resampling method; performing uniform focusing compensation on the re-sampled signal by using a uniform focusing compensation function, and performing improved Stolt interpolation on the re-sampled signal; and sequentially carrying out deskew processing and frequency modulation slope straightening processing on the interpolated signals by utilizing the unified deskew correction function to obtain a final high-resolution imaging result. The invention reduces space-variant, improves imaging quality and can be used for radar image matching positioning.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and further relates to a space variable nonlinear track expansion mapping high-resolution imaging method which can be used for radar image matching positioning.
Background
The FMCW SAR is a new system imaging radar, has the advantages of light volume, low cost and high resolution, and has wide development prospect in the low-cost civil application field. Because the pulse width of the frequency modulation continuous wave radar reaches millisecond level, the position change of the radar in a transmission pulse period is not negligible, the working mode suitable for pulse type SAR 'stop-go-stop' is not applicable any more, if the pulse type SAR 'stop-go-stop' is directly processed by a pulse type algorithm, the imaging quality is necessarily reduced, and therefore an imaging method suitable for FMCW SAR must be explored. In addition, the high maneuvering platform has larger three-axis speed and acceleration, and the flight track of the high maneuvering platform is a curved track, so that the traditional slope distance model established according to the uniform linear track is not applicable any more. Therefore, various solutions are proposed by numerous researchers at home and abroad according to the characteristics of the frequency modulation continuous wave radar.
Wangyu et al, in its published paper "Focus FMCW SAR Data Using the wave number Domain Algorithm" (IEEE trans. Geosci. Remote Sens., vol.48, no.4, april.2010.) proposed a FMCW-SAR wave number Domain imaging method. The wave number domain imaging is realized by multiplying the echo by a reference function and then carrying out Stolt interpolation. The method is only suitable for a level flight mode without acceleration, and frequency modulation continuous wave SAR imaging under a curve track cannot be realized.
Jianghenhong adopts frequency scale transformation in a published paper 'research on frequency modulation continuous wave SAR real-time imaging algorithm' (doctor paper 2007 of national defense science and technology university), corrects range migration in a range-Doppler domain, and realizes imaging through a phase retention factor. However, in the case of a large imaging width, the method has severe space-variant and low imaging quality.
Disclosure of Invention
The invention aims to provide a frequency modulation continuous wave high-resolution imaging method aiming at the defects of the prior art, so that an acceleration error is compensated through a new slope distance model, the method is suitable for a curve track mode with acceleration, and the focusing effect of a scene target point is improved through non-approximate distance migration space-variant correction.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
(1) Obtaining echo signals after the line-off frequency modulation processing, and carrying out instantaneous skew Taylor expansion on the echo signals to obtain echo signals S 1 (K r ,X a )，K r Support domain range, X, representing distance wavenumber a A slow time movement distance for the platform orientation;
(2) From the echo signal S 1 (K r ,X a ) For tilted two-dimensional wavenumber spectra, resulting in a reduction of the actually available support area and a continuous motion of the platform within the pulse, resulting in a shift of the echo in the range direction, causing a defocusing in the range direction, a two-dimensional rotational correction function H is constructed TDR (K r X) normalizing the two-dimensional wavenumber spectrum thereof while compensating for range-wise offset of the target echo:
H TDR (K r ,X)＝exp[-jK r X sinθ 0 ]
wherein j is an imaginary number unit, X is a platform full-time moving distance, and theta 0 Is the wave number center squint angle;
(3) Wave number domain echo signal S by two-dimensional rotation correction function 1 (K r ,X a ) Respectively carrying out distance walking compensation and distance deviation compensation to obtain a signal S after fast time distance compensation 2 (K r ,X a )；
(4) Post-compensation signal S for fast temporal distance 2 (K r ,X a ) The second exponential term of the acceleration compensation function H is over-large, so that the phenomena of wave number spectrum aliasing and influence of acceleration high-order terms on imaging focusing are caused, and the acceleration consistent compensation function H is constructed AC (K r ；X a ) And (3) restoring a two-dimensional wave number spectrum:
wherein k' = k x +K r sinθ 0 ，k x Is the azimuth wave number, k 2 Is a second order error coefficient, k i For error coefficients of each order, X a For slow time movement distance of platform orientation, R 0 Is the slant range at the center doppler;
(5) Using acceleration consistent compensation function H AC (K r ；X a ) For the signal S after fast time distance compensation 2 (K r ,k x ) Compensating to obtain a signal form S after high-order acceleration error compensation 3 (K r ,k x )；
(6) Using the existing fast-time unified compensation function H FC (K r ,k x ) Compensating the signal S after the error of the high-order acceleration 3 (k r ,k x ) Then compensation is carried out to obtain a signal S after fast time unified compensation 4 (k r ,k x )；
(7) Introducing a new variable k in azimuth interpolation by adopting a wavenumber domain azimuth resampling method x ', eliminating wave number k x Second order and higher order terms of (a) and (b) n To obtain a resampled signal S 5 (k r ,k x ')；
(8) Using the existing uniform focus compensation function H FC (k r ,k x ') performing uniform focusing compensation on the resampled signal to obtain a signal S after uniform focusing compensation processing 6 (k r ,k x ')；
(9) For the signal S after uniform focusing compensation 6 (k r ,k x ') performing a modified Stolt interpolation to obtain an interpolated signal S 7 (k y ,k x ')；
(10) For the interpolated signal S 7 (k y ,k x ') inverse Fourier transform of the distance and multiplying by the existing unified deskew function H (k) x ') to obtain a product subjected to deskew treatmentSignal S of 8 (R,k x ')；
(11) For the deskewed signal S 8 (R,k x ') performs an azimuthal inverse Fourier transform, and then uses the existing azimuthal spatial domain correction function H (X; r is 0 ') straightening the target frequency modulation slope of the signal after the azimuth inverse Fourier transform, and then carrying out the azimuth Fourier transform on the signal after the frequency modulation slope straightening to obtain a signal S focused in the final azimuth wavenumber domain 9 (R,k x ') to accomplish high resolution imaging of the frequency modulated continuous wave.
Compared with the prior art, the invention has the following advantages:
firstly, the invention recovers the two-dimensional wave number spectrum of the echo signal by using the constructed acceleration consistent compensation function, breaks through the limitation of acceleration on wave number domain algorithm imaging, is applicable to a curve track mode with acceleration, and realizes frequency modulation continuous wave radar imaging under the curve track.
Secondly, the invention carries out distance migration and distance offset compensation on the echo signal by constructing a two-dimensional rotation correction factor, realizes the correction of the distance migration without approximation, is suitable for the condition of large imaging width, avoids azimuth zero filling, reduces the operation amount, effectively improves the focusing effect of a scene target point and has good scene applicability compared with the traditional wave number domain imaging method.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is an imaging geometry and scene layout map used in the simulation of the present invention;
FIG. 3 is a graph of the results of imaging a point target using the method of the present invention;
FIG. 4 is a cross-sectional view of the pulse pressure at each point using a prior art wavenumber domain algorithm for imaging;
FIG. 5 is a cross-sectional view of azimuthal pulse pressure at various points for imaging using a prior art MFS algorithm;
FIG. 6 is a cross-sectional view of the pulse pressure at each point of the imaging process using the method of the present invention;
FIG. 7 is a two-dimensional contour plot of points imaged using a prior art wavenumber domain algorithm;
FIG. 8 is a two-dimensional contour plot of points imaged with a prior art MFS algorithm;
figure 9 is a two-dimensional contour plot of points imaged using the method of the present invention.
Detailed Description
The embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the embodiment of the high-resolution imaging method for expanding and mapping the spatially-variable nonlinear trajectory includes the following steps:
step 1, obtaining an echo signal, carrying out Taylor expansion on an instantaneous slope distance item of the echo signal, and carrying out wave number domain transformation on the echo signal.
(1.1) transmitting a linear frequency modulation continuous wave LFMCW signal by a radar, obtaining a difference frequency output echo signal after the line frequency modulation is carried out by a receiver
Neglecting the influence of RVP term and the change of window function to obtain the target echo signal
Is represented as follows:
wherein the content of the first and second substances,
for a fast time, t m Is the slow time, j is the imaginary unit, λ is the wavelength, c is the speed of light, f c Is the carrier frequency, and is,
for the time error term affected by the fast time and the slow time,
in order to obtain the integral slope distance error,
for instantaneous target-to-radar slope, R ref For reference distance, γ is the modulation frequency, B is the signal bandwidth, T p Is the pulse width;
(1.2) dividing the time error term Δ t r,a At t m ＝t n The Taylor's expansion is the slope without acceleration and the slope error expression generated by the acceleration:
wherein, t n Moving time of the platform beam center irradiating the target, Δ x is the difference of the full-time moving distance, Δ x a Is the difference of slow time shift distance of azimuth, k i Error coefficients of each order;
(1.3) time error term Δ t of Taylor expansion r,a Output echo signal brought into difference frequency
Obtaining a signal S of a distance wave number azimuth position domain 1 (K r ,X a )：
Wherein, K r Representing the range of the support domain of the distance wave number, X a The platform orientation is moved a distance in a slow time.
Step two, constructing a two-dimensional rotation correction function, and utilizing the two-dimensional rotation correction function to perform wave number domain echo signal S 1 (K r ,X a ) Distance walking is performed and the distance offset caused by fast time is compensated.
(2.1) constructing a two-dimensional rotation correction function:
since the radar operates in an oblique view imaging state, the echo signal S 1 (K r ,X a ) In a two-dimensional wavenumber spectrum ofThe tilted wave number spectrum is more inclined and the tilted angle of view is larger, and the tilted wave number spectrum can reduce the practically available support area, and finally influence the imaging result. In addition, due to the continuous motion of the platform in the pulse, a fast distance time error is generated, so that the echo is shifted in the distance direction, and defocusing in the distance direction is caused. Therefore, it is necessary to construct a two-dimensional rotation correction function to correct the two-dimensional wavenumber spectrum and to compensate for the range shift of the target echo.
The platform of the present example moves the distance X in full time and the wave number center squint angle theta 0 The constructed two-dimensional rotational corrective function is expressed as follows:
H TDR (K r ,X)＝exp[-jK r X sinθ 0 ]
wherein j is an imaginary unit, K r A support domain range representing a distance wavenumber;
(2.2) combining the two-dimensional rotation correction function with the signal S of the distance wave number azimuth position domain 1 (K r ,X a ) Multiplying to obtain signal S after fast time distance offset compensation 2 (K r ,X a )：
Wherein j is an imaginary unit, R 0 Is the slope distance at center Doppler, Δ x is the difference in full time movement distance, R ref For reference distance, X is the full time displacement distance of the platform, k i For error coefficients of each order, Δ x a Is the azimuth slow time movement distance difference.
Step three, constructing an acceleration consistent compensation function, and utilizing the function to compensate the signal S after the fast time distance offset compensation 2 (K r ,X a ) And (6) compensation.
(3.1) constructing an acceleration consistency compensation function:
signal S after compensation due to fast time distance offset 2 (K r ,X a ) The second exponential term of (2) is too large in error, which results in broadening of the azimuth wavenumber spectrum and thus aliasingPhenomenon, and the existence of acceleration high-order terms affects the imaging focus, so it is necessary to construct an acceleration consistent compensation function to recover the two-dimensional wave number spectrum, example k x Is the azimuth wave number, k 2 Is a second order error coefficient, k i For each order of error coefficient, the constructed acceleration consistent compensation function is expressed as follows:
wherein k' = k x +K r sinθ 0 ，k x Is the azimuth wave number, k 2 Is a second order error coefficient, k i For error coefficients of each order, X a For slow time movement distance of platform orientation, R 0 Is the slope distance at the center doppler;
(3.2) applying acceleration consistent compensation function to two-dimensional wave number domain signal S 2 (K r ,X a ) Compensating to obtain a signal form S after high-order acceleration error compensation 3 (K r ,k x )：
Wherein, the first and the second end of the pipe are connected with each other,
k n ＝2K r ·k 2 x n ，x n moving distance, k, for the center of the platform beam to impinge on the target 2 Is a second order error coefficient.
Step four, utilizing a fast time unified compensation function H FC (K r ；X a ) For signal S 3 (K r ,k x ) Compensation is performed.
Additional Doppler frequency shift index term k specific to continuous wave SAR due to continuous motion of the airborne platform during the sweep period x X r It needs to be compensated and the space variant item K is compensated at the same time r R ref And the implementation stepThe following:
(4.1) selecting the following fast time unified compensation functions:
H FC (K r ,k x )＝exp[-jk x X r -jK r R ref ]
wherein, K r Representing the range of the support domain, k, of the distance wavenumber x Is the azimuthal wavenumber, X r For fast time displacement of the platform, R ref Is a reference distance;
(4.2) Using fast time unified Compensation function H FC (K r ,k x ) For signal S 3 (K r ,k x ) Compensating to obtain a compensated signal S 4 (K r ,k x ) The expression is as follows:
wherein k "= (k) x +K r sinθ 0 )·cosθ 0 ,R 0 Is the slant distance, theta, at the center Doppler 0 At wave number center oblique view, x n The distance traveled for the platform beam center to illuminate the target.
Step five, adopting a wave number domain azimuth resampling method to introduce a new variable k to azimuth interpolation x ', obtaining a resampled signal S 5 (k r ,k x ')。
(5.1) introducing a variable k by interpolating the azimuth direction x ', eliminating azimuth wave number and moving distance x from beam center to target n Coupled term of (2)
Order:
wherein k "= (k) x +K r sinθ 0 )·cosθ 0 ，K r Branch representing distance wave numberSpan range, k x Is the azimuth wave number, θ 0 Is a central squint angle;
(5.2) adding k x ' substitution of Signal S 4 (k r ,k x ) And obtaining a two-dimensional wave number spectrum after azimuth resampling as follows:
wherein k is x ' Azimuth wavenumber, x, introduced for azimuth interpolation n Moving distance, R, for the center of the platform beam to impinge on the target 0 ' is the target range location.
Step six, utilizing a uniform focusing compensation function H FC (k r ,k x ') performing uniform focusing compensation on the resampled signal to obtain a uniform compensated signal S 6 (k r ,k x ')。
(6.1) using a uniform focus compensation function:
wherein, K r Representing the range of the support domain, k, of the distance wavenumber x ' is the interpolated azimuth wavenumber, R ref Is a reference distance;
(6.2) multiplying the uniform focusing compensation function with the resampled signal, performing uniform focusing treatment on the resampled signal, and obtaining a reference distance center decoupling signal form through uniform focusing:
step seven, the signal S after the consistent compensation processing is processed 6 (k r ,k x ') performing a modified Stolt interpolation to obtain an interpolated two-dimensional wave number spectrum S 7 (k y ,k x ')。
(7.1) constructing a Stolt interpolation factor:
wherein, K r Representing the range of the support domain, k, of the distance wavenumber x ' is the interpolated azimuth wavenumber, k y Is the distance wave number;
(7.2) bringing the Stolt interpolation factor into the reference off-center decoupled signal S 6 (K r ,k x ') to obtain a two-dimensional wavenumber spectrum S after Stolt interpolation 7 (k y ,k x ')：
Wherein, K rc Variables introduced to improve Stolt interpolation, k x ' is the interpolated azimuth wavenumber, R ref As a reference distance, x n Moving distance, R, for the center of the platform beam to impinge on the target 0 ' is the target range position.
Step eight, the signal S after the expansion Stolt interpolation is carried out 7 (k y ,k x ') distance inverse Fourier transform and multiplying by a unified deskew correction function to obtain a deskewed signal S 8 (R,k x ')。
(8.1) the unified deskew function selected for use, expressed as:
wherein, K rc Variables introduced to improve Stolt interpolation, k x ' is the interpolated azimuth wavenumber, R ref Is a reference distance;
(8.2) reacting H (k) x ') and the signal S after Stolt interpolation 7 (k y ,k x ') to obtain a signal S after deskew 8 (R,k x ')：
Wherein, theta 0 Is a central oblique angle, x n Moving distance, R, for the center of the platform beam to impinge on the target 0 ' is the target range position.
Step nine, the signal S after the deskew processing 8 (R,k x ') straightening the target frequency modulation slope of the unified distance unit to obtain the final azimuth wave number domain focused signal.
(9.1) deskew-processed Signal S 8 (R,k x ') performing an inverse Fourier transform of the azimuth to obtain a transformed deskew-processed signal S 91 (R,X a )：
S 91 (R,X a )＝Sinc((R-(R 0 '-R ref )))·exp(-jK a (X a -x n ') 2 )
Wherein R is the distance position, R 0 ' is the target distance position, R ref As a reference distance, K a Is the slope, x, of the phase and azimuth position of the target after rotational shifting n '＝cosθ 0 x n ，x n Moving distance, θ, for the center of the platform beam to impinge on the target 0 Is a central squint angle;
(9.2) selecting the existing azimuth space domain correction function H (X) a ；R 0 ') expressed as:
H(X a ；R 0 ')＝exp[jK a X a 2 ]
(9.3) correcting the function H (X) in the azimuth space domain a ；R 0 ') and S 91 (R,X a ) Multiplying to obtain a signal S after azimuth compression 92 (R,k x ')：
S 92 (R,X a )＝Sinc((R-(R 0 '-R ref )))·exp(jK a x n 'X a )·exp(-jK a (x n ') 2 )
Wherein k is x ' is the interpolated azimuth wavenumber;
(9.4) orientationCompressed signal S 92 (R,k x ') performing azimuth Fourier transform to obtain a final azimuth wavenumber domain focused signal S 9 (R,k x ') i.e. the result of the high-resolution imaging after two-dimensional focusing.
The effect of the present invention can be further illustrated by the following simulation experiments:
simulation conditions
The signal carrier frequency of the frequency modulation continuous wave radar system is set to be 16GHz, the pulse repetition frequency is set to be 2KHz, and the frequency modulation continuous wave radar system moves along a curve track. The imaging geometry and scene layout of the FMCW SAR are shown in fig. 2, where fig. 2 (a) is a three-dimensional schematic diagram of the imaging geometry of the SAR, fig. 2 (b) is a schematic diagram of the scene layout, and as can be seen from fig. 2 (b), the initial layout of the imaging field is a 3 × 3 rectangular lattice.
(II) simulation content
Simulation 1, under the above conditions, the method of the present invention is used to simulate a nine-point target scene, and an imaging result is obtained, as shown in fig. 3.
As can be seen from FIG. 3, the focusing effect of the point target is good, and meanwhile, the imaging result focused by the target point is a rectangular dot matrix with three rows and three columns, the transverse direction represents the distance direction, the longitudinal direction represents the azimuth direction, and the imaging result is consistent with the initial dot distribution diagram, so that the accuracy of the invention is proved.
As can be seen from fig. 4, the scene edge points 1 and 9 processed by the existing wavenumber domain algorithm cannot be focused precisely in the azimuth direction because the platform has an upward altitude speed and an acceleration in the three-dimensional direction, and the linearization operation of the doppler frequency modulation term in the echo on the distance space-variant has a large phase error due to the existing wavenumber domain algorithm processing.
And (3) selecting edge points 1 and 9 and a center point 5 in an imaging scene, performing imaging simulation on the three points by using an MFS algorithm provided by the literature, "frequency modulation continuous wave real-time imaging algorithm research", wherein an azimuth pulse pressure cross-sectional view of each point obtained by the simulation is shown in fig. 5, wherein fig. 5 (a) shows an azimuth pulse pressure cross-sectional view of the edge point 1, fig. 5 (b) shows an azimuth pulse pressure cross-sectional view of the center point 5, and fig. 5 (c) shows an azimuth pulse pressure cross-sectional view of the edge point 9.
As can be seen from fig. 5, the azimuth peak-to-peak side lobe ratio of the scene edge points 1 and 9 is too large, so that a defocus phenomenon occurs, which indicates that when the scene width is large, the residual doppler modulation azimuth space-variant term is not negligible.
And 4, selecting edge points 1 and 9 and a central point 5 in an imaging scene, performing imaging simulation on the three points by using the method of the invention, wherein an azimuth pulse pressure cross-sectional view of each point obtained by simulation is shown in fig. 6, wherein fig. 6 (a) shows an azimuth pulse pressure cross-sectional view of the edge point 1, fig. 6 (b) shows an azimuth pulse pressure cross-sectional view of the central point 5, and fig. 6 (c) shows an azimuth pulse pressure cross-sectional view of the edge point 9.
As can be seen from fig. 6, since the space-variant effect caused by the acceleration error and the too large scene width is considered at the same time for each target point subjected to the simulation processing in the present invention, the scene edge points 1 and 9 and the scene center point 5 both exhibit a good focusing effect, and the peak side lobe of each point is relatively low, the main lobe and the first side lobe are clearly distinguished, and the focusing depth is good.
Simulation 6, selecting edge points 1 and 9 and a central point 5 in an imaging scene, performing imaging simulation on the three points by using an MFS algorithm provided by the literature, "frequency modulation continuous wave real-time imaging algorithm research", and obtaining a two-dimensional contour map of each point, as shown in fig. 8, wherein fig. 8 (a) shows the two-dimensional contour map of the edge point 1; FIG. 8 (b) is a two-dimensional contour diagram of the center point 5; fig. 8 (c) shows a two-dimensional contour diagram of the edge point 9;
as can be seen from fig. 7 and 8, the distortion phenomenon occurs in the two-dimensional main lobe at the edge points 1 and 9 in the prior art, which indicates that there is a residual amount of RCM at these two points, and there is a significant coupling between the main lobe and the side lobe.
Simulation 7, selecting edge points 1 and 9 and a central point 5 in an imaging scene, performing imaging simulation on the three points by using the method of the invention, and obtaining a two-dimensional contour map of each point as shown in fig. 9, wherein fig. 9 (a) shows the two-dimensional contour map of the edge point 1; fig. 9 (b) shows a two-dimensional contour diagram of the center point 5; fig. 9 (c) shows a two-dimensional contour diagram of the edge point 9;
as can be seen from fig. 9, the scene edge points 1 and 9 and the scene center point 5 both present a good "cross" effect.
In conclusion, the method combines the wave number domain imaging algorithm and the motion compensation through acceleration error compensation, two-dimensional rotation correction factor construction and Stolt interpolation expansion, realizes the accurate focusing of the frequency modulation continuous wave radar on the scene target point, and verifies the accuracy and the effectiveness of the method.
Claims (10)
1. A space variable nonlinear track expansion mapping high-resolution imaging method is characterized by comprising the following steps:
(1) Obtaining echo signals after the line-off frequency modulation processing, and carrying out instantaneous skew Taylor expansion on the echo signals to obtain echo signals S 1 (K r ,X a )，K r Representing the range of the support domain of the distance wave number, X a Slow time movement distance for platform orientation;
(2) From the echo signal S 1 (K r ,X a ) For the two-dimensional wave number spectrum with inclination, which causes the practically available support area to be reduced and the continuous motion of the platform in the pulse, which causes the distance direction defocusing caused by the deviation of the echo in the distance direction, a two-dimensional rotation correction function H is constructed TDR (K r And X) normalizing the two-dimensional wave number spectrum, and simultaneously compensating the range offset of the target echo:
H TDR (K r ,X)＝exp[-jK r Xsinθ 0 ]
wherein j is an imaginary unit, X is a platform full-time moving distance, and theta 0 The wave number center squint angle;
(3) Wave number domain echo signal S by two-dimensional rotation correction function 1 (K r ,X a ) Respectively carrying out distance walking compensation and distance deviation compensation to obtain a signal S after fast time distance compensation 2 (K r ,X a )；
(4) Post-compensation signal S for fast temporal distance 2 (K r ,X a ) The second exponential term of the acceleration sensor has overlarge error, causes the phenomena that the beam spectrum is aliased and the imaging focusing is influenced by the acceleration high-order term, and constructs an acceleration consistent compensation function H AC (K r ；X a ) And (3) recovering a two-dimensional wave number spectrum:
wherein k' = k x +K r sinθ 0 ，k x Is the azimuth wave number, k 2 Is a second order error coefficient, k i For error coefficients of each order, X a For slow time-of-travel distance of platform orientation, R 0 Is the slant range at the center doppler;
(5) Using acceleration consistent compensation function H AC (K r ；X a ) For the signal S after fast time distance compensation 2 (K r ,k x ) Compensating to obtain a signal form S after high-order acceleration error compensation 3 (K r ,k x )；
(6) Utilizing an existing fast-time unified compensation function H FC (K r ,k x ) Compensating the higher order acceleration error signal S 3 (k r ,k x ) Then compensation is carried out to obtain the signal S after fast time unified compensation 4 (k r ,k x )；
(7) By adopting a wave number domain azimuth resampling method, a new interpolation is introduced in the azimuth directionVariable k x ', eliminating wave number k x Second order and higher order terms of (a) and (b) n To obtain a resampled signal S 5 (k r ,k x ')；
(8) Using the existing uniform focus compensation function H FC (k r ,k x ') performing uniform focusing compensation on the resampled signal to obtain a signal S after uniform focusing compensation processing 6 (k r ,k x ')；
(9) For the signal S after the consistent focusing compensation 6 (k r ,k x ') performing a modified Stolt interpolation to obtain an interpolated signal S 7 (k y ,k x ')；
(10) For the interpolated signal S 7 (k y ,k x ') inverse Fourier transform of the distance and multiplication by the existing unified deskew function H (k) x ') to obtain a deskewed signal S 8 (R,k x ')；
(11) For the signal S after the deskew processing 8 (R,k x ') performs an azimuthal inverse Fourier transform, and then uses the existing azimuthal spatial domain correction function H (X; r 0 ') straightening the target frequency modulation slope of the signal after the azimuth inverse Fourier transform, and then performing the azimuth Fourier transform on the signal after the frequency modulation slope straightening to obtain a signal S focused in the final azimuth wave number domain 9 (R,k x ') to accomplish high resolution imaging of the frequency modulated continuous wave.
2. The method according to claim 1, wherein the echo signal obtained in (1) is expressed in the wavenumber domain as S 1 (K r ,X a ) Expressed as follows:
wherein j is an imaginary unit, K r Representing the range of the support domain of the distance wave number, X a For slow time movement distance of platform orientation, R 0 Is the slope distance at the center Doppler, Δ x is the full time displacementDeviation, theta 0 At an oblique viewing angle at the center of the wave number, R ref As a reference distance, k i For each order of error coefficient, Δ x a The azimuth is moved by the difference in distance in a slow time.
3. The method of claim 1, wherein step (3) utilizes a two-dimensional rotational correction function H TDR (K r X) echo signal S in the log domain 1 (K r ,X a ) Compensating by applying a two-dimensional rotation correction function H TDR (K r X) and echo signal S 1 (K r ,X a ) Multiplying to obtain a fast time distance compensated signal S 2 (K r ,X a ) Is represented as follows:
wherein j is an imaginary unit, K r Representing the range of the support domain of the distance wave number, R 0 Is the slope distance at center Doppler, Δ x is the difference in full time movement distance, θ 0 At wave number center oblique view angle, R ref For reference distance, X is the full time displacement distance of the platform, k i For each order of error coefficient, Δ x a The azimuth is the slow time movement distance difference.
4. The method of claim 1, wherein step (5) utilizes an acceleration consistent compensation function H AC (K r ；X a ) For the fast time distance compensated signal S 2 (K r ,k x ) Compensating by making the acceleration consistent with a compensation function H AC (K r ；X a ) And echo signal S 2 (K r ,k x ) Multiplying to obtain a signal form S after high-order acceleration error compensation 3 (K r ,k x ) Expressed as follows:
wherein, K r Representing the range of the support domain, k, of the distance wavenumber x Is the azimuthal wavenumber, X a For slow time movement distance of platform orientation, k' = k x +K r sinθ 0 ，K r Support domain range, θ, representing distance wavenumber 0 At wave number center oblique view, x n Moving distance, R, for the center of the platform beam to impinge on the target 0 Is the slant range at central Doppler, R ref As reference distance, k i For each order of the error coefficients,
k n ＝2K r ·k 2 x n ，k 2 is a second order error coefficient.
5. The method of claim 1, wherein (6) utilizes a fast-time uniform compensation function H FC (K r ,k x ) For signal S 3 (K r ,k x ) Compensation is performed to achieve the following:
6a) Selected fast time unified compensation function H FC (K r ；X a ) Expressed as:
H FC (K r ,k x )＝exp[-jk x X r -jK r R ref ]，
wherein, K r Representing the range of the support domain, k, of the distance wavenumber x Is the azimuthal wavenumber, X r For fast time displacement of the platform, R ref Is a reference distance;
6b) Unifying fast time compensation function H FC (K r ,k x ) And signal S 3 (K r ,k x ) Multiplying to obtain signal S with fast time uniform compensation 4 (K r ,k x ) The expression is as follows:
wherein k "= (k) x +K r sinθ 0 )·cosθ 0 ，R 0 Is the slant distance, theta, at the center Doppler 0 At wave number center oblique view, x n The distance traveled for the platform beam center to illuminate the target.
6. The method according to claim 1, characterized in that said step (7) is carried out as follows:
7a) Introducing a variable k by azimuth interpolation x '：
Wherein k "= (k) x +K r sinθ 0 )·cosθ 0 ，K r Representing the range of the support domain, k, of the distance wavenumber x Is the azimuthal wavenumber, θ 0 Is a central squint angle;
7b) Will k x ' substitution fast time unified compensated Signal S 4 (k r ,k x ) In order to eliminate wave number k x Second order and higher order terms of (a) and (b) n The two-dimensional wave number spectrum after azimuth resampling is obtained by the coupling term of (1):
wherein k is x ' Azimuth wavenumber, x, introduced for azimuth interpolation n Moving distance, R, for the center of the platform beam to impinge on the target 0 ' is the target range position.
7. The method according to claim 1, characterized in that said step (8) is carried out as follows:
8a) The chosen uniform focus compensation function is expressed as:
wherein, K r Representing the range of the support domain, k, of the distance wavenumber x ' is the interpolated azimuth wavenumber, R ref Is a reference distance;
8b) Will be consistent with the focus compensation function H UFC (k r ,k x ') and the resampled signal S 5 (K r ,k x ') are multiplied to obtain a signal S after reference distance center decoupling 6 (K r ,k x ') indicated below:
wherein x is n Moving distance, R, for the center of the platform beam to impinge on the target 0 ' is the target range location.
8. The method of claim 1, wherein the step (9) is performed on the uniform compensation processed signal S 6 (k r ,k x ') perform a modified Stolt interpolation, which is implemented as follows:
9a) Constructing a Stolt interpolation factor:
wherein, K r Support domain range, k, representing distance wavenumber x ' is the interpolated azimuth wavenumber, k y Is the distance wave number;
9b) Signal S with Stolt interpolation factor brought into reference distance center decoupling 6 (K r ,k x ') to obtain a two-dimensional wavenumber spectrum S after Stolt interpolation 7 (k y ,k x ')：
Wherein, K rc Variables introduced to improve Stolt interpolation, k x ' is the interpolated azimuth wavenumber, R ref As a reference distance, x n Moving distance, R, for the center of the platform beam to impinge on the target 0 ' is the target range location.
9. Method according to claim 1, characterized in that said step (10) is carried out as follows:
10a) The selected unified deskew correction function is expressed as:
wherein, K rc Variables introduced to improve Stolt interpolation, k x ' is the interpolated azimuth wavenumber, R ref Is a reference distance;
10b) H (k) is reacted with x ') and the signal S after Stolt interpolation 7 (k y ,k x ') to obtain a signal S after deskew 8 (R,k x ')：
Wherein, theta 0 At an oblique angle of view at the center, x n Moving distance, R, for the center of the platform beam to impinge on the target 0 ' is the target range location.
10. Method according to claim 1, characterized in that said step (11) is carried out as follows:
11a) The chosen azimuth-space domain correction function is expressed as:
H(X a ；R 0 ')＝exp[jK a X a 2 ]
wherein, K a Is the slope, X, of the phase and azimuth position of the target after rotational movement a Is the azimuth position;
11b) Correcting function of azimuth space domain and deskew processed signal S 8 (R,k x ') are multiplied to obtain a signal S focused in the azimuth wave number domain 9 (R,k x ')：
S 9 (R,k x ')＝Sinc[R-(R 0 '-R ref )]Sinc[k x '-K a x n ']
·exp[-jK a (x n ') 2 ]
Wherein x is n '＝cosθ 0 x n R is the distance position, R 0 ' is the target range position, R ref As a reference distance, k x ' is the interpolated azimuth wavenumber, θ 0 Is a central squint angle.
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| CN116299464A (en) * | 2023-05-17 | 2023-06-23 | 西安电子科技大学 | High-speed high-mobility wide-range fan-scan SAR imaging method |
| CN117056676A (en) * | 2023-08-21 | 2023-11-14 | 国家卫星海洋应用中心 | Data preprocessing method, device and equipment for omnidirectional-wave high-spectrum correction |
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| CN116299464A (en) * | 2023-05-17 | 2023-06-23 | 西安电子科技大学 | High-speed high-mobility wide-range fan-scan SAR imaging method |
| CN116299464B (en) * | 2023-05-17 | 2023-07-21 | 西安电子科技大学 | High-speed high-mobility wide-range fan-scan SAR imaging method |
| CN117056676A (en) * | 2023-08-21 | 2023-11-14 | 国家卫星海洋应用中心 | Data preprocessing method, device and equipment for omnidirectional-wave high-spectrum correction |
| CN117056676B (en) * | 2023-08-21 | 2024-03-19 | 国家卫星海洋应用中心 | Data preprocessing method, device and equipment for omnidirectional-wave high-spectrum correction |
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