CN116719027A - Star-machine double-base SAR imaging method in bidirectional sliding beam focusing mode - Google Patents
Star-machine double-base SAR imaging method in bidirectional sliding beam focusing mode Download PDFInfo
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Abstract
The invention discloses a satellite-machine double-base SAR frequency domain imaging method under a bidirectional sliding beam focusing mode, which aims at a low PRF satellite-machine double-base SAR system, firstly carries out preprocessing on echo signals, combines the thought of a spectrum analysis technology, and utilizes equivalent convolution transformation and compensation to remove azimuth spectrum aliasing of the signals; then, approximating the slant range by utilizing a Legendre polynomial expansion method, and establishing a high-precision slant range model; combining the thought of the series inversion to obtain an accurate two-dimensional spectrum phase analysis type of the point target; and finally, obtaining a high-resolution image in a frequency domain design algorithm. The implementation process is as follows: (1) establishing a slant range expression of a satellite-machine bistatic SAR; (2) acquiring point target echo data; (3) performing antialiasing pretreatment on the point target echo; (4) utilizing Legend polynomials to approximate the slant distance; (5) Unfolding by utilizing a Legendre polynomial to obtain a spectrum phase analysis formula; and (6) designing a frequency domain imaging algorithm to obtain an imaging result.
Description
Technical Field
The invention relates to the field of radar signal processing methods, in particular to a satellite-machine double-base SAR imaging method in a bidirectional sliding beam focusing mode, which has an effect of improving the imaging quality of scene edge points.
Background
The dual-base SAR system can be applied to a plurality of different configurations due to the separate operation of the receiving and transmitting platforms, so that the dual-base SAR system has higher flexibility and practicability compared with single-base SAR systems, and can acquire more abundant information. The star-computer bistatic SAR has the characteristics of long acting distance and wide coverage range, and has the advantages of strong anti-interference capability and high safety. But simultaneously, the corresponding technical problems are brought to the double-base SAR system due to the split arrangement of the receiving and transmitting platforms.
First is the problem of the slope distance function approximation. Unlike conventional single-base SAR, the total slant range of double-base SAR is the sum of corresponding slant ranges from the transceiver platform to the target point, and is in the form of the sum of double root marks, so that the system and echo characteristics have higher complexity. Aiming at the approximation of the double-way inclined distance, students at home and abroad have proposed a plurality of methods for solving the problem. In document [1], xiong Tao, li Yachao, li Qi et al propose to approximate a two-way pitch using a combination of a single-basis equivalent component and a double-basis compensation component, wherein the single-basis equivalent component includes three equivalent parameters of equivalent pitch, speed, and squint angle. In document [2], li Dong, liao guide et al approximate the approach of using Taylor series expansion for the slope distance. In document [3], hua methong, guangyong Zheng, ronghua Zhao et al propose a derivation scheme based on a distance equivalent elliptical model of highly squint BiSAR focusing. In document [4], li Menghui, tan Gewei et al propose to approximate the slant range using a fourth order chebyshev polynomial, but simulation verification is performed only for on-board bistatic SAR, and the possibility and applicability under more configurations (such as on-board bistatic SAR, etc.) are not considered.
Secondly, the design problem of an imaging algorithm is that the signal processing of the bistatic SAR is more complex, and the imaging method of the monostatic SAR is not directly applicable any more. The FBP algorithm mentioned in document [5] is a typical representative of a time domain imaging algorithm, and is regarded as a preferred algorithm for bistatic SAR imaging, and the algorithm can be used for any bistatic SAR, and theoretically there are no limitations on configuration and flight trajectory, but the disadvantage is that the calculation amount is large, the calculation efficiency is low, and the influence of platform motion errors and inertial navigation measurement errors is large. In the aspect of frequency domain imaging, deriving a two-dimensional spectrum analytic formula of a target is the primary work. The current mainstream frequency spectrum solving method is a series inversion (Method ofSeries Reversion, MSR) method, which adopts a Taylor series high-order approximation mode, can solve the high-precision two-dimensional frequency spectrum of the bistatic SAR point target with any configuration, and is most widely applied. Based on the two-dimensional spectrum, the target imaging task can be completed by selecting a RD, NCS, OMEGA-K classical algorithm. Under the satellite-machine double-base SAR system, due to the large speed difference of the receiving and transmitting platforms, the problem of spectrum blurring can exist at the edge of an imaging scene, and the imaging quality is influenced. The step of eliminating spectral blur must therefore be considered in the design of frequency domain imaging algorithms. The current solutions mainly include sub-aperture segmentation described in document [6] and the upsampling-based full aperture processing schemes mentioned in documents [7], [8 ].
Relevant documents for retrieval in the background art are given below:
[1]Xiong Tao,Li Yachao,Li Qi,et al.Using an Equivalence-Based Approach to Derive 2-D Spectrum ofBiSAR Data and Implementation Into an RDA Processor[J].IEEE Transactions on Geoscience andRemote Sensing,2021,59(6):4765-4774.
[2]Li Dong,Liao Guisheng,Wang Wei,et al.Extended azimuth nonlinear chirp scaling algorithm for bistatic SAR processing in high-resolution highly squinted mode[J].IEEE Geoscience and Remote Sensing Letters,2014,11(6):1134-1138.
[3]Hua Zhong,Guangyong Zheng,Ronghua Zhao,et al.Focus Improvement for Highly Squinted One-Stationary BISAR Imaging Based On A Range Equivalent Model[C].IGARSS 2019.
[4] li Menghui, tan Gewei, yang Jingjing, etc. motion compensation and quadrature decoupling based bistatic SAR imaging algorithm [ J ]. Signal processing, 2021,37 (1): 75-85.
[5]Shi Tianyue,Mao Xinhua,Andreas Jakobsson,Liu Yanqi.Parametric Model-Based 2-D Autofocus Approach for General BiSAR Filtered Backprojection Imagery[J].IEEE Transactions on Geoscience and Remote Sensing,2022,60:1-14.
[6] Zhang Jindong, chen Gurui, zhu Daiyin, etc. A squint sliding bunching SAR subaperture processing imaging method [ J ]. Data acquisition and processing 2017,32 (04): 776-784.
[7] Guan Yifu, yang Yuan, gu Wentong, et al, on-board TOPS mode two-step imaging algorithm study [ J ]. Air force early warning academy of sciences 2020,34 (03): 167-172.
[8]LUO X L,DENG Y K,WANG R,et al.Image formation procfessing for sliding spotlight SAR with stepped frequency chirps[J].IEEE Geoscience and Remote Sensing Letters,2014,11(10):1692-1696.
Disclosure of Invention
Aiming at the difficulties existing in the prior art, namely the oblique distance approximation precision and the design problem of a satellite-machine bistatic SAR imaging algorithm, the invention provides a satellite-machine bistatic SAR imaging method under a bidirectional sliding beam focusing mode, so as to realize the non-fuzzy imaging of a scene edge point target under the condition of low Pulse Repetition Frequency (PRF), and the effect is superior to that of the traditional frequency domain imaging algorithm based on Taylor series expansion.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a star-computer double-base SAR imaging method in a bidirectional sliding beam focusing mode comprises the following steps:
step 1, establishing an oblique distance expression of a bidirectional sliding bunching mode according to a geometric model of a satellite-machine bistatic SAR system;
step 2, acquiring a ground point target echo signal generated when the low-orbit satellite platform transmits the linear frequency modulation signal;
step 3, performing antialiasing pretreatment on the point target echo to obtain a non-fuzzy frequency spectrum;
step 4, approximating the oblique distance expression established in the step 1 by utilizing a Legendre polynomial to obtain a Legendre expansion of a double-pass oblique distance;
step 5, combining a series inversion method, and acquiring the phase psi (f) of the original two-dimensional spectrum of the point target by utilizing the Legend expansion of the double-pass skew r ,f a ) Phase ψ (f r ,f a ) Spread out as distance frequency domain f r And discard the distance frequency domain f in power series form r And azimuth frequency domain f a Obtaining a two-dimensional spectrum phase based on the Legendre polynomial expansion;
and step 6, combining the two-dimensional spectrum phase terms based on the Legendre polynomial expansion obtained in the step 5, and performing distance compression, secondary compression, distance migration correction, constant term and higher term compensation, azimuth compression and the like on the non-fuzzy spectrum obtained in the step 3 to obtain an imaging result.
In a further step 3, the process of performing the antialiasing preprocessing on the point target echo is as follows:
3a) Constructing a reference function:
firstly, constructing a reference function of an azimuth time domain tau as shown in a formula (1):
H ref (τ)＝exp(jπητ 2 ) (1)，
wherein eta is a frequency modulation coefficient and is related to the actual configuration parameter of the star-machine bistatic SAR system, thereby satisfying the relationLambda is the wavelength of the carrier wave, v T and vR Respectively the moving speeds of the receiving and transmitting platforms, R tef and Rref The distances from the receiving and transmitting platform to the virtual rotation center point in the bidirectional sliding beam focusing mode are respectively shown.
Performing distance FFT on the time domain echo signal S (t, tau) obtained in the step 2, and converting the time domain echo signal S (t, tau) into a distance frequency domain to obtain S (f) r τ), and S (f) r τ) and a reference function H ref (τ) multiplying;
3b) Equivalent convolution transformation:
performing azimuth FFT on the result of the step 3 a) and performing azimuth FFT with a reference function H under a new time domain coordinate tau' ref Multiplying (τ') to obtain the signal S (f) without ambiguity in azimuth frequency domain under new time domain coordinate τ r τ'). This step can in turn be regarded as a time-domain echo S (f r τ) and a reference function H ref Performing equivalent convolution transformation on (tau) to obtain S (f) r τ'), wherein:
the FFT transformation corresponds to a transformation between the time-frequency axes. Before and after FFT conversion, the original time domain coordinate tau, the new time domain coordinate tau' of the echo signal and the original frequency coordinate f of the echo signal a New frequency coordinate f' a Satisfy the relation between
3c) Conjugate compensation:
for S (f) obtained in step 3 b) r Performing azimuth FFT again to obtain a new two-dimensional frequency domain signal S (f) r ,f′ a ) For S (f) r ,f′ a ) Multiplying by a frequency domain conjugate compensation function H ref * (f′ a ) The resulting aliasing free spectrum is shown in equation (2):
S'(f r ,f′ a )＝S(f r ,f′ a )·H ref * (f′ a ) (2)，
in a further step 4, the procedure for obtaining the two-dimensional spectrum expression based on the legendre polynomial expansion is as follows:
4a) Normalizing the azimuth slow time tau, namelyT a Is the synthetic aperture time. Then to the slant distance R bi (τ) Legend orthogonal decomposition and expansion into the form of a fourth order power series of x is shown below:
R bi (x)＝α 0 +α 1 x+α 2 x 2 +α 3 x 3 +α 4 x 4 (3)，
wherein the corresponding term coefficient alpha i The method meets the following conditions:
wherein Ln (x) For Legendre polynomials, satisfy the formula
In the formula (4), the operation process in the bracket { } is a fixed integral operation, and the corresponding calculation result of the order n is brought in the operation, and the specific operation content satisfies the formula:
4b) Will beIn the substitute return type (3), the double-way inclined distance R is obtained by rearrangement bi (τ) the fourth-order power series expansion in slow time τ, i.e., the legendre polynomial approximation of the skew is:
R bi (τ)＝k 0 +k 1 τ+k 2 τ 2 +k 3 τ 3 +k 4 τ 4 (5)，
wherein ,the Legend decomposition coefficient corresponding to the skew.
In a further step 5, the procedure for obtaining the two-dimensional spectral expression based on the legendre polynomial expansion is as follows:
5a) Firstly, azimuth time-frequency conversion of the nonlinear phase is completed by utilizing the principle of stationary phase, and the result is shown in a formula (6):
and obtaining the corresponding relation between the azimuth slow time and the frequency by a series inversion method:
in formulas (6) and (7), k n (n=2, 3, 4) is the corresponding skewLegend decomposition coefficient, f r For distance frequency, f a For azimuth frequency, f c The carrier frequency, c, is the speed of light.
5b) The linear phase removed before the compensation is utilized, and the frequency shift property of Fourier transformation is utilized to obtain an original two-dimensional frequency spectrum as shown in a formula (8):
S(f r ,f a )＝W r (f r )W a (f a )exp(jψ(f r ,f a )) (8)，
wherein ,Wr Represents the distance envelope, W a Represents the azimuth envelope, ψ (f r ,f a ) Representing the original two-dimensional spectrum phase, the specific expression is shown in formula (9):
wherein ,kn (n=0, 1,2,3, 4) is Legend decomposition coefficient corresponding to the skew, f r For distance frequency, f a For azimuth frequency, f c The carrier frequency, c, is the speed of light.
By means of Legendre polynomial pairs (9)And (5) unfolding. Firstly, normalizing, namely, making ∈ ->B is the signal bandwidth. The three fractional formulas are respectively arranged into a three-order power series form of y:
wherein the coefficients preceding y of the different power terms satisfy the relation as shown in formula (11):
the operation process in the bracket { } is fixed integral operation, and the corresponding order n calculation result is brought in during operation, and the specific operation content satisfies the formula:and then will beIn the power series with y, the power series is arranged as f r In the form of a third-order power series, to yield equation (12):
wherein ,is->Corresponding Legend decomposition coefficients.
5c) Bringing the result of formula (12) into formula (9) for sorting and merging, discarding f r and fa After the higher order term of (2), the legend spectral phase expression can be obtained as shown in equation (13):
wherein the distance frequency f r The coefficients corresponding to the different power terms satisfy the following relationship:
wherein ,kn (n=0, 1,2,3, 4) is Legend decomposition coefficient corresponding to the skew, f r For distance frequency, f a For azimuth frequency, f c The carrier frequency, c, is the speed of light.
Each phase term found in equation (13),and f r and fa Are all independent and are constant phase terms; />Is f r Linear term coefficients of (2) corresponding to range migration; />Is f r Square term coefficients, corresponding to distance compression; />Is a cubic term coefficient; />Then only with f a The term is the azimuth modulation term, and corresponds to azimuth compression.
In a further step 6, the two-dimensional spectrum S' (f) without aliasing r ,f′ a ) The method comprises the following steps of performing operations such as distance compression, secondary compression, migration correction, constant term compensation, higher term compensation, azimuth compression and the like in sequence, wherein the specific process is as follows:
6a) First, a distance compression and secondary compression function is constructed as shown in formula (16), where γ is the tuning frequency:
secondly, performing range migration correction, and constructing a compensation function as shown in formula (17):
and then constant term and higher term compensation are carried out, and the compensation function is shown as a formula (18):
6b) Compensating the two-dimensional frequency domain signal S' (f) after compensation by the distance compression, migration correction, constant term and higher term r ,f′ a ) Performing distance IFFT, and converting the signal back to time domain to obtain S '(t, f' a ) Combining with Dechirp processing idea, constructing azimuth compression function to convert the phase of the IFFT signal, as shown in formula (19)
For S '(t, f' a ) And H is az And (3) performing azimuth IFFT on the multiplied result to obtain an azimuth time domain unambiguous signal, and multiplying the azimuth time domain unambiguous signal by a Dechirp function to obtain a formula (20):
in the formulas (19) and (20), xi satisfies the relationη satisfies the relationshipLambda is the wavelength of the carrier wave, v T and vR Respectively the moving speeds of the receiving and transmitting platforms, R tef and Rref Respectively the distance from the receiving and transmitting platform to the virtual rotation center point in the bidirectional sliding beam focusing mode, R Tcen and RRcen Respectively, the minimum value of the target slant distance from the receiving and transmitting platform to the ground point.
6c) And finally, carrying out azimuth FFT (fast Fourier transform) on the azimuth time domain non-blurred signals subjected to the series of operations, and converting the azimuth time domain non-blurred signals back to a frequency domain to obtain non-blurred imaging.
Compared with the prior art, the invention has the advantages that:
(1) The traditional method for approximating the pitch by using the taylor series is to approximate the pitch near the moment by using the value of the pitch model at the central moment of the synthetic aperture, and when the azimuth time is far away from the central moment, the pitch approximation error of the target point is increased. The invention uses the Legendre polynomial expansion method to carry out fourth-order approximation on the slope distance expression of the satellite-machine bistatic SAR, and the method uses the instantaneous slope distance at the corresponding azimuth moment to carry out weighting operation, so that compared with the traditional Taylor series expansion approximation method, the precision is higher, and the error is smaller;
(2) The invention designs an echo antialiasing preprocessing scheme under the condition of low PRF. Because the flight speed difference between the low orbit satellite transmitting platform and the unmanned aerial vehicle receiving platform is huge, the PRFs actually required by the low orbit satellite transmitting platform and the unmanned aerial vehicle receiving platform have larger difference, for a satellite-based double-base SAR system under the low PRF condition, the Doppler bandwidth of a target point positioned at the edge of an imaging scene is obviously higher than that of the PRFs, and if the target point is directly processed by using a conventional frequency domain imaging method, the phenomenon of spectrum aliasing is necessarily generated. The invention pre-processes the echo, and the PRF after pre-processing is larger than Doppler bandwidth by the method of equivalent convolution transformation and compensation. According to the scheme, not only is the frequency spectrum blurring in the azimuth direction eliminated, but also excessive echo data quantity and distance blurring caused by directly expanding the PRF are avoided, so that efficient frequency domain blurring-free imaging can be realized in a subsequent design algorithm;
(3) The invention expands the application range of frequency domain imaging which uses Legendre polynomial to spread the target frequency spectrum. The application background of the research developed by the Li Le let de polynomial is the airborne double-base SAR system. The invention expands the two-way sliding beam focusing working mode under a more complex satellite-machine double-base SAR system, and overcomes the problem of frequency spectrum blurring of the satellite-machine double-base SAR system, and the working mode can realize the coordination of mapping width and resolution by setting reasonable sliding coefficients;
(4) The invention designs a set of processing flow aiming at the low PRF star-computer double-base SAR system imaging. Firstly, preprocessing echo signals, and combining the thought of spectrum analysis technology, and removing azimuth aliasing of the signals by utilizing equivalent convolution transformation and compensation; then, approximating the double-pass slant range by utilizing a Legend polynomial expansion method, and establishing a high-precision slant range model; then, combining the thought of the series inversion to obtain a phase expression of an accurate two-dimensional frequency spectrum of the point target; and finally, obtaining an imaging result in a frequency domain design algorithm.
Drawings
Fig. 1 is a flowchart of a frequency domain imaging algorithm according to the present embodiment.
Fig. 2 is a schematic diagram of a bistatic SAR geometric model.
FIG. 3 is a schematic diagram of a satellite-machine bistatic SAR bi-directional sliding beaming mode of operation, wherein: (a) satellite forward sliding beaming; (b) reversely sliding the beam for the unmanned plane.
Fig. 4 is a schematic diagram of simulation of a 5×5 uniform distribution point target array on the ground.
Fig. 5 is a graph comparing the skew errors under different skew approximation methods.
Fig. 6 is a two-dimensional spectrum contrast diagram before and after echo dealiasing preprocessing, in which: (a) is a two-dimensional spectrum prior to de-aliasing; (b) is the two-dimensional spectrum after de-aliasing.
FIG. 7 is a contrast of image point height maps at different positions of a scene, wherein: (a) is an imaging height map of the central point P1 under the algorithm of the invention; (b) is an imaging height map of the lower edge point P3 of the algorithm of the invention; (c) An imaging height map of a central point P3 under a Taylor series expansion method; (d) An imaging height map of the edge point P3 under the taylor series expansion method.
Fig. 8 is a comparison of distance and azimuth cross-sectional views of a scene edge imaging point P3 under different imaging algorithms, wherein: (a) The distance profile of the scene edge point P3 under the algorithm of the invention; (b) The azimuth section view of the scene edge point P3 under the algorithm of the invention; (c) Expanding a distance profile of a lower edge point P3 of the frequency domain algorithm for the Taylor series; (d) The azimuthal cross-section of the lower edge point P3 of the frequency domain algorithm is developed for the Taylor series.
Detailed Description
The invention will be further described with reference to the drawings and examples.
Example 1
The embodiment discloses a star-computer bistatic SAR two-dimensional frequency domain imaging method combining echo preprocessing with Legend polynomials, which comprises the following steps as shown in figure 1:
step 1, establishing a slant range expression of a bidirectional sliding bunching mode according to a geometric model of a satellite-machine bistatic SAR system.
A schematic diagram of the bi-directional sliding beamforming mode is shown in FIG. 3, wherein W, U is the virtual center of rotation of the transmitter and receiver, R tef and Rref The distance between the transmitting platform and the receiving platform and the rotation center is R tcen and Rrcen The shortest range of the transceiver to the ground.
The geometric model of the bistatic SAR system is shown in figure 2, and the point P represents any scattering point in the scene, and the coordinates are (x 0 ,y 0 0), the three-dimensional real-time positions of the receiving and transmitting radar platform are respectively (x) t ,y t ,z t) and (xr ,y r ,z r ). Establishing an oblique distance expression R under a bidirectional sliding bunching working mode according to a geometric model of a satellite-machine bistatic SAR system bi (τ) is as follows:
step 2, obtaining ground point target echo signals generated when the low-orbit satellite platform transmits the linear frequency modulation signals, wherein the ground point target echo signals are as follows:
where σ is the backscattering coefficient of the point target, t and τ are the distance-fast time and azimuth-slow time, W, respectively r and Wa Respectively a distance window function and an azimuth window function, c is the speed of light, lambda is the carrier wavelength, gamma is the transmission signal toneFrequency.
And step 3, performing antialiasing pretreatment on the point target echo to obtain a non-fuzzy frequency spectrum. The specific process is as follows:
3a) Constructing a reference function:
first, a reference function of the azimuth time domain τ is constructed as follows:
H ref (τ)＝exp(jπητ 2 ) (1)，
wherein eta is a frequency modulation coefficient and is related to the actual configuration parameter of the star-machine bistatic SAR system, thereby satisfying the relationLambda is the wavelength of the carrier wave, v T and vR Respectively the moving speeds of the receiving and transmitting platforms, R tef and Rref The distances from the receiving and transmitting platform to the virtual rotation center point in the bidirectional sliding beam focusing mode are respectively shown.
Performing distance FFT on the time domain echo signal S (t, tau) obtained in the step 2, and converting the time domain echo signal S (t, tau) into a distance frequency domain to obtain S (f) r τ), and S (f) r τ) and a reference function H ref (τ) multiplying;
3b) Equivalent convolution transformation:
performing azimuth FFT on the result of the step 3 a) and performing azimuth FFT with a reference function H under a new time domain coordinate tau' ref Multiplying (τ') to obtain the signal S (f) without ambiguity in azimuth frequency domain under new time domain coordinate τ r τ'). This step can in turn be regarded as a time-domain echo S (f r τ) and a reference function H ref Performing equivalent convolution transformation on (tau) to obtain S (f) r τ'), wherein:
the FFT transformation corresponds to a transformation between the time-frequency axes. Before and after FFT conversion, the original time domain coordinate tau, the new time domain coordinate tau' of the echo signal and the original frequency coordinate f of the echo signal a New frequency coordinate f' a Satisfy the relation between
3c) Conjugate compensation:
for S (f) obtained in step 3 b) r Performing azimuth FFT again to obtain a new two-dimensional frequency domain signal S (f) r ,f′ a ) For S (f) r ,f′ a ) Multiplying by a frequency domain conjugate compensation function H ref * (f′ a ) The resulting aliasing free spectrum is shown in equation (2):
S'(f r ,f′ a )＝S(f r ,f′ a )·H ref * (f′ a ) (2)，
and 4, approximating the oblique distance expression established in the step 1 by utilizing a Legendre polynomial to obtain a Legendre expansion of the double-pass oblique distance. The specific process is as follows:
in this embodiment, for the slant distance R described in step 1 bi (τ) power series arrangement in azimuth slow time when four-order approximation is performed using Legend polynomials.
4a) Normalizing the azimuth slow time tau, namelyTa is the synthetic aperture time. Then to the slant distance R bi (τ) performing Legend orthogonal decomposition and expansion into a fourth order power series form of x as shown in equation (3):
R bi (x)＝α 0 +α 1 x+α 2 x 2 +α 3 x 3 +α 4 x 4 (3)，
wherein the corresponding term coefficient alpha i The method meets the following conditions:
wherein Ln (x) For Legendre polynomials, satisfy the formula
In the formula (4), the operation process in the bracket { } is a fixed integral operation, and the corresponding calculation result of the order n is carried in during the operation, namelyThe calculated content satisfies the formula:
4b) Will beIn the substitution return type (5), the double-way inclined distance R is obtained by rearrangement bi (τ) the fourth-order power series expansion in slow time τ, i.e., the legendre polynomial approximation of the skew is shown in equation (5):
R bi (τ)＝k 0 +k 1 τ+k 2 τ 2 +k 3 τ 3 +k 4 τ 4 (5)，
wherein ,the Legend decomposition coefficient corresponding to the skew.
Step 5, combining a series inversion method, and acquiring the phase psi (f) of the original two-dimensional spectrum of the point target by utilizing the Legend expansion of the double-pass skew r ,f a ) Phase ψ (f r ,f a ) Spread out as distance frequency domain f r And discard the distance frequency domain f in power series form r And azimuth frequency domain f a And (3) obtaining a two-dimensional spectrum phase based on the Legendre polynomial expansion. The specific process is as follows:
5a) Firstly, azimuth time-frequency conversion of the nonlinear phase is completed by utilizing the principle of stationary phase, and the result is shown in a formula (6):
and obtaining the corresponding relation between the azimuth slow time and the frequency by a series inversion method:
in formulas (6) and (7), k n (n=2, 3, 4) is Legend decomposition coefficient corresponding to the skew, f r For distance frequency, f a For azimuth frequency, f c The carrier frequency, c, is the speed of light.
5b) The linear phase removed before the compensation is utilized, and the frequency shift property of Fourier transformation is utilized to obtain an original two-dimensional frequency spectrum as shown in a formula (8):
S(f r ,f a )＝W r (f r )W a (f a )exp(jψ(f r ,f a )) (8)，
wherein ,Wr Represents the distance envelope, W a Represents the azimuth envelope, ψ (f r ,f a ) Representing the original two-dimensional spectrum phase, the specific expression is shown in formula (9):
wherein ,kn (n=0, 1,2,3, 4) is Legend decomposition coefficient corresponding to the skew, f r For distance frequency, f a For azimuth frequency, f c The carrier frequency, c, is the speed of light.
In the Legendre polynomial pair (11)And (5) unfolding. Firstly, normalizing, namely, making ∈ ->B is the signal bandwidth. The three power series forms of three fractional formulas respectively arranged into y are shown as a formula (10):
wherein the coefficients preceding y of the different power terms satisfy the relation as shown in formula (11):
the operation process in the bracket { } is fixed integral operation, and the corresponding order n calculation result is brought in during operation, and the specific operation content satisfies the formula:and then->In the power series with y, the power series is arranged as f r In the form of a third-order power series, to yield equation (12): />
wherein ,is->Corresponding Legend decomposition coefficients.
5c) Bringing the result of formula (12) into formula (9) for sorting and merging, discarding f r and fa After the higher order term of (2), the legend spectral phase expression can be obtained as shown in equation (13):
wherein the distance frequency f r The coefficients corresponding to the different power terms satisfy the following relationship:
wherein ,kn (n=0, 1,2,3, 4) is Legend decomposition coefficient corresponding to the skew, f r For distance frequency, f a For azimuth frequency, f c The carrier frequency, c, is the speed of light.
Each phase term found in equation (13),and f r and fa Are all independent and are constant phase terms; />Is f r Linear term coefficients of (2) corresponding to range migration; />Is f r Square term coefficients, corresponding to distance compression; />Is a cubic term coefficient; />Then only with f a The term is the azimuth modulation term, and corresponds to azimuth compression.
And step 6, combining the two-dimensional spectrum phase terms based on the Legendre polynomial expansion obtained in the step 5, and performing distance compression, secondary compression, distance migration correction, constant term and higher term compensation, azimuth compression and the like on the non-fuzzy spectrum obtained in the step 3 to obtain an imaging result. The specific process is as follows:
6a) First, a distance compression and secondary compression function is constructed as shown in formula (16), where γ is the tuning frequency:
/>
secondly, performing range migration correction, and constructing a compensation function as shown in formula (17):
and then constant term and higher term compensation are carried out, and the compensation function is shown as a formula (18):
6b) Compensating the two-dimensional frequency domain signal S' (f) after compensation by the distance compression, migration correction, constant term and higher term r ,f′ a ) Performing distance IFFT, and converting the signal back to time domain to obtain S '(t, f' a ) Combining with Dechirp processing idea, constructing azimuth compression function to convert the phase of the IFFT signal, as shown in formula (19)
For S '(t, f' a ) And H is az And (3) performing azimuth IFFT on the multiplied result to obtain an azimuth time domain unambiguous signal, and multiplying the azimuth time domain unambiguous signal by a Dechirp function to obtain a formula (20):
in the formulas (19) and (20), xi satisfies the relationη satisfies the relationshipLambda is the wavelength of the carrier wave, v T and vR Respectively the moving speeds of the receiving and transmitting platforms, R tef and Rref Respectively the distance from the receiving and transmitting platform to the virtual rotation center point in the bidirectional sliding beam focusing mode, R Tcen and RRcen Respectively, the minimum value of the target slant distance from the receiving and transmitting platform to the ground point.
6c) And finally, carrying out azimuth FFT (fast Fourier transform) on the azimuth time domain non-blurred signals subjected to the series of operations, and converting the azimuth time domain non-blurred signals back to a frequency domain to obtain non-blurred imaging.
Example two
The embodiment provides a simulation experiment of the satellite-machine double-base SAR imaging method in the bidirectional sliding bunching mode, which is described as follows:
simulation conditions:
the simulation parameters in table 1 are used for carrying out ground point target array simulation experiments, and the focusing effect of the satellite-machine bistatic SAR frequency domain imaging method based on echo preprocessing and Legend polynomial is verified.
TABLE 1 Star-machine bistatic SAR simulation parameters
The size of the star-machine bistatic SAR ground imaging scene is set to 3km×3km by using the parameters of table 1, and 5×5 uniformly distributed point target arrays are arranged in the imaging scene, as shown in fig. 4, where P1 is the scene center point and P3 is the scene edge point.
(II) simulation content:
(1) Contrast of oblique distance approximation errors of two unfolding modes
The present embodiment compares the slope distance based on the legendre polynomial expansion with the conventional slope distance approximation error based on the taylor series expansion, and the result is shown in fig. 5. It can be seen that when the azimuth time is smaller, the error of the slant distance model of the two unfolding modes is not much different; when the azimuth time is increased, the fourth-order Legendre expansion approximation precision of the oblique distance model is higher than the fourth-order Taylor series approximation precision, and the error is smaller.
This is because the taylor series expansion method approximates the range around the synthetic aperture center time by the value of the range model at that time, and the target point range error increases as the azimuth time moves away from the center time. If the problem is to be solved, the slant distance needs to be expanded into an expression with a higher order, but the complexity and the calculated amount of formula derivation are further increased; the Legendre polynomial expansion rule is to utilize the instantaneous slope distance at the corresponding azimuth moment to carry out weighting operation, so that the approximate slope distance error of the target point far away from the center moment is reduced, and the stable approximation of the slope distance model is ensured.
(2) Echo antialiasing preprocessing effect display
According to the echo preprocessing scheme proposed in the first embodiment, a two-dimensional frequency domain result of the echo before and after the de-aliasing can be obtained as shown in fig. 6. Where (a) in fig. 6 is a two-dimensional spectrum before the demosaicing and (b) is a two-dimensional spectrum after the demosaicing. It can be seen that after the de-aliasing preprocessing procedure, the two-dimensional spectral width of the echo signal is shrunk and no aliasing occurs.
(3) Point target imaging contour map effect contrast
In order to evaluate the focusing effect of the imaging algorithm proposed in the first embodiment on targets at different positions in the scene, contour maps of two points of a center point P1 and an edge point P3 in the scene are selected for analysis, and the contour results are shown in fig. 7 (a) and fig. 7 (b), respectively. It can be seen that the energy concentration degree of the center point P1 and the edge point P3 is higher, so that the frequency domain imaging method proposed by the embodiment one is verified to have better focusing performance.
By applying the same thought, the conventional frequency domain imaging algorithm based on Taylor series expansion is adopted to perform two-dimensional frequency domain imaging on the P1 and P3 points, and the imaging results are shown in (c) and (d) of fig. 7. Comparing fig. 7 (a) and (c), the two imaging algorithms are not much different for the center point P1; as can be seen from comparison between fig. 7 (b) and fig. 7 (d), for the edge points of the scene, the conventional frequency domain algorithm based on taylor series expansion has obvious side lobe elongation in the azimuth direction of the imaging result, and the focusing effect is poor.
(4) Point target imaging contour map effect contrast
And then performing performance analysis on the imaging point results of the method of the first embodiment and the traditional Taylor expansion frequency domain algorithm, obtaining the distance and azimuth cross section results of the contour line of the edge point P3 as shown in (a) to (d) in fig. 8, calculating the distance corresponding to the center point P1 and the edge point P3, and recording the Peak Side Lobe Ratio (PSLR) and the Integral Side Lobe Ratio (ISLR) of the azimuth cross section in table 2.
In fig. 8, (a) and (b) are respectively distance and azimuth sectional views of the algorithm proposed by the present invention for the edge point P3, and (c) and (d) are respectively distance and azimuth sectional views of the taylor expansion frequency domain algorithm for the edge point P3. Comparing the observations (a) and (c) can find that the two imaging algorithms are not far apart from each other in terms of the edge point P3 of the scene; and comparing the observation (b) and (d) to obviously show that the main lobe widening and side lobe increasing phenomena exist in the orientation cross section diagram of the Taylor expansion imaging algorithm at the edge point P3, the imaging quality is reduced, and the cross section result of the method proposed by the first embodiment is closer to the result of the center point.
Table 2 imaging quality assessment for both methods
As can be seen from the data in table 2, the effect of the method proposed in the first embodiment is slightly improved with respect to the conventional taylor-expanded MSR algorithm in terms of the performance parameter in the distance direction, and is below-13.2 dB; for the performance parameters of the azimuth direction, at the edge point P3, the PSLR is increased from-12.773 dB to-13.311 dB and the ISLR is increased from-8.557 dB to-10.728 dB by the method proposed by the first embodiment compared with the Taylor expansion algorithm. In summary, the star-computer bistatic SAR two-dimensional frequency domain imaging method provided by the embodiment enables the point target to obtain better performance parameters generally, and can effectively improve the imaging quality of scene edge points.
The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, and the examples described herein are merely illustrative of the preferred embodiments of the present invention and are not intended to limit the spirit and scope of the present invention. The individual technical features described in the above-described embodiments may be combined in any suitable manner without contradiction, and such combination should also be regarded as the disclosure of the present disclosure as long as it does not deviate from the idea of the present invention. The various possible combinations of the invention are not described in detail in order to avoid unnecessary repetition.
The present invention is not limited to the specific details of the above embodiments, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the protection scope of the present invention without departing from the scope of the technical concept of the present invention, and the technical content of the present invention is fully described in the claims.
Claims (5)
1. The star-computer double-base SAR imaging method in the bidirectional sliding beam focusing mode is characterized by comprising the following steps of:
step 1, establishing an oblique distance expression of a bidirectional sliding bunching mode according to a geometric model of a satellite-machine bistatic SAR system;
step 2, acquiring a ground point target echo signal generated when the low-orbit satellite platform transmits the linear frequency modulation signal;
step 3, performing antialiasing pretreatment on the point target echo to obtain a non-fuzzy frequency spectrum;
step 4, approximating the oblique distance expression established in the step 1 by utilizing a Legendre polynomial to obtain a Legendre expansion of a double-pass oblique distance;
step 5, combining a series inversion method, and acquiring the phase psi (f) of the original two-dimensional spectrum of the point target by utilizing the Legend expansion of the double-pass skew r ,f a ) Phase ψ (f r ,f a ) Spread out as distance frequency domain f r And discard the distance frequency domain f in power series form r And azimuth frequency domain f a Obtaining a two-dimensional spectrum phase based on the Legendre polynomial expansion;
and step 6, combining the two-dimensional spectrum phase terms based on the Legendre polynomial expansion obtained in the step 5, and performing distance compression, secondary compression, distance migration correction, constant term and higher term compensation, azimuth compression and the like on the non-fuzzy spectrum obtained in the step 3 to obtain an imaging result.
2. The method for imaging a satellite-machine bistatic SAR in a bidirectional sliding beam-focusing mode according to claim 1, wherein in step 3, the specific process of performing the antialiasing pretreatment on the point target echo is as follows:
3a) Constructing a reference function:
firstly, constructing a reference function of an azimuth time domain tau as shown in a formula (1):
H ref (τ)＝exp(jπητ 2 ) (1)，
wherein eta is a frequency modulation coefficient and is related to the actual configuration parameter of the star-machine bistatic SAR system, thereby satisfying the relationLambda is the wavelength of the carrier wave, v T and vR Respectively the moving speeds of the receiving and transmitting platforms, R tef and Rref Respectively the distances from the receiving and transmitting platform to the virtual rotation center point in the bidirectional sliding beam focusing mode;
performing distance FFT on the time domain echo signal S (t, tau) obtained in the step 2, and converting the time domain echo signal S (t, tau) into a distance frequency domain to obtain S (f) r τ), and S (f) r τ) and a reference function H ref (τ) multiplying;
3b) Equivalent convolution transformation:
performing azimuth FFT on the result of the step 3 a) and performing azimuth FFT with a reference function H under a new time domain coordinate tau' ref Multiplying (τ') to obtain the signal S (f) without ambiguity in azimuth frequency domain under new time domain coordinate τ r τ'); this step can in turn be regarded as a time-domain echo S (f r τ) and a reference function H ref Performing equivalent convolution transformation on (tau) to obtain S (f) r τ'), wherein:
the FFT conversion corresponds to the conversion between time-frequency axes, and before and after the FFT conversion, the original time-domain coordinate tau, the new time-domain coordinate tau' and the original frequency coordinate f of the echo signal a New frequency coordinate f' a Satisfy the relation between
3c) Conjugate compensation:
for S (f) obtained in step 3 b) r Performing azimuth FFT again to obtain a new two-dimensional frequency domain signal S (f) r ,f′ a ) For S (f) r ,f′ a ) Multiplying by a frequency domain conjugate compensation function H ref * (f′ a ) The resulting aliasing free spectrum is shown in equation (2):
S(f r ,f′ a )＝S(f r ,f′ a )·H ref * (f′ a ) (2)。
3. the method for imaging a satellite-machine bistatic SAR in a bidirectional sliding beamforming mode according to claim 2, wherein in step 4, the approximation of the slope distance using the legendre polynomial is performed as follows:
4a) Normalizing the azimuth slow time tau, namelyT a Is the synthetic aperture time; then to the slant distance R bi (τ) Legend orthogonal decomposition and expansion into the form of a fourth order power series of x is shown below:
R bi (x)＝α 0 +α 1 x+α 2 x 2 +α 3 x 3 +α 4 x 4 (3)，
wherein the corresponding term coefficient alpha i The method meets the following conditions:
wherein Ln (x) For Legendre polynomials, satisfy the formula
In formula (4), however, the brackets are within { }The operation process is fixed integral operation, and the corresponding order n calculation result is brought in during operation, and the specific operation content satisfies the formula:
4b) Will beIn the substitute return type (3), the double-way inclined distance R is obtained by rearrangement bi (τ) the fourth-order power series expansion in slow time τ, i.e., the legendre polynomial approximation of the skew is:
R bi (τ)＝k 0 +k 1 τ+k 2 τ 2 +k 3 τ 3 +k 4 τ 4 (5)，
wherein ,the Legend decomposition coefficient corresponding to the skew.
4. The method for satellite-machine bistatic SAR imaging under the bidirectional sliding beam-focusing mode according to claim 3, wherein in step 5, the procedure of obtaining the spread two-dimensional spectrum phase based on the Legendre polynomial is as follows:
5a) Firstly, azimuth time-frequency conversion of the nonlinear phase is completed by utilizing the principle of stationary phase, and the result is shown in a formula (6):
and obtaining the corresponding relation between the azimuth slow time and the frequency by a series inversion method:
in formulas (6) and (7), k n (n=2, 3, 4) is Legend decomposition coefficient corresponding to the skew, f r For distance frequency, f a For azimuth frequency, f c C is the speed of light, which is the carrier frequency;
5b) The linear phase removed before the compensation is utilized, and the frequency shift property of Fourier transformation is utilized to obtain an original two-dimensional frequency spectrum as shown in a formula (8):
S(f r ,f a )＝W r (f r )W a (f a )exp(jψ(f r ,f a )) (8)
wherein ,Wr Represents the distance envelope, W a Represents the azimuth envelope, ψ (f r ,f a ) Representing the original two-dimensional spectrum phase, the specific expression is shown in formula (9):
wherein ,kn (n=0, 1,2,3, 4) is Legend decomposition coefficient corresponding to the skew, f r For distance frequency, f a For azimuth frequency, f c C is the speed of light, which is the carrier frequency;
in Legendre polynomial (9)Performing development, and performing normalization treatment to obtain ∈ ->B is the signal bandwidth; the three power series forms of three fractional formulas respectively arranged into y are shown as a formula (10):
wherein the coefficients preceding y of the different power terms satisfy the relation as shown in formula (11):
the operation process in the bracket { } is fixed integral operation, and the corresponding order n calculation result is brought in during operation, and the specific operation content satisfies the formula:and then->In the power series with y, the power series is arranged as f r In the form of a third-order power series, to yield equation (12):
wherein ,is->Corresponding Legend decomposition coefficients;
5c) Bringing the result of formula (12) into formula (9) for sorting and merging, discarding f r and fa After the higher order term of (2), the legend spectral phase expression can be obtained as shown in equation (13):
wherein the distance frequency f r The coefficients corresponding to the different power terms satisfy the following relationship:
wherein ,kn (n=0, 1,2,3, 4) is Legend decomposition coefficient corresponding to the skew, f r For distance frequency, f a For azimuth frequency, f c C is the speed of light, which is the carrier frequency;
each phase term found in equation (13),and f r and fa Are all independent and are constant phase terms; />Is f r Linear term coefficients of (2) corresponding to range migration; />Is f r Square term coefficients, corresponding to distance compression; />Is a cubic term coefficient;then only with f a The term is the azimuth modulation term, and corresponds to azimuth compression.
5. The method for satellite-machine bistatic SAR imaging in bi-directional sliding beamforming mode according to claim 4, wherein in step 6, the aliasing free two-dimensional spectrum S' (f) r ,f′ a ) The method comprises the following steps of performing operations such as distance compression, secondary compression, migration correction, constant term compensation, higher term compensation, azimuth compression and the like in sequence, wherein the specific process is as follows:
6a) First, a distance compression and secondary compression function is constructed as shown in formula (16), where γ is the tuning frequency:
secondly, performing range migration correction, and constructing a compensation function as shown in formula (17):
and then constant term and higher term compensation are carried out, and the compensation function is shown as a formula (18):
6b) Compensating the two-dimensional frequency domain signal S' (f) after compensation by the distance compression, migration correction, constant term and higher term r ,f′ a ) Performing distance IFFT, and converting the signal back to time domain to obtain S '(t, f' a ) Combining with Dechirp processing idea, constructing azimuth compensation function to convert the phase of the IFFT signal, as shown in formula (19)
For S '(t, f' a ) And H is az And (3) performing azimuth IFFT on the multiplied result to obtain an azimuth time domain unambiguous signal, and multiplying the azimuth time domain unambiguous signal by a Dechirp function to obtain a formula (20):
in the formulas (19) and (20), xi satisfies the relationEta satisfies the relationship->Lambda is the wavelength of the carrier wave, v T and vR Respectively the moving speeds of the receiving and transmitting platforms, R tef and Rref Respectively the distance from the receiving and transmitting platform to the virtual rotation center point in the bidirectional sliding beam focusing mode, R Tcen and RRcen Respectively the minimum value of the target slant distance from the receiving and transmitting platform to the ground point;
6c) And finally, carrying out azimuth FFT (fast Fourier transform) on the azimuth time domain non-blurred signals subjected to the series of operations, and converting the azimuth time domain non-blurred signals back to a frequency domain to obtain non-blurred imaging.
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