CN103033811A - Bistatic synthetic aperture radar imaging method based on similar single static equivalence - Google Patents

Abstract

The invention discloses a bistatic synthetic aperture radar imaging method based on similar single static equivalence. A double radical sign slant distance of bistatic is equivalent to a single radical sign slant distance of a similar single static, an analytical expression of a two dimensional spectrum of a system is obtained, a solving question of a double radical sign of the bistatic is simplified, mature single static imaging methods are fully used, such as an omega-K (wk) algorithm and a range-Doppler algorithm (RD algorithm), a two dimensional STOLT relation of the system is obtained according to the expression of the two dimensional spectrum, and finally, a two dimensional STOLT interpolation is approximated according to the two dimensional non-uniform Fourier transformation, and imaging of the system is achieved. Therefore, complicated degree of an imaging algorithm of the bistatic is largely reduced, and successive imaging process is facilitated.

Description

A kind of double-base synthetic aperture radar imaging method based on the single base equivalence of class

Technical field

The present technique invention belongs to the Radar Technology field, and it has been particularly related to double-base synthetic aperture (BiSAR) radar imagery technical field.

Background technology

Double-base synthetic aperture radar (Bistatic synthetic aperture radar is abbreviated as BiSAR) refers to the be placed in radar system of two different motion platforms of dual-mode antenna.Compare with single base SAR, Bistatic SAR has good concealment, and is safe, and antijamming capability is strong, the low-cost and strong advantage of dirigibility, and can realize the special pattern that some single base SAR can't realize, such as the forward sight imaging.The double-basis imaging is a kind of imaging pattern that has very much using value, can be applicable to the aspects such as aircraft navigation under guided missile navigation, the inclement weather and landing.In view of the multiple advantage of double-base SAR, significant to the research of double-base SAR imaging technique.

Although double-base SAR has above advantage, brought two radical sign problems of oblique distance history, cause the complicated of finding the solution of 2-d spectrum, cause the expression formula of 2-d spectrum to find the solution.At present, the approximate expression that some are found the solution bistatic 2-d spectrum has appearred, such as Extending Loffeld ' s bistatic formula (ELBF), Method of Series Reversion (MSR) and the Method of air-phase (AP), see R.Wang.et al for details, " Extending loffeld ' sbistatic formula for the general bistatic sar configuration ", Yew Lam Neo.et al, " A Two-DimensionalSpectrum for Bistatic SAR Processing Using Series Reversion " and Liu.z.et al, " Study on spaceborne/airborne hybrid bistatic sar image formation in frrequency domain ".These methods can be similar to and obtain the 2-d spectrum expression formula, but expression formula is too complicated, and it is very loaded down with trivial details to cause 2-d spectrum to find the solution, and is unfavorable for follow-up imaging processing.

Summary of the invention

The objective of the invention is to find the solution complicated shortcoming for the two radical sign problems and the 2-d spectrum that overcome bistatic oblique distance history in the prior art, a kind of double-base synthetic aperture radar system imaging method based on the single base equivalence of class is provided.The method has been simplified the Solve problems of bistatic pair of radical sign on the one hand, therefore can obtain simply bistatic 2-d spectrum, can take full advantage of on the other hand ripe single base formation method, such as omega-K (wk) algorithm, range Doppler algorithm (RD algorithm), thereby reduce to a great extent the complexity of bistatic imaging algorithm, for follow-up imaging processing is provided convenience.

Content of the present invention for convenience of description, at first make following term definition:

Definition 1, slow time and fast time

The slow time is that the orientation is to time t _a, refer to that transmit-receive platform flies over a flight needed time of aperture, because radar is with certain repetition period T _rThe emission received pulse, the slow time can be expressed as the time variable t of a discretize _a=nT _r, wherein, n is the orientation to constantly, the span of n is: and n=1 ... N, N are the discrete number of slow time in the synthetic aperture, T _rBe the repetition period.

The fast time refers to that distance is to time t.

Definition 2, zero Doppler are constantly

Slow time when zero Doppler refers to constantly that Doppler frequency is zero.

Definition 3, Bistatic SAR System Dependent parametric description

Transmitter platform oblique distance history: $R_s\left(t_a\right)=\sqrt{R_{\mathrm{so}}^2+V_s^2{(t_a-T_{s0})}^2}$

Wherein, t _aBe slow time, T _S0Be the zero Doppler moment of flat pad with respect to impact point: R _S0For flat pad zero Doppler constantly apart from the nearest oblique distance of target: Vs is the movement velocity size of the relative target of flat pad, and s represents transmitter, and x and y represent to observe scene transverse and longitudinal coordinate, X _S0, Y _S0, H _SThe initial three-dimensional coordinate of expression flat pad;

Receiver platform oblique distance history: $R_r\left(t_a\right)=\sqrt{R_{\mathrm{ro}}^2+V_r^2{(t_a-T_{r0})}^2}$

Wherein, t _aBe slow time, T _R0Be the zero Doppler moment of receiving platform with respect to impact point:

R _R0For receiving platform zero Doppler constantly apart from the nearest oblique distance of target:

V _rBe the movement velocity size of the relative target of receiving platform, r represents receiver, and x and y represent to observe scene transverse and longitudinal coordinate, X _R0, Y _R0, H _rThe initial three-dimensional coordinate of expression flat pad;

Bistatic SAR system oblique distance history: R (t _a)=R _s(t _a)+R _r(t _a)

The wavenumber domain frequency: $k=2\mathrm{\π}\frac{f+F_0}{C}$

Wherein, f is the frequency corresponding to the fast time, F ₀Be the centre frequency that transmits, C is light velocity size;

Transmitter platform phase place history: θ _s(t _a)=kR _s(t _a)

Receiver platform phase place history: θ _r(t _a)=kR _r(t _a)

Wherein, k is the wavenumber domain frequency, R _s(t _a) and R _r(t _a) be respectively the oblique distance history of flat pad and receiver platform;

Bistatic SAR system oblique distance history: θ (t _a)=θ _s(t _a)+θ _r(t _a)+2 π f _at _a

Wherein, f _aBe the Doppler frequency corresponding to the slow time;

The t of time point in the phase bit _A1Satisfy θ ' (t _A1)=0

Definition 4, least square method

Least square method (LS) is a kind of optimization algorithm, and the quadratic sum of the mould by minimizing evaluated error is sought the optimal function coupling.Utilize least square method so that these data of trying to achieve and the error between the real data are minimum.

Definition 5, based on the single basic mode type of the class of least square method (LS)

The single basic mode type of class oblique distance history based on least square method:

$R_m\left(t_a\right)=\sqrt{R_M^2+V^2{(t_a-T_M)}^2}$

Wherein, R _MThe shortest oblique distance history of the single basic SAR of equivalence: T _MSingle zero Doppler's moment of base of equivalence:

V is the single basic movement velocity of equivalence:

a ₀, a ₁, a ₂Be the optimum solution of finding the solution based on least square method, $[a_0,a_1,a_2]=\stackrel{\‾}{R}{\stackrel{\‾}{T}}_a^H\mathrm{inv}\left({\stackrel{\‾}{T}}_a{\stackrel{\‾}{T}}_a^H\right),$ H represents transpose conjugate, and inv () represents matrix inversion,

Each matrix of corresponding Bistatic SAR system oblique distance history square constantly of slow time: $\stackrel{\‾}{R}=[\frac{R^2\left(0\right)}{4},\frac{R^2\left(\mathrm{PRT}\right)}{4},\·\·\·,\frac{R^2\left((\mathrm{Nplus}-1)\mathrm{PRT}\right)}{4}],$ R ²(0) be the 0th constantly Bistatic SAR system oblique distance history square, R ²(PRT) be PRT Bistatic SAR system oblique distance history constantly square, R ²((Nplus-1) PRT) be (Nplus-1) PRT Bistatic SAR system oblique distance history constantly square,

The time parameter matrix, ${\stackrel{\‾}{T}}_a=\left[\begin{array}{c}\mathrm{1,1},\·\·\·,1\\ 0,\mathrm{PRT},\·\·\·(\mathrm{Nplus}-1)\mathrm{PRT}\\ 0,{\mathrm{PRT}}^2,\·\·\·{\left((\mathrm{Nplus}-1)\mathrm{PRT}\right)}^2\end{array}\right],$ PRT is the slow time sampling interval time, and Nplus is that slow time-sampling is counted.

Definition 6, based on the frequency spectrum of the single basic mode type of the class of LS

2-d spectrum based on the class Dan Ji of LS:

$S(f,f_a)=\exp (-j4\mathrm{\π}{R}_M\sqrt{{\left(\frac{f+F_0}{C}\right)}^2-{\left(\frac{f_a}{2V}\right)}^2}-j2\mathrm{\π}{f}_a{T}_M)$

Wherein, f is the Doppler frequency corresponding to the fast time, f _aThe Doppler frequency corresponding to the slow time, F _oBe the centre frequency that transmits, C represents light velocity size, R _MBe the shortest oblique distance history of the single basic SAR of equivalence, T _MBe single zero Doppler's moment of base of equivalence, V is the single basic movement velocity of equivalence, and j represents-1 square root.

Definition 7, synthetic-aperture radar gauged distance compression method

Synthetic-aperture radar gauged distance compression method refers to utilize the synthetic-aperture radar transmission signal parameters, the distance of employing matched filtering technique Technologies Against Synthetic Aperture Radar is carried out process from filtering to signal.See document " radar imagery technology " for details, protect polished grade and write, the Electronic Industry Press publishes.

Definition 8, two-dimentional nonuniform fast Fourier transform

Signal S (f _d, f _Az) two-dimentional non-homogeneous fast Fourier change NUFFT (S (f _d, f _Az)) be

NUFFT(S(f _d,f _az))＝∫∫S(f _d,f _az)exp(-j2πf _dt _d-j2πf _azt _az)df _ddf _az

Wherein, f _dAnd f _AzRight and wrong are equally distributed, and j represents-1 square root.See document " An Accurate Algorithm for Nonuniform Fast Fourier Transforms (NUFFT ' s) " for details, Q.H.Liu and N.Nguyen.

Definition 9, double-basis radar system imaging coordinate system and observation scene coordinate system

Double-basis radar imagery coordinate system: [Δ R _M, Δ T _M]

Observation scene coordinate system: [x, y]

Wherein, Δ R _MPoor for the shortest oblique distance history of equivalent Dan Ji of non-reference point and reference point: Δ R _M=R _Mno-R _Mref, Δ T _MBe constantly poor of single base zero Doppler of the equivalence of non-reference point and reference point: Δ T _M=T _Mno-T _Mref, R _MnoThe shortest oblique distance history of non-reference point equivalence Dan Ji, R _MrefThe shortest oblique distance history of reference point equivalence Dan Ji, T _MnoThe shortest oblique distance history of non-reference point equivalence Dan Ji, T _MrefBe the shortest oblique distance history of reference point equivalence Dan Ji, reference point is the central point in the observation scene, and x represents to observe scene transverse axis coordinate, and y represents to observe the scene ordinate of orthogonal axes.

The invention provides a kind of method of the double-base synthetic aperture radar imaging based on the single base equivalence of class, the step of the method is as follows:

Step 1, the bistatic echoed signal of initialization

Bistatic Forward-Looking SAR System parameter is as follows: the transmit-receive platform initial position, note is P respectively _S0(X _S0, Y _S0, H _s) and P _R0(X _R0, Y _R0, H _r), wherein, X _S0The initial position of expression flat pad on X-axis, Y _S0The initial position of expression flat pad on Y-axis, H _sThe initial position of expression flat pad on Z axis; X _R0The initial position of expression receiving platform on X-axis, Y _R0The initial position of expression receiving platform on Y-axis, H _rThe initial position of expression receiving platform on Z axis; V _S(0, v _S, 0) and expression flat pad velocity, V _R(0, v _R, 0) and expression receiving platform velocity, wherein, v _SThe value of expression flat pad speed on Y-axis, v _RThe value of expression receiving platform speed on Y-axis; Radar emission linear FM signal, the frequency of its CF signal are F ₀, the pulse repetition time is PRF, wide T when exomonental, exomonental chirp rate K, exomonental bandwidth B, echo bearing is to sampling number Nplus, the sampling number N that the echo distance makes progress, wherein Nplus and N are positive integer, the sample frequency F that distance makes progress.The distance of observation scene is R rice to total length, and the orientation is Z rice to total length.Bistatic Forward-Looking SAR System parameter is known;

Echo data s (t, t _a) be a data matrix that Nplus is capable and N is listed as, the each row of data of echo data matrix is the echoed signal sampled data of fast time, every column data is the echo samples data of slow time.Reference point is the target's center's point in the observation scene, square R of reference point the 0th Bistatic SAR system oblique distance history constantly ²(0), square R of reference point PRT Bistatic SAR system oblique distance history constantly ²(PRT), square R of reference point (Nplus-1) PRT Bistatic SAR system oblique distance history constantly ²((Nplus-1) PRT), PRT are that slow time sampling interval provides by radar system, for known.

Step 2, echoed signal distance are to compression

With the echoed signal s in the step 1 (t, t _a) carry out traditional Fast Fourier Transform (FFT) in the fast time after, carry out again traditional gauged distance compression and process, obtain distance after the compression apart from frequency domain echo signal S ₁(f, t _a), wherein, t is the fast time, t _aBe the slow time, f is the frequency corresponding to the fast time.

The orientation of step 3, echoed signal is to Fourier transform

To the distance that obtains in the step 2 after the compression apart from frequency domain echo signal S ₁(f, t _a) do traditional Fast Fourier Transform (FFT) in the slow time, then obtain the 2-d spectrum S of echoed signal ₁(f, f _a), wherein, t _aBe slow time, f _aBe the frequency corresponding to the slow time, f is the frequency corresponding to the fast time;

Step 4, find the solution the single basic 2-d spectrum S of reference point class ₀(f, f _a)

The definition reference point is the target's center's point in the observation scene, the single basic 2-d spectrum S of reference point class ₀(f, f _a) be to be obtained by the spectral method (formula (1)) based on the single basic mode type of the class of LS:

$S_0(f,f_a)=\exp (-j4\mathrm{\π}{R}_{\mathrm{Mref}}\sqrt{{\left(\frac{f+F_0}{C}\right)}^2-{\left(\frac{f_a}{{2V}_{\mathrm{ref}}}\right)}^2}-j2\mathrm{\π}{f}_a{T}_{\mathrm{Mref}})---\left(1\right)$

Wherein, f is the frequency corresponding to the fast time, f _aThe frequency corresponding to the slow time, F ₀Be the centre frequency that transmits, C represents light velocity size, and j represents-1 square root, R _MrefBe the basic oblique distance history of the list of reference point equivalence, T _MrefBe zero Doppler's moment of single base of reference point equivalence, V _RefSingle base movement velocity for the reference point equivalence.

The basic oblique distance history of the list of reference point equivalence R _Mref, be to utilize formula (2) to obtain:

$R_{\mathrm{Mref}}=\sqrt{a_0-\frac{{a_1}^2}{4a_2}}---\left(2\right)$

Single base zero Doppler of reference point equivalence is T constantly _MrefTo utilize formula (3) to obtain:

$T_{\mathrm{Mref}}=-\frac{a_1}{2a_2}---\left(3\right)$

Single base movement velocity V of reference point equivalence _RefTo utilize formula (4) to obtain:

$V_{\mathrm{ref}}=\sqrt{a_2}---\left(4\right)$

In formula (2), (3), (4), a ₀, a ₁, a ₂Be the optimum solution of finding the solution based on the single basic mode type of the class of least square method (LS), they satisfy formula (5)

$[a_0,a_1,a_2]=\stackrel{\‾}{R}{\stackrel{\‾}{T}}_a^H{\left({\stackrel{\‾}{T}}_a{\stackrel{\‾}{T}}_a^H\right)}^{-1}---\left(5\right)$

In formula (5),

Each of slow time of reference point constantly corresponding Bistatic SAR system oblique distance history square matrix To utilize formula (6) to obtain:

$\stackrel{\‾}{R}=[\frac{R^2\left(0\right)}{4},\frac{R^2\left(\mathrm{PRT}\right)}{4},\·\·\·,\frac{R^2\left((\mathrm{Nplus}-1)\mathrm{PRT}\right)}{4}]---\left(6\right)$

In the formula (6), R ²(0) be reference point the 0th Bistatic SAR system oblique distance history constantly that provides of step 1 square, R ²(PRT) be the reference point PRT that provides of step 1 Bistatic SAR system oblique distance history constantly square, R ²((Nplus-1) PRT) be reference point (Nplus-1) PRT that provides of step 1 Bistatic SAR system oblique distance history constantly square, PRT is the slow time sampling interval that step 1 provides; Nplus counts for the slow time-sampling that step 1 provides.

Slow time parameter matrix To utilize formula (7) to obtain:

${\stackrel{\‾}{T}}_a=\left[\begin{array}{c}\mathrm{1,1},\·\·\·,1\\ 0,\mathrm{PRT},\·\·\·(\mathrm{Nplus}-1)\mathrm{PRT}\\ 0,{\mathrm{PRT}}^2,\·\·\·{\left((\mathrm{Nplus}-1)\mathrm{PRT}\right)}^2\end{array}\right]---\left(7\right)$

In formula (5), Represent slow time parameter matrix

Transpose conjugate;

Expression is found the solution

Contrary.

Step 5, reference point phase compensation

2-d spectrum S with the echoed signal that obtains in the step 3 ₁(f, f _a) with step 4 in the single basic 2-d spectrum S of the reference point class that obtains ₀(f, f _a) complex conjugate Pointwise is multiplied each other, and obtains the 2-d spectrum S of reference point phase compensation echoed signal afterwards ₂(f, f _a), as shown in Equation (8)

$S_2(f,f_a)=S_1(f,f_a)\×S_0^{*}(f,f_a)---\left(8\right)$

In the formula (8),

That reference point is based on the single basic 2-d spectrum S of the class of LS ₀(f, f _a) complex conjugate, S ₀(f, f _a) be the single basic 2-d spectrum of reference point class, S ₁(f, f _a) be the 2-d spectrum that step 3 provides echoed signal, reference point is the target's center's point in the observation scene, f is the frequency corresponding to the fast time, f _aIt is the frequency corresponding to the slow time.

Step 6, non-reference target point Phase Equivalent

Formula (8) in formula from step 4 (1) and the step 5 obtains conclusion: the 2-d spectrum S of the echoed signal after the reference point phase compensation ₂(f, f _a) comprise coupling terms

2-d spectrum S with the echoed signal after the reference point phase compensation that obtains in the step 5 ₂(f, f _a) middle coupling terms $\sqrt{\frac{{(f+F_0)}^2}{C^2}-\frac{{f_a}^2}{{4V}_{\mathrm{ref}}^2}}$ Equivalence is $\frac{F_0+f^{\′}}{C},$ Even

$\sqrt{\frac{{(f+F_0)}^2}{C^2}-\frac{{f_a}^2}{{4V}_{\mathrm{ref}}^2}}=\frac{F_0+f^{\′}}{C}---\left(9\right)$

In the formula (9), f' is the equivalent frequency corresponding to the fast time, and f is the frequency corresponding to the fast time, f _aThe frequency corresponding to the slow time, F ₀Be the centre frequency that transmits, C represents light velocity size, V _RefSingle base movement velocity for the reference point equivalence; Solve equivalent frequency f ' corresponding to the fast time by formula (9).

2-d spectrum S with the echoed signal after the reference point phase compensation that obtains in the step 5 ₂(f, f _a) project on the equivalent frequency f ' corresponding to the fast time, obtain the 2-d spectrum S of equivalent frequency domain ₃(f ', f _a), as shown in Equation (10):

$S_3(f^{\′},f_a)=\exp (-j4\mathrm{\π\Δ}{R}_M\left(\frac{f^{\′}+F_0}{C}\right)-j2\mathrm{\π}{f}_a\mathrm{\Δ}{T}_M)---\left(10\right)$

In the formula (10), f' is the equivalent frequency corresponding to the fast time, and C represents light velocity size, f _aExpression is corresponding to the frequency of slow time, Δ R _MPoor for the shortest oblique distance history of equivalent Dan Ji of non-reference point and reference point, definition Δ R _M=R _Mno-R _Mref, R _MnoThe shortest oblique distance history of non-reference point equivalence Dan Ji, R _MrefThe shortest oblique distance history of reference point equivalence Dan Ji, Δ T _MBe constantly poor of single base zero Doppler of the equivalence of non-reference point and reference point, Δ T _M=T _Mno-T _Mref, T _MnoThe shortest oblique distance history of non-reference point equivalence Dan Ji, T _MrefBe the shortest oblique distance history of reference point equivalence Dan Ji, reference point is the target's center's point in the observation scene, and non-reference point is to remove other impact points of target's center's point in the observation scene;

Step 7, two-dimentional nonuniform fast Fourier transform

To obtaining the 2-d spectrum S of equivalent frequency domain in the step 6 ₃(f', f _a), utilize formula (11) to do two-dimentional nonuniform fast Fourier transform, then realize and will obtain the 2-d spectrum S of equivalent frequency domain in the step 6 ₃(f', f _a) transform to oblique distance history image area-orientation in image area, NUFFT (S ₃(f ', f _a))=∫ ∫ S ₃(f ', f _a) exp (j2 π f ' t-j2 π f _at _a) df ' df _a(11)

In the formula (11), f' is corresponding equivalent frequency of fast time,

f _aExpression is corresponding to the frequency of slow time, and f represents the frequency corresponding to the fast time, V _RefBe the single base of reference point equivalence movement velocity, F ₀Be the centre frequency that transmits, C represents light velocity size.

Process the observation area echo data s (t, the t that receive from the double-base synthetic aperture radar system through above-mentioned steps _a) in obtain the target imaging result with high-resolution.

Ultimate principle of the present invention is by least square method the two radical sign problems in the double-basis oblique distance history to be converted to single number, therefore simplify and find the solution, thereby obtain the analytical expression of the 2-d spectrum of system, and utilize the thought of omega-k algorithm, according to the expression formula of 2-d spectrum, obtain the two-dimentional STOLT relation of system, at last by study two-dimensional STOLT relation, utilize two-dimentional Nonuniform fast Fourier transform to be similar to two-dimentional STOLT interpolation, to finish the imaging to this system.

Innovative point of the present invention is that the two radical sign oblique distance histories equivalence with double-basis is the single oblique distance history of similar Dan Ji, thereby obtain the analytical expression of the 2-d spectrum of system, simplified the Solve problems of bistatic pair of radical sign, therefore can obtain simply bistatic 2-d spectrum, take full advantage of ripe single base formation method, such as omega-K (wk) algorithm, range Doppler algorithm (RD algorithm), expression formula according to 2-d spectrum, obtain the two-dimentional STOLT relation of system, by study two-dimensional STOLT relation, utilize two-dimentional Nonuniform fast Fourier transform to be similar to two-dimentional STOLT interpolation, to finish the imaging to this system at last.Thereby reduce to a great extent the complexity of bistatic imaging algorithm, for follow-up imaging processing is provided convenience.

Advantage of the present invention mainly is to carry out equivalence for two radical sign problems that oblique distance history in the double-base SAR exists, and finds the solution the 2-d spectrum expression formula thereby simplified, and has effectively utilized the thought of single base imaging algorithm; Can analyze by the analytical expression of 2-d spectrum and to obtain STOLT mapping relations and approximate processing way thereof, the large and high problem of complexity of the operand of having avoided two-dimentional STOLT interpolation to bring.Thereby reduce to a great extent the complexity of bistatic imaging algorithm, for follow-up imaging processing is provided convenience.

Description of drawings

Fig. 1 is the double-base synthetic aperture radar flight geometric relationship figure that the specific embodiment of the invention adopts

Wherein, P _tExpress the flight path of flat pad, P _rExpress the flight path of receiving platform,

The movement velocity vector of expression flat pad,

The movement velocity vector of expression receiving platform; O represents to observe the reference point in the scene; X, Y, Z represent the scene coordinate axis.

The radar beam of expression flat pad points to vector,

The radar beam of expression receiving platform points to vector, A ₀Reference point in the expression observation scene, A ₁, A ₂..., A ₁₄14 non-reference point in the expression observation scene.

Fig. 2 is workflow block diagram of the present invention

Fig. 3 is the result schematic diagram after the double-base SAR echo data is processed through step 3 of the present invention ~ step 6

Wherein, transverse axis is expressed as the fast time, and the longitudinal axis is expressed as slow time A ₀Reference point in the expression observation scene, A ₁, A ₂..., A ₁₄14 non-reference point in the expression observation scene.

Fig. 4 is the result schematic diagram after the double-base SAR echo data is processed through step 1 of the present invention ~ step 8

Wherein, transverse axis is expressed as the fast time, and the longitudinal axis is expressed as slow time, A ₀Reference point in the expression observation scene, A ₁, A ₂..., A ₁₄14 non-reference point in the expression observation scene.

The double-base SAR system platform parameter of Fig. 5 for adopting in this experiment enforcement

Embodiment

The present invention mainly adopts the method for emulation experiment to verify the feasibility of this scheme, and institute in steps, conclusion is all correct in MATLAB7.0 checking.

Present embodiment adopts the parallel in the same way flight of transmit-receive platform, and the antenna beam speed of two platforms is respectively the 2100(metre per second (m/s)) and the 700(metre per second (m/s)).The centre frequency that transmits is 9.65GHz, and the pulse multiplicity is 2500Hz, and wide when transmitting is the 2(microsecond).The X-axis total length of observation area is 1000 meters, and the Y-axis total length is 200 meters, whole observation area 15 reflection spots that distributing, and the distance of adjacent two points is 250 meters to gap, the orientation is 100 meters to gap.Reference point A ₀Coordinate be (0,700).

The implementation step is as follows:

Step 1, the bistatic echoed signal of initialization

Use double-base SAR system parameter shown in Figure 5, emulation obtains the double-base SAR echo signal data s (t, the t that deposit with 1799 row, 1024 columns value matrixs _a); Each row of data is deposited is sampled data to fast time echoed signal, and every column data is deposited is sampled data to slow time echoed signal;

Step 2, echoed signal distance are to compression

S (t, t that step 1 is obtained _a) do the conventional fast Fourier transform of fast time and obtain (f, t apart from frequency domain S _a), with s emission signal s ₀(t) as the reference signal of Range compress, then reference signal is carried out distance and obtain apart from frequency domain S to Fourier transform ₀(f), with S (f, t _a) and S ₀(f) after multiplying each other line by line, conjugate multiplication obtains apart from the echoed signal S after compression ₁(f, t _a), thereby the distance of realization echoed signal is to compression;

The orientation of step 3, echoed signal is to Fourier transform

The echoed signal S of the distance that step 2 is obtained after the compression ₁(f, t _a) do the conventional fast Fourier transform of slow time, then obtain the 2-d spectrum S of echoed signal ₁(f, f _a);

Step 4, reference point phase compensation

Being chosen to image field scape central point is reference point target, utilizes formula in the definition (3): $T_{s0}=\frac{y-Y_{S0}}{V_t},$ $R_{s0}=\sqrt{{(X_{S0}-x)}^2+H_S^2},$ $T_{r0}=\frac{y-Y_{r0}}{V_r}$ With $R_{r0}=\sqrt{{(X_{r0}-x)}^2+H_r^2}$ Two platforms are respectively R with respect to the shortest oblique distance history of reference point _S0=627.48 (km) and R _R0=3 (kms), two platforms are T with respect to the nearest time point of reference point _S0=1.0504 (second) and T _R0=0.7375 (second), can be in the hope of the optimum solution a based on least square method according to definition (5) ₀=1.0045 * 10 ¹¹, a ₁=-5.8585 * 10 ⁷, a ₂=1.4645 * 10 ⁷, recycle formula (2) ~ (4), obtain the basic oblique distance history of the list R of reference point equivalence _Mref=346.85 (kms), single base zero Doppler's time T of reference point equivalence _Mref=2.001 (seconds), the basic movement velocity V of the list of reference point equivalence _Ref=3.8269 (km per seconds), according to defining (6):

$S(f,f_a)=\exp \{-j4\mathrm{\π}{R}_{\mathrm{ref}}\sqrt{\frac{{(f+F_0)}^2}{C^2}-\frac{{\left(f_a\right)}^2}{{4V}^2}}-j2\mathrm{\π}{f}_a{T}_M\},$ Obtain the 2-d spectrum S based on the class Dan Ji of LS of reference point ₀(f, f _a), with its complex conjugate 2-d spectrum S with echoed signal ₁(f, f _a) pointwise multiplies each other and obtain 2-d spectrum S after the reference point phase compensation ₂(f, f _a).With S ₂(f, f _a) by two-dimentional inverse Fourier transform to showing preliminary imaging results to the territory apart from history territory-orientation.Result as shown in Figure 4;

Step 5, non-reference target point Phase Equivalent

With reference to the 2-d spectrum S after the phase compensation ₂(f, f _a) in coupling terms

Equivalence is F _c+ f' is with S ₂(f, f _a) projected to new frequency field f ', obtain the 2-d spectrum S of equivalent frequency domain ₃(f', f _a);

Step 6, two-dimentional nonuniform fast Fourier transform

2-d spectrum S to the equivalent frequency domain that obtains in the step 5 ₃(f', f _a), utilize formula (11): NUFFT (S ₃(f ', f _a))=∫ ∫ S ₃(f ', f _a) exp (j2 π f ' t-j2 π f _at _a) df ' df _a, do two-dimentional nonuniform fast Fourier transform, obtain

Then convert the signal into oblique distance history image area-orientation to image area, result as shown in Figure 5;

Step 7, imaging results show

We are with in the step 6

Obtain X-Y scheme by traditional Matlab drawing practice; The present invention uses MATLAB's " contour " function for obtaining isocontour two-dimensional imaging result.

Through the processing of above-mentioned steps, just can from the double-base SAR echo data, obtain the scene image of existing high-resolution.

Emulation and test by specific embodiments of the present invention, imaging scheme provided by the present invention can realize the Bistatic SAR imaging, not only simplify the expression formula of finding the solution of double-base SAR 2-d spectrum, and take full advantage of mature single base imaging algorithm, also obtained simultaneously high-quality imaging results.

Claims (1)

1. method based on the double-base synthetic aperture radar imaging of the single base equivalence of class is characterized in that it may further comprise the steps:

Step 1, the bistatic echoed signal of initialization

Bistatic Forward-Looking SAR System parameter is as follows: the transmit-receive platform initial position, note is P respectively _S0(X _S0, Y _S0, H _s) and P _R0(X _R0, Y _R0, H _r), wherein, X _S0The initial position of expression flat pad on X-axis, Y _S0The initial position of expression flat pad on Y-axis, H _sThe initial position of expression flat pad on Z axis; X _R0The initial position of expression receiving platform on X-axis, Y _R0The initial position of expression receiving platform on Y-axis, H _rThe initial position of expression receiving platform on Z axis; V _S(0, v _S, 0) and expression flat pad velocity, V _R(0, v _R, 0) and expression receiving platform velocity, wherein, v _SThe value of expression flat pad speed on Y-axis, v _RThe value of expression receiving platform speed on Y-axis; Radar emission linear FM signal, the frequency of its CF signal are F ₀, the pulse repetition time is PRF, wide T when exomonental, exomonental chirp rate K, exomonental bandwidth B, echo bearing is to sampling number Nplus, the sampling number N that the echo distance makes progress, wherein Nplus and N are positive integer, the sample frequency F that distance makes progress.The distance of observation scene is R rice to total length, and the orientation is Z rice to total length.Bistatic Forward-Looking SAR System parameter is known;

Echo data s (t, t _a) be a data matrix that Nplus is capable and N is listed as, the each row of data of echo data matrix is the echoed signal sampled data of fast time, every column data is the echo samples data of slow time.Reference point is the target's center's point in the observation scene, square R of reference point the 0th Bistatic SAR system oblique distance history constantly ²(0), square R of reference point PRT Bistatic SAR system oblique distance history constantly ²(PRT), square R of reference point (Nplus-1) PRT Bistatic SAR system oblique distance history constantly ²((Nplus-1) PRT), PRT are that slow time sampling interval provides by radar system, for known.

Step 2, echoed signal distance are to compression

With the echoed signal s in the step 1 (t, t _a) carry out traditional Fast Fourier Transform (FFT) in the fast time after, carry out again traditional gauged distance compression and process, obtain distance after the compression apart from frequency domain echo signal S ₁(f, t _a), wherein, t is the fast time, t _aBe the slow time, f is the frequency corresponding to the fast time.

The orientation of step 3, echoed signal is to Fourier transform

To the distance that obtains in the step 2 after the compression apart from frequency domain echo signal S ₁(f, t _a) do traditional Fast Fourier Transform (FFT) in the slow time, then obtain the 2-d spectrum S of echoed signal ₁(f, f _a), wherein, t _aBe slow time, f _aBe the frequency corresponding to the slow time, f is the frequency corresponding to the fast time;

Step 4, find the solution the single basic 2-d spectrum S of reference point class ₀(f, f _a)

The definition reference point is the target's center's point in the observation scene, the single basic 2-d spectrum S of reference point class ₀(f, f _a) be to be obtained by the spectral method (formula (1)) based on the single basic mode type of the class of LS:

$S_0(f,f_a)=\exp (-j4\mathrm{\π}{R}_{\mathrm{Mref}}\sqrt{{\left(\frac{f+F_0}{C}\right)}^2-{\left(\frac{f_a}{{2V}_{\mathrm{ref}}}\right)}^2}-j2\mathrm{\π}{f}_a{T}_{\mathrm{Mref}})---\left(1\right)$

Wherein, f is the frequency corresponding to the fast time, f _aThe frequency corresponding to the slow time, F ₀Be the centre frequency that transmits, C represents light velocity size, and j represents-1 square root, R _MrefBe the basic oblique distance history of the list of reference point equivalence, T _MrefBe zero Doppler's moment of single base of reference point equivalence, V _RefSingle base movement velocity for the reference point equivalence.

The basic oblique distance history of the list of reference point equivalence R _Mref, be to utilize formula (2) to obtain:

$R_{\mathrm{Mref}}=\sqrt{a_0-\frac{{a_1}^2}{4a_2}}---\left(2\right)$

Single base zero Doppler of reference point equivalence is T constantly _MrefTo utilize formula (3) to obtain:

$T_{\mathrm{Mref}}=-\frac{a_1}{2a_2}---\left(3\right)$

Single base movement velocity V of reference point equivalence _RefTo utilize formula (4) to obtain:

$V_{\mathrm{ref}}=\sqrt{a_2}---\left(4\right)$

In formula (2), (3), (4), a ₀, a ₁, a ₂Be the optimum solution of finding the solution based on the single basic mode type of the class of least square method (LS), they satisfy formula (5)

$[a_0,a_1,a_2]=\stackrel{\‾}{R}{\stackrel{\‾}{T}}_a^H{\left({\stackrel{\‾}{T}}_a{\stackrel{\‾}{T}}_a^H\right)}^{-1}---\left(5\right)$

In formula (5),

Each of slow time of reference point constantly corresponding Bistatic SAR system oblique distance history square matrix To utilize formula (6) to obtain:

$\stackrel{\‾}{R}=[\frac{R^2\left(0\right)}{4},\frac{R^2\left(\mathrm{PRT}\right)}{4},\·\·\·,\frac{R^2\left((\mathrm{Nplus}-1)\mathrm{PRT}\right)}{4}]---\left(6\right)$

In the formula (6), R ²(0) be reference point the 0th Bistatic SAR system oblique distance history constantly that provides of step 1 square, R ²(PRT) be the reference point PRT that provides of step 1 Bistatic SAR system oblique distance history constantly square, R ²((Nplus-1) PRT) be reference point (Nplus-1) PRT that provides of step 1 Bistatic SAR system oblique distance history constantly square, PRT is the slow time sampling interval that step 1 provides; Nplus counts for the slow time-sampling that step 1 provides.

Slow time parameter matrix

To utilize formula (7) to obtain:

${\stackrel{\‾}{T}}_a=\left[\begin{array}{c}\mathrm{1,1},\·\·\·,1\\ 0,\mathrm{PRT},\·\·\·(\mathrm{Nplus}-1)\mathrm{PRT}\\ 0,{\mathrm{PRT}}^2,\·\·\·{\left((\mathrm{Nplus}-1)\mathrm{PRT}\right)}^2\end{array}\right]---\left(7\right)$

In formula (5),

Represent slow time parameter matrix

Transpose conjugate; Expression is found the solution Contrary.

Step 5, reference point phase compensation

2-d spectrum S with the echoed signal that obtains in the step 3 ₁(f, f _a) with step 4 in the single basic 2-d spectrum S of the reference point class that obtains ₀(f, f _a) complex conjugate

Pointwise is multiplied each other, and obtains the 2-d spectrum S of reference point phase compensation echoed signal afterwards ₂(f, f _a), as shown in Equation (8)

$S_2(f,f_a)=S_1(f,f_a)\×S_0^{*}(f,f_a)---\left(8\right)$

In the formula (8),

That reference point is based on the single basic 2-d spectrum S of the class of LS ₀(f, f _a) complex conjugate, S ₀(f, f _a) be the single basic 2-d spectrum of reference point class, S ₁(f, f _a) be the 2-d spectrum that step 3 provides echoed signal, reference point is the target's center's point in the observation scene, f is the frequency corresponding to the fast time, f _aIt is the frequency corresponding to the slow time.

Step 6, non-reference target point Phase Equivalent

Formula (8) in formula from step 4 (1) and the step 5 obtains conclusion: the 2-d spectrum S of the echoed signal after the reference point phase compensation ₂(f, f _a) comprise coupling terms

2-d spectrum S with the echoed signal after the reference point phase compensation that obtains in the step 5 ₂(f, f _a) middle coupling terms $\sqrt{\frac{{(f+F_0)}^2}{C^2}-\frac{{f_a}^2}{{4V}_{\mathrm{ref}}^2}}$ Equivalence is $\frac{F_0+f^{\′}}{C},$ Even

$\sqrt{\frac{{(f+F_0)}^2}{C^2}-\frac{{f_a}^2}{{4V}_{\mathrm{ref}}^2}}=\frac{F_0+f^{\′}}{C}---\left(9\right)$

In the formula (9), f' is the equivalent frequency corresponding to the fast time, and f is the frequency corresponding to the fast time, f _aThe frequency corresponding to the slow time, F ₀Be the centre frequency that transmits, C represents light velocity size, V _RefSingle base movement velocity for the reference point equivalence; Solve equivalent frequency f ' corresponding to the fast time by formula (9).

2-d spectrum S with the echoed signal after the reference point phase compensation that obtains in the step 5 ₂(f, f _a) project on the equivalent frequency f ' corresponding to the fast time, obtain the 2-d spectrum S of equivalent frequency domain ₃(f ', f _a), as shown in Equation (10):

$S_3(f^{\′},f_a)=\exp (-j4\mathrm{\π\Δ}{R}_M\left(\frac{f^{\′}+F_0}{C}\right)-j2\mathrm{\π}{f}_a\mathrm{\Δ}{T}_M)---\left(10\right)$

In the formula (10), f' is the equivalent frequency corresponding to the fast time, and C represents light velocity size, f _aExpression is corresponding to the frequency of slow time, Δ R _MPoor for the shortest oblique distance history of equivalent Dan Ji of non-reference point and reference point, definition Δ R _M=R _Mno-R _Mref, R _MnoThe shortest oblique distance history of non-reference point equivalence Dan Ji, R _MrefThe shortest oblique distance history of reference point equivalence Dan Ji, Δ T _MBe constantly poor of single base zero Doppler of the equivalence of non-reference point and reference point, Δ T _M=T _Mno-T _Mref, T _MnoThe shortest oblique distance history of non-reference point equivalence Dan Ji, T _MrefBe the shortest oblique distance history of reference point equivalence Dan Ji, reference point is the target's center's point in the observation scene, and non-reference point is to remove other impact points of target's center's point in the observation scene;

Step 7, two-dimentional nonuniform fast Fourier transform

To obtaining the 2-d spectrum S of equivalent frequency domain in the step 6 ₃(f', f _a), utilize formula (11) to do two-dimentional nonuniform fast Fourier transform, then realize and will obtain the 2-d spectrum S of equivalent frequency domain in the step 6 ₃(f', f _a) transform to oblique distance history image area-orientation in image area, NUFFT (S ₃(f ', f _a))=∫ ∫ S ₃(f ', f _a) exp (j2 π f ' t-j2 π f _at _a) df ' df _a(11)

In the formula (11), f' is corresponding equivalent frequency of fast time,

f _aExpression is corresponding to the frequency of slow time, and f represents the frequency corresponding to the fast time, V _RefBe the single base of reference point equivalence movement velocity, F ₀Be the centre frequency that transmits, C represents light velocity size.

Process the observation area echo data s (t, the t that receive from the double-base synthetic aperture radar system through above-mentioned steps _a) in obtain the target imaging result with high-resolution.

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