CN103487808B - A kind of track Simulation method of variable element locking mode missile-borne Spotlight SAR Imaging - Google Patents

Abstract

The invention discloses a kind of variable element locking mode missile-borne Spotlight SAR Imaging track Simulation method, comprise step one, determine four coordinate systems of employing in emulating, step 2, obtain the transformed matrix that coordinate system asks, step 3, setting radar system fundamental simulation parameter, step 4, utilize runge kutta method to emulate to obtain body at flight path plane coordinate system E _min thick emulation flight path coordinates matrix, step 5, to obtain in the synthetic aperture time SAR at earth rotation coordinate system E _gin thick emulation flight path coordinates matrix, step 6, obtain accurately body emulation flight path.The present invention proposes a kind of locking mode of operation of variable element missile-borne Spotlight SAR Imaging, the distinctive fixed strabismus angle of this pattern is that body guidance is provided convenience.

Description

A kind of track Simulation method of variable element locking mode missile-borne Spotlight SAR Imaging

Technical field

The present invention relates to synthetic-aperture radar (Synthetic Aperture Radar is called for short SAR) technical field, specifically say, refer to a kind of track Simulation method of variable element locking mode missile-borne Spotlight SAR Imaging.

Background technology

Synthetic-aperture radar is that a kind of signal analysis technology that relies on builds equivalent vast of heaven line, to obtain beam elevation upwards high-resolution round-the-clock two-dimensional imaging radar.The beam bunching mode synthetic-aperture radar of variable element system is for the high precision mapping of large stravismus zonule, the application demand of investigation and proposing, its by adjust carrier frequency of SAR system, frequency modulation rate, pulse width, sampling rate and pulse repeat to ask every, be provided with following advantage: compared to the SAR system of the constant parameter of routine, variable element SAR has the imaging processing flow process more simplified, higher image processing speed, the space availability ratio of data in higher SAR data storer, thus total amount of data is reduced, the volume of transmitted data that reduction SAR and ground base station are asked.

Variable element system SAR is particularly applicable to being applied in Missile-borne SAR guidance.In Missile-borne SAR guidance task, SAR often needs to work in large stravismus or super large strabismus mode.Different and airborne or satellite-borne SAR, for evading interception, the movement locus of Missile-borne SAR is not straight line usually, under missile-borne locking beam bunching mode, the direction of motion of body with play angle that order oblique distance asks in imaging process, need to be maintained a fixing angle, the flight path plane of body also no longer with ground level keeping parallelism.This demand is the difficulties in the track Simulation of variable element locking mode missile-borne Spotlight SAR Imaging.

Summary of the invention

The object of the invention is to solve the problem to solve, for variable element locking mode missile-borne Spotlight SAR Imaging, proposing a kind of track Simulation method.The flight path of setting body is restrained in three-dimensional single plane, angle is being locked according to known, fourth-order Runge-Kutta method is adopted to generate the flight path of thick emulation, and then according to the sampling location of the accurate flight path of variable element SAR system design Missile-borne SAR, utilize the method for interpolation to generate the flight path of body emulation accurately.

A kind of variable element locking mode missile-borne Spotlight SAR Imaging track Simulation method of the present invention, comprises following step:

Step one, determine emulate in adopt four coordinate systems: earth rotation coordinate system E _g, imaging scene coordinate system E _s, direction of visual lines polar coordinate system E _lwith body flight path plane coordinate system E _m.

In step 2, determining step one, four coordinate systems ask the method for transformation of coordinate, obtain the transformed matrix that coordinate system is asked.

Step 3, setting radar system fundamental simulation parameter, determine the accumulation corner Δ θ of SAR in the synthetic aperture time, determine the quantity N of the sampling pulse launched along flight path direction SAR _a.

The time step t of step 4, the emulation of setting runge kutta method _h.Utilize runge kutta method to emulate and obtain body at flight path plane coordinate system E _min thick emulation flight path coordinates matrix.

Step 5, integrating step four and the result in step 2, to obtain in the synthetic aperture time SAR at earth rotation coordinate system E after coordinate transformation _gin thick emulation flight path coordinates matrix.

Step 6, in conjunction with variable element SAR system design interpolation method, interpolation is carried out to the thick emulation flight path obtained in step 5, obtain the flight path of body emulation accurately.

The invention has the advantages that:

(1) propose a kind of locking mode of operation of variable element missile-borne Spotlight SAR Imaging, the distinctive fixed strabismus angle of this pattern is that body guidance is provided convenience;

(2) utilize runge kutta method to carry out the recursion calculation of body flight path, carry out interpolation processing in conjunction with variable element system, obtain the accurate flight path of locking mode missile-borne Spotlight SAR Imaging;

(3) this method is applicable to the body track Simulation of single flight path plane, and imaging scene center can not be arctic point.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention;

Fig. 2 is the schematic diagram of four coordinate systems of the present invention;

Fig. 3 is along orientation to the schematic diagram data be spacedly distributed in wavenumber domain of the present invention;

Fig. 4 is the flight path schematic diagram of gained body of the present invention under earth rotation coordinate system.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The present invention is a kind of track Simulation method of variable element locking mode missile-borne Spotlight SAR Imaging, and process flow diagram as shown in Figure 1, comprises following step:

Step one, determine emulate in adopt four coordinate systems: earth rotation coordinate system E _g, imaging scene coordinate system E _s, direction of visual lines polar coordinate system E _lwith body flight path plane coordinate system E _m, four coordinate systems as shown in Figure 2.Be specially:

Set with the earth tangent plane of scene center formation as the flight path plane of L, SAR is for P.

(1) earth rotation coordinate system E _g

True origin: the earth's core is designated as O _g;

X-axis is designated as X _g: under the line in plane, point to zero degree warp direction;

Y-axis is designated as Y _g: under the line in plane, point to east longitude 90 degree of warp directions;

Z axis is designated as Z _g: along earth's axis, point to the positive arctic (north latitude 90 degree of directions).

(2) imaging scene coordinate system E _s

True origin: scene center is designated as O _s;

X-axis is designated as X _s: in plane L, point to the east of scene;

Y-axis is designated as Y _s: in plane L, point to the north of scene;

Z axis is designated as Z _s: cross scene central point, deviate from direction, the earth's core perpendicular to the earth tangent plane formed with scene center.

(3) the polar coordinate system E of direction of visual lines _l

True origin is designated as O _l: scene center;

X-axis is designated as X _l: in plane L, with Y _laxle, Z _laxle forms right-handed coordinate system;

Y-axis is designated as Y _l: in plane L, point to SAR sensor along the projection of synthetic aperture central instant oblique distance in this plane;

Z axis is designated as Z _l: cross scene central point, deviate from direction, the earth's core perpendicular to the earth tangent plane formed with scene center.

(4) body flight path plane coordinate system E _m

True origin is designated as O _m: scene center;

X-axis is designated as X _m: in body flight path plane, with Y _maxle, Z _maxle forms right-handed coordinate system;

Y-axis is designated as Y _m: in body flight path plane, point to the direction of target and SAR sensor;

Z axis is designated as Z _m: deviate from direction, the earth's core, directed in orthogonal is in the direction of body flight path plane P.

In step 2, determining step one, four coordinate systems ask the method for transformation of coordinate, obtain the transformed matrix that coordinate system is asked.

If SAR is at earth rotation coordinate system E _gin synthetic aperture central instant (be designated as t ₀) coordinate is (x _g0, y _g0, z _g0), at imaging scene coordinate system E _smiddle t ₀the coordinate in moment is (x _s0, y _s0, z _s0), scene center is at E _gcoordinate (x in coordinate system _p, y _p, z _p).Certain moment SAR is at earth rotation coordinate system E _gin coordinate be (x _g, y _g, z _g), SAR is at imaging scene coordinate system E in the same time _sin coordinate be (x _s, y _s, z _s), at the polar coordinate system E of direction of visual lines _lin coordinate be (x _l, y _l, z _l), at body flight path plane coordinate system E _min coordinate be (x _m, y _m, z _m).

(1) imaging scene coordinate system E is obtained _sto earth rotation coordinate system E _gtransition matrix A _sg, earth rotation coordinate system E _gto imaging scene coordinate system E _stransition matrix A _gs.

The longitude φ of SAR at synthetic aperture central instant is obtained according to formula (1) and formula (2) _lowith latitude φ _la:

${\mathrm{\φ}}_{l0}=\arctan \left(\frac{y_{g0}}{x_{g0}}\right)---\left(1\right)$

${\mathrm{\φ}}_{\mathrm{la}}=\arctan \left(\frac{z_{g0}}{\sqrt{x_{g0}^2+y_{g0}^2}}\right)---\left(2\right)$

A _sgmeet the relation that formula (3) represents, can A be obtained according to formula (4) _sg

$\left[\begin{array}{ccc}{x}_g& y_g& z_g\end{array}\right]=\left[\begin{array}{ccc}{x}_s& y_s& z_s+\sqrt{x_{g0}^2+y_{g0}^2+z_{g0}^2}\end{array}\right]A_{\mathrm{sg}}---\left(3\right)$

$A_{\mathrm{sg}}=\left[\begin{array}{ccc}\sin {\mathrm{\φ}}_{\mathrm{la}}& 0& \cos {\mathrm{\φ}}_{\mathrm{la}}\\ 0& 1& 0\\ -\cos {\mathrm{\φ}}_{\mathrm{la}}& 0& \sin {\mathrm{\φ}}_{\mathrm{la}}\end{array}\right]\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_{\mathrm{lo}}& -\sin {\mathrm{\φ}}_{\mathrm{lo}}& 0\\ \sin {\mathrm{\φ}}_{\mathrm{lo}}& \cos {\mathrm{\φ}}_{\mathrm{lo}}& 0\\ 0& 0& 1\end{array}\right]---\left(4\right)$

A _sga is obtained through inversion operation _gs.

(2) imaging scene coordinate system E is obtained _sto the polar coordinate system E of direction of visual lines _ltransition matrix A _sl, the polar coordinate system E of direction of visual lines _lto imaging scene coordinate system E _stransition matrix A _ls.

Obtain synthetic aperture central instant SAR according to formula (5) and depart from imaging scene coordinate system E _sthe angle of Y direction is α, then

$\mathrm{\α}=\arctan \frac{x_{s0}}{y_{s0}}---\left(5\right)$

A _slmeet the relation that formula (6) represents, can A be obtained according to formula (7) _sl

[x _ly _lz _l]=[x _sy _sz _s]A _sl(6)

$A_{\mathrm{sl}}=\left[\begin{array}{ccc}\cos \mathrm{\α}& \sin \mathrm{\α}& 0\\ -\sin \mathrm{\α}& \cos \mathrm{\α}& 0\\ 0& 0& 1\end{array}\right]---\left(7\right)$

A _sla is obtained through inversion operation _ls.

(3) the polar coordinate system E of direction of visual lines is obtained _lto body flight path plane coordinate system E _mtransition matrix A _lm, body flight path plane coordinate system E _mto the polar coordinate system E of direction of visual lines _ltransition matrix A _ml.

Obtaining synthetic aperture central instant SAR to the incident angle of scene center according to formula (8) is β, then

$\mathrm{\β}=\arcsin \frac{\sqrt{x_{s0}^2+y_{s0}^2}}{\sqrt{x_{s0}^2+y_{s0}^2+z_{s0}^2}}---\left(8\right)$

Setting flight path plane P and plane L angle are γ, obtain flight path plane relative rotation angle Ω to be according to formula (9)

$\mathrm{\Ω}=\arccos \frac{\cos \mathrm{\γ}}{\sin \mathrm{\β}}---\left(9\right)$

A _lmmeet the relation that formula (10) represents, can A be obtained according to formula (11) _sl

$\left[\begin{array}{ccc}{x}_m& y_m& z_m\end{array}\right]=\left[\begin{array}{ccc}{x}_l& y_l& z_l\end{array}\right]A_{\mathrm{lm}}---\left(10\right)$

$A_{\mathrm{lm}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \sin \mathrm{\β}& \cos \mathrm{\β}\\ 0& -\cos \mathrm{\β}& \sin \mathrm{\β}\end{array}\right]\left[\begin{array}{ccc}\cos \mathrm{\Ω}& 0& -\sin \mathrm{\Ω}\\ 0& 1& 0\\ \sin \mathrm{\Ω}& 0& \cos \mathrm{\Ω}\end{array}\right]---\left(11\right)$

A _lma is obtained through inversion operation _ml.

Step 3, setting radar system fundamental simulation parameter, determine the accumulation corner Δ θ of SAR in the synthetic aperture time, determine the quantity N of the sampling pulse launched along flight path direction SAR _a.

(1) the reference carrier frequency f of radar system is set ₀, light velocity c, simulating scenes radius D, duration of pulse μ, ρ _a, ρ _rbe respectively azimuth resolution and the range resolution of system expection, obtaining according to formula (12) corner that in the synthetic aperture time, SAR accumulates in plane L is Δ θ, then

$\mathrm{\Δ\θ}=2\tan \frac{c}{4f_0{\mathrm{\ρ}}_a\sin \mathrm{\β}}---\left(12\right)$

(2) set function nextpow2 () as rreturn value be greater than independent variable minimum 2 the function of integer corresponding to integral number power, obtained the quantity N of the sampling pulse launched along flight path direction SAR by formula (13) _a

$N_a=2^{\mathrm{nextpow}2\left(\frac{3D}{{\mathrm{\ρ}}_a}\right)}---\left(13\right)$

The time step t of step 4, the emulation of setting runge kutta method _h.Utilize runge kutta method to emulate and obtain body at flight path plane coordinate system E _min sample coordinate matrix Posm.

(1) setting projectile flight speed is V, Texas tower velocity reversal and the locking angle θ played between order oblique distance, the time step t of runge kutta method emulation _h.If synthetic aperture initial time is t ₁, finish time is t ₂, t ₁< t ₀< t ₂, utilize runge kutta method to generate t ₀~ t ₂the thick emulation in moment slightly emulates flight path.If (x _f, y _f, 0) and be t _mmoment SAR is at body flight path plane coordinate system E _min coordinate, (x _1f, y _1f, 0) and be t _m+ t _hmoment SAR is at body flight path plane coordinate system E _min coordinate.If x _fy _finitial value be that synthetic aperture central instant SAR platform is at body flight path plane coordinate system E _min coordinate.Intermediate parameters k is calculated according to formula (14)-formula (18) _1xf, k _1yf, k _2xf, k _2yf, k _3xf, k _3yf, k _4xf, k _4yf.

$\left\{\begin{array}{c}{k}_{1\mathrm{xf}}=V\sin \left(\mathrm{arccot}\right|\frac{x_f}{y_f}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\\ k_{1\mathrm{yf}}=-V\cos \left(\mathrm{arccot}\right|\frac{x_f}{y_f}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\end{array}\right.---\left(14\right)$

$\left\{\begin{array}{c}{k}_{2\mathrm{xf}}=V\sin \left(\mathrm{arccot}\right|\frac{x_f+k_{1\mathrm{xf}}{t}_h/2}{y_f+k_{1\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\\ k_{2\mathrm{yf}}=-V\cos \left(\mathrm{arccot}\right|\frac{x_f+k_{1\mathrm{xf}}{t}_h/2}{y_f+k_{1\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\end{array}\right.---\left(15\right)$

$\left\{\begin{array}{c}{k}_{3\mathrm{xf}}=V\sin \left(\mathrm{arccot}\right|\frac{x_f+k_{2\mathrm{xf}}{t}_h/2}{y_f+k_{2\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\\ k_{3\mathrm{yf}}=-V\cos \left(\mathrm{arccot}\right|\frac{x_f+k_{2\mathrm{xf}}{t}_h/2}{y_f+k_{2\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\end{array}\right.---\left(16\right)$

$\left\{\begin{array}{c}{k}_{4\mathrm{xf}}=V\sin \left(\mathrm{arccot}\right|\frac{x_f+k_{3\mathrm{xf}}{t}_h/2}{y_f+k_{3\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\\ k_{4\mathrm{yf}}=-V\cos \left(\mathrm{arccot}\right|\frac{x_f+k_{3\mathrm{xf}}{t}_h/2}{y_f+k_{3\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\end{array}\right.---\left(17\right)$

$\left\{\begin{array}{c}{x}_{1f}=x_f+\frac{(k_{1\mathrm{xf}}+{2k}_{2\mathrm{xf}}+2k_{2\mathrm{xf}}+k_{4\mathrm{xf}})t_h}{6}\\ y_{1f}=y_f+\frac{(k_{1\mathrm{yf}}+2k_{2\mathrm{yf}}+2k_{2\mathrm{yf}}+k_{4\mathrm{yf}})t_h}{6}\end{array}\right.---\left(18\right)$

(2) repeat (1) of step 4, utilize runge kutta method to generate t ₁~ t ₀the thick emulation flight path of moment SAR is at body flight path plane coordinate system E _min coordinate.(1) and (2) of combining step four, to obtain in the synthetic aperture time SAR at body flight path plane coordinate system E _min thick emulation flight path coordinates matrix, be expressed as matrix Posm.

Step 5, integrating step four and the result in step 2, to obtain in the synthetic aperture time SAR at earth rotation coordinate system E after coordinate transformation _gin thick emulation flight path coordinates matrix.

Poss is that this flight path is at earth rotation coordinate system E _gin flight path coordinates matrix.In integrating step two, coordinate system transforms rule, obtains Poss according to formula (19)

Poss＝PosmA _mlA _lsA _sg(19)

Step 6, in conjunction with variable element SAR system design interpolation method, interpolation is carried out to the thick emulation flight path obtained in step 5, obtain the flight path of body emulation accurately.

Application claims SAR echo data at wavenumber domain along orientation to being spacedly distributed, as shown in Figure 3.Be located at imaging scene coordinate system E _sin, the angle sequence that SAR departs from Y-axis in plane L is Δ ε, then

$\mathrm{\&Delta;\&epsiv;}=\arctan \frac{2\tan \frac{\mathrm{\&Delta;\&theta;}}{2}}{N_a}i,i=-\frac{N_a}{2},...\frac{N_a}{2}.---\left(20\right)$

Flight path slightly can be emulated at imaging scene coordinate system E by matrix Poss _sin, the angle sequence that SAR departs from Y-axis in plane L is Δ ε ₀.With Δ ε ₀for raw data position, Poss is raw data value, and Δ ε is Data Position after interpolation, and after obtaining interpolation after carrying out interpolation operation, SAR is at imaging scene coordinate system E _sin coordinate Possl accurately, the SAR flight path namely obtained after the present invention's emulation.

embodiment

Variable element locking mode missile-borne Spotlight SAR Imaging track Simulation performance parameter, systematic parameter, Space geometric parameter, derived parameter are as shown in table 1,

Table 1 variable element locking mode missile-borne Spotlight SAR Imaging track Simulation parameter list

Step one, as Fig. 2 determine emulate in adopt four coordinate systems: earth rotation coordinate system E _g, imaging scene coordinate system E _s, direction of visual lines polar coordinate system E _lwith body flight path plane coordinate system E _m, shown in four coordinate systems.

Step 2, establish SAR at earth rotation coordinate system E _gthe coordinate of middle synthetic aperture central instant is (1253.3 ,-3392.7,5247.6) (km), at imaging scene coordinate system E _smiddle t ₀the coordinate in moment is (0,11.491,9.642) (km), and scene center is at E _gcoordinate in coordinate system is (1240.6 ,-3391.5,5239.7) (km),

(1) imaging scene coordinate system E _sto earth rotation coordinate system E _stransition matrix A _sg, earth rotation coordinate system E _gto imaging scene coordinate system E _stransition matrix A _gs.

Base area spherical model can obtain the longitude φ of SAR at synthetic aperture central instant _lowith φ _la:

φ _l0＝-69.91°

φ _la＝55.42°

$A_{\mathrm{sg}}=\left[\begin{array}{ccc}0.2829& -0.7733& -0.5675\\ 0.9391& 0.3435& 0\\ 0.1950& -0.5330& 0.8234\end{array}\right]$

$A_{\mathrm{gs}}=\left[\begin{array}{ccc}0.2829& 0.9391& 0.1950\\ -0.7733& 0.3435& -0.5330\\ -0.5675& 0& 0.8234\end{array}\right]$

(2) imaging scene coordinate system E _sto the polar coordinate system E of direction of visual lines _ltransition matrix A _sl, the polar coordinate system E of direction of visual lines _lto imaging scene coordinate system E _stransition matrix A _ls.

If synthetic aperture central instant SAR departs from imaging scene coordinate system E _sangle [alpha]=0 of Y direction.

$A_{\mathrm{sl}}=A_{\mathrm{ls}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

(3) the polar coordinate system E of direction of visual lines _lto body flight path plane coordinate system E _mtransition matrix A _lm, body flight path plane coordinate system E _mto the polar coordinate system E of direction of visual lines _ltransition matrix A _ml.

Setting synthetic aperture central instant SAR is β to the incident angle of scene center, and β=50 °, flight path plane relative rotation angle Ω=0 °.

$A_{\mathrm{lm}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0.7660& 0.6428\\ 0& -0.6428& 0.7660\end{array}\right]$

$A_{\mathrm{ml}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0.7602& -0.6379\\ 0& 0.6379& 0.7701\end{array}\right]$

Parameter in step 3, foundation table 1, calculates Δ θ=0.347 °, N according to formula (12) and (13) _a=1024.

The time step t of step 4, the emulation of setting runge kutta method _h=0.001s.Utilize runge kutta method to emulate and obtain body at flight path plane coordinate system E _min sample coordinate matrix Posm.

Step 5, integrating step four and the result in step 2, to obtain in the synthetic aperture time SAR at earth rotation coordinate system E after coordinate transformation _gin thick emulation flight path coordinates matrix.If Poss is that this flight path is at earth rotation coordinate system E _gin flight path coordinates matrix.In integrating step two, coordinate system transforms rule, obtains Poss.

Step 6, in conjunction with simulation parameter list 1, obtaining by formula (20) the angle sequence that SAR departs from Y-axis in plane L is Δ ε.Flight path slightly can be emulated at imaging scene coordinate system E by matrix Poss _sin, the angle sequence that SAR departs from Y-axis in plane L is Δ ε ₀.Comprehensive Δ ε ₀, Δ ε and Poss, the accurate SAR after interpolation can be obtained at imaging scene coordinate system E _sin coordinate represent Possl.Schematic diagram is as shown in Figure 4 in earth rotation coordinate system for the body flight path of emulation gained.

Process provides a kind of track Simulation method being applicable to the variable element locking mode missile-borne Spotlight SAR Imaging of single flight path plane, simulation result is that subsequent echoes emulation provides the foundation with imaging processing.

Claims (1)

1. a track Simulation method for variable element locking mode missile-borne Spotlight SAR Imaging, comprises following step:

Step one, determine emulate in adopt four coordinate systems: earth rotation coordinate system E _g, imaging scene coordinate system E _s, direction of visual lines polar coordinate system E _lwith body flight path plane coordinate system E _m, be specially:

Set with the earth tangent plane of scene center formation as the flight path plane of L, SAR is for P;

(1) earth rotation coordinate system E _g

True origin: the earth's core is designated as O _g;

X-axis is designated as X _g: under the line in plane, point to zero degree warp direction;

Y-axis is designated as Y _g: under the line in plane, point to east longitude 90 degree of warp directions;

Z axis is designated as Z _g: along earth's axis, point to the positive arctic;

(2) imaging scene coordinate system E _s

True origin: scene center is designated as O _s;

X-axis is designated as X _s: in plane L, point to the east of scene;

Y-axis is designated as Y _s: in plane L, point to the north of scene;

Z axis is designated as Z _s: cross scene central point, deviate from direction, the earth's core perpendicular to the earth tangent plane formed with scene center;

(3) the polar coordinate system E of direction of visual lines _l

True origin is designated as O _l: scene center;

X-axis is designated as X _l: in plane L, with Y _laxle, Z _laxle forms right-handed coordinate system;

Y-axis is designated as Y _l: in plane L, point to SAR sensor along the projection of synthetic aperture central instant oblique distance in this plane;

Z axis is designated as Z _l: cross scene central point, deviate from direction, the earth's core perpendicular to the earth tangent plane formed with scene center;

(4) body flight path plane coordinate system E _m

True origin is designated as O _m: scene center;

X-axis is designated as X _m: in body flight path plane, with Y _maxle, Z _maxle forms right-handed coordinate system;

Y-axis is designated as Y _m: in body flight path plane, point to the direction of target and SAR sensor;

Z axis is designated as Z _m: deviate from direction, the earth's core, directed in orthogonal is in the direction of body flight path plane P;

In step 2, determining step one, the method for transformation of coordinate between four coordinate systems, obtains the transformed matrix between coordinate system;

If SAR is at earth rotation coordinate system E _gin synthetic aperture central instant coordinate be (x _g0, y _g0, z _g0), at imaging scene coordinate system E _sin synthetic aperture central instant coordinate be (x _s0, y _s0, z _s0), scene center is at E _gcoordinate (x in coordinate system _p, y _p, z _p); Certain moment SAR is at earth rotation coordinate system E _gin coordinate be (x _g, y _g, z _g), SAR is at imaging scene coordinate system E in the same time _sin coordinate be (x _s, y _s, z _s), at the polar coordinate system E of direction of visual lines _lin coordinate be (x _l, y _l, z _l), at body flight path plane coordinate system E _min coordinate be (x _m, y _m, z _m);

(1) imaging scene coordinate system E is obtained _sto earth rotation coordinate system E _gtransition matrix A _sg, earth rotation coordinate system E _gto imaging scene coordinate system E _stransition matrix A _gs;

SAR is obtained at synthetic aperture central instant t according to formula (1) and formula (2) ₀longitude φ _lowith latitude φ _la:

${\mathrm{\&phi;}}_{10}=\arctan \left(\frac{y_{g0}}{x_{g0}}\right)---\left(1\right)$

${\mathrm{\&phi;}}_{\mathrm{la}}=\arctan \left(\frac{z_{g0}}{\sqrt{x_{g0}^2+y_{g0}^2}}\right)---\left(2\right)$

A _sgmeet the relation that formula (3) represents, can A be obtained according to formula (4) _sg

$\left[\begin{array}{ccc}{x}_g& y_g& z_g\end{array}\right]\left[\begin{array}{ccc}{x}_s& y_s& z_s+\sqrt{x_{g0}^2+y_{g0}^2+z_{g0}^2}\end{array}\right]A_{\mathrm{sg}}---\left(3\right)$

$A_{\mathrm{sg}}=\left[\begin{array}{ccc}\sin {\mathrm{\&phi;}}_{\mathrm{la}}& 0& \cos {\mathrm{\&phi;}}_{\mathrm{la}}\\ 0& 1& 0\\ -\cos {\mathrm{\&phi;}}_{\mathrm{la}}& 0& \sin {\mathrm{\&phi;}}_{\mathrm{la}}\end{array}\right]\left[\begin{array}{ccc}\cos {\mathrm{\&phi;}}_{\mathrm{lo}}& -{\sin \mathrm{\&phi;}}_{\mathrm{lo}}& 0\\ \sin {\mathrm{\&phi;}}_{\mathrm{lo}}& \cos {\mathrm{\&phi;}}_{\mathrm{lo}}& 0\\ 0& 0& 1\end{array}\right]---\left(4\right)$

A _sga is obtained through inversion operation _gs;

(2) imaging scene coordinate system E is obtained _sto the polar coordinate system E of direction of visual lines _ltransition matrix A _sl, the polar coordinate system E of direction of visual lines _lto imaging scene coordinate system E _stransition matrix A _ls;

Obtain synthetic aperture central instant SAR according to formula (5) and depart from imaging scene coordinate system E _sthe angle of Y direction is α, then

$\mathrm{\&alpha;}=\arctan \frac{x_{s0}}{y_{s0}}---\left(5\right)$

A _slmeet the relation that formula (6) represents, can A be obtained according to formula (7) _sl

[x _ly _lz _l]＝[x _sy _sz _s]A _sl(6)

$A_{s1}=\left[\begin{array}{ccc}\cos \mathrm{\&alpha;}& \sin \mathrm{\&alpha;}& 0\\ -\sin \mathrm{\&alpha;}& \cos \mathrm{\&alpha;}& 0\\ 0& 0& 1\end{array}\right]---\left(7\right)$

A _sla is obtained through inversion operation _ls;

(3) the polar coordinate system E of direction of visual lines is obtained _lto body flight path plane coordinate system E _mtransition matrix A _lm, body flight path plane coordinate system E _mto the polar coordinate system E of direction of visual lines _ltransition matrix A _ml;

Obtaining synthetic aperture central instant SAR to the incident angle of scene center according to formula (8) is β, then

$\mathrm{\&beta;}=\arcsin \frac{\sqrt{x_{s0}^2+y_{s0}^2}}{\sqrt{x_{s0}^2+y_{s0}^2+z_{s0}^2}}---\left(8\right)$

Setting flight path plane P and plane L angle are γ, obtain flight path plane relative rotation angle Ω to be according to formula (9)

$\mathrm{\&Omega;}=\arccos \frac{\cos \mathrm{\&gamma;}}{\sin \mathrm{\&beta;}}---\left(9\right)$

A _lmmeet the relation that formula (10) represents, can A be obtained according to formula (11) _lm

[x _my _mz _m]＝[x _ly _lz _l]A _lm(10)

$A_{1m}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}\\ 0& -\cos \mathrm{\&beta;}& \sin \mathrm{\&beta;}\end{array}\right]\left[\begin{array}{ccc}\cos \mathrm{\&Omega;}& 0& -\sin \mathrm{\&Omega;}\\ 0& 1& 0\\ \sin \mathrm{\&Omega;}& 0& \cos \mathrm{\&Omega;}\end{array}\right]---\left(11\right)$

A _lma is obtained through inversion operation _ml;

Step 3, setting radar system fundamental simulation parameter, determine the accumulation corner Δ θ of SAR in the synthetic aperture time, determine the quantity N of the sampling pulse launched along flight path direction SAR _a;

(1) the reference carrier frequency f of radar system is set ₀, light velocity c, simulating scenes radius D, duration of pulse μ, ρ _afor the azimuth resolution of system expection, obtaining according to formula (12) corner that in the synthetic aperture time, SAR accumulates in plane L is Δ θ, then

$\mathrm{\&Delta;\&theta;}=2\tan \frac{c}{4f_0{\mathrm{\&rho;}}_a\sin \mathrm{\&beta;}}---\left(12\right)$

(2) set function nextpow2 () as rreturn value be greater than independent variable minimum 2 the function of integer corresponding to integral number power, obtained the quantity N of the sampling pulse launched along flight path direction SAR by formula (13) _a

$N_a=2^{\mathrm{nextpow}2\left(\frac{3D}{{\mathrm{\&rho;}}_a}\right)}---\left(13\right)$

The time step t of step 4, the emulation of setting runge kutta method _h; Utilize runge kutta method to emulate and obtain body at flight path plane coordinate system E _min sample coordinate matrix Posm;

(1) setting projectile flight speed is V, Texas tower velocity reversal and the locking angle θ played between order oblique distance, the time step t of runge kutta method emulation _h; If synthetic aperture initial time is t ₁, finish time is t ₂, t ₁<t ₀<t ₂, utilize runge kutta method to generate t ₀~ t ₂the thick emulation flight path in moment; If (x _f, y _f, 0) and be t _mmoment SAR is at body flight path plane coordinate system E _min coordinate, (x _1f, y _1f, 0) and be t _m+ t _hmoment SAR is at body flight path plane coordinate system E _min coordinate; If x _f, y _finitial value be that synthetic aperture central instant SAR platform is at body flight path plane coordinate system E _min coordinate; Intermediate parameters k is calculated according to formula (14)-formula (18) _1xf, k _1yf, k _2xf, k _2yf, k _3xf, k _3yf, k _4xf, k _4yf;

$\left\{\begin{array}{c}{k}_{1\mathrm{xf}}=V\sin \left(\mathrm{arccot}\right|\frac{x_f}{y_f}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\\ k_{1\mathrm{yf}}=-V\cos \left(\mathrm{arccot}\right|\frac{x_f}{y_f}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\end{array}\right.---\left(14\right)$

$\left\{\begin{array}{c}{k}_{2\mathrm{xf}}=V\sin \left(\mathrm{arccot}\right|\frac{x_f+k_{1\mathrm{xf}}{t}_h/2}{y_f+k_{1\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\\ k_{2\mathrm{yf}}=-V\cos \left(\mathrm{arccot}\right|\frac{x_f+k_{1\mathrm{xf}}{t}_h/2}{y_f+k_{1\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\end{array}\right.---\left(15\right)$

$\left\{\begin{array}{c}{k}_{3\mathrm{xf}}=V\sin \left(\mathrm{arccot}\right|\frac{x_f+k_{2\mathrm{xf}}{t}_h/2}{y_f+k_{2\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\\ k_{3\mathrm{yf}}=-V\cos \left(\mathrm{arccot}\right|\frac{x_f+k_{2\mathrm{xf}}{t}_h/2}{y_f+k_{2\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\end{array}\right.---\left(16\right)$

$\left\{\begin{array}{c}{k}_{4\mathrm{xf}}=V\sin \left(\mathrm{arccot}\right|\frac{x_f+k_{3\mathrm{xf}}{t}_h/2}{y_f+k_{3\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\\ k_{4\mathrm{yf}}=-V\cos \left(\mathrm{arccot}\right|\frac{x_f+k_{3\mathrm{xf}}{t}_h/2}{y_f+k_{3\mathrm{yf}}{t}_h/2}|+\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2})\end{array}\right.---\left(17\right)$

$\left\{\begin{array}{c}{x}_{1f}=x_f+\frac{(k_{1\mathrm{xf}}+{2k}_{2\mathrm{xf}}+{2k}_{2\mathrm{xf}}+k_{4\mathrm{xf}})t_h}{6}\\ y_{1f}=y_f+\frac{(k_{1\mathrm{yf}}+{2k}_{2\mathrm{yf}}+{2k}_{2\mathrm{yf}}+k_{4\mathrm{yf}})t_h}{6}\end{array}\right.---\left(18\right)$

(2) repeat (1) of step 4, utilize runge kutta method to generate t ₁~ t ₀the thick emulation flight path of moment SAR is at body flight path plane coordinate system E _min coordinate; (1) and (2) of combining step four, to obtain in the synthetic aperture time SAR at body flight path plane coordinate system E _min thick emulation flight path coordinates matrix, be expressed as matrix Posm;

Step 5, integrating step four and the result in step 2, to obtain in the synthetic aperture time SAR at earth rotation coordinate system E after coordinate transformation _gin thick emulation flight path coordinates matrix;

Poss is that this flight path is at earth rotation coordinate system E _gin flight path coordinates matrix; In integrating step two, coordinate system transforms rule, obtains Poss according to formula (19)

Poss＝PosmA _mlA _lsA _sg(19)

Step 6, in conjunction with variable element SAR system design interpolation method, interpolation is carried out to the thick emulation flight path obtained in step 5, obtain the flight path of body emulation accurately;

Application claims SAR echo data at wavenumber domain along orientation to being spacedly distributed;

Be located at imaging scene coordinate system E _sin, the angle sequence that SAR departs from Y-axis in plane L is Δ ε, then

$\mathrm{\&Delta;\&epsiv;}=\arctan \frac{2\tan \frac{\mathrm{\&Delta;\&theta;}}{2}}{N_a}i,i=-\frac{N_a}{2},...\frac{N_a}{2}.---\left(20\right)$

Flight path slightly can be emulated at imaging scene coordinate system E by matrix Poss _sin, the angle sequence that SAR departs from Y-axis in plane L is Δ ε ₀; With Δ ε ₀for raw data position, Poss is raw data value, and Δ ε is Data Position after interpolation, and after obtaining interpolation after carrying out interpolation operation, SAR is at imaging scene coordinate system E _sin coordinate Poss1 accurately, the SAR flight path obtained after being emulation.