CN106646409A - SAR echo signal simulation method based on quasi-double-station model - Google Patents

Abstract

The invention discloses a SAR echo signal simulation method based on a quasi-bistatic model. First, input simulation parameters and parameter initialization; the simulation parameters include the three-axis coordinate trajectory of the antenna phase center in the ground-fixed coordinate system [X(t _i ), Y(t _i ),Z(t _i )], ground target coordinates [x _k ,y _k ,z _k ], oblique angle of view The lower angle of view φ(t _i ), the simulation start time t _M ; then, according to the simulation start time, calculate the distance vector between each pulse transmission time and pulse reception time and the distance vector between the antenna phase center and each ground target at each pulse transmission and reception time; finally , combined with the mathematical model of the SAR echo signal, to obtain the corresponding echo data. The present invention is based on the quasi-bistatic model, based on the radar continuous motion model, can realize high-precision SAR echo simulation; avoids complex iterative calculations, and has high calculation efficiency under the premise of ensuring calculation accuracy; suitable for airborne And spaceborne SAR echo signal simulation, which can complete the echo simulation of SAR echo signals under various conditions.

Description

A Simulation Method of SAR Echo Signal Based on Quasi-bistatic Model

technical field

The invention belongs to the field of signal processing, and relates to a method for calculating simulation parameters, in particular to a method for calculating the receiving time of SAR echoes based on a quasi-bistatic model, which realizes the simulation of SAR echo signals under the quasi-bistatic model.

Background technique

Synthetic Aperture Radar (SAR) has become one of the main themes in the era of rapid development of space information remote sensing technology because it is not affected by weather and climate, and can observe the earth in all-weather, all-weather, high-resolution, and large areas. . Due to the complexity of SAR, algorithm verification, performance testing and system debugging are very difficult and complex, and the original echo data of SAR under specific conditions are required. These data are often not practical to obtain through radar carrier flight, and It cannot be replaced by the real data acquired by existing SAR satellites, so the SAR echo signal simulation plays an important role in the radar development process.

The SAR echo simulation model is divided into two types based on the stop-and-go model and the non-stop-and-go model. In the SAR echo simulation, six coordinate systems are used to describe the satellite radar and The relationship between the ground target, so that the mutual positional relationship between the radar antenna phase center and the ground target can be calculated at azimuth time, so as to calculate the slant distance between the radar antenna phase center and the ground target, and bring it into the SAR echo model , and finally complete the SAR echo simulation.

Under the stop-and-go model, the radar transmit signal time and the echo signal receive time are considered to be the same time during the echo simulation process. This model greatly simplifies the complexity of the SAR echo signal simulation, but ignores the signal transmit time and receive time. The change of radar position between moments, especially for high-orbit and high-speed radar platforms, the position change is more obvious, which inevitably brings certain errors and affects the quality of subsequent processing of SAR echoes; under the non-stop-and-go model, considering The change of the radar position at the time of signal transmission and reception, in order to accurately calculate the time of echo signal reception, iterative solution is required, which makes the algorithm very complicated.

Contents of the invention

The purpose of the present invention is to solve the error caused by the SAR echo simulation stop-and-go model and the problem of complex parameter calculation algorithms under the non-stop-and-go model, and proposes a method for quickly calculating the receiving time of SAR echo signals based on the quasi-bistatic model , within the allowable range of error, based on the quasi-bistatic model, the fast simulation is realized, which makes up for the deficiency of the stop-and-go model and the non-stop-and-go model.

In order to achieve the above object, the present invention provides a SAR echo signal simulation method based on a quasi-bistatic model, comprising:

Step 1. Input simulation parameters and initialization of simulation parameters;

The simulation parameters include: three-axis coordinate trajectory [X(t _i ), Y(t _i ), Z(t _i )] of the antenna phase center in the ground-fixed coordinate system, where i=1, 2...N is the phase center of each antenna , N is the total number of antenna phase centers, t _i is the moment corresponding to the antenna phase center coordinates; ground target coordinates [x _k , y _k , z _k ], k=1, 2...n is each ground target, n is the ground The total number of targets, the backscatter coefficient σ _k of each ground target, the antenna beam width β _a in azimuth direction, the antenna beam width β _b in range direction, and the oblique angle Downward viewing angle φ(t _i ), simulation start time t _M , pulse repetition frequency f _prf , pulse width T _prt of transmitted signal, number of simulated pulses N _p ; frequency modulation f _r of transmitted signal, wavelength λ of transmitted signal;

The simulation parameters are initialized to obtain antenna phase center coordinates, oblique viewing angles and downward viewing angle curves by means of curve fitting;

Step 2. Calculate each pulse transmission time and pulse reception time according to the start time of the simulation; while calculating the pulse transmission and reception time, calculate the distance vector between the antenna phase center and each ground target at each pulse transmission and reception time, and the distance vector between the antenna phase center and the ground Line-of-sight angle and line-of-sight incidence angle between targets;

Step 3, combining the mathematical model of the SAR echo signal to obtain corresponding echo data.

As a further improvement of the present invention, in step 1, the implementation method of the simulation parameter initialization is:

Let the third-order expressions of antenna phase center coordinates, oblique viewing angle and downward viewing angle curves be:

φ(t)＝e ₃ t ³ +e ₂ t ² +e ₁ t+e ₀ (3)

Among them, a _i , b _i , c _i , d _i , e _i i=0,1,2,3 are the coefficients to be fitted, and for the third-order polynomial, use the MATLAB polynomial fitting function command polyfit to perform the fitting;

a. Using [X(t _i ), Y(t _i ), Z(t _i )] and t _i , calculate a _i , b _i , c _i i=0, 1, 2, 3 through formula (4):

b. Use and t _i , calculate d _i i=0,1,2,3 through formula (5):

c. Using φ(t _i ) and t _i , calculate e _i i = 0, 1, 2, 3 through formula (6):

[e ₃ e ₂ e ₁ e ₀ ]=polyfit(φ(t _i ),t _i ,3) (6).

As a further improvement of the present invention, said step 2 includes:

Step 21, calculate each pulse emission time;

Substituting the simulation start time t _M and the sequence number ie=1,2...N _p of the transmitted pulse sequence into formula (7), the time t _ie of each pulse transmission is calculated:

Step 22. Calculate the corresponding antenna phase center position coordinates, oblique angle of view and downward angle of view according to each pulse transmission time;

Put the calculated coefficients a _i , b _i , c _i , d _i , e _i i = 0, 1, 2, 3 and each pulse transmission time t _ie into formulas (1), (2), ( 3) Obtain the corresponding antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) at each pulse transmission time, oblique angle and the lower viewing angle φ(t _ie ):

φ(t _ie )＝e ₃ t _ie ³ +e ₂ t _ie ² +e ₁ t _ie +e ₀

Step 23, obtain the distance vector between the antenna phase center and each ground target according to each pulse transmission time;

Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (9) , to get the distance vector between the antenna phase center and the ground target

Step 24, calculate the line-of-sight angle between the antenna phase center corresponding to each pulse transmission time and the ground target according to the geometric model;

Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (10) , to get the line-of-sight angle θ _ie between the antenna phase center corresponding to each pulse transmission time and the ground target:

Step 25, calculate the line-of-sight incident angle corresponding to each pulse emission time according to the geometric model;

Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (11) , to obtain the line-of-sight incident angle γ _ie corresponding to each pulse emission moment:

Step 26, using the quasi-bistation model to calculate the signal delay time, and calculate the receiving time of each pulse;

The distance vector between the antenna phase center and the ground target at the moment of pulse transmission Substituting into formula (12) to calculate the echo delay time τ _delay :

Wherein, | | is a modulo operation, and c is the speed of light;

Substitute the pulse emission time t _ie and the echo delay time τ _delay into formula (13) to calculate the pulse reception time t _r :

t _r =t _ie +τ _delay (13)

Step 27. Calculate the corresponding antenna phase center position coordinates, oblique angle of view and downward angle of view according to each pulse receiving moment;

Put the calculated coefficients a _i , b _i , c _i , d _i , e _i i=0, 1, 2, 3 and each pulse receiving time t _ir into formulas (1), (2), ( 3) Obtain the corresponding antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) at each pulse receiving moment, oblique angle and down angle φ(t _ir ):

φ(t _ir )＝e ₃ t _ir ³ +e ₂ t _ir ² +e ₁ t _ir +e ₀

Step 28, obtain the distance vector between the antenna phase center and each ground target according to each pulse receiving moment;

Substitute the calculated antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into the formula ( 15), get the distance vector between the antenna phase center and each ground target

Step 29, calculate the line-of-sight angle between the antenna phase center corresponding to each pulse receiving moment and the ground target according to the geometric model;

Substitute the calculated antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into the formula ( 16), get the line-of-sight angle θ _ir between the antenna phase center corresponding to the pulse receiving moment and the ground target:

Step 210, calculating the line-of-sight incident angle corresponding to each pulse receiving moment according to the geometric model;

Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (17) , to obtain the line-of-sight incident angle γ _ir corresponding to each pulse emission moment:

As a further improvement of the present invention, said step 3 includes:

Step 31, using the relative position vector of the antenna phase center corresponding to the pulse transmission time and the ground target and the relative position vector of the antenna phase center and the ground target corresponding to the pulse receiving time to calculate the two-way distance in the SAR echo simulation;

The calculated distance vector between the antenna phase center and each ground target at each pulse transmission time and the distance vector between the antenna phase center and each ground target at each pulse receiving moment Substitute into formula (18) to get the two-way distance R(t):

Step 32, calculating the azimuth antenna pattern;

The line-of-sight angle θ _ie between the antenna phase center corresponding to each pulse transmission moment and the ground target, and the oblique angle The line-of-sight angle θ _ir between the antenna phase center corresponding to each pulse receiving moment and the ground target, and the oblique angle The azimuth antenna beam width β _a is substituted into equation (19) to calculate the azimuth antenna directivity function W _a :

Step 33, calculating the range antenna pattern;

Substitute the line-of-sight incident angle γ _ie , oblique angle of view φ(t _ie ) corresponding to each pulse transmission time, the line-of-sight incident angle γ _ir , downward viewing angle φ(t _ir ) corresponding to each pulse receiving time, and the distance-to-antenna beamwidth β _b into the formula (20), calculate the range antenna directivity function W _r :

Step 34, using the two-way distance and the antenna pattern to calculate the SAR echo;

The azimuth antenna directivity function W _a , the range antenna directivity function W _r , the target backscatter coefficient σ _k , the pulse width T _prt of the transmitted signal, the frequency modulation f _r of the transmitted signal, the wavelength λ of the transmitted signal and the two-way The distance R(t) is substituted into formula (21), and the echo is calculated point by point:

Among them, τ represents the range time of the echo data, and n is the total number of targets.

Compared with prior art, the beneficial effect of the present invention is:

1. The present invention is based on the quasi-bistatic model, based on the radar continuous motion model, and can realize high-precision SAR echo simulation;

2. Based on the quasi-bistation model, the present invention proposes a fast calculation method for each pulse receiving time, which avoids complicated iterative calculations and has high calculation efficiency under the premise of ensuring calculation accuracy;

3. The present invention is based on a quasi-bistatic model, is suitable for airborne and spaceborne SAR echo signal simulation, and can complete the echo simulation of SAR echo signals under various conditions.

Description of drawings

Fig. 1 is the flow chart of the SAR echo signal simulation method based on the quasi-bistatic model disclosed by an embodiment of the present invention;

Fig. 2 is a SAR quasi-bi-station model figure among the present invention;

Fig. 3 is a contrasting figure of slant distance and continuous model slant distance in the present invention;

Fig. 4 is the slant distance error diagram of the stop-and-go model;

Fig. 5 is the slant distance error figure of the inventive method;

Fig. 6 is a diagram of the real part of the echo signal in the present invention.

detailed description

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Below in conjunction with accompanying drawing, the present invention is described in further detail:

The present invention proposes a method for calculating the receiving time of SAR echo signals based on a quasi-bistatic model, and realizes the simulation of continuous model SAR echo signals, which is suitable for airborne and spaceborne SAR echo signal simulations. The overall process is shown in Figure 1 . In the SAR echo simulation, the general stop-and-go model assumes that the radar receives the reflected pulse while transmitting the pulse, but this assumption ignores the movement of the radar platform during the pulse transmission process, which will bring certain errors; and In the non-stop-and-go model, in order to calculate the receiving time of each pulse, a large number of iterative calculations are required, which brings inconvenience to engineering applications. The invention is based on the quasi-bistatic model, uses the distance between the phase center of the radar antenna and the ground at the time of pulse transmission to calculate the pulse propagation delay time, and realizes fast approximate calculation of the two-way slant distance within the error allowable range. The SAR echo simulation method based on the quasi-bistatic model of the present invention comprises the following steps:

Step 1. Input simulation parameters and initialization of simulation parameters;

(1) The simulation parameters specifically include: the three-axis coordinate trajectory of the antenna phase center in the ground-fixed coordinate system [X(t _i ), Y(t _i ), Z(t _i )], where i=1, 2...N is each Antenna phase center, N is the total number of antenna phase centers, t _i is the moment corresponding to the antenna phase center coordinates; ground target coordinates [x _k , y _k , z _k ], k=1, 2...n is each ground target, n is the total number of ground targets, the backscatter coefficient σ _k of each ground target, the antenna beam width β _a in azimuth direction, the antenna beam width β _b in range direction, and the oblique angle Downward viewing angle φ(t _i ), simulation start time t _M , pulse repetition frequency f _prf , pulse width T _prt of transmitted signal, number of simulated pulses N _p ; frequency modulation f _r of transmitted signal, wavelength λ of transmitted signal.

(2), simulation parameter initialization;

Let the third-order expressions of antenna phase center coordinates, oblique viewing angle and downward viewing angle curves be:

φ(t)＝e ₃ t ³ +e ₂ t ² +e ₁ t+e ₀ (3)

Among them, a _i , b _i , c _i , d _i , e _i i=0,1,2,3 are the coefficients to be fitted, and for the third-order polynomial, use the MATLAB polynomial fitting function command polyfit to perform the fitting;

a. Using [X(t _i ), Y(t _i ), Z(t _i )] and t _i , calculate a _i , b _i , c _i i=0, 1, 2, 3 through formula (4):

b. Use and t _i , calculate d _i i=0,1,2,3 through formula (5):

c. Using φ(t _i ) and t _i , calculate e _i i = 0, 1, 2, 3 through formula (6):

[e ₃ e ₂ e ₁ e ₀ ]=polyfit(φ(t _i ),t _i ,3) (6)

Step 2. Calculate each pulse transmission time and pulse reception time according to the start time of the simulation; while calculating the pulse transmission and reception time, calculate the distance vector between the antenna phase center and each ground target at each pulse transmission and reception time, and the distance vector between the antenna phase center and the ground Line-of-sight angle and line-of-sight incident angle between targets; the present invention calculates the slant distance between the antenna phase center and the ground target at the moment of pulse transmission, calculates the one-way time delay of pulse propagation, and uses twice the one-way time delay to approximate the two-way time delay of pulse propagation, In order to calculate the pulse receiving time, this approximation avoids the complex iterative solution of the non-stop-and-go model. Through subsequent simulation analysis, it can be seen that the error caused by this approximation can meet the actual engineering application.

(1), calculate each pulse emission time;

Substituting the simulation start time t _M , the sequence number of the transmitted pulse sequence ie=1,2...N _p , N _p is the number of simulated pulses, into formula (7), and calculates the time t _ie of each pulse transmission:

(2) Calculate the corresponding antenna phase center position coordinates, oblique angle of view and downward angle of view according to each pulse transmission time;

Put the calculated a _i , b _i , c _i , d _i , e _i i = 0, 1, 2, 3 and other fitting coefficients and each pulse emission time t _ie into formula (1), ( 2), (3) Obtain the corresponding antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) at each pulse transmission time, and the oblique angle and the lower viewing angle φ(t _ie ):

φ(t _ie )＝e ₃ t _ie ³ +e ₂ t _ie ² +e ₁ t _ie +e ₀

(3), obtain the distance vector between the antenna phase center and each ground target according to each pulse transmission moment;

Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (9) , to get the distance vector between the antenna phase center and the ground target

(4), calculate the line-of-sight angle between the antenna phase center corresponding to each pulse transmission moment and the ground target according to the geometric model;

Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (10) , to get the line-of-sight angle θ _ie between the antenna phase center corresponding to each pulse transmission time and the ground target:

(5) According to the geometric model, the line-of-sight incident angle corresponding to each pulse emission moment is calculated;

Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (11) , to obtain the line-of-sight incident angle γ _ie corresponding to each pulse emission moment:

(6) Use the quasi-bistation model to calculate the signal delay time and calculate the receiving time of each pulse;

The schematic diagram of the quasi-bistatic model is shown in Figure 2. The distance vector between the antenna phase center and the ground target at the moment of pulse transmission is Substituting into formula (12) to calculate the echo delay time τ _delay :

Among them, || is a modulo operation, and c is the speed of light;

Substitute the pulse emission time t _ie and the echo delay time τ _delay into formula (13) to calculate the pulse reception time t _r :

t _r =t _ie +τ _delay (13)

(7) Calculate the corresponding antenna phase center position coordinates, oblique angle of view and downward angle of view according to each pulse receiving moment;

Put the calculated a _i , b _i , c _i , d _i , e _i i = 0, 1, 2, 3 and other fitting coefficients and each pulse receiving time t _ir into formula (1), ( 2), (3) Obtain the corresponding antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) at each pulse receiving moment, oblique angle and down angle φ(t _ir ):

φ(t _ir )＝e ₃ t _ir ³ +e ₂ t _ir ² +e ₁ t _ir +e ₀

(8), obtain the distance vector between the antenna phase center and each ground target according to each pulse receiving moment;

Substitute the calculated antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into the formula ( 15), get the distance vector between the antenna phase center and each ground target

(9), according to the geometric model, calculate the line-of-sight angle between the antenna phase center corresponding to each pulse receiving moment and the ground target;

Substitute the calculated antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into the formula ( 16), get the line-of-sight angle θ _ir between the antenna phase center corresponding to the pulse receiving moment and the ground target:

(10), calculate the line-of-sight incident angle corresponding to each pulse receiving moment according to the geometric model;

Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (17) , to obtain the line-of-sight incident angle γ _ir corresponding to each pulse emission moment:

Step 3, combining the mathematical model of the SAR echo signal, substituting the relevant data calculated in the first two steps into the echo model to obtain the corresponding echo data;

(1), using the relative position vector of the antenna phase center corresponding to the pulse transmission time and the ground target and the relative position vector of the antenna phase center and the ground target corresponding to the pulse receiving time to calculate the two-way distance in the SAR echo simulation;

The calculated distance vector between the antenna phase center and each ground target at each pulse transmission time and the distance vector between the antenna phase center and each ground target at each pulse receiving moment Substitute into formula (18) to get the two-way distance R(t):

(2) Calculate the azimuth antenna pattern;

The line-of-sight angle θ _ie between the antenna phase center corresponding to each pulse transmission moment and the ground target, and the oblique angle The line-of-sight angle θ _ir between the antenna phase center corresponding to each pulse receiving moment and the ground target, and the oblique angle The azimuth antenna beam width β _a is substituted into equation (19) to calculate the azimuth antenna directivity function W _a :

(3), calculate the distance to the antenna pattern;

Substitute the line-of-sight incident angle γ _ie , oblique angle of view φ(t _ie ) corresponding to each pulse transmission time, the line-of-sight incident angle γ _ir , downward viewing angle φ(t _ir ) corresponding to each pulse receiving time, and the distance-to-antenna beamwidth β _b into the formula (20), calculate the range antenna directivity function W _r :

(4), using the two-way distance and the antenna pattern to calculate the SAR echo;

The azimuth antenna directivity function W _a , the range antenna directivity function W _r , the target backscatter coefficient σ _k , the pulse width T _prt of the transmitted signal, the frequency modulation f _r of the transmitted signal, the wavelength λ of the transmitted signal and the two-way The distance R(t) is substituted into formula (21), and the echo is calculated point by point:

Among them, τ represents the range time of the echo data, and n is the total number of targets.

Example 1:

The present invention provides a kind of SAR echo signal simulation method based on quasi-bistatic model, comprising:

Step 1. Input simulation parameters and initialization of simulation parameters;

(1) The simulation parameters specifically include the three-axis coordinate trajectory of the antenna phase center in the ground-fixed coordinate system [X(t _i ), Y(t _i ), Z(t _i )], where i=1, 2...N is the antenna phase center The moment corresponding to the coordinates, N is the total number of antenna phase center coordinates, ground target coordinates [x _k , y _k , z _k ], k=1, 2...n is each ground target, and the backscatter coefficient σ _k k of each target =1,2...n, n is the total number of targets, antenna beam width β _a in azimuth direction, antenna beam width β _b in range direction, oblique angle of view Angle of view φ(t _i ) at i=1,2...N, i=1,2...N, simulation start time t _M , pulse repetition frequency f _prf , pulse width T _prt of transmitted signal, number of simulated pulses N _p , f _r is the frequency modulation of the transmitted signal, and λ is the wavelength of the transmitted signal. The specific parameters of this embodiment are: X(t _ie )=[0,0,…,0]m, Y(t _ie )=[0,7000,14000,…,700000]m, Z(t _ie )=[ 1.1*10 ⁶ ,1.1*10 ⁶ ,…,1.1*10 ⁶ ]m, the target coordinates are [x ₁ ,y ₁ ,z ₁ ]＝[1.1*10 ⁶ 5.584*10 ³ 0], σ ₁ ＝1, The number of targets is 1, β _a =2°, β _b =2°, φ _ie =[45,45,…,45]°, t _M =0s, f _prf =600Hz, T _prt =2*10 ^-6 s, simulated pulse number N _p =1000, f _r =2.5*10 ¹³ Hz, λ=0.02cm;

(2) Simulation parameter initialization;

a) Using [X(t _i ), Y(t _i ), Z(t _i )] and t _i , calculate a _i , bi , c _{i i} =0, 1, 2, 3 through formula (4):

[a ₃ a ₂ a ₁ a ₀ ]=[0 0 0 0]

[b ₃ b ₂ b ₁ b ₀ ]=[0 0 7000 0]

[c ₃ c ₂ c ₁ c ₀ ]=[0 0 0 1.1*10 ⁶ ]

b) use and t _i , calculate d _i i=0,1,2,3 through formula (5):

[d ₃ d ₂ d ₁ d ₀ ]=[0 0 0 90]

c) Using φ(t _i ) and t _i , calculate e _i i = 0, 1, 2, 3 through formula (6):

[e ₃ e ₂ e ₁ e ₀ ]=[0 0 0 45]

Step 2. Calculate each pulse transmission time and pulse reception time according to the start time of the simulation;

(1) Put the formula t _M =0, f _prf =600 and N _p =1000 into (7), and the calculation can be t _ie =[0.00170.0033,...,1.6667]s, t _ie is the pulse emission time;

(2) Put the calculated a _i , b _i , c _i , d _i , e _i i = 0, 1, 2, 3 and other fitting coefficients and each pulse emission time t _ie into the formula (1 ), (2), (3) to obtain the corresponding antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) at the moment of pulse transmission, and the oblique angle and the lower viewing angle φ(t _ie ):

φ(t _ie )＝[45,45,…,45]

(3) Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k ,y _k ,z _k ] of the ground scene target into the formula (9), get the distance vector between the antenna phase center and each ground target

(4) Substitute the calculated position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) of the phase center of the pulse transmitting antenna and the position coordinates [x _k ,y _k ,z _k ] of the ground scene target into the formula (10), the line-of-sight angle θ _ie between the antenna phase center corresponding to the pulse transmission moment and the ground target is obtained;

(5) Substitute the calculated position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) of the phase center of the pulse transmitting antenna and the position coordinates [x _k , y _k , z _k ] of the ground scene target into the formula (11), obtain the line-of-sight incident angle γ _ie corresponding to the moment of pulse emission;

(6) The schematic diagram of the quasi-bistatic model is shown in Figure 2. The distance vector between the radar and the ground target at the time of pulse transmission is Substituting formula (12) to calculate the echo delay time;

Substitute the pulse emission time t _ie and the echo delay time τ _delay into formula (13) to calculate the pulse reception time t _ir ;

(7) Put the calculated a _i , b _i , c _i , d _i , e _i i = 0, 1, 2, 3 and other fitting coefficients and pulse receiving time t _ir into formula (1) , (2), (3) Obtain the corresponding antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) at each pulse receiving moment, oblique angle and down angle φ(t _ir );

(8) Substitute the calculated antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target at the moment of pulse reception into Equation (15), the distance vector between the antenna phase center and each ground target is obtained

(9) Substitute the calculated antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) and the position coordinates [x _k ,y _k ,z _k ] of the ground scene target at the moment of pulse reception into Equation (16), the angle θ _ir between the antenna phase center corresponding to the pulse receiving moment and the line of sight of the ground target is obtained;

(10) Substitute the calculated position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) of the phase center of the pulse transmitting antenna and the position coordinates [x _k ,y _k ,z _k ] of the ground scene target into the formula (17), obtain the line-of-sight incident angle γ _ir corresponding to the pulse emission moment;

Step 3, combining the mathematical model of the SAR echo signal to obtain the echo data at any time;

(1) Calculate the distance vector between the antenna phase center and each ground target at the moment of pulse transmission and the distance vector between the antenna phase center and each ground target at the moment of pulse reception Substitute into formula (18) to get the two-way distance R(t);

(2) The line-of-sight angle θ _ie between the antenna phase center corresponding to the pulse transmission moment and the ground target, and the oblique angle The line-of-sight angle θ _ir between the antenna phase center corresponding to the pulse receiving moment and the ground target, and the oblique angle The azimuth antenna beam width β _a is substituted into formula (19) to calculate the azimuth antenna pattern W _a ;

(3) Substitute the line-of-sight incident angle γ _ie , oblique angle φ(t _ie ) corresponding to the moment of pulse transmission, the line-of-sight incident angle γ _ir , downward angle of view φ(t _ir ) corresponding to the pulse reception time, and the distance into the antenna beam width β _b Equation (20), calculate the range antenna pattern W _r ;

(4) The azimuth antenna directivity function W _a , the range antenna directivity function W _r , the target backscattering coefficient σ _k , the pulse width T _prt of the transmitted signal, the frequency modulation f _r of the transmitted signal, and the wavelength λ of the transmitted signal and the two-way distance R(t) are substituted into formula (21), and the echo is calculated point by point.

The present invention is based on the quasi-two-station model, and utilizes engineering approximation to propose a fast calculation method for the echo signal receiving time, which overcomes the complex problem of echo simulation calculation based on the non-stop model. Figure 3 compares the continuous model with that of the present invention. Figure 4 shows the slant distance error of the stop-and-go model for the two-way slant distance obtained by the calculation method, and Fig. 5 shows the slant distance error of the method of the present invention. Through error analysis, it can be known that the near error can meet the actual engineering needs. Fig. 6 is a result diagram of the echo signal in the present invention. Through the analysis of examples, the complete implementation process of the method of the present invention is further described in detail, and the rationality and correctness of the method of the present invention are verified.

The advantages of the present invention are:

1. The present invention is based on the quasi-bistatic model, based on the radar continuous motion model, and can realize high-precision SAR echo simulation;

2. Based on the quasi-bistation model, the present invention proposes a fast calculation method for each pulse receiving time, which avoids complicated iterative calculations and has high calculation efficiency under the premise of ensuring calculation accuracy;

3. The present invention is based on a quasi-bistatic model, is suitable for airborne and spaceborne SAR echo signal simulation, and can complete the echo simulation of SAR echo signals under various conditions.

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (4)

1. a kind of SAR echo signal simulation method based on quasi-bistatic model, it is characterized in that, comprising: Step 1. Input simulation parameters and initialization of simulation parameters; The simulation parameters include: three-axis coordinate trajectory [X(t _i ), Y(t _i ), Z(t _i )] of the antenna phase center in the ground-fixed coordinate system, where i=1, 2...N is the phase center of each antenna , N is the total number of antenna phase centers, t _i is the moment corresponding to the antenna phase center coordinates; ground target coordinates [x _k , y _k , z _k ], k=1, 2...n is each ground target, n is the ground The total number of targets, the backscatter coefficient σ _k of each ground target, the antenna beam width β _a in azimuth direction, the antenna beam width β _b in range direction, and the oblique angle Downward viewing angle φ(t _i ), simulation start time t _M , pulse repetition frequency f _prf , pulse width T _prt of transmitted signal, number of simulated pulses N _p ; frequency modulation f _r of transmitted signal, wavelength λ of transmitted signal; The simulation parameters are initialized to obtain antenna phase center coordinates, oblique viewing angles and downward viewing angle curves by means of curve fitting; Step 2. Calculate each pulse transmission time and pulse reception time according to the start time of the simulation; while calculating the pulse transmission and reception time, calculate the distance vector between the antenna phase center and each ground target at each pulse transmission and reception time, and the distance vector between the antenna phase center and the ground Line-of-sight angle and line-of-sight incidence angle between targets; Step 3, combining the mathematical model of the SAR echo signal to obtain corresponding echo data. 2. the SAR echo signal simulation method based on quasi-bistatic model as claimed in claim 1, is characterized in that, in step 1, the realization method of described simulation parameter initialization is: Let the third-order expressions of antenna phase center coordinates, oblique viewing angle and downward viewing angle curves be: $\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ φ(t)＝e ₃ t ³ +e ₂ t ² +e ₁ t+e ₀ (3) Among them, a _i , b _i , c _i , d _i , e _i i=0,1,2,3 are the coefficients to be fitted, and for the third-order polynomial, use the MATLAB polynomial fitting function command polyfit to perform the fitting; a. Using [X(t _i ), Y(t _i ), Z(t _i )] and t _i , calculate a _i , b _i , c _i i=0, 1, 2, 3 through formula (4): $\begin{array}{c}<span\; class="notranslate">\; \&lsqb;</span>\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&lsqb;</span>\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&lsqb;</span>\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ b. Use and t _i , calculate d _i i=0,1,2,3 through formula (5): c. Using φ(t _i ) and t _i , calculate e _i i = 0, 1, 2, 3 through formula (6): [e ₃ e ₂ e ₁ e ₀ ]=polyfit(φ(t _i ),t _i ,3) (6). 3. the SAR echo signal simulation method based on quasi-bistatic model as claimed in claim 2, is characterized in that, described step 2 comprises: Step 21, calculate each pulse emission time; Substituting the simulation start time t _M and the sequence number ie=1,2...N _p of the transmitted pulse sequence into formula (7), the time t _ie of each pulse transmission is calculated: ${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ Step 22. Calculate the corresponding antenna phase center position coordinates, oblique angle of view and downward angle of view according to each pulse transmission time; Put the calculated coefficients a _i , b _i , c _i , d _i , e _i i = 0, 1, 2, 3 and each pulse transmission time t _ie into formulas (1), (2), ( 3) Obtain the corresponding antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) at each pulse transmission time, oblique angle and the lower viewing angle φ(t _ie ): Step 23, obtain the distance vector between the antenna phase center and each ground target according to each pulse transmission time; Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (9) , to get the distance vector between the antenna phase center and the ground target Step 24, calculate the line-of-sight angle between the antenna phase center corresponding to each pulse transmission time and the ground target according to the geometric model; Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (10) , to get the line-of-sight angle θ _ie between the antenna phase center corresponding to each pulse transmission time and the ground target: ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\sqrt{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Z</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$ Step 25, calculate the line-of-sight incident angle corresponding to each pulse emission time according to the geometric model; Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (11) , to obtain the line-of-sight incident angle γ _ie corresponding to each pulse emission moment: ${\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Z</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$ Step 26, using the quasi-bistation model to calculate the signal delay time, and calculate the receiving time of each pulse; The distance vector between the antenna phase center and the ground target at the moment of pulse transmission Substituting into formula (12) to calculate the echo delay time τ _delay : Among them, || is a modulo operation, and c is the speed of light; Substitute the pulse emission time t _ie and the echo delay time τ _delay into formula (13) to calculate the pulse reception time t _r : t _r =t _ie +τ _delay (13) Step 27. Calculate the corresponding antenna phase center position coordinates, oblique angle of view and downward angle of view according to each pulse receiving moment; Put the calculated coefficients a _i , b _i , c _i , d _i , e _i i=0, 1, 2, 3 and each pulse receiving time t _ir into formulas (1), (2), ( 3) Obtain the corresponding antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ,) oblique angle of view at each pulse receiving moment and down angle φ(t _ir ): Step 28, obtain the distance vector between the antenna phase center and each ground target according to each pulse receiving moment; Substitute the calculated antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into the formula ( 15), get the distance vector between the antenna phase center and each ground target Step 29, calculate the line-of-sight angle between the antenna phase center corresponding to each pulse receiving moment and the ground target according to the geometric model; Substitute the calculated antenna phase center position coordinates X(t _ir ), Y(t _ir ), Z(t _ir ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into the formula ( 16), get the line-of-sight angle θ _ir between the antenna phase center corresponding to the pulse receiving moment and the ground target: ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\sqrt{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Z</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$ Step 210, calculating the line-of-sight incident angle corresponding to each pulse receiving moment according to the geometric model; Substitute the calculated pulse transmitting antenna phase center position coordinates X(t _ie ), Y(t _ie ), Z(t _ie ) and the position coordinates [x _k , y _k , z _k ] of the ground scene target into formula (17) , to obtain the line-of-sight incident angle γ _ir corresponding to each pulse emission moment: ${\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Z</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$ 4. the SAR echo signal simulation method based on quasi-bistatic model as claimed in claim 3, is characterized in that, described step 3 comprises: Step 31, using the relative position vector of the antenna phase center corresponding to the pulse transmission time and the ground target and the relative position vector of the antenna phase center and the ground target corresponding to the pulse receiving time to calculate the two-way distance in the SAR echo simulation; The calculated distance vector between the antenna phase center and each ground target at each pulse transmission time and the distance vector between the antenna phase center and each ground target at each pulse receiving moment Substitute into formula (18) to get the two-way distance R(t): Step 32, calculating the azimuth antenna pattern; The line-of-sight angle θ _ie between the antenna phase center corresponding to each pulse transmission moment and the ground target, and the oblique angle The line-of-sight angle θ _ir between the antenna phase center corresponding to each pulse receiving moment and the ground target, and the oblique angle The azimuth antenna beam width β _a is substituted into equation (19) to calculate the azimuth antenna directivity function W _a : Step 33, calculating the range antenna pattern; Substitute the line-of-sight incident angle γ _ie , oblique angle of view φ(t _ie ) corresponding to each pulse transmission time, the line-of-sight incident angle γ _ir , downward viewing angle φ(t _ir ) corresponding to each pulse receiving time, and the distance-to-antenna beamwidth β _b into the formula (20), calculate the range antenna directivity function W _r : ${\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 0.886</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 0.886</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$ Step 34, using the two-way distance and the antenna pattern to calculate the SAR echo; The azimuth antenna directivity function W _a , the range antenna directivity function W _r , the target backscatter coefficient σ _k , the pulse width T _prt of the transmitted signal, the frequency modulation f _r of the transmitted signal, the wavelength λ of the transmitted signal and the two-way The distance R(t) is substituted into formula (21), and the echo is calculated point by point: ${\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; j\&pi;f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}<span\; class="notranslate">\; )</span>$ Among them, τ represents the range time of the echo data, and n is the total number of targets.