CN103076607B

CN103076607B - Method for realizing sliding spotlight mode based on SAR (Synthetic Aperture Radar) satellite attitude control

Info

Publication number: CN103076607B
Application number: CN201310001124.7A
Authority: CN
Inventors: 陈杰; 邹德意; 王鹏波; 朱燕青
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2013-01-04
Filing date: 2013-01-04
Publication date: 2014-07-30
Anticipated expiration: 2033-01-04
Also published as: CN103076607A

Abstract

The invention discloses a method for realizing a sliding spotlight mode based on SAR (Synthetic Aperture Radar) satellite attitude control, which belongs to the technical field of signal processing. According to the method, a satellite attitude is regulated and controlled, so that the direction angle of a satellite antenna is changed continuously, and the problem of angular quantification is solved; and a complete space relation geometrical model is established, so that a sliding spotlight mode can be realized more accurately, and the SAR azimuth resolution is increased. Moreover, the antenna is simple in structure, the satellite cost can be lowered, the size and the weight of a satellite are reduced, and the satellite has a wide application prospect. Compared with the conventional method for realizing the sliding spotlight mode through a phase control array, the method disclosed by the invention has the advantages that the direction of the antenna is changed continuously, and the accuracy is higher; and the structure of the satellite antenna can be greatly simplified, the satellite cost is reduced, the satellite weight is reduced, and the satellite antenna has a very important application value.

Description

Method for realizing sliding beam-bunching mode based on SAR satellite attitude control

Technical Field

The invention provides a method for realizing a sliding beam-forming mode based on SAR satellite attitude control, and belongs to the technical field of signal processing.

Background

The sliding beam bunching mode is a novel Synthetic Aperture Radar (SAR) imaging mode, controls azimuth resolution by controlling the moving speed of an antenna irradiation area on the ground, has larger imaging area than the bunching mode, can have higher resolution than a stripe mode with the same antenna size, and can make good balance in high resolution and large area imaging. The phased array antenna is a main means for realizing a sliding beam-bunching mode at present, in a radar antenna scanning mode, the pointing angle of the phased array antenna is influenced by the quantization position of the digital phase shifter, an angle quantization error exists, continuous change is impossible to realize, and the quantization problem causes the discontinuity of echo main energy and influences the azimuth resolution of the SAR. The phased array antenna has a complex structure and high manufacturing cost, and needs a complex central processing unit for control.

Disclosure of Invention

The invention provides a method for realizing a sliding spotlight mode based on SAR satellite attitude control, which is implemented by adjusting the rolling angle theta of a satellite_rYaw angle theta_yAnd a pitch angle theta_pThe invention relates to a novel method for realizing a sliding beam-forming mode suitable for a high-mobility satellite.

A method for realizing a sliding spotlight mode based on SAR satellite attitude control comprises the following steps:

the method comprises the following steps: computing the satellite in a rotating earth-centered coordinate system E_gCoordinate of (x)_s,y_s,z_s)；

Step two: calculating the time T of the front side view beam center of the satellite pointing to the center of the observation target area₀Antenna coordinate system E_aThe unit vector (0,1,0) in the rotating earth center coordinate system E_gCoordinates of (5);

step three: calculating T₀Time antenna coordinate system E_aDistance R from unit vector (0,1,0) to ground₀；

Step four: calculating T₀Slope distance delta R from moment rotating point C to ground pointing point₀；

Step five: calculating the coordinate system E of the rotation point C in the rotation geocentric_gCoordinates of (5)

Step six: calculating the coordinate system E of the satellite and the rotation point C at the rotating earth center in the process of full sliding convergence (sliding bunching)_gRelative vector (R) in (1)_x,R_y,R_z)；

Step seven: calculating the coordinate system E of the antenna pointing at the rotating geocentric during the full sliding convergence process_gCoordinate of (x'₁,y′₁,z′₁)；

Step eight: calculating the antenna orientation in the antenna coordinate system E in the process of full sliding convergence_aCoordinate of (x ″)₁,y″₁，z″₁)；

Step nine: calculating the antenna coordinate System E_aLower unit vector (0,1,0), coordinate (x) after attitude control_ZT,y_ZT,z_ZT)；

Step ten: calculating a satellite attitude control angle in the full sliding convergence process;

step eleven: and calculating the control law of the satellite attitude and the control curve of the angular speed of each axis in the full sliding and gathering process.

The invention provides a method for realizing a sliding beam-forming mode based on SAR satellite attitude control, which realizes continuous change of a satellite antenna pointing angle by regulating and controlling the satellite attitude, does not have the problem of angle quantization, can more accurately realize the sliding beam-forming mode by establishing a more perfect spatial relation geometric model, and improves the SAR azimuth resolution. And the antenna has a simple structure, can reduce the cost of the satellite, reduce the volume and weight of the satellite, and has wide application prospect.

The invention has the advantages that:

(1) compared with the conventional method for realizing the sliding beam-bunching mode through a phased array, the method provided by the invention has the advantages that the antenna pointing direction is continuously changed, and the accuracy is higher;

(2) the method provided by the invention is realized in a very accurate star motion model, and the accuracy is very high;

(3) the method provided by the invention can greatly simplify the structure of the satellite antenna, reduce the cost of the satellite and reduce the weight of the satellite, and has very important application value.

Drawings

FIG. 1 is a flow chart of a method of the present invention;

FIG. 2 is a graph of pitch angle versus scan time in an embodiment;

FIG. 3 is a graph of yaw angle versus scan time for an embodiment;

FIG. 4 is a graph of angular velocity of the x-axis of the satellite versus scan time in an embodiment;

FIG. 5 is a graph of the angular velocity of the y-axis of the satellite versus the scan time in the example;

FIG. 6 is a graph of angular velocity of the z-axis of the satellite versus scan time in an embodiment;

FIG. 7 is an enlarged view of the imaging result of the SLIP mode of the phased array antenna in the embodiment;

FIG. 8 is an enlarged view of imaging results of the pose-controlled sliding mode in the embodiment;

FIG. 9 is a point target analysis result of the sliding mode of the phased array antenna in the embodiment;

FIG. 10 is a result of target analysis of pose-controlled slider-gather mode points in an embodiment.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and examples.

The invention discloses a formula parameter declaration part:

T₀the moment when the center of the wave beam points to the center of the observation target area is observed from the front side view of the satellite;

A_numin order to meet the requirement of the length of the observation belt in the azimuth direction, the pulse number is transmitted;

f_PRFis the pulse weightA complex frequency PRF;

θ_Lis the radar antenna view angle;

ρ_athe azimuth resolution is;

K_ais an azimuth beam broadening factor;

L_sis the equivalent antenna length;

the satellite on-orbit motion average angular velocity is obtained;

the earth mean rotation angular velocity;

a is the length of the earth's major semi-axis;

b is the length of the short half shaft of the earth;

m is the mean angle of approach;

e is an eccentric angle;

theta is the true proximal angle;

e is the eccentricity;

r is the radius;

p is a half positive focal length;

H_Ggreenwich mean hour angle at spring break;

omega is the right ascension of the orbit intersection point;

i is the track inclination angle;

omega is the amplitude angle of the orbit in the near place;

gamma is the track angle of the satellite;

θ_rfor rolling of satellites about the x-axisTurning;

θ_yis the yaw angle of the satellite about the y-axis;

θ_pis the pitch angle of the satellite around the z-axis;

θ_{y_c}the satellite yaw angle after yaw control;

ω₃₂is an equivalent angular velocity vector of rotation;

R₂a rotation matrix when the satellite yaws;

R₃is the rotation matrix when the satellite is pitching.

The coordinate system transformation matrix statement of the invention (for convenience of representation, cosine cos is denoted by c and sine sin is denoted by s):

A_{go} = (\begin{matrix} c_{H_{G}} & s_{H_{G}} & 0 \\ {- s}_{H_{G}} & c_{H_{G}} & 0 \\ 0 & 0 & 1 \end{matrix})

to a non-rotating earth-centered coordinate system E_oTo the rotating earth's center coordinate system E_gThe transformation matrix of (2);

as a plane coordinate system of the track E_vTo the non-rotating geocentric coordinate system E_oThe transformation matrix of (2);

for the satellite platform coordinate system E_rTo the orbital plane coordinate system E_vThe transformation matrix of (2);

as satellite star coordinate system E_eTo satellite platform coordinate system E_rThe transformation matrix of (2);

as an antenna coordinate system E_aSatellite-to-satellite star coordinate system E_eThe transformation matrix of (2);

the inverse transformation can be achieved by matrix inversion.

The invention realizes the sliding bunching mode through satellite attitude control, and the method flow is shown in figure 1 and specifically comprises the following steps.

At the time of transmitting the M-th pulse, the average proximal angle M is:

<math> <mrow> <mi>M</mi> <mo>=</mo> <msub> <mover> <mi>ω</mi> <mo>&OverBar;</mo> </mover> <mi>sat</mi> </msub> <mo>·</mo> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <mi>m</mi> <msub> <mi>f</mi> <mi>PRF</mi> </msub> </mfrac> <mo>-</mo> <mfrac> <msub> <mi>A</mi> <mi>num</mi> </msub> <mrow> <mn>2</mn> <mo>·</mo> <msub> <mi>f</mi> <mi>PRF</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

and then calculating the eccentric angle E as:

(2)

calculating the true paraxial angle θ as:

<math> <mrow> <mi>θ</mi> <mo>=</mo> <mn>2</mn> <mo>·</mo> <mi>arctan</mi> <mrow> <mo>(</mo> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>e</mi> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mi>e</mi> </mrow> </mfrac> </msqrt> <mo>·</mo> <mi>tan</mi> <mfrac> <mi>E</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

the calculated radius r is:

from the above-obtained satellite in the orbital plane coordinate system E_vCoordinate of (x)_vs,y_vs,z_vs) Comprises the following steps:

through coordinate system conversion, the coordinate system is converted into a rotating earth center coordinate system E_gObtaining the coordinate system E of the satellite in the rotating geocentric_gCoordinate of (x)_s,y_s,z_s) Comprises the following steps:

get T out of₀Time of day satellite in rotating earth center coordinate system E_gHas the coordinates of

Step two: calculating T₀Time antenna coordinate system E_aThe unit vector (0,1,0) in the rotating earth center coordinate system E_gCoordinate of (x)₁,y₁,z₁)；

Through coordinate system conversion, the coordinate system is converted into a satellite star coordinate system E_eTo the satellite platform coordinate system E_rConversion to orbital plane coordinate system E_vTo a non-rotating earth-centered orbital coordinate system E_oThen converted into a rotating earth center coordinate system E_gObtaining an antenna coordinate system E_aThe unit vector (0,1,0) in the rotating earth center coordinate system E_gCoordinate of (x)₁,y₁,z₁) Comprises the following steps:

note that: at this time, at A, attitude adjustment control is not taken into consideration_reThe mid-attitude angles are all zero. In a satellite-satellite coordinate system E_eConversion to satellite platform coordinate system E_rIn the process, yaw control is considered. By yaw control, the satellite yaw angle theta_{y_c}Comprises the following steps:

<math> <mrow> <msub> <mi>θ</mi> <mrow> <mi>y</mi> <mo>_</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>+</mo> <mi>arctan</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <mi>θ</mi> <mo>+</mo> <mi>ω</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>sin</mi> <mi>i</mi> </mrow> <mrow> <msub> <mover> <mi>ω</mi> <mo>&OverBar;</mo> </mover> <mi>sat</mi> </msub> <mo>/</mo> <msub> <mover> <mi>ω</mi> <mo>&OverBar;</mo> </mover> <mi>earth</mi> </msub> <mo>-</mo> <mi>cos</mi> <mi>i</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>

r_{1} = b^{2} x_{1}^{2} + b^{2} y_{1}^{2} + a^{2} z_{1}^{2} - - - (9)

r_{2} = 2 (b^{2} x_{1} x_{s_{0}} + b^{2} y_{1} y_{s_{0}} + a^{2} z_{1} z_{s_{0}}) - - - (10)

r_{3} = b^{2} x_{s_{0}}^{2} + b^{2} y_{s_{0}}^{2} + a^{2} z_{s_{0}}^{2} - a^{2} b^{2} - - - (11)

Wherein r is₁,r₂,r₃Respectively, intermediate variables.

Antenna coordinate system E_aDistance R from unit vector (0,1,0) to ground₀：

R_{0} = \frac{- \sqrt{r_{2}^{2} - {4 r}_{1} r_{3}} - r_{2}}{{2 r}_{1}} - - - (12)

The rotating point C is a point of the antenna which fixedly points to the ground of the earth under a sliding beam-focusing mode, namely an antenna beam center focusing point. Calculating formula by sliding bunching azimuth resolutionObtaining:

Since the position of the rotation point C is not changed in the sliding bunching mode, the time T can be selected₀Now, the attitude angles of the satellites are all zero.

Step six: calculating the coordinate system E of the satellite and the rotation point C at the rotation earth center in the full sliding convergence process_gRelative vector (R) in (1)_x,R_y,R_z)；

\{\begin{matrix} R_{x} = x_{s} - x_{c_{0}} \\ R_{y} = y_{s} - y_{c_{0}} \\ R_{z} = z_{s} - z_{c_{0}} \end{matrix} - - - (15)

Step eight: calculating the antenna orientation in the antenna coordinate system E in the process of full sliding convergence_aCoordinate of (x ″)₁,y″₁,z″₁)；

Theoretically, sliding bunching attitude control can be completed by changing attitude angles of any two dimensions or all three dimensions, and the pitch angle theta is changed_pAnd yaw angle theta_yFor example, the pitch angle is controlled first and then the yaw angle is controlled to obtain the coordinate (x) after the attitude control_ZT,y_ZT,z_ZT) Comprises the following steps:

simplifying to obtain:

step ten: calculating a satellite attitude control angle in the full sliding and gathering process: pitch angle theta_pAnd yaw angle theta_y；

Solving equation (20) yields:

wherein,

step eleven: calculating a satellite attitude control rule and an angular speed control curve of each axis in the full sliding convergence process;

because different control results can be caused by different control sequences even if the control quantity is fixed, the change of the control angle needs to be expressed by using an Euler four-element formula, and the change rule of the attitude Euler angle is solved.

To be provided withRespectively representing sequential pivot vectors

\hat{1} = {(\begin{matrix} 1 & 0 & 0 \end{matrix})}^{T},

\hat{2} = {(\begin{matrix} 0 & 1 & 0 \end{matrix})}^{T},

\hat{3} = {(\begin{matrix} 0 & 0 & 1 \end{matrix})}^{T},

Then there are:

therefore, the attitude control rule, the rotation angular velocity omega of the three axes x, y and z can be obtained_x,ω_y,ω_zRespectively as follows:

through the eleven steps, the calculation of the posture control rule of the sliding bunching mode is completed.

Example (b):

the method provided by the invention is verified by a simulation experiment. The simulation verification is divided into two parts, and the first part calculates the attitude control rule provided by the invention through C + + language programming; the second part controls the satellite attitude according to the attitude control rule calculated by the first part through C + + language programming, generates echo data through simulation, images and evaluates the echo data, and verifies the correctness and superiority of the invention through comparison with simulation echo data in a phased array antenna mode.

A first part: calculating the attitude control rule provided by the invention;

parameters given in the simulation experiment: the method comprises the following steps of (1) 6378140.0m of the earth major semi-axis, 6356755.0m of the earth minor semi-axis, 6371140.0m of the average earth radius, 0.000073reg/s of the earth rotation angular velocity, 7003819.0m of the orbit semi-major axis, 97.889 of the orbit inclination angle, 90.0 of the argument of the perigee, 121.0 of right ascension at the ascending intersection point, 0.0011 of eccentricity, 0.03m of working wavelength, 20.0deg of the antenna central visual angle, 3.3m of antenna length, 350MHz of signal sampling rate, 300MHz of signal bandwidth, 5000Hz of pulse repetition frequency, 0.5m of azimuth resolution and 1.2 of beam spreading factor, wherein a point target is arranged at the center of a scene, and the specific calculation steps are:

1.1 computing the satellite in a rotating earth-centered coordinate system E_gCoordinate of (x)_s,y_s,z_s)；

Obtaining a satellite in-orbit plane coordinate system E according to the formulas (1) to (4)_vCoordinate of (x)_vs,y_vs,z_vs) As shown in equation (5), the coordinate system is converted into a rotating earth center coordinate system E_gObtaining the coordinate system E of the satellite in the rotating geocentric_gCoordinate of (x)_s,y_s,z_s) E.g. formula (6), and taking T therefrom₀Time of day satellite in rotating earth center coordinate system E_gHas the coordinates of

1.2 calculating T₀Time antenna coordinate system E_aThe unit vector (0,1,0) in the rotating earth center coordinate system E_gCoordinate of (x)₁,y₁,z₁)；

Conversion to a rotating earth-centered coordinate system E by coordinate system conversion in view of yaw control_gAs shown in formula (7).

1.3 calculating T₀Time antenna coordinate system E_aDistance R from unit vector (0,1,0) to ground₀；

According to the formulas (9) to (11), the result is calculated as the formula (12).

1.4 calculating T₀Slope distance delta R from moment rotating point C to ground pointing point₀；

Due to the fact that

Can obtain the Delta R₀As shown in formula (13).

1.5 calculating the rotation point C in the rotating geocentric coordinate system E_gCoordinates of (5)

Since the position of the rotation point is not changed in the sliding bunching mode, the time T can be selected₀At this time, the attitude angles of the satellites are all zero, and the calculation result is as shown in the formula (14).

1.6 calculating the coordinate system E of the satellite and the rotation point C at the rotating earth center in the full sliding and gathering process_gRelative vector (R) in (1)_x,R_y,R_z)；

Rotating earth center coordinate system E_gIn the process of full sliding aggregation, the position of the satellite changes, the rotation point C does not change, and a relative vector can be calculated as the formula (15).

1.7 calculation of antenna pointing in the course of full-slip focusing on the rotating geocentric coordinate System E_gCoordinate of (x'₁,y′₁,z′₁)；

The calculation result is as shown in equation (16).

1.8 calculation of antenna pointing in antenna coordinate System E during full sliding aggregation_aCoordinate of (x ″)₁,y″₁,z″₁)；

And (5) performing coordinate system conversion, as shown in formula (17).

1.9 calculating the antenna coordinate System E_aLower unit vector (0,1,0), coordinate (x) after attitude control_ZT,y_ZT,z_ZT)；

And (4) obtaining a result as shown in the formula (19) through coordinate system conversion and attitude control as shown in the formula (18).

1.10 calculating the satellite attitude control angle in the full sliding and gathering process: pitch angle theta_pAnd yaw angle theta_y；

According to equation (20), the equation can be solved to obtain the result as equation (21).

1.11 calculating a satellite attitude control rule and an angular speed control curve of each axis in the full sliding and gathering process;

according to the formula (22), the attitude control rule can be obtained, and the rotation angular velocity of the three axes x, y and z is as the formula (23).

In simulation, 65536 is taken as the number of azimuth sampling points, the maximum scanning angle is +/-2.808 degrees, different maximum scanning angles can be realized by changing the number of azimuth sampling points, in the example, for convenience of simulation program writing, 2 integral powers are taken as the number of azimuth sampling points, only-2.23 degrees to +223 degrees of scanning angle range is taken for actual processing, the length of the surveying and mapping belt is 10km, and the yaw angle theta is calculated_pAnd a pitch angle theta_yThe variation law is shown in fig. 2 and fig. 3, respectively, and the three-axis rotation angular velocities obtained for controlling the satellite attitude to realize the sliding bunching mode are shown in fig. 2 and fig. 3, respectivelyShown in fig. 4, 5 and 6.

A second part: and generating echo data by simulation, and imaging and evaluating the echo data.

Given parameters in simulation experiments are unchanged, echo data under a phased array antenna mode and an attitude control mode of the invention are generated through simulation by C + + programming respectively, results obtained through imaging are displayed in a graph 7 and a graph 8 respectively, the imaging data are evaluated, the results are displayed in a graph 9 and a graph 10 respectively, and as can be seen from analysis results, the azimuth resolution of the implementation of sliding beam bunching by attitude control is improved compared with that of the phased array antenna.

The two simulation experiments show that the method provided by the invention is a very accurate method.

Claims

1. A method for realizing a sliding spotlight mode based on SAR satellite attitude control is characterized by comprising the following steps:

At the time of transmitting the M-th pulse, the average proximal angle M is:

and then calculating the eccentric angle E as:

calculating the true paraxial angle θ as:

calculating the vector r as:

Step two: calculating T₀Time antenna coordinate system E_aThe unit vector (0,1,0) in the rotating earth center coordinate system E_gSeat inLabel (x)₁,y₁,z₁)；

Wherein r is₁,r₂,r₃Respectively intermediate variables;

Step four: calculating T₀Inclination from the moment of rotation C to the ground pointing pointDistance Δ R₀；

Calculating formula by sliding bunching azimuth resolutionObtaining:

Step seven: calculating the coordinate system E of the antenna pointing at the rotating geocentric during the full sliding convergence process_gCoordinate of (x)₁′,y₁′,z₁′)；

Step eight: calculating the antenna orientation in the antenna coordinate system E in the process of full sliding convergence_aCoordinate of (x)₁",y₁",z₁")；

Firstly controlling the pitch angle and then the yaw angle to obtain the coordinate (x) after the attitude control_ZT,y_ZT,z_ZT) Comprises the following steps:

simplifying to obtain:

Solving equation (20) yields:

and according toTo obtainAs follows below, the following description will be given,

wherein,

to be provided withRespectively representing sequential pivot vectors Then there are:

the attitude control law, namely the rotation angular velocity omega of the three axes x, y and z is obtained_x,ω_y,ω_zRespectively as follows:

through the eleven steps, the calculation of the attitude control law of the sliding bunching mode is completed;

in the above steps, the letter parameters are defined as follows:

T₀the moment when the center of the wave beam points to the center of the observation target area is observed from the front side view of the satellite; a. the_numIn order to meet the requirement of the length of the observation belt in the azimuth direction, the pulse number is transmitted; f. of_PRFIs the pulse repetition frequency PRF; theta_LIs the radar antenna view angle; rho_aThe azimuth resolution is; k_aIs an azimuth beam broadening factor; l is_sIs the equivalent antenna length;the satellite on-orbit motion average angular velocity is obtained;the earth mean rotation angular velocity; a is the length of the earth's major semi-axis; b is the length of the short half shaft of the earth; m is the mean angle of approach; e is an eccentric angle; theta is the true proximal angle; e is the eccentricity; r is the radius; p is a half positive focal length; h_GGreenwich mean hour angle at spring break; omega is the right ascension of the orbit intersection point; i is the track inclination angle; omega is the amplitude angle of the orbit in the near place; gamma is the track angle of the satellite; theta_rIs the roll angle of the satellite about the x-axis; theta_yIs the yaw angle of the satellite about the y-axis; theta_pIs the pitch angle of the satellite around the z-axis; theta_{y_c}The satellite yaw angle after yaw control; omega₃₂Is an equivalent angular velocity vector of rotation; r₂A rotation matrix when the satellite yaws; r₃A rotation matrix during satellite pitching; cosine cos is denoted by c and sine sin is denoted by s;

for the satellite platform coordinate system E_rTo the orbital plane coordinate system E_vIs rotatedChanging the matrix;

the inverse transformation is achieved by matrix inversion.