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 beamforming mode based on SAR satellite attitude control, and belongs to the technical field of signal processing. The method realizes the continuous change of the pointing angle of the satellite antenna by controlling the attitude of the satellite, and there is no angle quantification problem. By establishing a relatively complete geometric model of the spatial relationship, the sliding spotlight mode can be realized more accurately, and the resolution of the SAR azimuth direction can be improved. . Moreover, the antenna has a simple structure, can reduce the cost of the satellite, reduce the size and weight of the satellite, and has broad application prospects. Compared with the current method of realizing the sliding beamforming mode through the phased array, the method proposed by the present invention has a continuous change in antenna pointing and higher accuracy; it can greatly simplify the structure of the satellite antenna, reduce the cost of the satellite and reduce the weight of the satellite, which is very important. Value.

Description

A Method of Sliding Spotlight Mode Based on SAR Satellite Attitude Control

技术领域technical field

本发明提出一种基于SAR卫星姿态控制实现滑动聚束模式的方法，属于信号处理技术领域。The invention proposes a method for realizing a sliding beamforming mode based on SAR satellite attitude control, which belongs to the technical field of signal processing.

背景技术Background technique

滑动聚束模式是一种新颖的合成孔径雷达（SAR）成像模式，它通过控制天线辐照区在地面的移动速度来控制方位分辨率，其成像的面积比聚束模式大，并且其分辨率可以高于相同天线尺寸条带模式，它可以在高分辨率和大面积成像中做出很好的权衡。而相控阵天线是目前实现滑动聚束模式的主要手段，在雷达天线扫描方式上，相控阵天线指向角受数字移相器量化位影响，存在角度量化误差，实现连续变化是不可能的，这种量化问题导致回波主能量不连续，影响SAR的方位向分辨率。并且相控阵天线结构复杂，造价高昂，需要复杂的中央处理器进行控制。The sliding spotlight mode is a novel synthetic aperture radar (SAR) imaging mode. It controls the azimuth resolution by controlling the moving speed of the antenna irradiation area on the ground. Its imaging area is larger than that of the spotlight mode, and its resolution Can be higher than the same antenna size strip mode, it can make a good trade-off in high resolution and large area imaging. The phased array antenna is currently the main means to realize the sliding beamforming mode. In the scanning mode of the radar antenna, the pointing angle of the phased array antenna is affected by the quantization bit of the digital phase shifter, and there is an angle quantization error, so it is impossible to realize continuous change. , this quantization problem leads to the discontinuity of the main energy of the echo, which affects the azimuth resolution of SAR. Moreover, the structure of the phased array antenna is complicated, the cost is high, and a complex central processing unit is required for control.

发明内容Contents of the invention

本发明提出了一种基于SAR卫星姿态控制实现滑动聚束模式的方法，该方法通过对卫星滚动角θ_r、偏航角θ_y和俯仰角θ_p的控制，调整卫星天线指向，使之保持指向地下旋转点C，从而实现滑动聚束模式，本发明是一种适用于高机动性卫星实现滑动聚束模式的新方法。The present invention proposes _a method for realizing the sliding beamforming mode based on SAR satellite attitude control _. The method adjusts the pointing of the satellite antenna to maintain _the Pointing to the underground rotation point C to realize the sliding beamforming mode, the invention is a new method suitable for high mobility satellites to realize the sliding beamforming mode.

一种基于SAR卫星姿态控制实现滑动聚束模式的方法，包括以下几个步骤：A method for realizing sliding spotlight mode based on SAR satellite attitude control, comprising the following steps:

步骤一：计算卫星在转动地心坐标系E_g中的坐标(x_s,y_s,z_s)；Step 1: Calculate the coordinates (x _s , y _s , z _s ) of the satellite in the rotating geocentric coordinate system E _g ;

步骤二：计算卫星正侧视波束中心指向观测目标区域中心的时刻T₀，天线坐标系E_a中单位矢量(0,1,0)在转动地心坐标系E_g中的坐标；Step 2: Calculate the coordinates of the unit vector (0,1,0) in the antenna coordinate system E _a in the rotating geocentric coordinate system E _g at the time T ₀ when the center of the side-looking beam of the satellite points to the center of the observation target area;

步骤三：计算T₀时刻天线坐标系E_a中单位矢量(0,1,0)到地面的距离R₀；Step 3: Calculate the distance R ₀ from the unit vector (0,1,0) to the ground in the antenna coordinate system E _a at time T ₀ ;

步骤四：计算T₀时刻旋转点C到地面指向点的斜距ΔR₀；Step 4: Calculate the slant distance ΔR ₀ from the rotation point C to the ground pointing point at time T ₀ ;

步骤五：计算旋转点C在转动地心坐标系E_g中的坐标 Step 5: Calculate the coordinates of the rotation point C in the rotating geocentric coordinate system E _g

步骤六：计算全滑聚(滑动聚束)过程中卫星与旋转点C在转动地心坐标系E_g中的相对矢量(R_x,R_y,R_z)；Step 6: Calculate the relative vector (R _x , R _y , R _z ) between the satellite and the rotation point C in the rotating geocentric coordinate system E _g during the full sliding (sliding beamforming) process;

步骤七：计算全滑聚过程中天线指向在转动地心坐标系E_g中的坐标(x′₁,y′₁,z′₁)；Step 7: Calculate the coordinates (x′ ₁ , y′ ₁ , z′ ₁ ) of the antenna pointing in the rotating earth-centered coordinate system E _g during the full sliding process;

步骤八：计算全滑聚过程中天线指向在天线坐标系E_a中的坐标(x″₁,y″₁，z″₁)；Step 8: Calculate the coordinates (x″ ₁ , y″ ₁ , z″ ₁ ) that the antenna points to in the antenna coordinate system E _a during the full sliding process;

步骤九：计算天线坐标系E_a下单位矢量(0,1,0)，经姿态控制后的坐标(x_ZT,y_ZT,z_ZT)；Step 9: Calculate the unit vector (0,1,0) in the antenna coordinate system E _a , and the coordinates (x _ZT , y _ZT , z _ZT ) after attitude control;

步骤十：计算全滑聚过程中卫星姿态控制角；Step 10: Calculate the satellite attitude control angle in the process of full sliding and gathering;

步骤十一：计算全滑聚过程中卫星姿态控制规律，及各轴角速度控制曲线。Step 11: Calculate the satellite attitude control law and the angular velocity control curves of each axis in the process of full sliding and gathering.

本发明提出一种基于SAR卫星姿态控制实现滑动聚束模式的方法，该方法通过对卫星姿态进行调控，实现卫星天线指向角连续变化，不存在角度量化问题，通过建立较完善的空间关系几何模型，可更精确地实现滑动聚束模式，提高SAR方位向分辨率。而且，天线结构简单，可以降低卫星成本，减小卫星体积和重量，具有广阔的应用前景。The present invention proposes a method for realizing the sliding beamforming mode based on SAR satellite attitude control. The method realizes the continuous change of the pointing angle of the satellite antenna by regulating the attitude of the satellite, and there is no problem of angle quantization. By establishing a relatively complete spatial relationship geometric model , which can realize the sliding spotlight mode more accurately and improve the resolution of SAR in azimuth direction. Moreover, the antenna has a simple structure, can reduce the cost of the satellite, reduce the size and weight of the satellite, and has broad application prospects.

本发明的优点在于：The advantages of the present invention are:

（1）本发明提出的方法相比于目前通过相控阵实现滑动聚束模式的方法，天线指向连续变化，准确度更高；(1) Compared with the current method of realizing the sliding beamforming mode through the phased array, the method proposed by the present invention can continuously change the antenna pointing, and the accuracy is higher;

（2）本发明提出的方法，是在十分精确的星体运动模型中实现的，精确度十分高；(2) The method proposed by the present invention is realized in a very accurate astral motion model, and the accuracy is very high;

（3）本发明提出的方法可以大大简化卫星天线结构，降低卫星成本和减轻卫星重量，具有十分重要的应用价值。(3) The method proposed by the present invention can greatly simplify the structure of the satellite antenna, reduce the cost and weight of the satellite, and has very important application value.

附图说明Description of drawings

图1是本发明的方法流程图；Fig. 1 is method flowchart of the present invention;

图2是实施例中俯仰角随扫描时间变化曲线；Fig. 2 is the variation curve of pitch angle with scanning time in the embodiment;

图3是实施例中偏航角随扫描时间变化曲线；Fig. 3 is the variation curve of yaw angle with scanning time in the embodiment;

图4是实施例中卫星x轴角速度随扫描时间变化曲线；Fig. 4 is the variation curve of satellite x-axis angular velocity with scanning time in the embodiment;

图5是实施例中卫星y轴角速度随扫描时间变化曲线；Fig. 5 is the change curve of satellite y-axis angular velocity with scanning time in the embodiment;

图6是实施例中卫星z轴角速度随扫描时间变化曲线；Fig. 6 is the change curve of satellite z-axis angular velocity with scanning time in the embodiment;

图7是实施例中相控阵天线滑聚模式成像结果放大图；Fig. 7 is an enlarged view of the imaging result of the phased array antenna sliding convergence mode in the embodiment;

图8是实施例中姿态调控滑聚模式成像结果放大图；Fig. 8 is an enlarged view of the imaging result of attitude control sliding mode in the embodiment;

图9是实施例中相控阵天线滑聚模式点目标分析结果；Fig. 9 is the point target analysis result of phased array antenna sliding mode in the embodiment;

图10是实施例中姿态调控滑聚模式点目标分析结果。Fig. 10 is the point target analysis result of attitude control sliding convergence mode in the embodiment.

具体实施方式Detailed ways

下面将结合附图及实施例对本发明作进一步的详细说明。The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

本发明公式参数声明部分：The formula parameter declaration part of the present invention:

T₀为卫星正侧视波束中心指向观测目标区域中心的时刻；T ₀ is the moment when the center of the side-looking beam of the satellite points to the center of the observed target area;

A_num为满足观测带方位向长度要求，发射脉冲数；A _num is the number of transmitted pulses to meet the azimuth length requirement of the observation zone;

f_PRF为脉冲重复频率PRF；f _PRF is the pulse repetition frequency PRF;

θ_L为雷达天线视角；θ _L is the angle of view of the radar antenna;

ρ_a为方位向分辨率；ρ _a is the azimuth resolution;

K_a为方位向波束展宽因子；K _a is the azimuth beam broadening factor;

L_s为等效天线长度；L _s is the equivalent antenna length;

为卫星在轨运动平均角速度； is the average angular velocity of the satellite in orbit;

为地球平均自转角速度； is the mean angular velocity of the earth's rotation;

a为地球长半轴长度；a is the length of the semi-major axis of the earth;

b为地球短半轴长度；b is the length of the semi-minor axis of the earth;

M为平均近心角；M is the average pericardial angle;

E为偏心角；E is the eccentric angle;

θ为真近心角；θ is the true pericardial angle;

e为偏心率；e is the eccentricity;

r为矢径；r is the vector radius;

P为半正焦距；P is the half positive focal length;

H_G为春分点的格林威治时角；H _G is the Greenwich hour angle of the vernal equinox;

Ω为轨道升交点赤经；Ω is the right ascension of ascending node of the orbit;

i为轨道倾角；i is the orbital inclination;

ω为轨道近地点幅角；ω is the argument of perigee;

γ为卫星的航迹角；γ is the track angle of the satellite;

θ_r为卫星绕x轴的滚转角；θ _r is the roll angle of the satellite around the x-axis;

θ_y为卫星绕y轴的偏航角；θ _y is the yaw angle of the satellite around the y-axis;

θ_p为卫星绕z轴的俯仰角；θ _p is the pitch angle of the satellite around the z axis;

θ_{y_c}为偏航控制后的卫星偏航角；θ _{y_c} is the satellite yaw angle after yaw control;

ω₃₂为等效旋转角速度矢量；ω ₃₂ is the equivalent rotational angular velocity vector;

R₂为卫星偏航时旋转矩阵；R ₂ is the rotation matrix of satellite yaw;

R₃为卫星俯仰时旋转矩阵。R ₃ is the rotation matrix when the satellite is pitching.

本发明的坐标系转换矩阵声明（为方便表示，用c表示余弦cos，用s表示正弦sin）：The coordinate system conversion matrix statement of the present invention (for convenience, use c to represent cosine cos, and s to represent sine sin):

$A_{go} = (\begin{matrix} c_{H_{G}} & s_{H_{G}} & 0 \\ {- s}_{H_{G}} & c_{H_{G}} & 0 \\ 0 & 0 & 1 \end{matrix})$ 为不转动地心坐标系E_o到转动地心坐标系E_g的转换矩阵； $A_{go} = (\begin{matrix} c_{h_{G}} & {the s}_{h_{G}} & 0 \\ {- the s}_{h_{G}} & c_{h_{G}} & 0 \\ 0 & 0 & 1 \end{matrix})$ is the transformation matrix from the non-rotating geocentric coordinate system E _o to the rotating geocentric coordinate system E _g ;

$A_{ov} = (\begin{matrix} c_{Ω} & s_{Ω} & 0 \\ {- s}_{Ω} & c_{Ω} & 0 \\ 0 & 0 & 1 \end{matrix}) \cdot (\begin{matrix} 1 & 0 & 0 \\ 0 & c_{i} & s_{i} \\ 0 & {- s}_{i} & c_{i} \end{matrix}) \cdot (\begin{matrix} c_{ω} & s_{ω} & 0 \\ {- s}_{ω} & c_{ω} & 0 \\ 0 & 0 & 1 \end{matrix})$ 为轨道平面坐标系E_v到不转动地心坐标系E_o的转换矩阵； $A_{ov} = (\begin{matrix} c_{Ω} & {the s}_{Ω} & 0 \\ {- the s}_{Ω} & c_{Ω} & 0 \\ 0 & 0 & 1 \end{matrix}) \cdot (\begin{matrix} 1 & 0 & 0 \\ 0 & c_{i} & {the s}_{i} \\ 0 & {- the s}_{i} & c_{i} \end{matrix}) \cdot (\begin{matrix} c_{ω} & {the s}_{ω} & 0 \\ {- the s}_{ω} & c_{ω} & 0 \\ 0 & 0 & 1 \end{matrix})$ is the conversion matrix from the orbit plane coordinate system E _v to the non-rotating geocentric coordinate system E _o ;

$A_{vr} = (\begin{matrix} {- s}_{(θ - γ)} & {- c}_{(θ - γ)} & 0 \\ c_{(θ - γ)} & {- s}_{(θ - γ)} & 0 \\ 0 & 0 & 1 \end{matrix})$ 为卫星平台坐标系E_r到轨道平面坐标系E_v的转换矩阵； $A_{vr} = (\begin{matrix} {- the s}_{(θ - γ)} & {- c}_{(θ - γ)} & 0 \\ c_{(θ - γ)} & {- the s}_{(θ - γ)} & 0 \\ 0 & 0 & 1 \end{matrix})$ is the transformation matrix from the satellite platform coordinate system E _r to the orbit plane coordinate system E _v ;

$A_{re} = (\begin{matrix} c_{θ_{r}} & 0 & {- s}_{θ_{r}} \\ 0 & 1 & 0 \\ s_{θ_{r}} & 0 & c_{θ_{r}} \end{matrix}) \cdot (\begin{matrix} c_{θ_{p}} & {- s}_{θ_{p}} & 0 \\ s_{θ_{p}} & c_{θ_{p}} & 0 \\ 0 & 0 & 1 \end{matrix}) \cdot (\begin{matrix} 1 & 0 & 0 \\ 0 & c_{θ_{y}} & {- s}_{θ_{y}} \\ 0 & s_{θ_{y}} & c_{θ_{y}} \end{matrix})$ 为卫星星体坐标系E_e到卫星平台坐标系E_r的转换矩阵； $A_{re} = (\begin{matrix} c_{θ_{r}} & 0 & {- the s}_{θ_{r}} \\ 0 & 1 & 0 \\ {the s}_{θ_{r}} & 0 & c_{θ_{r}} \end{matrix}) &Center Dot; (\begin{matrix} c_{θ_{p}} & {- the s}_{θ_{p}} & 0 \\ {the s}_{θ_{p}} & c_{θ_{p}} & 0 \\ 0 & 0 & 1 \end{matrix}) &Center Dot; (\begin{matrix} 1 & 0 & 0 \\ 0 & c_{θ_{the y}} & {- the s}_{θ_{the y}} \\ 0 & {the s}_{θ_{the y}} & c_{θ_{the y}} \end{matrix})$ is the transformation matrix from the satellite star coordinate system E _e to the satellite platform coordinate system E _r ;

$A_{ea} = (\begin{matrix} 1 & 0 & 0 \\ 0 & c_{θ_{L}} & s_{θ_{L}} \\ 0 & {- s}_{θ_{L}} & c_{θ_{L}} \end{matrix})$ 为天线坐标系E_a到卫星星体坐标系E_e的转换矩阵； $A_{ea} = (\begin{matrix} 1 & 0 & 0 \\ 0 & c_{θ_{L}} & {the s}_{θ_{L}} \\ 0 & {- the s}_{θ_{L}} & c_{θ_{L}} \end{matrix})$ is the transformation matrix from the antenna coordinate system E _a to the satellite star coordinate system E _e ;

相反转换可通过矩阵求逆实现。The opposite transformation can be achieved by matrix inversion.

本发明通过卫星姿态控制实现滑动聚束模式，方法流程如图1所示，具体包括以下几个步骤。The present invention realizes the sliding beamforming mode through satellite attitude control, and the method flow is shown in FIG. 1 , which specifically includes the following steps.

发射第m个脉冲时，平均近心角M为：When the mth pulse is emitted, the average pericardial angle M is:

$M m = = {\overset{&OverBar; &OverBar;}{ω ω}}_{sat sat} \cdot &Center Dot; (({T T}_{00} + + \frac{m m}{{f f}_{PRF PRF}} - - \frac{{A A}_{num num}}{22 \cdot &Center Dot; {f f}_{PRF PRF}})) - - - - - - ((11))$

进而计算偏心角E为：Then calculate the eccentric angle E as:

$E E. = = M m + + e e \cdot &Center Dot; ((11 - - \frac{{e e}^{22}}{88} + + \frac{{e e}^{44}}{192192})) \cdot &Center Dot; sin sin M m + + {e e}^{22} \cdot &Center Dot; ((\frac{11}{22} - - \frac{{e e}^{22}}{66})) \cdot &Center Dot; sin sin ((22 M m)) + +$ $((22))$

${e e}^{33} \cdot &Center Dot; ((\frac{33}{88} - - \frac{{2727 e e}^{22}}{128128})) \cdot &Center Dot; sin sin ((33 M m)) + + \frac{11}{33} {e e}^{44} \cdot \cdot sin sin ((44 M m)) + + \frac{125125}{384384} {e e}^{55} \cdot \cdot sin sin ((55 M m))$

计算真近心角θ为：Calculate the true pericardial angle θ as:

$θ θ = = 22 \cdot &Center Dot; arctan arctan ((\sqrt{\frac{11 + + e e}{11 - - e e}} \cdot &Center Dot; tan the tan \frac{E E.}{22})) - - - - - - ((33))$

计算矢径r为：Calculate the radius r as:

$r r = = \frac{P P}{11 + + e e \cdot \cdot cos cos θ θ} - - - - - - ((44))$

由上可得卫星在轨道平面坐标系E_v中的坐标(x_vs,y_vs,z_vs)为：From the above, the coordinates (x _vs , y _vs , z _vs ) of the satellite in the orbit plane coordinate system E _v are:

$(\begin{matrix} {x x}_{vs vs} \\ {y the y}_{vs vs} \\ {z z}_{vs vs} \end{matrix}) = = (\begin{matrix} r r \cdot &Center Dot; cos cos θ θ \\ r r \cdot &Center Dot; sin sin θ θ \\ 00 \end{matrix}) - - - - - - ((55))$

通过坐标系转换，转换至转动地心坐标系E_g，得到卫星在转动地心坐标系E_g中的坐标(x_s,y_s,z_s)为：Through coordinate system transformation, transform to the rotating earth-centered coordinate system E _g , and obtain the coordinates (x _s , y _s , z _s ) of the satellite in the rotating earth-centered coordinate system E _g as:

$(\begin{matrix} {x x}_{s the s} \\ {y the y}_{s the s} \\ {z z}_{s the s} \end{matrix}) = = {A A}_{go go} \cdot &Center Dot; {A A}_{ov ov} \cdot &Center Dot; (\begin{matrix} {x x}_{vs vs} \\ {y the y}_{vs vs} \\ {z z}_{vs vs} \end{matrix}) - - - - - - ((66))$

从中取T₀时刻卫星在转动地心坐标系E_g的坐标为 From it, the coordinates of the satellite in the rotating earth-centered coordinate system E _g at time T ₀ are

步骤二：计算T₀时刻天线坐标系E_a中单位矢量(0,1,0)在转动地心坐标系E_g中的坐标(x₁,y₁,z₁)；Step 2: Calculate the coordinates ₍ x ₁ , y ₁ , z ₁ ) of the unit vector (0,1,0) in the antenna coordinate system E _a in the rotating geocentric coordinate system E g at time T ₀ ;

通过坐标系转换，转换至卫星星体坐标系E_e，转换至卫星平台坐标系E_r，转换至轨道平面坐标系E_v，转换至不转动的地心轨道坐标系E_o，再转换至转动地心坐标系E_g，得到天线坐标系E_a中单位矢量(0,1,0)在转动地心坐标系E_g中的坐标(x₁,y₁,z₁)为：Through coordinate system conversion, it is converted to the satellite star coordinate system E _e , to the satellite platform coordinate system E _r , to the orbital plane coordinate system E _v , to the non-rotating earth-centered orbital coordinate system E _o , and then to the rotating earth coordinate system. center coordinate system E _g , the coordinates (x ₁ , y ₁ , z ₁ ) of the unit vector (0,1,0) in the antenna coordinate system E _a in the rotating geocentric coordinate system E _g are obtained as:

$(\begin{matrix} {x x}_{11} \\ {y the y}_{11} \\ {z z}_{11} \end{matrix}) = = {A A}_{go go} \cdot \cdot {A A}_{ov ov} \cdot \cdot {A A}_{vr vr} \cdot \cdot {A A}_{re re} \cdot \cdot {A A}_{ea ea} \cdot \cdot (\begin{matrix} 00 \\ 11 \\ 00 \end{matrix}) - - - - - - ((77))$

注意：此时不考虑姿态调整控制，在A_re中姿态角都为零。在从卫星星体坐标系E_e转换至卫星平台坐标系E_r过程中，考虑偏航控制。经偏航控制，卫星偏航角θ_{y_c}为：Note: The attitude adjustment control is not considered at this time, and the attitude angles are all zero in _Are . In the process of transforming from the satellite star coordinate system E _e to the satellite platform coordinate system E _r , the yaw control is considered. After yaw control, the satellite yaw angle θ _{y_c} is:

${θ θ}_{y the y__c c} = = {θ θ}_{y the y} + + arctan arctan ((\frac{cos cos ((θ θ + + ω ω)) - - sin sin i i}{{\overset{&OverBar; &OverBar;}{ω ω}}_{sat sat} / / {\overset{&OverBar; &OverBar;}{ω ω}}_{earth earth} - - cos cos i i})) - - - - - - ((88))$

${r r}_{11} = = {b b}^{22} {x x}_{11}^{22} + + {b b}^{22} {y the y}_{11}^{22} + + {a a}^{22} {z z}_{11}^{22} - - - - - - ((99))$

${r r}_{22} = = 22 (({b b}^{22} {x x}_{11} {x x}_{{s the s}_{00}} + + {b b}^{22} {y the y}_{11} {y the y}_{{s the s}_{00}} + + {a a}^{22} {z z}_{11} {z z}_{{s the s}_{00}})) - - - - - - ((1010))$

${r r}_{33} = = {b b}^{22} {x x}_{{s the s}_{00}}^{22} + + {b b}^{22} {y the y}_{{s the s}_{00}}^{22} + + {a a}^{22} {z z}_{{s the s}_{00}}^{22} - - {a a}^{22} {b b}^{22} - - - - - - ((1111))$

其中，r₁,r₂,r₃分别为中间变量。Among them, r ₁ , r ₂ , and r ₃ are intermediate variables respectively.

天线坐标系E_a中单位矢量(0,1,0)到地面的距离R₀：The distance R ₀ from the unit vector (0,1,0) in the antenna coordinate system E _a to the ground:

${R R}_{00} = = \frac{- - \sqrt{{r r}_{22}^{22} - - {44 r r}_{11} {r r}_{33}} - - {r r}_{22}}{{22 r r}_{11}} - - - - - - ((1212))$

旋转点C为滑动聚束模式下，天线固定指向地球地面下的一点，即为天线波束中心聚焦点。由滑动聚束方位向分辨率计算公式得：Rotation point C is in the sliding beamforming mode, and the antenna is fixedly pointing to a point under the ground of the earth, which is the central focus point of the antenna beam. Calculation formula of azimuth resolution by sliding beamforming have to:

${ΔR ΔR}_{00} = = \frac{{22 ρ ρ}_{a a} {R R}_{00}}{{K K}_{a a} {L L}_{s the s} - - 22 {ρ ρ}_{a a}} - - - - - - ((1313))$

$\{\begin{matrix} {x x}_{{c c}_{00}} = = {x x}_{11} \cdot &Center Dot; (({R R}_{00} + + {ΔR ΔR}_{00})) + + {x x}_{{s the s}_{00}} \\ {y the y}_{{c c}_{00}} = = {y the y}_{11} \cdot &Center Dot; (({R R}_{00} + + {ΔR ΔR}_{00})) + + {y the y}_{{s the s}_{00}} \\ {z z}_{{c c}_{00}} = = {z z}_{11} \cdot &Center Dot; (({R R}_{00} + + {ΔR ΔR}_{00})) + + {z z}_{{s the s}_{00}} \end{matrix} - - - - - - ((1414))$

由于滑动聚束模式下，旋转点C位置不变，可以选择时刻T₀下，此时卫星姿态角都为零。Since the position of the rotation point C remains unchanged in the sliding beamforming mode, the time T ₀ can be selected, and the attitude angles of the satellites are all zero at this time.

步骤六：计算全滑聚过程中卫星与旋转点C在转动地心坐标系E_g中的相对矢量(R_x,R_y,R_z)；Step 6: Calculate the relative vectors (R _x , R _y , R _z ) between the satellite and the rotating point C in the rotating geocentric coordinate system E _g during the full sliding and gathering process;

$\{\begin{matrix} {R R}_{x x} = = {x x}_{s the s} - - {x x}_{{c c}_{00}} \\ {R R}_{y the y} = = {y the y}_{s the s} - - {y the y}_{{c c}_{00}} \\ {R R}_{z z} = = {z z}_{s the s} - - {z z}_{{c c}_{00}} \end{matrix} - - - - - - ((1515))$

$\{\begin{matrix} {x x}_{11}^{' '} = = \frac{{x x}_{{c c}_{00}} - - {x x}_{s the s}}{\sqrt{{R R}_{x x}^{22} + + {R R}_{y the y}^{22} + + {R R}_{z z}^{22}}} \\ {y the y}_{11}^{' '} = = \frac{{y the y}_{{c c}_{00}} - - {y the y}_{s the s}}{\sqrt{{R R}_{x x}^{22} + + {R R}_{y the y}^{22} + + {R R}_{z z}^{22}}} \\ {z z}_{11}^{' '} = = \frac{{z z}_{{c c}_{00}} - - {z z}_{s the s}}{\sqrt{{R R}_{x x}^{22} + + {R R}_{y the y}^{22} + + {R R}_{z z}^{22}}} \end{matrix} - - - - - - ((1616))$

步骤八：计算全滑聚过程中天线指向在天线坐标系E_a中的坐标(x″₁,y″₁,z″₁)；Step 8: Calculate the coordinates (x″ ₁ , y″ ₁ , z″ ₁ ) that the antenna points to in the antenna coordinate system E _a during the full sliding process;

$(\begin{matrix} {x x}_{11}^{' '' '} \\ {y the y}_{11}^{' '' '} \\ {z z}_{11}^{' '' '} \end{matrix}) = = {A A}_{ae ae} \cdot \cdot {A A}_{er er} \cdot \cdot {A A}_{rv rv} \cdot \cdot {A A}_{vo vo} \cdot \cdot {A A}_{og og} \cdot \cdot (\begin{matrix} {x x}_{11}^{' '} \\ {y the y}_{11}^{' '} \\ {z z}_{11}^{' '} \end{matrix}) - - - - - - ((1717))$

理论上，改变任意两个维度或全部三个维度的姿态角都可以完成滑动聚束姿态控制，取改变俯仰角θ_p和偏航角θ_y为例，先控制俯仰角再控制偏航角得到姿态控制后的坐标(x_ZT,y_ZT,z_ZT)为：Theoretically, changing the attitude angles of any two dimensions or all three dimensions can complete the sliding beamforming attitude control. Taking changing the pitch angle θ _p and yaw angle θ _y as an example, first control the pitch angle and then control the yaw angle to obtain The coordinates (x _ZT , y _ZT , z _ZT ) after attitude control are:

$(\begin{matrix} {x x}_{ZT ZT} \\ {y the y}_{ZT ZT} \\ {z z}_{ZT ZT} \end{matrix}) = = {A A}_{ae ae} \cdot \cdot (\begin{matrix} {c c}_{{θ θ}_{y the y}} & 00 & {s the s}_{{θ θ}_{y the y}} \\ 00 & 11 & 00 \\ - - {s the s}_{{θ θ}_{y the y}} & 00 & {c c}_{{θ θ}_{y the y}} \end{matrix}) \cdot \cdot (\begin{matrix} {c c}_{{θ θ}_{p p}} & {s the s}_{{θ θ}_{p p}} & 00 \\ {- - s the s}_{{θ θ}_{p p}} & {c c}_{{θ θ}_{p p}} & 00 \\ 00 & 00 & 11 \end{matrix}) \cdot &Center Dot; {A A}_{ea ea} \cdot \cdot (\begin{matrix} 00 \\ 11 \\ 00 \end{matrix}) - - - - - - ((1818))$

化简得：Simplified:

$\{\begin{matrix} {x x}_{ZT ZT} = = {c c}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{p p}} {c c}_{{θ θ}_{L L}} - - {s the s}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{L L}} \\ {y the y}_{ZT ZT} = = {c c}_{{θ θ}_{p p}} {c c}_{{θ θ}_{L L}}^{22} + + {c c}_{{θ θ}_{L L}} {s the s}_{{θ θ}_{L L}} {s the s}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{p p}} + + {s the s}_{{θ θ}_{L L}}^{22} {c c}_{{θ θ}_{y the y}} \\ {z z}_{ZT ZT} = = {s the s}_{{θ θ}_{L L}} {c c}_{{θ θ}_{L L}} {c c}_{{θ θ}_{p p}} - - {c c}_{{θ θ}_{L L}}^{22} {s the s}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{p p}} - - {s the s}_{{θ θ}_{L L}} {c c}_{{θ θ}_{L L}} {c c}_{{θ θ}_{y the y}} \end{matrix} - - - - - - ((1919))$

步骤十：计算全滑聚过程中卫星姿态控制角：俯仰角θ_p和偏航角θ_y；Step 10: Calculate the satellite attitude control angle during the full sliding process: pitch angle θ _p and yaw angle θ _y ;

$\{\begin{matrix} {x x}_{11}^{' '' '} = = {x x}_{ZT ZT} = = {c c}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{p p}} {c c}_{{θ θ}_{L L}} - - {s the s}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{L L}} \\ {y the y}_{11}^{' '' '} = = {y the y}_{ZT ZT} = = {c c}_{{θ θ}_{p p}} {c c}_{{θ θ}_{L L}}^{22} + + {c c}_{{θ θ}_{L L}} {s the s}_{{θ θ}_{L L}} {s the s}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{p p}} + + {s the s}_{{θ θ}_{L L}}^{22} {c c}_{{θ θ}_{y the y}} \\ {z z}_{11}^{' '' '} = = {z z}_{ZT ZT} = = {s the s}_{{θ θ}_{L L}} {c c}_{{θ θ}_{L L}} {c c}_{{θ θ}_{p p}} - - {c c}_{{θ θ}_{L L}}^{22} {s the s}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{p p}} - - {s the s}_{{θ θ}_{L L}} {c c}_{{θ θ}_{L L}} {c c}_{{θ θ}_{y the y}} \end{matrix} - - - - - - ((2020))$

解方程（20）可得：Solving Equation (20) gives:

$\{\begin{matrix} {s the s}_{{θ θ}_{y the y}} = = \frac{- - A A \cdot &Center Dot; B B - - \sqrt{11 - - {A A}^{22} + + {B B}^{22}}}{11 + + {B B}^{22}} \\ {c c}_{{θ θ}_{y the y}} = = A A + + B B \cdot &Center Dot; {s the s}_{{θ θ}_{y the y}} \\ {s the s}_{{θ θ}_{p p}} = = \frac{{x x}_{11}^{' '' '} + + {s the s}_{{θ θ}_{y the y}} {s the s}_{{θ θ}_{L L}}}{{c c}_{{θ θ}_{y the y}} {c c}_{{θ θ}_{L L}}} \\ {c c}_{{θ θ}_{p p}} = = \frac{{z z}_{11}^{' '' '}}{{c c}_{{θ θ}_{L L}} {c c}_{{θ θ}_{L L}}} + + \frac{11}{{c c}_{{θ θ}_{y the y}}} + + \frac{{s the s}_{{θ θ}_{y the y}} \cdot \cdot {x x}_{11}^{' '' '}}{{c c}_{{θ θ}_{y the y}} \cdot \cdot {s the s}_{{θ θ}_{L L}}} \end{matrix} - - - - - - ((21 twenty one))$

其中， $\{\begin{matrix} A = \frac{s_{θ_{L}}}{y_{1}^{''} s_{θ_{L}} - z_{1}^{''} c_{θ_{L}}} \\ B = \frac{x_{1}^{''}}{y_{1}^{''} s_{θ_{L}} - z_{1}^{''} c_{θ_{L}}} \end{matrix} .$ in, $\{\begin{matrix} A = \frac{{the s}_{θ_{L}}}{{the y}_{1}^{''} {the s}_{θ_{L}} - z_{1}^{''} c_{θ_{L}}} \\ B = \frac{x_{1}^{''}}{{the y}_{1}^{''} {the s}_{θ_{L}} - z_{1}^{''} c_{θ_{L}}} \end{matrix} .$

步骤十一：计算全滑聚过程中卫星姿态控制规律，及各轴角速度控制曲线；Step 11: Calculate the satellite attitude control law and the angular velocity control curve of each axis during the full sliding and gathering process;

由于即使控制量一定，控制的先后顺序不同也会造成不同的控制结果，需将控制角度的变化使用欧拉四元素式表示，求出姿态欧拉角的变化规律。Even if the control amount is constant, different control sequences will result in different control results. It is necessary to express the change of the control angle using the Euler four-element formula to find the change law of the attitude Euler angle.

以分别表示顺序转轴矢量 $\hat{1} = {(\begin{matrix} 1 & 0 & 0 \end{matrix})}^{T},$ $\hat{2} = {(\begin{matrix} 0 & 1 & 0 \end{matrix})}^{T},$ $\hat{3} = {(\begin{matrix} 0 & 0 & 1 \end{matrix})}^{T},$ 则有：by Respectively represent the sequential rotation axis vector $\hat{1} = {(\begin{matrix} 1 & 0 & 0 \end{matrix})}^{T},$ $\hat{2} = {(\begin{matrix} 0 & 1 & 0 \end{matrix})}^{T},$ $\hat{3} = {(\begin{matrix} 0 & 0 & 1 \end{matrix})}^{T},$ Then there are:

${ω ω}_{3232} = = {R R}_{22} (({θ θ}_{y the y})) \cdot &Center Dot; [[{\overset{\cdot &Center Dot;}{θ θ}}_{y the y} \cdot &Center Dot; \overset{^^}{22} + + {R R}_{33} (({θ θ}_{p p})) \cdot \cdot {\overset{\cdot \cdot}{θ θ}}_{p p} \cdot &Center Dot; \overset{^^}{33}]]$

$= = (\begin{matrix} {c c}_{{θ θ}_{y the y}} & 00 & {s the s}_{{θ θ}_{y the y}} \\ 00 & 11 & 00 \\ {- - s the s}_{{θ θ}_{y the y}} & 00 & {c c}_{{θ θ}_{y the y}} \end{matrix}) \cdot \cdot [\begin{matrix} {\overset{\cdot \cdot}{θ θ}}_{y the y} \end{matrix} (\begin{matrix} 00 \\ 11 \\ 00 \end{matrix}) + + (\begin{matrix} {c c}_{{θ θ}_{p p}} & {s the s}_{{θ θ}_{p p}} & 00 \\ {- - s the s}_{{θ θ}_{p p}} & {c c}_{{θ θ}_{p p}} & 00 \\ 00 & 00 & 11 \end{matrix}) \cdot \cdot {\overset{\cdot \cdot}{θ θ}}_{p p} (\begin{matrix} 00 \\ 00 \\ 11 \end{matrix})] - - - - - - ((22 twenty two))$

$= = (\begin{matrix} {s the s}_{{θ θ}_{y the y}} \cdot \cdot {\overset{\cdot \cdot}{θ θ}}_{p p} \\ {\overset{\cdot \cdot}{θ θ}}_{y the y} \\ {c c}_{{θ θ}_{y the y}} \cdot \cdot {\overset{\cdot \cdot}{θ θ}}_{p p} \end{matrix})$

由此可得姿态控制规律，x,y,z三轴的旋转角速度ω_x,ω_y,ω_z分别为：From this, the attitude control law can be obtained. The rotational angular velocities ω x , ω y , and ω z of the three axes of _x , _y , and _z are respectively:

$(\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}) = = (\begin{matrix} {s the s}_{{θ θ}_{y the y}} \cdot \cdot {\overset{\cdot \cdot}{θ θ}}_{p p} \\ {\overset{\cdot \cdot}{θ θ}}_{y the y} \\ {c c}_{{θ θ}_{y the y}} \cdot \cdot {\overset{\cdot \cdot}{θ θ}}_{p p} \end{matrix}) - - - - - - ((23 twenty three))$

经过以上十一个步骤，完成了对滑动聚束模式姿态控制规律的计算。After the above eleven steps, the calculation of the attitude control law of the sliding beamforming mode is completed.

实施例：Example:

对本发明提出的方法进行了仿真实验验证。仿真验证分为两部分，第一部分通过C++语言编程，计算出本发明提出的姿态控制规律；第二部分通过C++语言编程，根据第一部分计算出的姿态控制规律对卫星姿态进行控制，仿真生成回波数据，并对回波数据进行成像和评估，通过与相控阵天线方式的仿真回波数据对比，验证了本发明的正确性以及优越性。The method proposed in the present invention is verified by simulation experiments. The simulation verification is divided into two parts. The first part calculates the attitude control law proposed by the present invention through C++ language programming; the second part uses C++ language programming to control the satellite attitude according to the attitude control law calculated in the first part, and the simulation generates a return The echo data is imaged and evaluated, and the correctness and superiority of the present invention are verified by comparing with the simulated echo data of the phased array antenna.

第一部分：计算出本发明提出的姿态控制规律；The first part: calculate the attitude control law that the present invention proposes;

仿真实验中给定参数：地球长半轴6378140.0m、地球短半轴6356755.0m、平均地球半径6371140.0m、地球自转角速度0.000073reg/s、轨道半长轴7003819.0m、轨道倾角97.889、近地点幅角90.0、升交点赤经121.0、偏心率0.0011、工作波长0.03m、天线中心视角20.0deg、天线长度3.3m、信号采样率350MHz、信号带宽300MHz、脉冲重复频率5000Hz、方位向分辨率0.5m、波束展开因子1.2，通过在场景中心布置一个点目标，具体计算步骤为：The given parameters in the simulation experiment: the major semi-axis of the earth is 6378140.0m, the semi-minor axis of the earth is 6356755.0m, the average earth radius is 6371140.0m, the angular velocity of the earth's rotation is 0.000073reg/s, the semi-major axis of the orbit is 7003819.0m, the orbital inclination is 97.889, and the argument of perigee is 90.0 , ascending node right ascension 121.0, eccentricity 0.0011, working wavelength 0.03m, antenna center viewing angle 20.0deg, antenna length 3.3m, signal sampling rate 350MHz, signal bandwidth 300MHz, pulse repetition frequency 5000Hz, azimuth resolution 0.5m, beam spread Factor 1.2, by arranging a point target in the center of the scene, the specific calculation steps are:

1.1计算卫星在转动地心坐标系E_g中的坐标(x_s,y_s,z_s)；1.1 Calculate the coordinates (x _s , y _s , z _s ) of the satellite in the rotating geocentric coordinate system E _g ;

根据式（1）-（4）得到卫星在轨道平面坐标系E_v中的坐标(x_vs,y_vs,z_vs)，如式（5），通过坐标系转换，转换至转动地心坐标系E_g，得到卫星在转动地心坐标系E_g中的坐标(x_s,y_s,z_s)，如式（6），并从中取T₀时刻卫星在转动地心坐标系E_g的坐标为 According to formulas (1)-(4), the coordinates (x _vs , y _vs , z _vs ) of the satellite in the orbital plane coordinate system E _v are obtained, such as formula (5), through coordinate system conversion, converted to the rotating geocentric coordinate system E _g , get the coordinates (x _s , y _s , z _s ) of the satellite in the rotating earth-centered coordinate system E _g , as shown in formula (6), and take the coordinates of the satellite in the rotating earth-centered coordinate system E _g at time T ₀ for

1.2计算T₀时刻天线坐标系E_a中单位矢量(0,1,0)在转动地心坐标系E_g中的坐标(x₁,y₁,z₁)；1.2 Calculate the coordinates (x ₁ , y ₁ , z ₁ ) of the unit vector (0,1,0) in the antenna coordinate system E _a in the rotating geocentric coordinate system E _g at time T ₀ ;

考虑偏航控制，通过坐标系转换，转换至转动地心坐标系E_g，如式（7）。Considering the yaw control, through the transformation of the coordinate system, it is converted to the rotating earth-centered coordinate system E _g , as shown in formula (7).

1.3计算T₀时刻天线坐标系E_a中单位矢量(0,1,0)到地面的距离R₀；1.3 Calculate the distance R ₀ from the unit vector (0,1,0) to the ground in the antenna coordinate system E _a at time T ₀ ;

根据式（9）-（11），计算出结果如式（12）。According to formula (9)-(11), the calculated result is as formula (12).

1.4计算T₀时刻旋转点C到地面指向点的斜距ΔR₀；1.4 Calculate the slant distance ΔR ₀ from the rotation point C to the point on the ground at time T ₀ ;

由于 $\frac{Δ R_{0}}{R_{0} + {ΔR}_{0}} \cdot K_{a} \frac{L_{s}}{2} = ρ_{a},$ 可得ΔR₀如式（13）。because $\frac{Δ R_{0}}{R_{0} + {ΔR}_{0}} &Center Dot; K_{a} \frac{L_{the s}}{2} = ρ_{a},$ ΔR ₀ can be obtained as formula (13).

1.5计算旋转点C在转动地心坐标系E_g中的坐标 1.5 Calculate the coordinates of the rotation point C in the rotating geocentric coordinate system E _g

由于滑动聚束模式下，旋转点位置不变，可以选择时刻T₀下，此时卫星姿态角都为零，计算出结果如式（14）。Since the position of the rotation point remains unchanged in the sliding beamforming mode, the time T ₀ can be selected, at which point the satellite attitude angles are all zero, and the calculated result is shown in formula (14).

1.6计算全滑聚过程中卫星与旋转点C在转动地心坐标系E_g中的相对矢量(R_x,R_y,R_z)；1.6 Calculate the relative vectors (R _x , R _y , R _z ) between the satellite and the rotating point C in the rotating geocentric coordinate system E _g during the full sliding process;

转动地心坐标系E_g下，全滑聚过程中，卫星位置变化，旋转点C不变，可计算相对矢量如式（15）。Under the rotating earth-centered coordinate system E _g , during the process of full sliding and gathering, the position of the satellite changes and the rotation point C remains unchanged. The relative vector can be calculated as formula (15).

1.7计算全滑聚过程中天线指向在转动地心坐标系E_g中的坐标(x′₁,y′₁,z′₁)；1.7 Calculate the coordinates (x′ ₁ , y′ ₁ , z′ ₁ ) of the antenna pointing in the rotating earth-centered coordinate system E _g in the process of full sliding convergence;

计算结果如式（16）。The calculation result is as formula (16).

1.8计算全滑聚过程中天线指向在天线坐标系E_a中的坐标(x″₁,y″₁,z″₁)；1.8 Calculate the coordinates (x″ ₁ , y″ ₁ , z″ ₁ ) of the antenna pointing in the antenna coordinate system E _a during the full sliding process;

做坐标系转换，如式（17）。Do coordinate system conversion, such as formula (17).

1.9计算天线坐标系E_a下单位矢量(0,1,0)，经姿态控制后的坐标(x_ZT,y_ZT,z_ZT)；1.9 Calculate the unit vector (0,1,0) in the antenna coordinate system E _a , and the coordinates (x _ZT , y _ZT , z _ZT ) after attitude control;

经坐标系转换和姿态控制，如式（18），得到结果如式（19）。After coordinate system conversion and attitude control, as in formula (18), the result is as in formula (19).

1.10计算全滑聚过程中卫星姿态控制角：俯仰角θ_p和偏航角θ_y；1.10 Calculate the attitude control angle of the satellite during the full sliding process: pitch angle θ _p and yaw angle θ _y ;

根据式（20），可解方程得到结果如式（21）。According to formula (20), the equation can be solved to obtain the result as formula (21).

1.11计算全滑聚过程中卫星姿态控制规律，及各轴角速度控制曲线；1.11 Calculate the satellite attitude control law and the angular velocity control curve of each axis during the full sliding and gathering process;

根据式（22），可得姿态控制规律，x,y,z三轴的旋转角速度如式（23）。According to Equation (22), the attitude control law can be obtained, and the rotational angular velocity of the x, y, and z axes is as in Equation (23).

仿真时，方位向采样点数取65536，此时最大扫描角有±2.808度，不同最大扫描角可通过改变方位向采用点数实现，本例中为了方便仿真程序编写，方位向采样点数取2的整数次方，实际处理只取扫描角范围为-2.23度到+223度，此时测绘带长度10km，计算出偏航角θ_p和俯仰角θ_y变化规律分别显示在图2和图3中，进而得到控制卫星姿态以实现滑动聚束模式的三轴旋转角速度分别在图4、图5和图6中显示。During the simulation, the number of azimuth sampling points is 65536. At this time, the maximum scanning angle is ±2.808 degrees. Different maximum scanning angles can be realized by changing the number of points in the azimuth direction. In this example, for the convenience of writing the simulation program, the number of azimuth sampling points is an integer of 2. The second power, the actual processing only takes the scanning angle range from -2.23 degrees to +223 degrees, and the length of the surveying strip is 10km at this time, the calculated variation laws of the yaw angle θ _p and the pitch angle θ _y are shown in Fig. 2 and Fig. 3, respectively. The three-axis rotational angular velocity obtained to control the attitude of the satellite to realize the sliding beamforming mode is shown in Fig. 4, Fig. 5 and Fig. 6, respectively.

第二部分：仿真生成回波数据，并对回波数据进行成像和评估。Part II: The simulation generates echo data, and performs imaging and evaluation of the echo data.

仿真实验中给定的参数不变，通过C++编程，分别仿真产生相控阵天线方式和本发明的姿态控制方式下的回波数据，再通过成像，分别得到结果显示在图7和图8中，再对成像数据进行评估，结果分别显示在图9和图10中，从分析结果中可以看出，姿态控制实现滑动聚束在方位分辨率上较相控阵天线有所提升。The given parameters in the simulation experiment remain unchanged, and through C++ programming, the echo data under the phased array antenna mode and the attitude control mode of the present invention are respectively simulated, and then through imaging, the results obtained are shown in Fig. 7 and Fig. 8 respectively , and then evaluate the imaging data, the results are shown in Fig. 9 and Fig. 10 respectively. From the analysis results, it can be seen that the azimuth resolution of the sliding beamforming achieved by attitude control is improved compared with that of the phased array antenna.

上述两部分仿真实验说明本发明提出的方法是一种十分精确的方法。The above two parts of the simulation experiment show that the method proposed by the present 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:

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)；

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:

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_gSeat inLabel (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:

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

Wherein r is₁,r₂,r₃Respectively intermediate variables;

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

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 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 rotation earth center in the full sliding convergence process_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′,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")；

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

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:

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:

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

wherein,

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

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;

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_vIs rotatedChanging the matrix;

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 is achieved by matrix inversion.