CN102736073B

CN102736073B - Method for computing range ambiguity of satellite-borne synthetic aperture radar (SAR) in universal mode

Info

Publication number: CN102736073B
Application number: CN 201210208826
Authority: CN
Inventors: 王鹏波; 门志荣; 陈杰; 刘月珊; 杨威
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2012-06-19
Filing date: 2012-06-19
Publication date: 2013-08-14
Anticipated expiration: 2032-06-19
Also published as: CN102736073A

Abstract

The present invention proposes a method for calculating the range ambiguity of spaceborne SAR in a general mode, which belongs to the field of signal processing, including reading the relevant parameters of the spaceborne SAR system, obtaining the range parameters in the squint state, widening the range antenna width, Get the number of fuzzy areas, get the energy of the fuzzy areas, calculate the distance ambiguity of the jth position, and draw the change curve of the range ambiguity with the distance position. When the invention acquires the antenna pattern of the distance and the slant distance between the satellite platform and the target point, the spherical model of the earth is adopted, which is closer to the actual situation, and the result is more accurate and reliable. The present invention fully considers the spatial geometric characteristics under the condition of large scanning angle when acquiring the ambiguity in the range direction, and the result has higher reliability. For different designs of scanning angles in system design, the present invention can obtain different change curves of range-to-ambiguity, and by analyzing these different change curves, different scanning angles can be compared and optimized.

Description

A Calculation Method of Range Ambiguity of Spaceborne SAR in General Mode

技术领域 technical field

本发明属于信号处理领域，具体涉及一种通用模式下星载SAR距离向模糊度的计算方法。The invention belongs to the field of signal processing, and in particular relates to a method for calculating the range ambiguity of a spaceborne SAR in a general mode.

背景技术 Background technique

合成孔径雷达（Synthetic Aperture Radar,SAR）卫星近些年来发展迅速，由于SAR卫星不受天气、地理、时间等因素的限制，能够对地进行全天时的观测，且具有一定的穿透力，因而被广泛的应用于军事侦察、地形测绘、资源探测、海洋观测、生态监测、自然灾害监测、快速救援等方面。Synthetic Aperture Radar (SAR) satellites have developed rapidly in recent years. Since SAR satellites are not limited by factors such as weather, geography, and time, they can observe the earth all day long and have certain penetrating power. Therefore, it is widely used in military reconnaissance, topographic mapping, resource detection, ocean observation, ecological monitoring, natural disaster monitoring, rapid rescue, etc.

距离向模糊度是星载SAR中的一个重要指标，其直接反映了距离向副瓣信号对主瓣信号的干扰程度，在系统设计、波位选取时，距离模糊度是主要的考核指标之一。合成孔径雷达采用脉冲工作体制，其必然带来方位向和距离向的模糊问题。由于雷达作用距离远、运行速度快，合成孔径雷达的方位和距离模糊比较突出。The range ambiguity is an important indicator in spaceborne SAR, which directly reflects the interference degree of the range sidelobe signal to the main lobe signal. In the system design and wave position selection, the range ambiguity is one of the main assessment indicators . Synthetic aperture radar adopts the pulse working system, which will inevitably bring about the ambiguity of azimuth and range. Due to the long range and fast operation speed of the radar, the ambiguity of the azimuth and range of the synthetic aperture radar is relatively prominent.

SAR图像的模糊是来自测绘带外的回波信号对测绘带回波信号的干扰，造成图像质量下降，给SAR图像的应用造成困难。模糊问题也是SAR工程设计中要解决的一个重要问题，特别是在星载SAR设计中模糊问题更为重要。SAR图像的模糊可分为距离向模糊和方位向模糊，方位向模糊是由于发射脉冲的脉冲重复频率(PRF)过低，回波信号的多普勒频谱欠采样引起的。而距离向模糊是由于雷达发射脉冲的重复频率过高引起的，主要是在测绘带内有用回波信号到达的同时，此脉冲之前或之后发射的脉冲也会有从距离合适的其他目标回来的回波信号到达，它们的能量混入目标回波信号中造成距离模糊，如图1所示为距离向模糊示意图。目前，传统的距离向模糊度的计算方法主要针对于正侧视情况，而大扫描角情况下的距离向模糊度计算的研究很少。因此，本发明提出了一种适用于大扫描角通用星载SAR模式下的距离向模糊度的精细算法，利用本发明能够准确的反映出距离向模糊度随距离向位置变化的现象，实现距离向模糊度的优化。The blurring of SAR image is the interference of the echo signal from outside the surveying zone to the echo signal of the surveying zone, resulting in the degradation of image quality and making it difficult for the application of SAR image. Fuzzy problem is also an important problem to be solved in SAR engineering design, especially in the design of spaceborne SAR. The ambiguity of SAR images can be divided into range ambiguity and azimuth ambiguity. The azimuth ambiguity is caused by the low pulse repetition frequency (PRF) of the transmitted pulse and the undersampling of the Doppler spectrum of the echo signal. The range ambiguity is caused by the high repetition frequency of the radar transmitted pulse, mainly because when the useful echo signal arrives in the surveying zone, the pulses transmitted before or after this pulse will also return from other targets with a suitable distance When the echo signals arrive, their energy is mixed into the target echo signal to cause range ambiguity, as shown in Figure 1 for a schematic diagram of range ambiguity. At present, the traditional range ambiguity calculation method is mainly aimed at the side-view situation, but there are few studies on the range ambiguity calculation in the case of large scanning angle. Therefore, the present invention proposes a fine algorithm suitable for the range ambiguity in the general-purpose spaceborne SAR mode with a large scanning angle. The invention can accurately reflect the phenomenon that the range ambiguity changes with the range position, and realize the range ambiguity. optimization towards ambiguity.

发明内容 Contents of the invention

本发明提出了一种通用星载SAR模式下的距离向模糊度的计算方法，该方法以地球模型、卫星地距几何关系为基础，通过分析在大扫描角情况下的地球模型中模糊区与测绘带的位置关系，结合距离向天线方向图，得到模糊区信号能量和测绘带的信号能量，最后得出距离向模糊度的值。The present invention proposes a method for calculating the range ambiguity under the general spaceborne SAR mode. The method is based on the geometric relationship between the earth model and the satellite ground distance, and analyzes the relationship between the ambiguity area and the Combining the positional relationship of the surveying zone with the antenna pattern in the range direction, the signal energy in the ambiguity area and the signal energy in the surveying zone are obtained, and finally the value of the range ambiguity is obtained.

本发明提出了一种通用星载SAR模式下的距离向模糊度的计算方法，具体包括以下几个步骤：The present invention proposes a method for calculating the range ambiguity in a general-purpose spaceborne SAR mode, which specifically includes the following steps:

步骤一：读入星载SAR系统的相关参数，包括轨道高度H，天线距离向尺寸L_r，雷达工作波长λ，平均地球半径R_e，光速c，脉冲重复频率PRF，天线中心视角θ_m，起始扫描角终止扫描角

中间扫描角

距离向测绘带宽度SW_r，距离向选取位置数目Fr。Step 1: Read in the relevant parameters of the spaceborne SAR system, including the orbital height H, the antenna range dimension L _r , the radar operating wavelength λ, the average earth radius R _e , the speed of light c, the pulse repetition frequency PRF, the antenna center angle of view θ _m , start scan angle end scan angle

middle scan angle

The width of the range survey strip SW_r, the number of selected positions Fr in the range direction.

步骤二：获取斜视状态下距离向参数；；Step 2: Obtain the distance parameter in the squint state;

（1）建立坐标系，；坐标原点为地球球心；Z轴方向为由地球球心指向卫星；Y轴方向为以地球球心为起点，方向与卫星速度方向平行；X轴方向为以地球球心为起点，垂直于卫星航迹方向，使该坐标系构成右手直角坐标系；(1) Establish a coordinate system; the origin of the coordinates is the center of the earth; the direction of the Z-axis is from the center of the earth to the satellite; the direction of the Y-axis is starting from the center of the earth, and the direction is parallel to the speed direction of the satellite; the direction of the X-axis is from the center of the earth The center of the sphere is the starting point, perpendicular to the direction of the satellite track, so that the coordinate system constitutes a right-handed rectangular coordinate system;

（2）、获取斜视状态下波束中心视角θ_m′；；(2) Obtain the angle of view θ _m ′ of the beam center in the squint state;

其中θ_m为天线中心视角，

为中间扫描角；where θ _m is the viewing angle of the antenna center,

is the middle scan angle;

（3）、获取斜视下测绘带中心点斜距R_m；(3) Obtain the slant distance R _m of the center point of the surveying zone under the squint;

$\frac{{R R}_{e e} + + H h}{sin sin {β β}_{m m}^{' '}} = = \frac{{R R}_{e e}}{sin sin {θ θ}_{m m}^{' '}} - - - - - - ((22 a a))$

γ_m′＝β_m′-θ_m′ (2b)γ _m ′=β _m ′-θ _m ′ (2b)

${R R}_{m m} = = \sqrt{{(({R R}_{e e} + + H h))}^{22} + + {R R}_{e e}^{22} - - 22 {R R}_{e e} \cdot \cdot (({R R}_{e e} + + H h)) \cdot &Center Dot; cos cos {γ γ}_{m m}^{' '}} - - - - - - ((22 c c))$

其中，β_m′和γ_m′为观测带中心点的入射角和地心角，H为轨道高度，R_e为平均地球半径，θ_m′为斜视状态下波束中心视角；Among them, β _m ′ and γ _m ′ are the incident angle and geocentric angle of the center point of the observation zone, H is the orbit height, R _e is the average earth radius, and θ _m ′ is the angle of view of the center of the beam in the squint state;

（4）、获取测绘带中心点B的坐标(x,y,z)；(4) Obtain the coordinates (x, y, z) of the center point B of the surveying belt;

z＝R_e+H-R_m·cosθ_m′ (3b)z=R _e +HR _m cosθ _m ′ (3b)

$x x = = \sqrt{{R R}_{e e}^{22} - - {y the y}^{22} - - {z z}^{22}} - - - - - - ((33 c c))$

其中，R_m为斜视下测绘带中心点斜距，

为中间扫描角，H为轨道高度，R_e为平均地球半径，θ_m′为斜视状态下波束中心视角，x、y和z分别为测绘带中心点B的X轴、Y轴和Z轴坐标；Among them, R _m is the slant distance of the center point of the surveying zone under the oblique view,

is the middle scanning angle, H is the orbit height, R _e is the average earth radius, θ _m ′ is the angle of view of the center of the beam in the squint state, x, y and z are the X-axis, Y-axis and Z-axis coordinates of the center point B of the survey zone respectively ;

（5）、获取测绘带中心点B点所在距离向的小圆半径r和距离向离轴角α_B；(5) Obtain the radius r of the small circle in the distance direction of the center point B of the surveying belt and the distance direction off-axis angle α _B ;

$r r = = \sqrt{{R R}_{e e}^{22} - - {y the y}^{22}} - - - - - - ((44 a a))$

$sin sin {γ γ}_{B B} = = \frac{x x}{r r} - - - - - - ((44 b b))$

$\frac{\sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot &Center Dot; (({R R}_{e e} + + H h)) \cdot &Center Dot; cos cos {γ γ}_{B B}}}{sin sin {γ γ}_{B B}} = = \frac{r r}{sin sin {α α}_{B B}} - - - - - - ((44 c c))$

其中，γ_B为测绘带中心点B点所在小圆的圆心角，R_e为平均地球半径，(x,y,z)为测绘带中心点B的坐标，H为轨道高度，y为测绘带中心点B的Y轴坐标。Among them, γ _B is the central angle of the small circle where the center point B of the survey belt is located, R _e is the average radius of the earth, (x, y, z) is the coordinate of the center point B of the survey belt, H is the orbital height, and y is the survey belt The Y-axis coordinate of the center point B.

步骤三：进行距离向天线宽度展宽；Step 3: Extend the distance to the antenna width;

（1）、获取距离向3dB波束宽度θ_3dB；(1) Obtain the 3dB beam width θ _3dB in the distance direction;

${θ θ}_{33 dB dB} = = \frac{0.886 0.886 λ λ}{{L L}_{r r}} - - - - - - ((55))$

其中λ为雷达工作波长，L_r为天线距离向尺寸；Where λ is the working wavelength of the radar, and L _r is the distance dimension of the antenna;

(2)、获取斜视下，距离向波束宽度α_r；(2) Obtain the range beam width α _r under squint;

${γ γ}_{11} = = \frac{SW SW__r r}{22 r r} - - - - - - ((66 a a))$

${R R}_{max max} = = \sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot \cdot (({R R}_{e e} + + H h)) \cdot \cdot cos cos (({γ γ}_{B B} + + {γ γ}_{11})) + + {y the y}^{22}} - - - - - - ((66 b b))$

$sin sin {α α}_{max max} = = \frac{r r \cdot &Center Dot; sin sin (({γ γ}_{B B} + + {γ γ}_{11}))}{\sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot \cdot (({R R}_{e e} + + H h)) \cdot \cdot cos cos (({γ γ}_{B B} + + {γ γ}_{11}))}} - - - - - - ((66 c c))$

${R R}_{min min} = = \sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot \cdot (({R R}_{e e} + + H h)) \cdot \cdot cos cos (({γ γ}_{B B} - - {γ γ}_{11})) + + {y the y}^{22}} - - - - - - ((66 d d))$

$sin sin {α α}_{min min} = = \frac{r r \cdot \cdot sin sin (({γ γ}_{B B} + + {γ γ}_{11}))}{\sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot &Center Dot; (({R R}_{e e} + + H h)) \cdot &Center Dot; cos cos (({γ γ}_{B B} - - {γ γ}_{11}))}} - - - - - - ((66 e e))$

α_r＝α_max-α_min (6f)α _r = α _max - α _min (6f)

其中，γ₁为半测绘带宽度在小圆内对应的圆心角，R_max和R_min分别为测绘带与卫星平台的最大斜距和最小斜距，α_max和α_min分别为测绘带在小圆平面内对应的距离向最大离轴角和最小离轴角，SW_r为距离向测绘带宽度，r为测绘带中心点B点所在距离向的小圆半径，R_e为平均地球半径，H为轨道高度，γ_B为测绘带中心点B点所在小圆的圆心角，y为测绘带中心点B的Y轴坐标；Among them, γ ₁ is the central angle corresponding to the half-swath width in the small circle, R _max and R _min are the maximum and minimum slant distances between the swath and the satellite platform, respectively, and α _max and α _min are the maximum and minimum slant distances between the swath and the satellite platform, respectively. The corresponding maximum off-axis angle and minimum off-axis angle in the circle plane, SW_r is the width of the survey zone in the distance direction, r is the radius of the small circle in the distance direction where the center point B of the survey zone is located, R _e is the average radius of the earth, and H is Orbital height, γ _B is the central angle of the small circle where the center point B of the survey belt is located, and y is the Y-axis coordinate of the center point B of the survey belt;

（3）、比较距离向波束宽度α_r和距离向3dB波束宽度θ_3dB的大小，判断是否需要展宽距离向天线宽度L_r，若距离向波束宽度α_r大于距离向3dB波束宽度θ_3dB，则进行展宽，展宽后的距离向天线宽度记为L_t：(3) Compare the size of the range beam width α _r and the range 3dB beam width θ _3dB to determine whether it is necessary to widen the range antenna width L _r , if the range beam width α _r is greater than the range 3dB beam width θ _3dB , then The widening is performed, and the distance to the antenna width after widening is denoted as L _t :

${L L}_{t t} = = \frac{0.886 0.886 λ λ}{{α α}_{r r} + + 0.001 0.001} - - - - - - ((77))$

若距离向波束宽度α_r小于距离向3dB波束宽度θ_3dB，则不进行展宽，L_t=L_r。If the range beam width α _r is smaller than the range 3dB beam width θ _3dB , no broadening is performed, L _t =L _r .

步骤四：获取模糊区数目Nr；Step 4: Obtain the number Nr of fuzzy regions;

${R R}_{a a max max} = = \sqrt{{(({R R}_{e e} + + H h))}^{22} - - {R R}_{e e}^{22}} - - - - - - ((88 a a))$

${R R}_{a a min min} = = \sqrt{{y the y}^{22} + + {(({R R}_{e e} + + H h - - r r))}^{22}} - - - - - - ((88 b b))$

${S S}_{min min} = = - - [[\frac{22 (({R R}_{min min} - - {R R}_{a a min min}))}{c c} \cdot &Center Dot; PRE PRE]] - - - - - - ((88 c c))$

${S S}_{max max} = = - - [[\frac{22 (({R R}_{max max} - - {R R}_{a a max max}))}{c c} \cdot &Center Dot; PRE PRE]] - - - - - - ((88 d d))$

Nr＝S_max-S_min (8e)Nr＝S _max -S _min (8e)

其中，R_a max和R_a min分别为模糊区最远斜距和最近斜距，S_max和S_min分别为模糊区最大序号和最小序号，[x]表示取不大于x的最大整数，R_e为平均地球半径，H为轨道高度，r为测绘带中心点B点所在距离向的小圆半径，c为光速，PRF为脉冲重复频率，y为测绘带中心点B的Y轴坐标。Among them, R _{a max} and R _{a min} are the farthest slope distance and the shortest slope distance in the fuzzy area respectively, S _max and S _min are the maximum serial number and the minimum serial number in the fuzzy area respectively, [x] means the largest integer not greater than x, R _e is the average earth radius, H is the orbital height, r is the radius of the small circle in the distance direction of the center point B of the survey zone, c is the speed of light, PRF is the pulse repetition frequency, and y is the Y-axis coordinate of the center point B of the survey zone.

步骤五：获取模糊区能量Ea；Step 5: Obtain the energy Ea of the fuzzy area;

(1)、在测绘带距离向上均匀选取Fr个位置；Fr为距离向选取位置数目；(1), Fr positions are evenly selected upwards in the survey zone distance; Fr is the number of selected positions in the distance direction;

(2)、求取测绘带距离向上第j个位置与卫星平台的斜距R_j；(2), obtain the slant distance R _j between the jth position and the satellite platform from the surveying zone;

$Δγ Δγ = = \frac{SW SW__r r}{r r \cdot &Center Dot; Fr Fr} - - - - - - ((99 b b))$

${R R}_{j j} = = \sqrt{{((sin sin (({γ γ}_{B B} - - {γ γ}_{11})) + + j j \cdot \cdot Δγ Δγ))}^{22} \cdot &Center Dot; {r r}^{22} + + {y the y}^{22} + + {((((cos cos (({γ γ}_{B B} - - {γ γ}_{11})) + + j j \cdot \cdot Δγ Δγ)) \cdot \cdot r r - - (({R R}_{e e} + + H h))))}^{22}} - - - - - - ((99 d d))$

其中，Δγ为圆心角步距，SW_r为距离向测绘带宽度，r为测绘带中心点B点所在距离向的小圆半径，Fr为距离向选取位置数目，r为测绘带中心点B点所在距离向的小圆半径，c，R_e为平均地球半径，H为轨道高度，γ₁为半测绘带宽度在小圆内对应的圆心角，γ_B为测绘带中心点B点所在小圆的圆心角，y为测绘带中心点B的Y轴坐标；Among them, Δγ is the center angle step distance, SW_r is the width of the survey zone in the distance direction, r is the radius of the small circle in the distance direction where the center point B of the survey zone is located, Fr is the number of selected positions in the distance direction, and r is the location of the center point B of the survey zone The radius of the small circle in the distance direction, c, Re _is the average earth radius, H is the orbital height, γ ₁ is the central angle corresponding to the half-swath width in the small circle, γ _B is the angle of the small circle where point B, the center point of the swath, is located Central angle, y is the Y-axis coordinate of the center point B of the surveying zone;

(3)、求取第S_i模糊区里第j个位置与卫星平台的斜距

和离轴角α_ij；(3), obtain the slant distance between the jth position and the satellite platform in the S _i fuzzy area

and off-axis angle α _ij ;

${R R}_{{a a}_{ij ij}} = = {R R}_{j j} + + \frac{{S S}_{i i} \cdot &Center Dot; c c}{22 \cdot &Center Dot; PRE PRE} - - - - - - ((1010 a a))$

$cos cos {γ γ}_{ij ij} = = \frac{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} + + {y the y}^{22} - - {R R}_{aij aij}^{22}}{22 r r \cdot &Center Dot; (({R R}_{e e} + + H h))} - - - - - - ((1010 b b))$

$\frac{r r}{sin sin {α α}_{ij ij}} = = \sqrt{\frac{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} + + {y the y}^{22} - - {R R}_{aij aij}^{22}}{sin sin {γ γ}_{ij ij}}} - - - - - - ((1010 c c))$

其中，γ_ij为所对应的圆心角，S_i为模糊区序号，PRF为脉冲重复频率，c为光速，R_j为测绘带距离向上第j个位置与卫星平台的斜距，r为测绘带中心点B点所在距离向的小圆半径，R_e为平均地球半径，H为轨道高度，y为测绘带中心点B的Y轴坐标；Among them, γ _ij is the corresponding central angle, S _i is the serial number of the fuzzy area, PRF is the pulse repetition frequency, c is the speed of light, R _j is the slant distance between the jth position upward from the surveying zone and the satellite platform, and r is the surveying zone The radius of the small circle in the distance direction where the center point B is located, R _e is the average earth radius, H is the orbital height, and y is the Y-axis coordinate of the center point B of the surveying zone;

(4)、求取第S_i模糊区里第j个位置的距离向天线方向图Wr_ij；(4), obtain the distance to the antenna pattern Wr _ij of the jth position in the S _i ambiguity zone;

${Wr Wr}_{ij ij} = = \frac{{sin sin}^{22} ((π π \cdot &Center Dot; {L L}_{t t} \cdot &Center Dot; ((sin sin {α α}_{ij ij} - - sin sin {α α}_{B B})) / / λ λ))}{{((π π \cdot &Center Dot; {L L}_{t t} \cdot &Center Dot; ((sin sin {α α}_{ij ij} - - sin sin {α α}_{B B})) / / λ λ))}^{22}} - - - - - - ((1111))$

其中α_ij为离轴角，λ为雷达工作波长，L_t为展宽后的距离向天线宽度，α_B为距离向离轴角；Among them, α _ij is the off-axis angle, λ is the working wavelength of the radar, L _t is the antenna width in the distance direction after broadening, and α _B is the off-axis angle in the distance direction;

(5)、求取第S_i模糊区里第j个位置返回的能量E_ij；(5), obtain the energy E _ij returned by the jth position in the S _i fuzzy zone;

$cos cos ((π π - - {β β}_{ij ij}^{' '})) = = \frac{{R R}_{{a a}_{ij ij}}^{22} + + {R R}_{e e}^{22} - - {(({R R}_{e e} + + H h))}^{22}}{22 {R R}_{e e} \cdot &Center Dot; {R R}_{{a a}_{ij ij}}} - - - - - - ((1212 a a))$

${E E.}_{ij ij} = = \frac{{Wr Wr}_{ij ij}^{22} \cdot \cdot {σ σ}_{00}}{sin sin {β β}_{ij ij}^{' '} \cdot \cdot {R R}_{aij aij}^{33}} - - - - - - ((1212 b b))$

其中，β_ij′为入射角序列，σ₀表示地面后向散射系数，R_e为平均地球半径，H为轨道高度，

表示第S_i模糊区里第j个位置与卫星平台的斜距；Among them, β _ij ′ is the incident angle sequence, σ ₀ is the ground backscatter coefficient, R _e is the average earth radius, H is the orbital height,

Indicates the slant distance between the j-th position and the satellite platform in the S _i-th ambiguity zone;

（6）、重复步骤（2）到（5），计算出所有位置返回的能量；(6) Repeat steps (2) to (5) to calculate the energy returned by all positions;

（7）、求取第j个位置返回的总能量E_allj和模糊区能量Ea_j；(7) Obtain the total energy E _allj returned from the jth position and the energy Ea _j of the fuzzy area;

${E E.}_{allj allj} = = \underset{i i}{Σ Σ} {E E.}_{ij ij} - - - - - - ((1313 a a))$

${Ea Ea}_{j j} = = {E E.}_{allj allj} - - {E E.}_{((| | {S S}_{min min} | | + + 11)) j j} - - - - - - ((1313 b b))$

其中s_min为模糊区最小序号，E_ij为第S_i模糊区里第j个位置返回的能量，

为i＝|s_min|+1时第S_i模糊区里第j个位置返回的能量。Where s _min is the minimum serial number of the fuzzy area, E _ij is the energy returned at the jth position in the S _i- th fuzzy area,

is the energy returned by the jth position in the S _i- th fuzzy area when i=|s _min |+1.

步骤六：求取第j个位置的距离向模糊度RASR_j;Step 6: Calculate the range ambiguity RASR _j of the jth position;

${RASR RASR}_{j j} = = 1010 \cdot &Center Dot; log log 1010 ((\frac{E E. {a a}_{j j}}{{E E.}_{((| | {S S}_{min min} | | + + 11)) j j}})) - - - - - - ((1414))$

其中Ea_j为模糊区能量，s_min为模糊区最小序号。Where Ea _j is the energy of the fuzzy area, and s _min is the minimum serial number of the fuzzy area.

步骤七：绘制距离向模糊度随距离向位置的变化曲线。Step 7: Draw the change curve of range ambiguity with range position.

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

（1）本发明提出一种通用星载SAR模式下的距离向模糊度计算方法，该方法精确度高。本发明获取距离向天线方向图和卫星平台与目标点的斜距时，采用的是地球球体模型，和实际情况更加的逼近，因此结果更加准确和可靠。(1) The present invention proposes a method for calculating range ambiguity in general spaceborne SAR mode, which has high accuracy. When the present invention acquires the antenna pattern of the distance and the slant distance between the satellite platform and the target point, the spherical model of the earth is adopted, which is closer to the actual situation, so the result is more accurate and reliable.

（2）本发明提出一种通用星载SAR模式下的距离向模糊度计算方法，该方法可靠性高。在进行系统设计的过程中，距离向模糊度的精确对于后续工作的展开和决策具有重要意义，本发明在获取距离向模糊度时，充分考虑了大扫描角情况下的空间几何特性，因此结果具有更高的可靠性。(2) The present invention proposes a method for calculating range ambiguity in general spaceborne SAR mode, which has high reliability. In the process of system design, the accuracy of the range ambiguity is of great significance for the development and decision-making of follow-up work. The present invention fully considers the spatial geometric characteristics under the condition of large scanning angle when obtaining the range ambiguity, so the result With higher reliability.

（3）本发明提出一种通用星载SAR模式下的距离向模糊度计算方法，该方法实用性强。对于系统设计中对扫描角的不同设计，本发明可得到不同的距离向模糊度的变化曲线，通过分析这些不同的变化曲线，可以对不同的扫描角进行比较和优化。(3) The present invention proposes a method for calculating range ambiguity in general spaceborne SAR mode, which is highly practical. For different designs of scanning angles in system design, the present invention can obtain different variation curves of range-to-ambiguity, and by analyzing these different variation curves, different scanning angles can be compared and optimized.

（4）本发明提出一种通用星载SAR模式下的距离向模糊度计算方法，该方法直观性好。通过本发明可得到距离向模糊度随距离向位置变化的曲线，因此可以很直观的反映距离向模糊度在整个场景内的变化情况，因此结果表现形式直观性强，便于系统设计者及决策者通过曲线做出正确的判断。(4) The present invention proposes a method for calculating range ambiguity in general spaceborne SAR mode, which is intuitive. Through the present invention, the curve of range ambiguity changing with distance position can be obtained, so it can intuitively reflect the change of range ambiguity in the whole scene, so the result expression form is intuitive, which is convenient for system designers and decision makers Make the right judgment through the curve.

附图说明 Description of drawings

图1是本发明的距离向模糊示意图；Fig. 1 is a schematic diagram of distance direction fuzziness of the present invention;

图2是本发明提出的一种通用星载SAR模式下的距离向模糊度计算方法的流程图；Fig. 2 is the flow chart of the range ambiguity calculation method under a kind of general space-borne SAR mode that the present invention proposes;

图3是本发明的计算斜视状态下，距离向参数计算的流程图；Fig. 3 is the flow chart of calculating distance to parameter under the calculation strabismus state of the present invention;

图4是本发明的正侧视到斜视的转换示意图；Fig. 4 is a schematic diagram of the conversion from the front side view to the oblique view of the present invention;

图5是本发明斜视状态下，波束中心视角示意图；Fig. 5 is a schematic diagram of the angle of view of the center of the beam under the squint state of the present invention;

图6是本发明的斜视状态下，垂直于卫星航迹方向的几何关系示意图；Fig. 6 is a schematic diagram of the geometric relationship perpendicular to the direction of the satellite track under the squint state of the present invention;

图7是本发明的计算斜视状态下，距离向天线宽度展宽的流程图；Fig. 7 is a flow chart of widening the distance to the antenna width under the calculation squint state of the present invention;

图8是本发明斜视状态下，测绘带中心点B所在小圆的剖面图；Fig. 8 is a sectional view of the small circle where the central point B of the surveying tape is located under the squint state of the present invention;

图9是本发明的计算模糊区能量的流程图；Fig. 9 is a flow chart of calculating the fuzzy region energy of the present invention;

图10是本发明的仿真数据绘制所得距离向模糊度的曲线；Fig. 10 is the curve of the obtained distance direction ambiguity drawn by the simulation data of the present invention;

具体实施方式 Detailed ways

下面将结合附图和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 with reference to the accompanying drawings and embodiments.

本发明提出一种通用星载SAR模式下的距离向模糊度计算方法，如图2所示，包括以下几个步骤：The present invention proposes a method for calculating range ambiguity in a general spaceborne SAR mode, as shown in Figure 2, including the following steps:

步骤一：读入星载SAR系统的相关参数，包括：轨道高度H，天线距离向尺寸L_r，雷达工作波长λ，平均地球半径R_e，光速c，脉冲重复频率PRF，天线中心视角θ_m，起始扫描角

终止扫描角

中间扫描角

距离向测绘带宽度SW_r，距离向选取位置数目Fr。Step 1: Read in the relevant parameters of the spaceborne SAR system, including: orbital height H, antenna range dimension L _r , radar operating wavelength λ, average earth radius R _e , light speed c, pulse repetition frequency PRF, antenna center viewing angle θ _m , the starting scan angle

end scan angle

middle scan angle

步骤二：获取斜视状态下距离向参数，如图3所示；Step 2: Obtain the distance parameter in the squint state, as shown in Figure 3;

（1）建立坐标系，如图4所示，坐标原点为地球球心；Z轴方向为由地球球心指向卫星；Y轴方向为以地球球心为起点，方向与卫星速度方向平行；X轴方向为以地球球心为起点，垂直于卫星航迹方向，使该坐标系构成右手直角坐标系。(1) Establish a coordinate system, as shown in Figure 4, the origin of the coordinates is the center of the earth; the direction of the Z axis is from the center of the earth to the satellite; the direction of the Y axis is starting from the center of the earth, and the direction is parallel to the direction of the satellite velocity; The axis direction starts from the center of the earth and is perpendicular to the direction of the satellite track, so that the coordinate system constitutes a right-handed rectangular coordinate system.

（2）、获取斜视状态下波束中心视角θ_m′，如图5所示；(2) Obtain the angle of view θ _m ′ of the center of the beam in the squint state, as shown in Figure 5;

其中θ_m为天线中心视角，

为中间扫描角。where θ _m is the viewing angle of the antenna center,

is the middle scan angle.

（3）、获取斜视下测绘带中心点斜距R_m，如图6所示；(3) Obtain the slope distance R _m of the center point of the surveying zone under the squint view, as shown in Figure 6;

γ_m′＝β_m′-θ_m′ (2b)γ _m ′=β _m ′-θ _m ′ (2b)

${R R}_{m m} = = \sqrt{{(({R R}_{e e} + + H h))}^{22} + + {R R}_{e e}^{22} - - 22 {R R}_{e e} \cdot &Center Dot; (({R R}_{e e} + + H h)) \cdot &Center Dot; cos cos {γ γ}_{m m}^{' '}} - - - - - - ((22 c c))$

其中，β_m′和γ_m′为观测带中心点的入射角和地心角，H为轨道高度，R_e为平均地球半径，θ_m′为斜视状态下波束中心视角。Among them, β _m ′ and γ _m ′ are the incident angle and geocentric angle of the center point of the observation zone, H is the orbit height, R _e is the average earth radius, and θ _m ′ is the angle of view of the center of the beam in the squint state.

（4）、获取测绘带中心点B的坐标(x,y,z)，如图4所示；(4) Obtain the coordinates (x, y, z) of the center point B of the surveying belt, as shown in Figure 4;

z＝R_e+H-R_m·cosθ_m′ (3b)z=R _e +HR _m cosθ _m ′ (3b)

其中，R_m为斜视下测绘带中心点斜距，

为中间扫描角，H为轨道高度，R_e为平均地球半径，θ_m′为斜视状态下波束中心视角，x、y和z分别为测绘带中心点B的X轴、Y轴和Z轴坐标。Among them, R _m is the slant distance of the center point of the surveying zone under the oblique view,

is the middle scanning angle, H is the orbit height, R _e is the average earth radius, θ _m ′ is the angle of view of the center of the beam in the squint state, x, y and z are the X-axis, Y-axis and Z-axis coordinates of the center point B of the survey zone respectively .

（5）、获取测绘带中心点B点所在距离向的小圆半径r和距离向离轴角α_B，如图4所示；(5) Obtain the radius r of the small circle in the distance direction of the center point B of the surveying belt and the distance direction off-axis angle α _B , as shown in Figure 4;

$r r = = \sqrt{{R R}_{e e}^{22} - - {y the y}^{22}} - - - - - - ((44 a a))$

$sin sin {γ γ}_{B B} = = \frac{x x}{r r} - - - - - - ((44 b b))$

步骤三：进行距离向天线宽度展宽，如图7所示；Step 3: Extend the distance to the antenna width, as shown in Figure 7;

其中λ为雷达工作波长，L_r为天线距离向尺寸。Where λ is the working wavelength of the radar, and L _r is the distance dimension of the antenna.

（2）、获取斜视下，距离向波束宽度α_r，如图8所示；(2) Obtain the range beam width α _r under squint, as shown in Figure 8;

${γ γ}_{11} = = \frac{SW SW__r r}{22 r r} - - - - - - ((66 a a))$

$sin sin {α α}_{max max} = = \frac{r r \cdot &Center Dot; sin sin (({γ γ}_{B B} + + {γ γ}_{11}))}{\sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot \cdot (({R R}_{e e} + + H h)) \cdot &Center Dot; cos cos (({γ γ}_{B B} + + {γ γ}_{11}))}} - - - - - - ((66 c c))$

${R R}_{min min} = = \sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot &Center Dot; (({R R}_{e e} + + H h)) \cdot &Center Dot; cos cos (({γ γ}_{B B} - - {γ γ}_{11})) + + {y the y}^{22}} - - - - - - ((66 d d))$

$sin sin {α α}_{min min} = = \frac{r r \cdot &Center Dot; sin sin (({γ γ}_{B B} + + {γ γ}_{11}))}{\sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot &Center Dot; (({R R}_{e e} + + H h)) \cdot \cdot cos cos (({γ γ}_{B B} - - {γ γ}_{11}))}} - - - - - - ((66 e e))$

α_r＝α_max-α_min (6f)α _r = α _max - α _min (6f)

其中，γ₁为半测绘带宽度在小圆内对应的圆心角，R_max和R_min分别为测绘带与卫星平台的最大斜距和最小斜距，α_max和α_min分别为测绘带在小圆平面内对应的距离向最大离轴角和最小离轴角，SW_r为距离向测绘带宽度，r为测绘带中心点B点所在距离向的小圆半径，R_e为平均地球半径，H为轨道高度，γ_B为测绘带中心点B点所在小圆的圆心角，y为测绘带中心点B的Y轴坐标。Among them, γ ₁ is the central angle corresponding to the half-swath width in the small circle, R _max and R _min are the maximum and minimum slant distances between the swath and the satellite platform, respectively, and α _max and α _min are the maximum and minimum slant distances between the swath and the satellite platform, respectively. The corresponding maximum off-axis angle and minimum off-axis angle in the circle plane, SW_r is the width of the survey zone in the distance direction, r is the radius of the small circle in the distance direction where the center point B of the survey zone is located, R _e is the average radius of the earth, and H is Orbit height, γ _B is the central angle of the small circle where the center point B of the survey zone is located, and y is the Y-axis coordinate of the center point B of the survey zone.

（3）、比较距离向波束宽度α_r和距离向3dB波束宽度θ_3dB的大小，判断是否需要展宽距离向天线宽度L_r。若距离向波束宽度α_r大于距离向3dB波束宽度θ_3dB，则进行展宽，展宽后的距离向天线宽度记为L_t：(3) Compare the range beam width α _r with the range 3dB beam width θ _3dB to determine whether it is necessary to widen the range antenna width L _r . If the range beam width α _r is greater than the range 3dB beam width θ _3dB , the widening is performed, and the range antenna width after widening is denoted as L _t :

${S S}_{max max} = = - - [[\frac{22 (({R R}_{max max} - - {R R}_{a a max max}))}{c c} \cdot \cdot PRE PRE]] - - - - - - ((88 d d))$

Nr＝S_max-S_min (8e)Nr＝S _max -S _min (8e)

步骤五：获取模糊区能量Ea，如图9所示；Step 5: Obtain the energy Ea of the fuzzy area, as shown in Figure 9;

（1）、在测绘带距离向上均匀选取Fr个位置；Fr为距离向选取位置数目。(1) Fr positions are uniformly selected in the distance upward direction of the surveying belt; Fr is the number of selected positions in the distance direction.

（2）、求取测绘带距离向上第j个位置与卫星平台的斜距R_j；(2) Obtain the slant distance R _j between the jth position in the upward direction of the surveying zone and the satellite platform;

$Δγ Δγ = = \frac{SW SW__r r}{r r \cdot \cdot Fr Fr} - - - - - - ((99 b b))$

${R R}_{j j} = = \sqrt{{((sin sin (({γ γ}_{B B} - - {γ γ}_{11})) + + j j \cdot \cdot Δγ Δγ))}^{22} \cdot \cdot {r r}^{22} + + {y the y}^{22} + + {((((cos cos (({γ γ}_{B B} - - {γ γ}_{11})) + + j j \cdot &Center Dot; Δγ Δγ)) \cdot &Center Dot; r r - - (({R R}_{e e} + + H h))))}^{22}} - - - - - - ((99 d d))$

其中，Δγ为圆心角歩距，SW_r为距离向测绘带宽度，r为测绘带中心点B点所在距离向的小圆半径，Fr为距离向选取位置数目，r为测绘带中心点B点所在距离向的小圆半径，c，R_e为平均地球半径，H为轨道高度，γ₁为半测绘带宽度在小圆内对应的圆心角，γ_B为测绘带中心点B点所在小圆的圆心角，y为测绘带中心点B的Y轴坐标。Among them, Δγ is the center angle step distance, SW_r is the width of the survey zone in the distance direction, r is the radius of the small circle in the distance direction where the center point B of the survey zone is located, Fr is the number of selected positions in the distance direction, and r is the location of the center point B of the survey zone The radius of the small circle in the distance direction, c, Re _is the average earth radius, H is the orbital height, γ ₁ is the central angle corresponding to the half-swath width in the small circle, γ _B is the angle of the small circle where point B, the center point of the swath, is located The central angle, y is the Y-axis coordinate of the center point B of the survey zone.

（3）、求取第S_i模糊区里第j个位置与卫星平台的斜距和离轴角α_ij；(3) Calculate the slant distance between the jth position in the S _i fuzzy area and the satellite platform and off-axis angle α _ij ;

$cos cos {γ γ}_{ij ij} = = \frac{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} + + {y the y}^{22} - - {R R}_{aij aij}^{22}}{22 r r \cdot \cdot (({R R}_{e e} + + H h))} - - - - - - ((1010 b b))$

其中，γ_ij为所对应的圆心角，S_i为模糊区序号，PRF为脉冲重复频率，c为光速，R_j为测绘带距离向上第j个位置与卫星平台的斜距，r为测绘带中心点B点所在距离向的小圆半径，R_e为平均地球半径，H为轨道高度，y为测绘带中心点B的Y轴坐标。Among them, γ _ij is the corresponding central angle, S _i is the serial number of the fuzzy area, PRF is the pulse repetition frequency, c is the speed of light, R _j is the slant distance between the jth position upward from the surveying zone and the satellite platform, and r is the surveying zone The radius of the small circle in the distance direction where the center point B is located, Re _is the average earth radius, H is the orbital height, and y is the Y-axis coordinate of the center point B of the surveying zone.

（4）、求取第S_i模糊区里第j个位置的距离向天线方向图Wr_ij；(4) Obtain the range antenna pattern Wr _ij of the jth position in the S _i ambiguity zone;

${Wr Wr}_{ij ij} = = \frac{{sin sin}^{22} ((π π \cdot \cdot {L L}_{t t} \cdot \cdot ((sin sin {α α}_{ij ij} - - sin sin {α α}_{B B})) / / λ λ))}{{((π π \cdot &Center Dot; {L L}_{t t} \cdot &Center Dot; ((sin sin {α α}_{ij ij} - - sin sin {α α}_{B B})) / / λ λ))}^{22}} - - - - - - ((1111))$

其中α_ij为离轴角，λ为雷达工作波长，L_t为展宽后的距离向天线宽度，α_B为距离向离轴角Among them, α _ij is the off-axis angle, λ is the radar working wavelength, L _t is the distance antenna width after broadening, and α _B is the distance off-axis angle

（5）、求取第S_i模糊区里第j个位置返回的能量E_ij；(5) Calculate the energy E _ij returned by the jth position in the S _i fuzzy area;

${E E.}_{ij ij} = = \frac{{Wr Wr}_{ij ij}^{22} \cdot &Center Dot; {σ σ}_{00}}{sin sin {β β}_{ij ij}^{' '} \cdot &Center Dot; {R R}_{aij aij}^{33}} - - - - - - ((1212 b b))$

表示第S_i模糊区里第j个位置与卫星平台的斜距。Among them, β _ij ′ is the incident angle sequence, σ ₀ is the ground backscatter coefficient, R _e is the average earth radius, H is the orbital height,

Indicates the slant distance between the jth position and the satellite platform in the S _i- th fuzzy area.

（6）、重复步骤（2）到（5），计算出所有位置返回的能量。(6). Repeat steps (2) to (5) to calculate the energy returned by all positions.

${RASR RASR}_{j j} = = 1010 \cdot \cdot log log 1010 ((\frac{E E. {a a}_{j j}}{{E E.}_{((| | {S S}_{min min} | | + + 11)) j j}})) - - - - - - ((1414))$

实施例Example

本实施例提供一种通用星载SAR模式下的距离向模糊度计算方法，包括以下几个步骤，流程图，如图2所示：This embodiment provides a method for calculating the range ambiguity in the general spaceborne SAR mode, which includes the following steps and a flow chart, as shown in Figure 2:

步骤一：读入星载SAR系统的相关参数，包括：轨道高度H，距离向天线宽度L_r，雷达工作波长λ，平均地球半径R_e，光速c，脉冲重复频率PRF，天线中心视角θ_m，起始扫描角终止扫描角

中间扫描角

距离向测绘带宽度SW_r，距离向选取位置数目Fr；Step 1: Read in the relevant parameters of the spaceborne SAR system, including: orbital height H, range antenna width L _r , radar operating wavelength λ, average earth radius R _e , light speed c, pulse repetition frequency PRF, and antenna center angle of view θ _m , the starting scan angle end scan angle

middle scan angle

The width of the range mapping swath SW_r, the number of selected positions Fr in the range direction;

其中，本实施例中具体参数为：H＝800km，L_r＝2m，λ＝0.03m，R_e＝6371140m，c＝3×10⁸m/s，PRF＝2000Hz，θ_m＝30°，

SW_r＝15000m，Fr＝1001；Wherein, the specific parameters in this embodiment are: H=800km, L _r =2m, λ=0.03m, _Re =6371140m, c=3×10 ⁸ m/s, PRF=2000Hz, θ _m =30°,

SW_r=15000m, Fr=1001;

步骤二：获取斜视状态下距离向参数，流程图如图3所示；Step 2: Obtain the distance parameters in the squint state, the flow chart is shown in Figure 3;

A、建立坐标系，如图4所示；A, establish a coordinate system, as shown in Figure 4;

坐标原点：地球球心Coordinate origin: the center of the earth

Z轴：由地球球心指向卫星Z axis: from the center of the earth to the satellite

Y轴：以地球球心为起点，方向与卫星速度方向平行Y axis: Starting from the center of the earth, the direction is parallel to the direction of the satellite speed

X轴：以地球球心为起点，垂直于卫星航迹方向，使该坐标系构成右手直角坐标系X-axis: starting from the center of the earth, perpendicular to the direction of the satellite track, so that the coordinate system forms a right-handed rectangular coordinate system

B、获取斜视状态下波束中心视角θ_m′，如图5所示；B. Obtain the angle of view θ _m ′ of the center of the beam in the squint state, as shown in FIG. 5 ;

方法如公式(1)所示:The method is shown in formula (1):

其中，本实施例中具体参数为：θ_m＝30°，

得到θ_m′＝31.6942°。Wherein, the specific parameters in this embodiment are: θ _m =30°,

θ _m ' = 31.6942° is obtained.

C、获取斜视下测绘带中心点斜距R_m，如图6所示；C. Obtain the slant distance R _m of the center point of the surveying zone under the squint view, as shown in Figure 6;

方法如公式(2a~2c)所示：The method is shown in formula (2a~2c):

γ_m′＝β_m′-θ_m′ (2b)γ _m ′=β _m ′-θ _m ′ (2b)

${R R}_{m m} = = \sqrt{{(({R R}_{e e} + + H h))}^{22} + + {R R}_{e e}^{22} - - 22 {R R}_{e e} \cdot \cdot (({R R}_{e e} + + H h)) \cdot \cdot cos cos {γ γ}_{m m}^{' '}} - - - - - - ((22 c c))$

其中，本实施例中的具体参数为：R_e＝6371140m，H＝800km，θ_m′按公式(1)获得，得到R_m＝963.91km。Wherein, the specific parameters in this embodiment are: R _e =6371140m, H=800km, θ _m ' is obtained according to formula (1), and R _m =963.91km.

D、获取测绘带中心点B的坐标(X，Y，Z)，如图4所示；D, obtain the coordinates (X, Y, Z) of the center point B of the surveying belt, as shown in Figure 4;

方法如公式(3a~3c)所示：The method is shown in formula (3a~3c):

z＝R_e+H-R_m·cosθ_m′ (3b)z=R _e +HR _m cosθ _m ′ (3b)

其中，本实施例中的具体参数为：

R_e＝6371140m，θ_m′按公式(1)获得，R_m按公式(2a～2c)获得，得到Y＝179.58km，Z＝6351km，X＝473.52km。Wherein, the concrete parameter among the present embodiment is:

R _e =6371140m, θ _m 'is obtained according to formula (1), R _m is obtained according to formula (2a-2c), and Y=179.58km, Z=6351km, X=473.52km.

E、获取B点所在距离向的小圆半径r和距离向离轴角α_B，如图4所示；E. Obtain the radius r of the small circle in the distance direction of point B and the off-axis angle α _B in the distance direction, as shown in Figure 4;

方法如公式(4a~4c)所示：The method is shown in formula (4a~4c):

$r r = = \sqrt{{R R}_{e e}^{22} - - {y the y}^{22}} - - - - - - ((44 a a))$

$sin sin {γ γ}_{B B} = = \frac{x x}{r r} - - - - - - ((44 b b))$

$\frac{\sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot &Center Dot; (({R R}_{e e} + + H h)) \cdot \cdot cos cos {γ γ}_{B B}}}{sin sin {γ γ}_{B B}} = = \frac{r r}{sin sin {α α}_{B B}} - - - - - - ((44 c c))$

其中，本实施例中的具体参数为：R_e＝6371140m，H＝800km，X、Y按公式(3a~3c)获得，得到r＝6368.6km，α_B＝30°。Wherein, the specific parameters in this embodiment are: _Re = 6371140m, H = 800km, X and Y are obtained according to formulas (3a~3c), and r = 6368.6km, α _B = 30°.

步骤三：距离向天线宽度展宽，流程图如图7所示。Step 3: The distance is widened toward the width of the antenna. The flow chart is shown in FIG. 7 .

A、获取距离向3dB波束宽度θ_3dB；A. Obtain the 3dB beam width θ _3dB in the distance direction;

方法如公式(5)所示：The method is shown in formula (5):

其中，本实施例中的具体参数为：L_r＝2m，λ＝0.03m，得到θ_3dB＝0.0133rad。Wherein, the specific parameters in this embodiment are: L _r =2m, λ=0.03m, and θ _3dB =0.0133rad is obtained.

B、获取斜视下，距离向波束宽度α_r，如图8所示；B. Obtain the range beam width α _r under squint, as shown in Figure 8;

方法如公式(6a~6f)所示：The method is shown in formula (6a~6f):

${γ γ}_{11} = = \frac{SW SW__r r}{22 r r} - - - - - - ((66 a a))$

$sin sin {α α}_{max max} = = \frac{r r \cdot &Center Dot; sin sin (({γ γ}_{B B} + + {γ γ}_{11}))}{\sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot &Center Dot; (({R R}_{e e} + + H h)) \cdot &Center Dot; cos cos (({γ γ}_{B B} + + {γ γ}_{11}))}} - - - - - - ((66 c c))$

$sin sin {α α}_{min min} = = \frac{r r \cdot &Center Dot; sin sin (({γ γ}_{B B} + + {γ γ}_{11}))}{\sqrt{{r r}^{22} + + {(({R R}_{e e} + + H h))}^{22} - - 22 r r \cdot \cdot (({R R}_{e e} + + H h)) \cdot &Center Dot; cos cos (({γ γ}_{B B} - - {γ γ}_{11}))}} - - - - - - ((66 e e))$

α_r＝α_max-α_min (6f)α _r = α _max - α _min (6f)

其中，本实施例中的具体参数为：R_e＝6371140m，H＝800km，SW_r＝15000m，r按公式(4a)获得，γ_B按公式(4b)获得，得到α_r＝0.0131rad。Wherein, the specific parameters in this embodiment are: R _e =6371140m, H=800km, SW_r=15000m, r is obtained according to formula (4a), γ _B is obtained according to formula (4b), and α _r =0.0131rad is obtained.

C、比较距离向波束宽度α_r和距离向3dB波束宽度θ_3dB的大小，判断是否需要展宽距离向天线宽度L_r。若α_r大于θ_3dB，则进行展宽，展宽后的距离向天线宽度记为L_t；C. Compare the range beam width α _r and the range 3dB beam width θ _3dB to determine whether it is necessary to widen the range antenna width L _r . If α _r is greater than θ _3dB , perform widening, and the distance to the antenna width after widening is recorded as L _t ;

方法如公式(7)所示：The method is shown in formula (7):

其中，本实施例中的具体参数为：λ＝0.03m，θ_3dB按公式(5)获得，α_r按公式(6a~6f)获得，得到L_t＝1.8798。Wherein, the specific parameters in this embodiment are: λ=0.03m, θ _3dB is obtained according to formula (5), α _r is obtained according to formula (6a~6f), and L _t =1.8798.

方法如公式(8a~8e)所示：The method is shown in formula (8a~8e):

Nr＝S_max-S_min (8e)Nr＝S _max -S _min (8e)

其中，本实施例中的具体参数为：R_e＝6371140m，H＝800km，PRF＝2000Hz，Y按公式(3a)获得，R_max按公式(6b)获得，R_min按公式(6d)获得，得到Nr＝26。Wherein, the specific parameters in this embodiment are: _Re =6371140m, H=800km, PRF=2000Hz, Y is obtained according to formula (3a), R _max is obtained according to formula (6b), R _min is obtained according to formula (6d), This gives Nr=26.

步骤五：获取模糊区能量Ea，流程图如图9所示;Step 5: Obtain the energy Ea of the fuzzy area, the flow chart is shown in Figure 9;

A、给出以下表示，在测绘带距离向上均匀选取Fr个位置；A. Given the following representation, Fr positions are uniformly selected upwards in the survey zone distance;

B、求取测绘带距离向上第j个位置与卫星平台的斜距R_j；B. Obtain the slope distance R _j between the jth position and the satellite platform in the upward distance of the surveying zone;

方法如公式(9a~9b)所示：The method is shown in formula (9a~9b):

${R R}_{j j} = = \sqrt{{((sin sin (({γ γ}_{B B} - - {γ γ}_{11})) + + j j \cdot &Center Dot; Δγ Δγ))}^{22} \cdot &Center Dot; {r r}^{22} + + {y the y}^{22} + + {((((cos cos (({γ γ}_{B B} - - {γ γ}_{11})) + + j j \cdot &Center Dot; Δγ Δγ)) \cdot \cdot r r - - (({R R}_{e e} + + H h))))}^{22}} - - - - - - ((99 d d))$

其中，本实施例中的具体参数为：R_e＝6371140m，H＝800km，SW_r＝15000m，Fr＝1001，r按公式(4a)获得，Y按公式(3a)获得，γ_B按公式(4b)获得，γ₁按公式(6a)获得，根据j的不同取值得到R_j。Wherein, the specific parameters in this embodiment are: _Re =6371140m, H=800km, SW_r=15000m, Fr=1001, r is obtained according to formula (4a), Y is obtained according to formula (3a), and γ _B is obtained according to formula (4b ), γ ₁ is obtained according to formula (6a), and R _j is obtained according to different values of j.

C、求取第S_i模糊区里第j个位置与卫星平台的斜距Ra_ij和离轴角α_ij；C, obtain the slant distance Ra _ij and the off-axis angle α _ij between the jth position and the satellite platform in the S _i ambiguity zone;

方法如公式(10a~10c)所示：The method is shown in formula (10a~10c):

其中，本实施例中的具体参数为：c＝3×108m/s，R_e＝6371140m，H＝800km，PRF＝2000Hz，r按公式(4a)获得，Y按公式(3a)获得，R_j按公式(9d)获得，根据j和S_i的不同取值得到Ra_ij和α_ij。Among them, the specific parameters in this embodiment are: c=3×108m/s, _Re =6371140m, H=800km, PRF=2000Hz, r is obtained according to formula (4a), Y is obtained according to formula (3a), R _j According to formula (9d), Ra _ij and α _ij are obtained according to different values of j and S _i .

D、求取第S_i模糊区里第j个位置的距离向天线方向图Wrij；D, obtain the distance to the antenna pattern Wrij of the jth position in the S _i ambiguity zone;

方法如公式(11a~11b)所示：The method is shown in formula (11a~11b):

其中，本实施例中的具体参数为：λ＝0.03m，α_B按公式(4a～4c)获得，α_ij按公式(10a~10c)获得，L_t按公式(7)获得，根据j和S_i的不同取值得到Wr_ij。Among them, the specific parameters in this embodiment are: λ=0.03m, α _B is obtained according to formula (4a-4c), α _ij is obtained according to formula (10a-10c), L _t is obtained according to formula (7), according to j and Different values of S _i get Wr _ij .

E、求取第S_i模糊区里第j个位置返回的能量E_ij；E, obtain the energy E _ij returned by the jth position in the S _i fuzzy area;

方法如公式(12a～12b)所示：The method is shown in formula (12a~12b):

其中，本实施例中的具体参数为：σ₀＝1，R_e＝6371140m，H＝800km，Ra_ij按公式(10a)获得，Wr_ij按公式(11a~11b)获得，根据j和S_i的不同取值得到E_ij。Among them, the specific parameters in this embodiment are: σ ₀ =1, R _e =6371140m, H=800km, Ra _ij is obtained according to formula (10a), Wr _ij is obtained according to formula (11a~11b), according to j and S _i Different values of E _ij can be obtained.

F、重复步骤B到E，计算出所有位置返回的能量。F. Repeat steps B to E to calculate the energy returned by all positions.

G、求取第j个位置返回的总能量E_allj和模糊区能量Ea_j；G. Obtain the total energy E _allj and the fuzzy area energy Ea _j returned by the jth position;

方法如公式(13a～13b)所示：The method is shown in formula (13a~13b):

${E E.}_{aj aj} = = {E E.}_{allj allj} - - {E E.}_{((| | {S S}_{min min} | | + + 11)) j j} - - - - - - ((1313 b b))$

其中，本实施例中的具体参数为：E_ij按公式(12a～12b)获得，根据j的不同取值得到E_allj和Ea_j。Wherein, the specific parameters in this embodiment are: E _ij is obtained according to formulas (12a-12b), and E _allj and Ea _j are obtained according to different values of j.

方法如公式(14)所示：The method is shown in formula (14):

其中，本实施例中的具体参数为：E_ij按公式(12a～12b)获得，Ea_j按公式(13~13)获得，根据j的不同取值得到RASR_j。Wherein, the specific parameters in this embodiment are: E _ij is obtained according to formula (12a-12b), Ea _j is obtained according to formula (13-13), and RASR _j is obtained according to different values of j.

采用本发明提出一种通用星载SAR模式下的距离向模糊度计算方法进行计算，得出的本实施例的仿真数据，对仿真数据进行绘制得到距离向模糊度的曲线，如图10所示，该曲线直观反映距离向模糊度在整个场景内的变化情况，结果表现形式直观性强，便于系统设计者及决策者通过曲线做出正确的判断。Using the calculation method of the range ambiguity in the general spaceborne SAR mode proposed by the present invention to calculate, obtain the simulation data of this embodiment, draw the simulation data to obtain the curve of the range ambiguity, as shown in Figure 10 , the curve intuitively reflects the change of the distance ambiguity in the whole scene, and the result expression form is intuitive, which is convenient for system designers and decision makers to make correct judgments through the curve.

Claims

1. the distance under the general satellite-borne SAR pattern comprises to the acquisition methods of blur level:

Step 1: read in the correlation parameter of Spaceborne SAR System, comprise orbit altitude H, antenna distance is to size L _r, radar operation wavelength λ, radius of a ball R fifty-fifty _e, light velocity c, pulse repetition rate PRF, center of antenna view angle theta _m, initial scan angle

Stop scan angle

The interscan angle

Distance is to mapping bandwidth SW_r, and distance is to chosen position number Fr;

It is characterized in that also comprising:

Step 2: obtain under the stravismus state distance to parameter;

(1) sets up coordinate system; True origin is the earth centre of sphere; Z-direction is to point to satellite by the earth centre of sphere; Y direction is for being starting point with the earth centre of sphere, and direction is parallel with the satellite velocities direction; X-direction perpendicular to satellite flight path direction, makes this coordinate system constitute right hand rectangular coordinate system for being starting point with the earth centre of sphere;

(2), obtain beam center view angle theta under the stravismus state _m';

θ wherein _mBe the center of antenna visual angle,

Be the interscan angle;

(3), obtain stravismus mapping band central point oblique distance R down _m

\frac{R_{e} + H}{\sin {β_{m}}^{'}} = \frac{R_{e}}{\sin {θ_{m}}^{'}} - - - (2 a)

γ _m'＝β _m'-θ _m' (2b)

R_{m} = \sqrt{{(R_{e} + H)}^{2} + {R_{e}}^{2} - {2 R}_{e} \cdot (R_{e} + H) \cdot \cos {γ_{m}}^{'}} - - - (2 c)

Wherein, β _m' and γ _m' being incident angle and the geocentric angle of observation band central point, H is orbit altitude, R _eBe the radius of a ball fifty-fifty, θ _m' be beam center visual angle under the stravismus state;

(4), obtain mapping band central point B coordinate (x, y, z);

z＝R _e+H-R _m·cosθ _m' (3b)

x = \sqrt{{R_{e}}^{2} - y^{2} - z^{2}} - - - (3 c)

Wherein, R _mBe with the central point oblique distance for looking side ways mapping down,

Be the interscan angle, H is orbit altitude, R _eBe the radius of a ball fifty-fifty, θ _m' be beam center visual angle under the stravismus state, x, y and z are respectively X-axis, Y-axis and the Z axial coordinate of mapping band central point B;

(5), obtain mapping band central point B point place distance to the roundlet radius r and apart to off-axis angle α _B

r = \sqrt{{R_{e}}^{2} - y^{2}} - - - (4 a)

\sin γ_{B} = \frac{x}{r} - - - (4 b)

\frac{\sqrt{r^{2} + {(R_{e} + H)}^{2} - 2 r \cdot (R_{e} + H) \cdot \cos γ_{B}}}{\sin γ_{B}} = \frac{r}{\sin α_{B}} - - - (4 c)

Wherein, γ _BBe the central angle of mapping band central point B point place roundlet, R _eBe the radius of a ball fifty-fifty, (x, y z) are the coordinate of mapping band central point B, and H is orbit altitude, and y is the Y-axis coordinate of mapping band central point B;

Step 3: carry out distance to sky line width broadening;

(1), obtains distance to 3dB beam angle θ _3dB

θ_{3 dB} = \frac{0.886 λ}{L_{r}} - - - (5)

Wherein λ is the radar operation wavelength, L _rFor antenna distance to size;

(2), obtain stravismus down, distance is to beam angle α _r

γ_{1} = \frac{SW_r}{2 r} - - - (6 a)

R_{\max} = \sqrt{r^{2} + {(R_{e} + H)}^{2} - 2 r \cdot (R_{e} + H) \cdot \cos (γ_{B} + γ_{1}) + y^{2}} - - - (6 b)

\sin α_{\max} = \frac{r \cdot \sin (γ_{B} + γ_{1})}{\sqrt{r^{2} + {(R_{e} + H)}^{2} - 2 r \cdot (R_{e} + H) \cdot \cos (γ_{B} + γ_{1})}} - - - (6 c)

R_{\min} = \sqrt{r^{2} + {(R_{e} + H)}^{2} - 2 r \cdot (R_{e} + H) \cdot \cos (γ_{B} + γ_{1}) + y^{2}} - - - (6 d)

\sin α_{\min} = \frac{r \cdot \sin (γ_{B} + γ_{1})}{\sqrt{r^{2} + {(R_{e} + H)}^{2} - 2 r \cdot (R_{e} + H) \cdot \cos (γ_{B} + γ_{1})}} - - - (6 e)

α _r＝α _max-α _min (6f)

Wherein, γ ₁Be the central angle of half mapping bandwidth correspondence in roundlet, R _MaxAnd R _MinBe respectively maximum oblique distance and the minimum oblique distance of mapping band and satellite platform, α _MaxAnd α _MinBe respectively mapping band in little disk corresponding distance to maximal off-axis angles and minimal off-axis angle, SW_r be distance to the mapping bandwidth, r for mapping band central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, γ _BBe the central angle of mapping band central point B point place roundlet, y is the Y-axis coordinate of mapping band central point B;

(3), compare distance to beam angle α _rWith the distance to 3dB beam angle θ _3dBSize, need to judge whether broadening distance to sky line width L _r, if distance is to beam angle α _rGreater than the distance to 3dB beam angle θ _3dB, then carry out broadening, the distance behind the broadening is designated as L to the sky line width _t:

L_{t} = \frac{0.886 λ}{α_{r} + 0.001} - - - (7)

If distance is to beam angle α _rLess than the distance to 3dB beam angle θ _3dB, then do not carry out broadening, L _t=L _r

Step 4: obtain confusion region number N r;

R_{a \max} = \sqrt{{(R_{e} + H)}^{2} - {R_{e}}^{2}} - - - (8 a)

R_{a \min} = \sqrt{y^{2} + {(R_{e} + H - r)}^{2}} - - - (8 b)

S_{\min} = - [\frac{2 (R_{\min} - R_{a \min})}{c} \cdot PRF] - - - (8 c)

S_{\max} = - [\frac{2 (R_{\max} - R_{a \max})}{c} \cdot PRF] - - - (8 d)

Nr＝S _max-S _min (8e)

Wherein, R _AmaxAnd R _AminBe respectively confusion region oblique distance and nearest oblique distance farthest, S _MaxAnd S _MinBe respectively the maximum sequence number in confusion region and smallest sequence number, the maximum integer that is not more than x, R are got in [x] expression _eBe the radius of a ball fifty-fifty, H is orbit altitude, r for mapping band central point B point place distance to little radius of circle, c is the light velocity, PRF is pulse repetition rate, y is with the Y-axis coordinate of central point B for mapping;

Step 5: obtain confusion region energy E a;

(1), upwards evenly chooses Fr position in mapping band distance; Fr is that distance is to the chosen position number;

(2), ask for the oblique distance R that surveys and draws band apart from make progress j position and satellite platform _j

Δγ = \frac{SW_r}{r \cdot Fr} - - - (9 b)

R_{j} = \sqrt{{(\sin (γ_{B} - γ_{1}) + j \cdot Δγ)}^{2} \cdot r^{2} + y^{2} + {((\cos (γ_{B} - γ_{1}) + j \cdot Δγ) \cdot r - (R_{e} + H))}^{2}} - - - (9 d)

Wherein, Δ γ is circle heart angle Walk distance, SW_r be distance to the mapping bandwidth, r for mapping band central point B point place distance to little radius of circle, Fr be distance to the chosen position number, r for survey and draw be with central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, γ ₁Be the central angle of half mapping bandwidth correspondence in roundlet, γ _BBe the central angle of mapping band central point B point place roundlet, y is the Y-axis coordinate of mapping band central point B;

(3), ask for S _iThe oblique distance of j position and satellite platform in the confusion region With off-axis angle α _Ij

R_{a_{ij}} = R_{j} + \frac{S_{i} \cdot c}{2 \cdot PRF} - - - (10 a)

\cos γ_{ij} = \frac{r^{2} + {(R_{e} + H)}^{2} + y^{2} - {R_{aij}}^{2}}{2 r \cdot (R_{e} + H)} - - - (10 b)

\frac{r}{{\sin a}_{ij}} = \frac{\sqrt{r^{2} + {(R_{e} + H)}^{2} + y^{2} - {R_{aij}}^{2}}}{\sin γ_{ij}} - - - (10 c)

Wherein, γ _IjBe corresponding central angle, S _iBe the confusion region sequence number, PRF is pulse repetition rate, and c is the light velocity, R _jBe the upwards oblique distance of j position and satellite platform of mapping band distance, r for mapping be with central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, and y is the Y-axis coordinate of mapping band central point B;

(4), ask for S _iThe distance of j position is to antenna radiation pattern Wr in the confusion region _Ij

{Wr}_{ij} = \frac{\sin^{2} (π \cdot L_{t} \cdot (\sin α_{ij} - \sin α_{B}) / λ)}{{(π \cdot L_{t} \cdot (\sin α_{ij} - \sin α_{B}) / λ)}^{2}} - - - (11)

α wherein _IjBe off-axis angle, λ is the radar operation wavelength, L _tFor the distance behind the broadening to sky line width, α _BFor the distance to off-axis angle;

(5), ask for S _iJ energy E that the position is returned in the confusion region _Ij

\cos (π - {β_{ij}}^{'}) = \frac{{R_{a_{ij}}}^{2} + {R_{e}}^{2} - {(R_{e} + H)}^{2}}{2 R_{e} \cdot R_{a_{ij}}} - - - (12 a)

E_{ij} = \frac{{Wr}_{ij}^{2} \cdot σ_{0}}{\sin {β_{ij}}^{'} \cdot {R_{aij}}^{3}} - - - (12 b)

Wherein, β _Ij' be the incident angle sequence, σ ₀Expression ground backscattering coefficient, R _eBe the radius of a ball fifty-fifty, H is orbit altitude,

Represent S _iThe oblique distance of j position and satellite platform in the confusion region;

(6), repeating step (2) is to (5), calculates the energy that all positions are returned;

(7), ask for the gross energy E that returns j position _AlljWith confusion region energy E a _j

E_{allj} = \underset{i}{Σ} E_{ij} - - - (13 a)

{Ea}_{j} = E_{allj} - E_{(| S_{\min} | + 1) j} - - - (13 b)

S wherein _MinBe confusion region smallest sequence number, E _IjBe S _iJ energy that the position is returned in the confusion region,

Be i=|s _Min|+1 o'clock S _iJ energy that the position is returned in the confusion region;

Step 6: ask for the distance of j position to blur level RASR _j;

{RASR}_{j} = 10 \cdot \log 10 (\frac{{Ea}_{j}}{E_{(| S_{\min} | + 1) j}}) - - - (14)

Ea wherein _jBe confusion region energy, S _MinBe the confusion region smallest sequence number;

Step 7: draw distance to blur level with the change curve of distance to the position.