CN102135612B

CN102135612B - Bistatic forward-looking synthetic aperture radar swath range calculation method

Info

Publication number: CN102135612B
Application number: CN201010611174A
Authority: CN
Inventors: 武俊杰; 黄钰林; 杨建宇; 杨海光; 李文超; 张晓玲; 孔令讲; 杨晓波
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2010-12-29
Filing date: 2010-12-29
Publication date: 2012-08-29
Anticipated expiration: 2030-12-29
Also published as: CN102135612A

Abstract

The invention discloses a method for calculating the range of a bistatic forward-looking synthetic aperture radar surveying zone. According to the bistatic forward-looking SAR resolution theory, the present invention determines the imageable and non-imaging boundaries in the bistatic forward-looking SAR forward-looking area. At the same time, it adopts the fuzzy theory and combines the particularity of the bistatic forward-looking SAR beam irradiation. The calculation system does not For the imaging swath range under fuzzy conditions, compare the swath range calculation results obtained by the resolution theory and the fuzzy theory, and take the intersection of the two to get the swath range of the bistatic forward-looking SAR. The method of the invention not only considers the fuzzy limitation of the width of the surveying swath in SAR imaging, but also considers the particularity of the bistatic forward-looking SAR receiving beam forward-looking. The method of the invention can be applied to the fields of high-resolution earth observation, autonomous navigation, etc., and is used for the design and configuration of the geometric structure of the bistatic forward-looking SAR system.

Description

A Calculation Method for the Range of Bistatic Forward-Looking Synthetic Aperture Radar Swath

技术领域 technical field

本发明属于雷达信号处理处理技术领域，尤其涉及双基地前视合成孔径雷达(SAR，Synthetic Aperture Radar)的测绘带范围计算方法。The invention belongs to the technical field of radar signal processing, and in particular relates to a method for calculating the range of a surveying zone of a bistatic forward-looking synthetic aperture radar (SAR, Synthetic Aperture Radar).

背景技术 Background technique

与光学传感器相比，合成孔径雷达具有穿透性强，能全天时、全天候工作的独特优点，目前已得到广泛的应用。双基地SAR是一种新的雷达体制，系统发射站和接收站分置于不同平台上，收发分置的特点使其具备了许多突出的优点和特点，如获取目标信息丰富、作用距离远、安全性好、抗干扰能力强等。Compared with optical sensors, synthetic aperture radar has the unique advantages of strong penetrability and ability to work all day and all day, and has been widely used at present. Bistatic SAR is a new radar system. The system’s transmitting station and receiving station are placed on different platforms. The characteristics of separate sending and receiving make it have many outstanding advantages and characteristics, such as the acquisition of rich target information, long range, Good security, strong anti-interference ability, etc.

双基地前视SAR是指收发波束共同指向运动接收站前方地面的双基地SAR系统。由于收发分置，发射站可为接收站提供方位向合成孔径，形成方位向高分辨，通过发射大带宽信号形成距离向高分辨，因此双基地前视SAR可以实现接收站前视高分辨成像。双基地前视SAR可以克服传统SAR技术不能实现飞行器正前方高分辨雷达成像的缺陷，使编队飞行的飞机具备前视成像的能力，从而可以应用于飞行器前视对地观测、自主导航、自主着陆、物资空投等领域。Bistatic forward-looking SAR refers to the bistatic SAR system in which the transmitting and receiving beams point to the ground in front of the moving receiving station. Due to the separation of transceivers, the transmitting station can provide azimuth synthetic aperture for the receiving station, forming high resolution in azimuth, and high resolution in range by transmitting large-bandwidth signals. Therefore, bistatic forward-looking SAR can realize high-resolution forward-looking imaging at the receiving station. Bistatic forward-looking SAR can overcome the defect that traditional SAR technology cannot realize high-resolution radar imaging directly in front of the aircraft, and enable aircraft flying in formation to have forward-looking imaging capabilities, which can be applied to aircraft forward-looking ground observation, autonomous navigation, and autonomous landing. , material airdrops and other fields.

测绘带范围是雷达成像和对地观测领域一个重要的概念和系统指标，也被称为辐照宽度和扫描宽度，它决定系统在地面的可成像区域范围。目前针对单基地SAR和双基地侧视SAR，测绘带范围通常采用系统模糊理论来确定，可见文献“保铮，邢梦道，王彤，《雷达成像技术》，电子工业出版社，2006年”、“John C.Curlander，Robert N.Mcdonough，《合成孔径雷达-系统与信号处理》，电子工业出版社，2006年”，即测绘带内的信号在距离和方位两个方向上都不存在模糊，从而由系统脉冲重复频率限制可以得到系统测绘带范围。但是在双基地前视SAR中，接收波束指向接收站运动的正前方，该区域内的目标并不都具有成像能力。所以不能只由模糊理论来确定双基地前视SAR的测绘带范围。The range of the swath is an important concept and system index in the field of radar imaging and earth observation. It is also called the irradiance width and the scan width. It determines the imageable area of the system on the ground. At present, for monostatic SAR and bistatic side-looking SAR, the range of the surveying zone is usually determined by the system fuzzy theory, as can be seen in the literature "Bao Zheng, Xing Mengdao, Wang Tong, "Radar Imaging Technology", Electronic Industry Press, 2006", " John C.Curlander, Robert N.Mcdonough, "Synthetic Aperture Radar-System and Signal Processing", Electronic Industry Press, 2006", that is, the signal in the survey zone has no ambiguity in the two directions of distance and azimuth, so The system swath range can be obtained limited by the system pulse repetition frequency. However, in bistatic forward-looking SAR, the receiving beam points directly in front of the receiving station, and not all targets in this area have imaging capabilities. Therefore, the swath range of bistatic forward-looking SAR cannot be determined only by fuzzy theory.

发明内容 Contents of the invention

本发明的目的是为了解决现有的方法在确定双基地前视SAR的测绘带范围时存在的问题，提出了一种双基地前视合成孔径雷达测绘带范围计算方法。The purpose of the present invention is to solve the existing problems in determining the swath range of bistatic forward-looking SAR in existing methods, and proposes a method for calculating the swath range of bistatic forward-looking synthetic aperture radar.

为了方便描述本发明的内容，首先对以下术语进行解释：In order to describe content of the present invention conveniently, at first the following terms are explained:

术语1：合成孔径雷达(SAR)Term 1: Synthetic Aperture Radar (SAR)

合成孔径雷达通常安装在空间中运动平台上，在距离向通过发射大时宽带宽积信号获取高的分辨率，在方位向通过雷达向前运动，产生一个等效的长阵列天线，达到波束锐化的目的，从而提高方位向的角度分辨率。Synthetic aperture radar is usually installed on a moving platform in space. In the distance direction, a large time-width-bandwidth product signal is emitted to obtain high resolution. In the azimuth direction, the radar moves forward to generate an equivalent long array antenna to achieve a sharp beam. The purpose of this is to improve the angular resolution of the azimuth direction.

术语2：双基地SAR(Bistatic SAR)Term 2: Bistatic SAR (Bistatic SAR)

双基地SAR是指系统发射站和接收站分置于不同平台上的SAR系统，其中至少有一个平台为运动平台，在概念上属于双基地雷达。Bistatic SAR refers to the SAR system in which the system transmitting station and receiving station are placed on different platforms, at least one of which is a moving platform, which is conceptually a bistatic radar.

术语3：双基地前视SAR(Forward-looking bistatic SAR)Term 3: Forward-looking bistatic SAR (Forward-looking bistatic SAR)

双基地前视SAR是指收发波束共同指向运动接收站前方地面的双基地SAR系统。由于收发分置，双基地SAR可以克服传统SAR技术不能实现飞行器正前方高分辨雷达成像的缺陷，使编队飞行的飞机具备前视成像的能力，从而可以应用于飞行器前视对地观测、自主导航、自主着陆、物资空投等领域。Bistatic forward-looking SAR refers to the bistatic SAR system in which the transmitting and receiving beams point to the ground in front of the moving receiving station. Due to the separation of transceivers, bistatic SAR can overcome the defect that traditional SAR technology cannot realize high-resolution radar imaging directly in front of the aircraft, so that the aircraft flying in formation can have the ability of forward-looking imaging, so that it can be applied to aircraft forward-looking ground observation and autonomous navigation. , autonomous landing, material airdrop and other fields.

术语4：双基地SAR梯度分辨率理论Term 4: Bistatic SAR Gradient Resolution Theory

梯度分辨率理论用来研究分析合成孔径雷达的分辨能力，系统时延的梯度决定距离分辨率，多普勒频率的梯度决定方位分辨率。The gradient resolution theory is used to study and analyze the resolution capability of synthetic aperture radar. The gradient of system time delay determines the range resolution, and the gradient of Doppler frequency determines the azimuth resolution.

术语5：SAR模糊理论Term 5: SAR Fuzzy Theory

在SAR成像技术中，较低的脉冲重复频率(PRF，Pulse RepetitionFrequency)会导致方位向频谱的混叠，产生方位模糊，使方位向的模糊电平提高。较高的PRF将减小脉冲间的持续时间，在时间上使接收脉冲间产生交叠，产生距离模糊。所以，PRF需要同时考虑方位和距离模糊的限制。In SAR imaging technology, a lower pulse repetition frequency (PRF, Pulse Repetition Frequency) will cause the azimuth spectrum to alias, resulting in azimuth ambiguity, which will increase the ambiguity level in the azimuth direction. A higher PRF will reduce the duration between pulses, causing overlapping in time between received pulses, resulting in range ambiguity. Therefore, PRF needs to consider the constraints of both azimuth and range ambiguity.

术语6：测绘带Term 6: Swap

测绘带是覆盖在地面上与平台运动方向平行的一条带状区域，决定系统在地面的可成像区域范围。传统单基地SAR中，测绘带与距离向垂直，测绘带范围由天线波束距离向在地面上的散布宽度决定。在系统设计时，为了避免距离模糊，测绘带受PRF的大小限制。The surveying zone is a belt-shaped area covering the ground parallel to the direction of platform movement, which determines the imaging area of the system on the ground. In traditional monostatic SAR, the mapping zone is perpendicular to the range direction, and the range of the mapping zone is determined by the spread width of the antenna beam range direction on the ground. During system design, in order to avoid distance ambiguity, the swath is limited by the size of the PRF.

本发明的一种双基地前视合成孔径雷达测绘带范围计算方法，具体包括如下步骤：A method for calculating the range of a bistatic forward-looking synthetic aperture radar surveying zone of the present invention specifically includes the following steps:

S1.初始化系统参数，系统坐标系以成像中心目标点为坐标原点，平台沿y轴运动，x轴为切航迹方向，z轴为垂直地面方向，初始化系统参数包括：发射站零时刻位置，记为(x_0T，y_0T，z_0T)；接收站零时刻位置，记为(0，y_0R，z_0R)；系统载频，记为f₀；波长，记为λ；发射信号带宽，记为B_r；平台运动速度，记为V；快时间变量，记为τ；慢时间变量，记为s；发射站天线斜视角，记为θ_sT；接收站天线下视角，记为θ_dR；发射站天线俯仰角为φ_T；发射站中心斜距，记为r_0T；接收站中心斜距，记为r_0R；脉冲重复频率，记为PRF；脉宽，记为T_r；距离分辨率，记为ρ_r；方位分辨率，记为ρ_a；合成孔径时间，记为T_s；则发射站距离为 $R_{T} (s) = \sqrt{r_{0 T}^{2} + V^{2} s^{2} - 2 r_{0 T} Vs \sin θ_{sT}};$ 接收站距离为 $R_{R} (s) = \sqrt{r_{0 R}^{2} + V^{2} s^{2} - 2 r_{0 R} Vs \cos θ_{dR}};$ 双基地前视SAR系统距离为R_bi(s)＝R_T(s)+R_R(s)；S1. Initialize the system parameters. The system coordinate system takes the imaging center target point as the coordinate origin, the platform moves along the y-axis, the x-axis is the direction tangential to the track, and the z-axis is the direction vertical to the ground. The initialization system parameters include: the position of the launch station at zero time, It is denoted as (x _0T , y _0T , z _0T ); the position of the receiving station at zero time is denoted as (0, y _0R , z _0R ); the system carrier frequency is denoted as f ₀ ; the wavelength is denoted as λ; the transmitting signal bandwidth is denoted as Denoted as B _r ; platform motion speed, denoted as V; fast time variable, denoted as τ; slow time variable, denoted as s; transmitting station antenna oblique angle, denoted as θ _sT ; receiving station antenna down angle, denoted as θ _dR ; Antenna elevation angle of transmitting station is φ _T ; center slant distance of transmitting station, denoted as r _0T ; center slant distance of receiving station, denoted as r _0R ; pulse repetition frequency, denoted as PRF; pulse width, denoted as T _r ; distance resolution rate, denoted as ρ _r ; azimuth resolution, denoted as ρ _a ; synthetic aperture time, denoted as T _s ; then the distance of the transmitting station is $R_{T} (the s) = \sqrt{r_{0 T}^{2} + V^{2} {the s}^{2} - 2 r_{0 T} vs. \sin θ_{s T}};$ The receiving station distance is $R_{R} (the s) = \sqrt{r_{0 R}^{2} + V^{2} {the s}^{2} - 2 r_{0 R} vs. \cos θ_{d}};$ The bistatic forward-looking SAR system distance is R _bi (s) = R _T (s) + R _R (s);

S2.采用梯度理论计算成像区域x轴上各点的分辨率方向，用分辨率与x轴的夹角的正切值来衡量分辨率方向，得到x轴上任意目标点P(x，0)的分辨率方向，结果如下：S2. Use the gradient theory to calculate the resolution direction of each point on the x-axis of the imaging area, use the tangent of the angle between the resolution and the x-axis to measure the resolution direction, and obtain any target point P(x, 0) on the x-axis Resolution direction, the result is as follows:

距离分辨率方向为 $dir (ρ_{r}) = \frac{\sin θ_{sT} (x) + \cos θ_{dR} (x)}{x / r_{0 R} (x) + \cos θ_{sT} (x) \sin φ_{T} (x)}$ The distance resolution direction is $dir (ρ_{r}) = \frac{\sin θ_{s T} (x) + \cos θ_{d} (x)}{x / r_{0 R} (x) + \cos θ_{s T} (x) \sin φ_{T} (x)}$

方位分辨率方向为：The azimuth resolution direction is:

$dir dir (({ρ ρ}_{a a})) = = \frac{{r r}_{00 T T} ((x x)) {sin sin}^{22} {θ θ}_{dR d} ((x x)) + + {r r}_{00 R R} ((x x)) {cos cos}^{22} {θ θ}_{sT s T} ((x x))}{{r r}_{00 T T} ((x x)) x x cos cos {θ θ}_{dR d} ((x x)) / / {r r}_{00 R R} ((x x)) + + {r r}_{00 R R} ((x x)) sin sin {θ θ}_{sT s T} ((x x)) sin sin {φ φ}_{T T} ((x x)) cos cos {θ θ}_{sT s T} ((x x))}$

其中 $r_{0 R} (x) = \sqrt{r_{0 R}^{2} (0) + x^{2}},$ $r_{0 T} (x) = \sqrt{r_{0 T}^{2} (0) + x^{2} - 2 r_{0 T} (0) x \cos θ_{sT} (0) \sin φ_{T}},$ $θ_{sT} (x) = a \sin (\frac{r_{0 T} (0) \sin θ_{sT} (0)}{r_{0 T} (x)}),$ $θ_{dR} (x) = a \cos (\cos θ_{dR} \frac{r_{0 R} (0)}{r_{0 R} (x)}),$ x表示目标点在x轴上的坐标；r_0R(x)表示P(x，0)点处的接收站中心斜距；r_0T(x)表示P(x，0)点处的发射站中心斜距；θ_dR(x)表示P(x，0)点处的接收站天线下视角；θ_sT(x)表示P(x，0)点处的发射站天线斜视角，φ_T(x)表示P(x，0)点处的发射站天线俯仰角；in $r_{0 R} (x) = \sqrt{r_{0 R}^{2} (0) + x^{2}},$ $r_{0 T} (x) = \sqrt{r_{0 T}^{2} (0) + x^{2} - 2 r_{0 T} (0) x \cos θ_{s T} (0) \sin φ_{T}},$ $θ_{s T} (x) = a \sin (\frac{r_{0 T} (0) \sin θ_{s T} (0)}{r_{0 T} (x)}),$ $θ_{d} (x) = a \cos (\cos θ_{d} \frac{r_{0 R} (0)}{r_{0 R} (x)}),$ x represents the coordinates of the target point on the x-axis; r _0R (x) represents the slant distance from the center of the receiving station at point P(x, 0); r _0T (x) represents the center of the transmitting station at point P(x, 0) slant distance; θ _dR (x) represents the downward angle of view of the antenna of the receiving station at point P(x, 0); θ _sT (x) represents the oblique angle of view of the antenna of the transmitting station at point P(x, 0), φ _T (x) Indicates the elevation angle of the transmitting station antenna at the point P(x, 0);

S3.设定双基地前视SAR可处理的分辨率夹角大小，并求解由该夹角确定的测绘带范围，由于SAR成像算法可以处理的距离分辨率和方位分辨率之间的夹角有限，设该角度为Δθ，则有atan{dir(ρ_r)}＝atan{dir(ρ_a)}-Δθ，采用步骤S2计算得到的距离分辨率方向和方位分辨率方向，求解该方程，可以得到该方程的解，记为x_reso，则由分辨率理论确定的双基地前视SAR测绘带范围为：x≥x_reso；S3. Set the resolution angle that can be processed by the bistatic forward-looking SAR, and solve the range of the survey zone determined by the angle. Since the angle between the range resolution and the azimuth resolution that the SAR imaging algorithm can handle is limited , assuming that the angle is Δθ, then there is atan{dir(ρ _r )}=atan{dir(ρ _a )}-Δθ, using the distance resolution direction and azimuth resolution direction calculated in step S2 to solve this equation, we can The solution of this equation is obtained, denoted as x _reso , then the range of the bistatic forward-looking SAR survey swath determined by the resolution theory is: x≥x _reso ;

S4.由模糊理论计算系统允许的回波最大散布宽度，记为Δτ＝1/PRF-T_r；S4. The maximum spread width of the echo allowed by the fuzzy theory calculation system is recorded as Δτ=1/PRF-T _r ;

S5.计算由模糊理论确定的双基地前视SAR测绘带范围，具体如下：S5. Calculate the range of the bistatic forward-looking SAR survey zone determined by the fuzzy theory, as follows:

S51.求解系统允许的最大双基地距离和、最小双基地距离和与收发站中较小的波束宽度之间的关系。设最大双基地距离和为R_bix，最小距离和为R_bin，则回波最大散布宽度为：(R_bix-R_bin)/c，其中c为光速，所以可求得系统允许的最大和最小收发站距离和之差为L＝R_bix-R_bin＝cΔτ，同时，假设在前视成像区域，收发站中较小的波束一直被较大的波束覆盖，并且较小的波束脚印形状为椭圆，该椭圆的两个半轴分别与x轴和y轴平行，半轴长度分别为a和b，由于最大和最小双基地距离和一定发生在较小波束脚印形成的椭圆上，可以计算出最小收发站距离和为： $R_{bin} = \min {\sqrt{{(x - x_{0 T})}^{2} + {(y - y_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(y - y_{0 R})}^{2} + z_{0 R}^{2}}};$ 最大收发站距离和为： $R_{bix} = \max {\sqrt{{(x - x_{0 T})}^{2} + {(y - y_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(y - y_{0 R})}^{2} + z_{0 R}^{2}}},$ 其中x，y满足

得到R_bin和R_bix为a和b的函数；S51. Solve the relationship between the maximum bistatic distance sum allowed by the system, the minimum bistatic distance sum and the smaller beam width in the transceiver station. Let the maximum bistatic distance sum be R _bix and the minimum distance sum be R _bin , then the maximum spread width of the echo is: (R _bix -R _bin )/c, where c is the speed of light, so the maximum and minimum allowed by the system can be obtained The difference between the distance sum of the transceiver station is L=R _bix -R _bin =cΔτ, and at the same time, it is assumed that in the forward-looking imaging area, the smaller beam in the transceiver station is always covered by the larger beam, and the shape of the footprint of the smaller beam is an ellipse , the two semi-axes of the ellipse are parallel to the x-axis and y-axis respectively, and the lengths of the semi-axes are a and b, respectively. Since the maximum and minimum bistatic distance sum must occur on the ellipse formed by the smaller beam footprint, the minimum The sum of transceiver station distances is:

R_{bin} = \min {\sqrt{{(x - x_{0 T})}^{2} + {(the y - {the y}_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(the y - {the y}_{0 R})}^{2} + z_{0 R}^{2}}};

The maximum transceiver station distance sum is:

R_{bix} = \max {\sqrt{{(x - x_{0 T})}^{2} + {(the y - {the y}_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(the y - {the y}_{0 R})}^{2} + z_{0 R}^{2}}},

where x, y satisfy

Get R _bin and R _bix as functions of a and b;

S52.利用步骤S51中得到的系统允许的最大和最小收发站距离和之差L，计算由模糊理论确定的双基地前视SAR测绘带范围，求解方程R_bix(a；b)-R_bin(a；b)＝L，可以求出确定b条件下的较小波束沿x轴的散布宽度，记为a(T_r，PRF，b)，则由模糊理论确定双基地前视SAR测绘带范围为：-a(T_r，PRF，b)≤x≤a(T_r，PRF，b)；S52. Utilize the difference L between the maximum and minimum transceiver station distances allowed by the system obtained in step S51, calculate the range of the bistatic forward-looking SAR survey zone determined by fuzzy theory, and solve the equation R _bix (a; b)-R _bin ( a; b) = L, the spread width of the smaller beam along the x-axis under the condition b can be obtained, denoted as a(T _r , PRF, b), then the range of the bistatic forward-looking SAR survey swath is determined by fuzzy theory is: -a(T _r , PRF, b)≤x≤a(T _r , PRF, b);

S6.计算双基地前视SAR测绘带范围，利用步骤S3和S52计算得到的测绘带范围边界条件，可以得到双基地前视SAR测绘带范围为：max{-a(T_r，PRF，b)，x_reso}≤x≤a(T_r，PRF，b)。S6. Calculate the range of the bistatic forward-looking SAR swath, using the boundary conditions of the swath range calculated in steps S3 and S52, the range of the bistatic forward-looking SAR swath can be obtained as: max{-a(T _r , PRF, b) , x _reso }≤x≤a(T _r , PRF, b).

本发明的有益效果：本发明根据双基地前视SAR分辨率理论，确定双基地前视SAR前视区域内可成像与不可成像的界限，同时采用模糊理论，结合双基地前视SAR波束照射的特殊性，计算系统不模糊条件下的成像测绘带范围，比较分辨率理论和模糊理论得到的测绘带范围计算结果，取二者的交集，即可得到双基地前视SAR的测绘带范围。本发明的方法不但考虑了SAR成像中对测绘带范围的模糊限制，还考虑了双基地前视SAR接收波束前视的特殊性。本发明的方法可以应用于高分辨率对地观测、自主导航等领域，用于双基地前视SAR系统的设计和几何结构的配置。Beneficial effects of the present invention: According to the bistatic forward-looking SAR resolution theory, the present invention determines the imageable and non-imaging boundaries in the bistatic forward-looking SAR forward-looking area, and adopts the fuzzy theory at the same time, combined with the bistatic forward-looking SAR beam irradiation Particularity, calculate the imaging swath range under the condition that the system is not blurred, compare the swath range calculation results obtained by the resolution theory and the fuzzy theory, and take the intersection of the two to get the swath range of the bistatic forward-looking SAR. The method of the invention not only considers the fuzzy limitation of the range of the surveying zone in SAR imaging, but also considers the particularity of the bistatic forward-looking SAR receiving beam forward-looking. The method of the invention can be applied to the fields of high-resolution earth observation, autonomous navigation, etc., and is used for the design and configuration of the geometric structure of the bistatic forward-looking SAR system.

附图说明 Description of drawings

图1是本发明的双基地前视合成孔径雷达测绘带范围计算方法流程示意图。Fig. 1 is a schematic flow chart of the method for calculating the swath range of the bistatic forward-looking synthetic aperture radar of the present invention.

图2是本发明采用的成像几何模式图。Fig. 2 is a diagram of an imaging geometric model adopted by the present invention.

图3是本发明具体实施例中采用的系统参数图。Fig. 3 is a diagram of system parameters used in a specific embodiment of the present invention.

图4是双基地前视SAR的等多普勒线和等距离线示意图。Figure 4 is a schematic diagram of iso-Doppler lines and equidistance lines of bistatic forward-looking SAR.

图5为本发明具体实施例中得到的距离分辨率和方位分辨率方向随x的变化曲线图。Fig. 5 is a graph showing the variation of distance resolution and azimuth resolution direction with x obtained in a specific embodiment of the present invention.

图6是本发明具体实施例中采用的波束覆盖图。Fig. 6 is a beam coverage diagram used in a specific embodiment of the present invention.

图7是本发明具体实施例中得到的由模糊理论确定的测绘带范围。Fig. 7 is the range of the swath determined by the fuzzy theory obtained in the specific embodiment of the present invention.

具体实施方式 Detailed ways

下面结合附图和具体实施例对本发明作进一步的描述。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

本发明的双基地前视合成孔径雷达测绘带范围计算方法的流程示意图如图1所示，具体过程如下：The schematic flow chart of the method for calculating the range of the bistatic forward-looking synthetic aperture radar mapping zone of the present invention is as shown in Figure 1, and the specific process is as follows:

S1.初始化系统参数，本实施例采用的成像几何模式图如图2所示，系统坐标系以成像中心目标点O为坐标原点，平台沿y轴运动，x轴为切航迹方向，z轴为垂直地面方向。初始化系统参数，包括发射站零时刻位置，记为(x_0T，y_0T，z_0T)；接收站零时刻位置，记为(0，y_0R，z_0R)；系统载频，记为f₀；波长，记为λ；发射信号带宽，记为B_r；平台运动速度，记为V；快时间变量，记为τ；慢时间变量，记为s；发射站天线斜视角，记为θ_sT；接收站天线下视角，记为θ_dR；发射站天线俯仰角为φ_T；发射站中心斜距，记为r_0T；接收站中心斜距，记为r_0R；脉冲重复频率，记为PRF；脉宽，记为T_r；距离分辨率，记为ρ_r；方位分辨率，记为ρ_a；合成孔径时间，记为T_s；则发射站距离 $R_{T} (s) = \sqrt{r_{0 T}^{2} + V^{2} s^{2} - 2 r_{0 T} Vs \sin θ_{sT}};$ 接收站距离 $R_{R} (s) = \sqrt{r_{0 R}^{2} + V^{2} s^{2} - 2 r_{0 R} Vs \cos θ_{dR}};$ 双基地前视SAR系统距离R_bi(s)＝R_T(s)+R_R(s)；部分参数的初始值如图3所示。S1. Initialize the system parameters. The imaging geometric pattern used in this embodiment is shown in Figure 2. The system coordinate system takes the imaging center target point O as the coordinate origin, the platform moves along the y-axis, the x-axis is the tangential track direction, and the z-axis is vertical to the ground. Initialize system parameters, including the zero-time position of the transmitting station, denoted as (x _0T , y _0T , z _0T ); the zero-time position of the receiving station, denoted as (0, y _0R , z _0R ); system carrier frequency, denoted as f ₀ ; Wavelength, denoted as λ; Transmitted signal bandwidth, denoted as B _r ; Platform motion velocity, denoted as V; Fast time variable, denoted as τ; Slow time variable, denoted as s; Transmitting station antenna oblique angle, denoted as θ _sT ; The angle of view of the receiving station antenna is denoted as θ _dR ; the elevation angle of the transmitting station antenna is φ _T ; the slant distance from the center of the transmitting station is denoted as r _0T ; the slant distance from the center of the receiving station is denoted as r _0R ; the pulse repetition frequency is denoted as PRF ; pulse width, denoted as T _r ; distance resolution, denoted as ρ _r ; azimuth resolution, denoted as ρ _a ; synthetic aperture time, denoted as T _s ; $R_{T} (the s) = \sqrt{r_{0 T}^{2} + V^{2} {the s}^{2} - 2 r_{0 T} vs. \sin θ_{s T}};$ Receiving station distance $R_{R} (the s) = \sqrt{r_{0 R}^{2} + V^{2} {the s}^{2} - 2 r_{0 R} vs. \cos θ_{d}};$ Bistatic forward-looking SAR system distance R _bi (s) = R _T (s) + R _R (s); the initial values of some parameters are shown in Figure 3.

S2.采用梯度理论计算成像区域x轴上各点的分辨率方向，包括距离分辨率和方位分辨率，下面分别进行阐述。S2. Using gradient theory to calculate the resolution direction of each point on the x-axis of the imaging area, including distance resolution and azimuth resolution, which will be described separately below.

距离分辨率：地面上某点的回波延时为：Distance resolution: The echo delay at a point on the ground is:

${τ τ}_{d d} ((x x,, y the y)) = = \frac{11}{c c} [[\sqrt{{((x x - - {x x}_{00 T T}))}^{22} + + {((y the y - - {y the y}_{00 T T}))}^{22} + + {z z}_{00 T T}^{22}} + + \sqrt{{x x}^{22} + + {((y the y - - {y the y}_{00 R R}))}^{22} + + {z z}_{00 R R}^{22}}]]$

等距离线即τ_d(x，y)为常数在地面形成的曲线。根据梯度理论，可以求得该等值线的梯度值，如下 $&dtri; τ_{d} (x, y) = [\frac{&PartialD; τ_{d} (x, y)}{&PartialD; x} i + \frac{&PartialD; τ_{d} (x, y)}{&PartialD; y} j + \frac{&PartialD; τ_{d} (x, y)}{&PartialD; z} k] (s / m)$ The equidistance line is the curve formed on the ground when τ _d (x, y) is a constant. According to the gradient theory, the gradient value of the contour line can be obtained as follows $&dtri; τ_{d} (x, the y) = [\frac{&PartialD; τ_{d} (x, the y)}{&PartialD; x} i + \frac{&PartialD; τ_{d} (x, the y)}{&PartialD; the y} j + \frac{&PartialD; τ_{d} (x, the y)}{&PartialD; z} k] (the s / m)$

其中in

$\frac{&PartialD; &PartialD; {τ τ}_{d d} ((x x,, y the y))}{&PartialD; &PartialD; x x} = = \frac{x x - - {x x}_{00 T T}}{\sqrt{{((x x - - {x x}_{00 T T}))}^{22} + + {((y the y - - {y the y}_{00 T T}))}^{22} + + {z z}_{00 T T}^{22}}} + + \frac{x x}{\sqrt{{x x}^{22} + + {((y the y - - {y the y}_{00 R R}))}^{22} + + {z z}_{00 R R}^{22}}}$

$\frac{&PartialD; &PartialD; {τ τ}_{d d} ((x x,, y the y))}{&PartialD; &PartialD; y the y} = = \frac{y the y - - {y the y}_{00 T T}}{\sqrt{{((x x - - {x x}_{00 T T}))}^{22} + + {((y the y - - {y the y}_{00 T T}))}^{22} + + {z z}_{00 T T}^{22}}} + + \frac{y the y - - {y the y}_{00 R R}}{\sqrt{{x x}^{22} + + {((y the y - - {y the y}_{00 R R}))}^{22} + + {z z}_{00 R R}^{22}}}$

$\frac{&PartialD; &PartialD; {τ τ}_{d d} ((x x,, y the y))}{&PartialD; &PartialD; z z} = = \frac{z z - - {z z}_{00 T T}}{\sqrt{{((x x - - {x x}_{00 T T}))}^{22} + + {((y the y - - {y the y}_{00 T T}))}^{22} + + {z z}_{00 T T}^{22}}} + + \frac{z z - - {z z}_{00 R R}}{\sqrt{{x x}^{22} + + {((y the y - - {y the y}_{00 R R}))}^{22} + + {z z}_{00 R R}^{22}}}$

令y＝0，并且去除z分量，得到Let y=0, and remove the z component, we get

${ρ ρ}_{r r} ((x x)) = = \frac{11 / / {B B}_{r r}}{\sqrt{{((\frac{x x - - {x x}_{00 T T}}{\sqrt{{((x x - - {x x}_{00 T T}))}^{22} + + {y the y}_{00 T T}^{22} + + {z z}_{00 T T}^{22}}} + + \frac{x x - - {x x}_{00 R R}}{\sqrt{{((x x - - {x x}_{00 R R}))}^{22} + + {y the y}_{00 R R}^{22} + + {z z}_{00 R R}^{22}}}))}^{22} + + {((\frac{{y the y}_{00 T T}}{\sqrt{{((x x - - {x x}_{00 T T}))}^{22} + + {y the y}_{00 T T}^{22} + + {z z}_{00 T T}^{22}}} + + \frac{{y the y}_{00 R R}}{\sqrt{{x x}^{22} + + {y the y}_{00 R R}^{22} + + {z z}_{00 R R}^{22}}}))}^{22}}}$

并且有 $\frac{x - x_{0 T}}{\sqrt{{(x - x_{0 T})}^{2} + y_{0 T}^{2} + z_{0 T}^{2}}} = \cos θ_{sT} (x) \sin φ_{T} (x),$ $\frac{x}{\sqrt{x^{2} + y_{0 R}^{2} + z_{0 R}^{2}}} = x / r_{0 R} (x),$ $\frac{y_{0 T}}{\sqrt{{(x - x_{0 T})}^{2} + y_{0 T}^{2} + z_{0 T}^{2}}} = \sin θ_{sT} (x),$ $\frac{y_{0 R}}{\sqrt{x^{2} + y_{0 R}^{2} + z_{0 R}^{2}}} = \cos θ_{dR} (x) .$ and have $\frac{x - x_{0 T}}{\sqrt{{(x - x_{0 T})}^{2} + {the y}_{0 T}^{2} + z_{0 T}^{2}}} = \cos θ_{s T} (x) \sin φ_{T} (x),$ $\frac{x}{\sqrt{x^{2} + {the y}_{0 R}^{2} + z_{0 R}^{2}}} = x / r_{0 R} (x),$ $\frac{{the y}_{0 T}}{\sqrt{{(x - x_{0 T})}^{2} + {the y}_{0 T}^{2} + z_{0 T}^{2}}} = \sin θ_{s T} (x),$ $\frac{{the y}_{0 R}}{\sqrt{x^{2} + {the y}_{0 R}^{2} + z_{0 R}^{2}}} = \cos θ_{d} (x) .$

所以，距离分辨率大小为Therefore, the distance resolution size is

${ρ ρ}_{r r} ((x x)) = = \frac{c c / / {B B}_{r r}}{\sqrt{{((x x / / {r r}_{00 R R} ((x x)) + + cos cos {θ θ}_{sT s T} ((x x)) sin sin {φ φ}_{T T} ((x x))))}^{22} + + {((sin sin {θ θ}_{sT s T} ((x x)) + + cos cos {θ θ}_{dR d} ((x x))))}^{22}}}$

用分辨率与x轴夹角衡量ρ_r的方向为The direction of ρ _r measured by the angle between the resolution and the x-axis is

$dir dir (({ρ ρ}_{r r})) = = \frac{sin sin {θ θ}_{sT s T} ((x x)) + + cos cos {θ θ}_{dR d} ((x x))}{x x / / {r r}_{00 R R} ((x x)) + + cos cos {θ θ}_{sT s T} ((x x)) sin sin {φ φ}_{T T} ((x x))}$

方位分辨率：地面上某点的多普勒频率为：Azimuth resolution: The Doppler frequency at a point on the ground is:

${f f}_{d d} ((x x,, y the y)) = = \frac{V V}{λ λ} \frac{y the y - - {y the y}_{00 R R}}{\sqrt{{x x}^{22} + + {((y the y - - {y the y}_{00 R R}))}^{22} + + {z z}_{00 R R}^{22}}} + + \frac{V V}{λ λ} \frac{y the y - - {y the y}_{00 T T}}{\sqrt{{((x x - - {x x}_{00 T T}))}^{22} + + {((y the y - - {y the y}_{00 T T}))}^{22} + + {z z}_{00 T T}^{22}}}$

此等多普勒线在地面上任意点(x，0，0)处的梯度表达式为The gradient expression of these Doppler lines at any point (x, 0, 0) on the ground is

$&dtri; &dtri; {f f}_{d d} = = \frac{&PartialD; &PartialD; {f f}_{d d}}{&PartialD; &PartialD; x x} i i + + \frac{&PartialD; &PartialD; {f f}_{d d}}{&PartialD; &PartialD; y the y} j j$

其中in

$\frac{&PartialD; &PartialD; {f f}_{d d}}{&PartialD; &PartialD; x x} = = \frac{V V}{λ λ} \frac{{xy xy}_{00 R R}}{{[[{x x}^{22} + + {y the y}_{00 R R}^{22} + + {z z}_{00 R R}^{22}]]}^{33 / / 22}} + + \frac{V V}{λ λ} \frac{((x x - - {x x}_{00 T T})) {y the y}_{00 T T}}{{[[{((x x - - {x x}_{00 T T}))}^{22} + + {y the y}_{00 T T}^{22} + + {z z}_{00 T T}^{22}]]}^{33 / / 22}}$

$\frac{&PartialD; &PartialD; {f f}_{d d}}{&PartialD; &PartialD; y the y} = = \frac{V V}{λ λ} \frac{11}{\sqrt{{x x}^{22} + + {y the y}_{00 R R}^{22} + + {z z}_{00 R R}^{22}}} - - \frac{V V}{λ λ} \frac{{y the y}_{00 R R}^{22}}{{[[{x x}^{22} + + {y the y}_{00 R R}^{22} + + {z z}_{00 R R}^{22}]]}^{33 / / 22}}$

$+ + \frac{V V}{λ λ} \frac{11}{\sqrt{{((x x - - {x x}_{00 T T}))}^{22} + + {y the y}_{00 T T}^{22} + + {z z}_{00 T T}^{22}}} - - \frac{V V}{λ λ} \frac{{y the y}_{00 T T}^{22}}{{[[{((x x - - {x x}_{00 T T}))}^{22} + + {y the y}_{00 T T}^{22} + + {z z}_{00 T T}^{22}]]}^{33 / / 22}}$

并且 $\frac{x - x_{0 T}}{\sqrt{{(x - x_{0 T})}^{2} + y_{0 T}^{2} + z_{0 T}^{2}}} = \sin φ_{T} (x) \cos θ_{sT} (x),$ 所以方位分辨率为and $\frac{x - x_{0 T}}{\sqrt{{(x - x_{0 T})}^{2} + {the y}_{0 T}^{2} + z_{0 T}^{2}}} = \sin φ_{T} (x) \cos θ_{s T} (x),$ So the azimuth resolution is

${ρ ρ}_{a a} ((x x)) = = \frac{λ λ / / (({VT VT}_{s the s}))}{\sqrt{{((\frac{x x}{{r r}_{00 R R}^{22} ((x x))} cos cos {θ θ}_{dR d} ((x x)) + + \frac{11}{{r r}_{00 T T} ((x x))} sin sin {θ θ}_{sT s T} ((x x)) sin sin {φ φ}_{T T} ((x x)) cos cos {θ θ}_{sT s T} ((x x))))}^{22} + + {((\frac{11}{{r r}_{00 R R} ((x x))} {sin sin}^{22} {θ θ}_{dR d} ((x x)) + + \frac{11}{{r r}_{00 T T} ((x x))} {cos cos}^{22} {θ θ}_{sT s T} ((x x))))}^{22}}}$

用分辨率与x轴夹角衡量ρ_a的方向为The direction of _ρ a measured by the angle between the resolution and the x-axis is

S3.设定双基地前视SAR可处理的分辨率夹角大小，并求解由该夹角确定的测绘带范围。S3. Set the resolution angle that can be processed by the bistatic forward-looking SAR, and solve the range of the survey swath determined by the angle.

在本实施例中，设定双基地前视SAR可处理的分辨率夹角大小为Δθ＝π/6。从而有

其中atan{dir(ρ_r)}与atan{dir(ρ_a)}都为x的函数，通过求曲线atan{dir(ρ_r)}与atan{dir(ρ_a)}-π/6的交点，即可求得x_reso。由图4可知，随着x的增大，距离分辨率和方位分辨率的方向趋近于正交，所以由分辨率理论确定的双基地前视SAR测绘带范围为：x≥x_reso。In this embodiment, the included resolution angle that can be processed by the bistatic forward-looking SAR is set as Δθ=π/6. thus have

Where atan{dir(ρ _r )} and atan{dir(ρ _a )} are both functions of x, by finding the intersection of the curve atan{dir(ρ _r )} and atan{dir(ρ _a )}-π/6 , you can get x _reso . It can be seen from Fig. 4 that as x increases, the directions of range resolution and azimuth resolution tend to be orthogonal, so the bistatic forward-looking SAR swath range determined by the resolution theory is: x≥x _reso .

在本实施例中，距离分辨率方向和方位分辨率方向随x的变化如图5所示，图中实线为x轴上各点距离分辨率方向随x的变化关系，虚线为x轴上各点的方位分辨率方向减去π/6后随x的变化关系。两条线相交的点即为x_reso，从图5中可以看出x_reso为-1600m，则由分辨率理论确定的测绘带范围为x≥-1600m。In this embodiment, the change of the distance resolution direction and azimuth resolution direction with x is shown in Figure 5. The solid line in the figure is the relationship between the distance resolution direction of each point on the x-axis and the change relationship with x, and the dotted line is the change of the x-axis direction. The relationship between the azimuth resolution of each point and the change of x after subtracting π/6. The point where the two lines intersect is x _reso . It can be seen from Figure 5 that x _reso is -1600m, and the range of the survey zone determined by the resolution theory is x≥-1600m.

S4.由模糊理论计算系统允许的回波最大散布宽度，记为Δτ＝1/PRF-T_r。在本实施例中，Δτ＝80μs。S4. Calculate the maximum spread width of the echo allowed by the system according to the fuzzy theory, denoted as Δτ=1/PRF-T _r . In this embodiment, Δτ=80 μs.

S51.求解系统允许的最大双基地距离和、最小双基地距离和与收发站中较小的波束宽度之间的关系。在本发明具体实施方式中，可求得系统允许的最大和最小收发站距离和之差为L＝R_bix-R_bin＝cΔτ＝24000m。同时，假设在前视成像区域，收发站中较小的波束一直被较大的波束覆盖，并且较小的波束脚印形状为椭圆，该椭圆的两个半轴分别与x轴和y轴平行，半轴长度分别为a和b，如图6所示。由于最大和最小双基地距离和一定发生在较小波束脚印形成的椭圆上，可以计算出最小收发站距离和为： $R_{bin} = \min {\sqrt{{(x - x_{0 T})}^{2} + {(y - y_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(y - y_{0 R})}^{2} + z_{0 R}^{2}}};$ 最大收发站距离和为： $R_{bix} = \max {\sqrt{{(x - x_{0 T})}^{2} + {(y - y_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(y - y_{0 R})}^{2} + z_{0 R}^{2}}},$ 其中x，y满足

得到R_bin和R_bix为a和b的函数。S51. Solve the relationship between the maximum bistatic distance sum allowed by the system, the minimum bistatic distance sum and the smaller beam width in the transceiver station. In a specific embodiment of the present invention, the difference between the maximum and minimum distances between transceiver stations allowed by the system can be obtained as L=R _bix −R _bin =cΔτ=24000m. At the same time, it is assumed that in the forward-looking imaging area, the smaller beam in the transceiver station is always covered by the larger beam, and the shape of the footprint of the smaller beam is an ellipse, and the two semi-axes of the ellipse are parallel to the x-axis and y-axis respectively, The semi-axis lengths are a and b, respectively, as shown in Figure 6. Since the maximum and minimum bistatic distance sums must occur on the ellipse formed by the smaller beam footprint, the minimum transceiver station distance sum can be calculated as:

R_{bin} = \min {\sqrt{{(x - x_{0 T})}^{2} + {(the y - {the y}_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(the y - {the y}_{0 R})}^{2} + z_{0 R}^{2}}};

The maximum transceiver station distance sum is:

R_{bix} = \max {\sqrt{{(x - x_{0 T})}^{2} + {(the y - {the y}_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(the y - {the y}_{0 R})}^{2} + z_{0 R}^{2}}},

where x, y satisfy

Get R _bin and R _bix as functions of a and b.

S52.利用步骤S51中得到的系统允许的最大和最小收发站距离和之差L，计算由模糊理论确定的双基地前视SAR测绘带范围。在本实施例中，通过求曲线R_bix(a)与R_bin(a)+L的交点，即可求得确定b条件下的较小波束沿x轴的散布宽度，即波束切航迹宽度。在本实施例中，b＝15000m，从图7中可以求得a为19050m。则由模糊理论确定的测绘带范围为：-19050m≤x≤19050m；S52. Using the difference L between the maximum and minimum distance sums of transceiver stations allowed by the system obtained in step S51, calculate the range of the bistatic forward-looking SAR survey swath determined by fuzzy theory. In this embodiment, by finding the intersection point of the curve R _bix (a) and R _bin (a)+L, the spread width of the smaller beam along the x-axis under the condition b can be obtained, that is, the width of the beam cutting track . In this embodiment, b=15000m, and a can be calculated as 19050m from FIG. 7 . The range of the survey zone determined by the fuzzy theory is: -19050m≤x≤19050m;

S6.计算双基地前视SAR的测绘带范围，比较步骤S3和S52中求得的测绘带范围，即可求得在本实施例中双基地前视SAR有效测绘带的最大范围为：-1600m≤x≤19050m。S6. Calculate the survey zone range of the bistatic forward-looking SAR, compare the survey zone ranges obtained in steps S3 and S52, and obtain the maximum range of the effective survey zone of the bistatic forward-looking SAR in this embodiment: -1600m ≤x≤19050m.

本领域的普通技术人员将会意识到，这里所述的实施例是为了帮助读者理解本发明的原理，应被理解为发明的保护范围并不局限于这样的特别陈述和实施例。凡是根据上述描述做出各种可能的等同替换或改变，均被认为属于本发明的权利要求的保护范围。Those skilled in the art will appreciate that the embodiments described herein are to help readers understand the principles of the present invention, and it should be understood that the protection scope of the invention is not limited to such specific statements and embodiments. All possible equivalent replacements or changes made according to the above description are considered to belong to the protection scope of the claims of the present invention.

Claims

1. a bistatic forward sight synthetic-aperture radar mapping band range computation method is characterized in that, specifically comprises the steps:

S1. initialization system parameter, system coordinate system is a true origin with the imaging center impact point, and platform moves along the y axle, and the x axle is for cutting the flight path direction, and the z axle is the vertical ground direction, the initialization system parameter comprises: cell site zero is the position constantly, is designated as (x _0T, y _0T, z _0T); Receiving station zero is the position constantly, be designated as (0, y _0R, z _0R); System's carrier frequency is designated as f ₀Wavelength is designated as λ; Transmitted signal bandwidth is designated as B _rPlatform motion speed is designated as V; Fast time variable is designated as τ; Slow time variable is designated as s; Antenna angle of squint, cell site is designated as θ _STReceiving station's antenna downwards angle of visibility is designated as θ _DRCell site's antenna elevation angle is φ _TCenter, cell site oblique distance is designated as r _0TReceiving station's center oblique distance is designated as r _0RPulse repetition rate is designated as PRF; Pulsewidth is designated as T _rRange resolution is designated as ρ _rAzimuthal resolution is designated as ρ _aThe synthetic aperture time, be designated as T _sThen cell site's distance does

R_{T} (s) = \sqrt{r_{0 T}^{2} + V^{2} s^{2} - 2 r_{0 T} Vs Sin θ_{ST}};

Receiving station's distance does

R_{R} (s) = \sqrt{r_{0 R}^{2} + V^{2} s^{2} - 2 r_{0 R} Vs Cos θ_{DR}};

Bistatic Forward-looking SAR System distance is R _Bi(s)=R _T(s)+R _R(s);

S2. adopt gradient theory to calculate the resolution direction of each point on the imaging region x axle, weigh the resolution direction with the tangent value of the angle of resolution and x axle, obtain the resolution direction of any impact point P (x, 0) on the x axle, the result is following:

The range resolution direction does

Dir (ρ_{r}) = \frac{Sin θ_{ST} (x) + Cos θ_{DR} (x)}{x / r_{0 R} (x) + Cos θ_{ST} (x) Sin φ_{T} (x)}

The azimuthal resolution direction is:

dir (ρ_{a}) = \frac{r_{0 T} (x) \sin^{2} θ_{dR} (x) + r_{0 R} (x) \cos^{2} θ_{sT} (x)}{r_{0 T} (x) x \cos θ_{dR} (x) / r_{0 R} (x) + r_{0 R} (x) \sin θ_{sT} (x) \sin φ_{T} (x) \cos θ_{sT} (x)}

Wherein

r_{0 R} (x) = \sqrt{r_{0 R}^{2} (0) + x^{2}},

r_{0 T} (x) = \sqrt{r_{0 T}^{2} (0) + x^{2} - 2 r_{0 T} (0) x Cos θ_{ST} (0) Sin φ_{T}},

θ_{ST} (x) = a Sin (\frac{r_{0 T} (0) Sin θ_{ST} (0)}{r_{0 T} (x)}),

θ_{DR} (x) = a Cos (Cos θ_{DR} \frac{r_{0 R} (0)}{r_{0 R} (x)}),

X representes the coordinate of impact point on the x axle; r _0R(x) receiving station's center oblique distance at expression P (x, 0) some place; r _0T(x) center, the cell site oblique distance at expression P (x, 0) some place; θ _DR(x) receiving station's antenna downwards angle of visibility at expression P (x, 0) some place; θ _ST(x) the antenna angle of squint, cell site at expression P (x, 0) some place, φ _T(x) cell site's antenna elevation angle at expression P (x, 0) some place;

S3. set the accessible resolution corner dimension of bistatic Forward-looking SAR; And find the solution by the definite mapping band scope of this angle; Because the angle between manageable range resolution of SAR imaging algorithm and the azimuthal resolution is limited, establishing this angle is Δ θ, and atan{dir (ρ is then arranged _r)=atan{dir (ρ _a)-Δ θ, the range resolution direction and the azimuthal resolution direction that adopt step S2 to calculate are found the solution this equation, can obtain separating of this equation, are designated as x _Reso, then be: x>=x by the theoretical bistatic Forward-looking SAR mapping band scope of confirming of resolution _Reso

S4. the echo extreme spread width that is allowed by the fuzzy theory computing system is designated as Δ τ=1/PRF-T _r

S5. calculate the bistatic Forward-looking SAR mapping band scope of confirming by fuzzy theory, specific as follows:

S51. the maximum double base distance that allows of solving system and, minimum bistatic distance and and transmitting-receiving station in relation between the less beam angle, establish maximum double base distance and be R _Bix, minor increment and be R _Bin, then echo extreme spread width is: (R _Bix-R _Bin)/c, wherein c is the light velocity, so the minimum and maximum transmitting-receiving station distance that the system of can trying to achieve allows with difference be L=R _Bix-R _Bin=c Δ τ simultaneously, supposes at the forward sight imaging region; Wave beam less in the transmitting-receiving station is covered by bigger wave beam always; And less wave beam footprint is shaped as ellipse, and two semiaxis of this ellipse are parallel with the y axle with the x axle respectively, and semiaxis length is respectively a and b; Because on minimum and maximum bistatic distance and the ellipse that necessarily occurs in than minor beam footprint formation, can calculate minimum transmitting-receiving station distance and be:

R_{Bin} = Min {\sqrt{{(x - x_{0 T})}^{2} + {(y - y_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(y - y_{0 R})}^{2} + z_{0 R}^{2}}};

Maximum transmitting-receiving station distance and be:

R_{Bix} = Max {\sqrt{{(x - x_{0 T})}^{2} + {(y - y_{0 T})}^{2} + z_{0 T}^{2}} + \sqrt{x^{2} + {(y - y_{0 R})}^{2} + z_{0 R}^{2}}},

X wherein, y satisfies

Obtain R _BinAnd R _BixFunction for a and b;

S52. utilize minimum and maximum transmitting-receiving station distance that the system that obtains among the step S51 allows with difference L, calculate the bistatic Forward-looking SAR mapping band scope of confirming by fuzzy theory, solving equation R _Bix(a; B)-R _Bin(a; B)=L, can obtain confirm under the b condition than the distribution width of minor beam along the x axle, be designated as a (T _r, PRF b), then confirms that by fuzzy theory bistatic Forward-looking SAR mapping band scope is :-a (T _r, PRF, b)≤x≤a (T _r, PRF, b);

S6. calculate bistatic Forward-looking SAR mapping band scope, the mapping band range boundary condition of utilizing step S3 and S52 to calculate can obtain bistatic Forward-looking SAR and survey and draw the band scope and be: max{-a (T _r, PRF, b), x _Reso}≤x≤a (T _r, PRF, b).