CN102445690B - QR Decomposition Method for 3D Synthetic Aperture Radar Imaging - Google Patents

QR Decomposition Method for 3D Synthetic Aperture Radar Imaging Download PDF

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CN102445690B
CN102445690B CN201010513822.1A CN201010513822A CN102445690B CN 102445690 B CN102445690 B CN 102445690B CN 201010513822 A CN201010513822 A CN 201010513822A CN 102445690 B CN102445690 B CN 102445690B
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王彦平
王斌
谭维贤
洪文
吴一戎
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Abstract

本发明公开了一种合成孔径雷达三维成像的QR分解方法，涉及雷达三维成像技术，先将各条轨迹观测得到的原始回波数据通过二维聚焦得到观测目标的单视复图像，再将单视复图像序列配准，进行相位补偿的解斜处理，得到目标沿高度向的观测采样数据；根据各次观测的位置和雷达观测几何构建实现目标高程成像的运算矩阵，得到高度向采样数据和目标高程图像之间矩阵向量形式的线性方程；接着对运算矩阵进行QR分解，利用分解后得到的正交矩阵和上三角矩阵求解线性方程，得到目标的高程图像；结合每次二维成像得到的目标二维图像，完成对目标的三维成像。本发明基于QR分解的矩阵方程求逆技术获取目标沿高度向的图像，得到高分辨率的目标三维成像。

Figure 201010513822

The invention discloses a QR decomposition method for three-dimensional imaging of synthetic aperture radar, which relates to radar three-dimensional imaging technology. The complex image sequence is registered, and the phase compensation is de-slanted to obtain the observation sampling data of the target along the height direction; according to the position of each observation and the radar observation geometry, the operation matrix for realizing the target elevation imaging is constructed to obtain the height direction sampling data and A linear equation in the form of a matrix vector between the target elevation images; then perform QR decomposition on the operation matrix, and use the decomposed orthogonal matrix and upper triangular matrix to solve the linear equation to obtain the target elevation image; combined with each two-dimensional imaging obtained The two-dimensional image of the target completes the three-dimensional imaging of the target. The invention obtains the image of the target along the height direction based on the matrix equation inversion technology of QR decomposition, and obtains the high-resolution three-dimensional imaging of the target.

Figure 201010513822

Description

The QR decomposition method of synthetic aperture radar three-dimensional imaging
Technical field
The present invention relates to radar three-dimensional imaging technical field, is a kind of disposal route for synthetic aperture radar three-dimensional imaging.
Background technology
Synthetic-aperture radar is the repeatedly parallel observation in short transverse by Texas tower, has collected the echo data to target under different visual angles, along the repeatedly sampling of short transverse, has formed height to synthetic aperture; The pulse compression that aperture is synthetic and distance makes progress making progress in conjunction with orientation, has realized the three-dimensional imaging to observed object.2000, the people such as German scholar A.Reigber, in paper < < First Demonstration of Airborne SAR Tomography UsingMultibaseline L-Band Data > >, carry out the research of airborne many baselines SAR three-dimensional imaging, proposed the spectrum estimating processing method of three-dimensional imaging.In follow-up study, F.Lomdardini, the people such as S.Guillaso are respectively at paper < < Adaptive spectral estimation formultibaseline SAR tomography with airborne L-band data > >, in < < Polarimetric SAR Tomography > >, introduced Capon, the methods such as MUSIC are carried out Estimation of Spatial Spectrum, proposition realizes the high-resolution three-D imaging method of many baselines SAR.2003 and 2005, the people such as Italy scholar G.Fornaro have carried out three-dimensional imaging research to spaceborne many baselines SAR respectively in paper and < < Three-Dimensional Focusing with Multipass SAR Data > > and < < Three-Dimensional Multipass SAR Focusing:Experiments WithLong-Term Spaceborne Data > >, by signal modeling, obtained height to the matrix-vector linear equation between observation data and target elevation map picture, and use the methods such as wave beam formation and svd to carry out three-dimensional imaging experiment.First many baselines SAR three-dimensional imaging carries out two-dimensional imaging to the data of every track collection, obtain the two-dimension focusing data vector that target obtains under difference observation visual angle, then utilize height to the sampled data estimation space spectrum of synthetic aperture, or solve linear equation, obtain target along the image of short transverse, thereby the target range-orientation two dimensional image obtaining in conjunction with each observation is realized the three-dimensional imaging to target.
Summary of the invention
The object of the invention is to propose a kind of QR decomposition method of synthetic aperture radar three-dimensional imaging, be that the height gathering according to synthetic-aperture radar is to the linear equation between observation data and target elevation map picture, based on QR, decompose, to obtain high-resolution three-dimensional imaging result.
For achieving the above object, technical solution of the present invention is:
The QR decomposition method of synthetic aperture radar three-dimensional imaging is to use the height of QR decomposition technique Technologies Against Synthetic Aperture Radar collection to carry out target three-dimensional imaging processing to data of multiple angles;
Synthetic-aperture radar is by target is highly upwards being carried out to observation from various visual angles, obtain target along the sampled data of short transverse, it can realize by airborne radar or spaceborne radar in the flight that repeatedly repeats in differing heights position, also can in flight observation, realize by laying array antenna, also can in ground track radar system, move realization by the two dimensional surface of antenna;
Synthetic-aperture radar along orientation to each observation track keeping parallelism, can generate separately the two dimensional image of observation scene, can be positive side-looking, stravismus, strip-type or the imaging of bunching type observation mode; The orientation of each observation track, is to arrange along vertical height direction, or along continuous straight runs arrangement, or along having the direction of an angle to arrange with horizontal direction.
The QR decomposition method of described synthetic aperture radar three-dimensional imaging, it comprises the steps:
Steps A: the target scene original echo data to each observation collection are carried out two-dimensional imaging, generates the haplopia complex pattern of observing scene range-azimuth plane;
Step B: the two-dimensional image sequence that each observation is generated is carried out registration, the image that minimum observation position place obtains of take is master image;
Step C: the oblique solution of every width image being carried out to phase compensation is processed, and phase modulation factor is by the determining positions of each observation;
Step D: the object height obtaining after being processed by oblique solution, to the computing operator matrix of observed samples data and elevation imaging, obtains the linear equation between observation data and target elevation map picture;
Step e: use QR decomposition method to invert to the linear equation of Vector-Matrix Form, obtain target along the image in different resolution of short transverse;
The target scene two dimensional image that step F: integrating step A generates, obtains range-azimuth-height dimensional resolution image of target.
The QR decomposition method of described synthetic aperture radar three-dimensional imaging, described in it, in step D, the structure formula of the computing operator matrix of elevation imaging is:
Figure BSA00000312525500031
Φ is the matrix of N * M, and matrix element is
Figure BSA00000312525500032
Wherein, the track number that N is each observation, M be object height to vector length, n=1 ..., N, m=1 ..., M, j is imaginary unit, exp is exponential function, λ is radar wavelength, r ' is target oblique distance value, the reference viewing angle that θ is synthetic-aperture radar, for the angle of each observation with horizontal direction, l nbe the n time observation and with reference to the distance between observation position.
The QR decomposition method of described synthetic aperture radar three-dimensional imaging, described in it, in step e, QR decomposition solves linear equation method and obtains target elevation map picture, comprises the steps:
Step e 1: the computing operator matrix to elevation imaging carries out QR decomposition, is decomposed into the product of orthogonal matrix and upper triangular matrix;
Step e 2: invert to decomposing the orthogonal matrix obtaining, its inverse matrix is its associate matrix;
Step e 3: to the linear equation between observed samples data and target elevation map picture, equation both sides are distinguished to the inverse matrix of premultiplication orthogonal matrix by height, obtained the upper triangular matrix equation of inverting target elevation map picture;
Step e 4: solve upper triangular matrix equation, obtain the elevation of target to image.
The beneficial effect of the inventive method is: a kind of method that proposes synthetic aperture radar three-dimensional imaging, according to the observation of synthetic-aperture radar, build height for how much to the linear equation between observation data and target elevation map picture, and use QR decomposition method to solve this linear equation, obtain the elevation image in different resolution of target, thereby realize the high-resolution three-dimensional imaging of target.
Accompanying drawing explanation
Fig. 1 is synthetic aperture radar three-dimensional imaging observation geometric representation;
Fig. 2 is the processing flow chart of synthetic aperture radar three-dimensional imaging QR decomposition method of the present invention;
Fig. 3 is that in the inventive method, elevation imaging linear equation builds process flow diagram;
Fig. 4 is that in the inventive method, QR decomposes the processing flow chart that solves linear equation.
Embodiment
The present invention is the QR decomposition method of synthetic aperture radar three-dimensional imaging, how much of the observations of the SAR three-dimensional imaging of method institute foundation as shown in Figure 1, x be carrier aircraft flight orientation to, y is distance direction, z is vertical height direction.Carrier aircraft has been carried out N time parallel observation in short transverse altogether to target scene, the minimum track of definition height and position is reference position, H is its podium level, the visual angle of reference position beam center is θ, its central beam direction is with reference to oblique distance direction r, and the angle of each survey layout direction and horizontal direction is
Figure BSA00000312525500041
definition s is orthogonal to carrier aircraft heading x and with reference to the elevation direction of oblique distance direction r, has set up three-dimensional imaging coordinate system x-r-s, and true origin is positioned at reference to position of platform to be located.
The target scene original echo that each observation is obtained through range-azimuth to two-dimensional imaging after, obtain haplopia complex pattern data, now to the impact point in three dimensions, the target focus data that the n time observation station obtains is expressed as
f n ( x &prime; , r &prime; , s &prime; ) = &Integral; - a a &gamma; ( s ) exp [ - j 4 &pi; r n ( x &prime; , r &prime; , s &prime; ) &lambda; ] ds
Wherein, λ is radar wavelength, γ (s) be target along elevation to scattering function, the elevation that the size of twice a is observation scene is to scope, r n(x ', r ', s '), n=1 ..., N is the distance between target and the n time observation, according to Fresnel approximation, it can be expressed as
Figure BSA00000312525500043
Wherein, l nbe the n time observation and with reference to the distance between observation position.Therefore the phase bit position of the resulting target focus data of the n time flight observation can be expressed as
Figure BSA00000312525500044
According to the phase place of target focus data, the oblique solution phase factor of linear frequency modulation item is removed in definition
After oblique solution is processed, the focus data phase bit position that the n time observation obtains is
Figure BSA00000312525500052
Now, the height obtaining to the signal frequency of observation data is
Figure BSA00000312525500053
The target two-dimension focusing signal that the n time observation obtains is
Figure BSA00000312525500054
Therefore, to the target in each range-azimuth resolution element, obtained its along elevation to scatter distributions function and height to the linear equation relational expression between synthetic aperture sampled data, be expressed as Vector-Matrix Form and be
g＝Φγ
Wherein, the two-dimension focusing data vector that g obtains for each observation, γ be target elevation to scatter distributions function, Φ is the operation matrix between sampled data and elevation map picture, the distance dependent of it and each observation position and target and radar antenna, is expressed as
Figure BSA00000312525500055
Wherein, the number that N is each observation, the object height that M is required reconstruction is to vector length, n=1 ..., N, m=1 ..., M, j is imaginary unit, and exp is exponential function, and λ is radar wavelength, and r ' is target oblique distance value, the reference viewing angle that θ is synthetic-aperture radar,
Figure BSA00000312525500056
for the angle of each observation with horizontal direction, l nbe the n time observation and with reference to the distance between observation position.
According to observation data vector sum target elevation, to the linear equation between scattering function, utilize the inversion operation to matrix equation, inverting target elevation to image.
Below in conjunction with accompanying drawing, describe each related detailed problem of QR decomposition method of synthetic aperture radar three-dimensional imaging of the present invention in detail.Be to be noted that described embodiment is only intended to be convenient to the understanding of the present invention, and it is not played to any restriction effect.
The QR decomposition method of synthetic aperture radar three-dimensional imaging of the present invention, its concrete implementation step as shown in Figure 2, mainly contains:
Steps A: the target scene original echo data to each observation collection are carried out two-dimensional imaging, generates the haplopia complex pattern of observing scene range-azimuth plane;
Step B: the two-dimensional image sequence that each observation is generated is carried out registration, the image that minimum observation position place obtains of take is master image;
Step C: the oblique solution of every width image being carried out to phase compensation is processed, and phase modulation factor is by the determining positions of each observation;
Step D: the object height obtaining after being processed by oblique solution, to the computing operator matrix of observed samples data and elevation imaging, obtains the linear equation between observation data and target elevation map picture;
Step e: use QR decomposition method to invert to the linear equation of Vector-Matrix Form, obtain target along the image in different resolution of short transverse;
The target scene two dimensional image that step F: integrating step A generates, obtains range-azimuth-height dimensional resolution image of target.
Structure height in the inventive method is to the linear equation between observation data and target elevation map picture, and the computing operator matrix that calculates elevation imaging is one of core content of the present invention, and concrete implementation step as shown in Figure 3, mainly contains:
Step D1: according to each observation position of synthetic-aperture radar and radar parameter, calculate the computing operator matrix Φ of elevation imaging, computing formula is:
Figure BSA00000312525500061
Φ is the matrix of N * M, and matrix element is
Wherein, the number that N is each observation, M be object height to vector length, n=1 ..., N, m=1 ..., M, j is imaginary unit, exp is exponential function, λ is radar wavelength, r ' is target oblique distance value, the reference viewing angle that θ is synthetic-aperture radar,
Figure BSA00000312525500071
for the angle of each observation with horizontal direction, l nbe the n time observation and with reference to the distance between observation position.
Step D2: the object height obtaining after being processed by oblique solution, to observed samples data, obtains the linear equation between observation data and target elevation map picture, is expressed as g=Φ γ; Wherein, g be object height to observed samples data, γ be target elevation to scatter distributions function.
It is one of core content of the present invention that QR decomposition method in the inventive method solves linear equation, and concrete implementation step as shown in Figure 4, mainly contains:
Step e 1: the computing operator matrix to elevation imaging carries out QR decomposition, is decomposed into the product of orthogonal matrix Q and upper triangular matrix R, is expressed as Φ=QR;
Step e 2: invert to decomposing the orthogonal matrix obtaining, its inverse matrix is its associate matrix Q -1=Q h;
Step e 3: to the linear equation between observed samples data and target elevation map picture, equation both sides are distinguished to the inverse matrix of premultiplication orthogonal matrix by height, obtained the upper triangular matrix equation of inverting target elevation map picture, be expressed as R γ=Q hg;
Step e 4: solve upper triangular matrix equation, obtain the elevation of target to image.
The method that the present invention is above-mentioned, has applied on computers MATLAB software and has been verified, and Technologies Against Synthetic Aperture Radar emulated data and ground rail system image data carried out three-dimensional imaging processing, and the validity of method has obtained checking.
The above; it is only the embodiment in the present invention; but protection scope of the present invention is not limited to this; any people who is familiar with this technology is in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprise scope within, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (2)

1.一种合成孔径雷达三维成像的QR分解方法，是使用QR分解技术对合成孔径雷达沿高度方向采集的多角度数据进行目标三维成像处理，其特征在于：1. a QR decomposition method of synthetic aperture radar three-dimensional imaging is to use QR decomposition technology to carry out target three-dimensional imaging processing to the multi-angle data that synthetic aperture radar collects along height direction, it is characterized in that: 合成孔径雷达是通过对目标在高度方向上进行多视角的观测，获取目标沿高度方向的采样数据，它通过机载雷达或星载雷达在不同高度位置的多次重复飞行实现，或者通过安放阵列天线在一次飞行观测中实现，或者在地基轨道雷达系统中天线的二维平面移动实现；Synthetic aperture radar is to obtain the sampling data of the target along the height direction by observing the target from multiple perspectives in the height direction. It is realized by repeated flights of airborne radar or spaceborne radar at different height positions, or by placing an array The antenna is realized in one flight observation, or the two-dimensional planar movement of the antenna in the ground-based orbital radar system; 合成孔径雷达沿方位向的各次观测轨迹保持平行，能够单独生成观测场景的二维图像，是正侧视、斜视、条带式或聚束式观测模式成像；各次观测轨迹的排列方向，是沿垂直高度方向排列，或沿水平方向排列，或沿与水平方向有一夹角的方向排列；The observation trajectories of the synthetic aperture radar along the azimuth direction are kept parallel, and can generate a two-dimensional image of the observation scene independently, which is imaging in the side-view, squint, strip or spotlight observation modes; the arrangement direction of the observation trajectories is Arranged along the vertical height direction, or along the horizontal direction, or along an angle with the horizontal direction; 该合成孔径雷达三维成像的QR分解方法包括如下步骤：The QR decomposition method of the synthetic aperture radar three-dimensional imaging comprises the following steps: 步骤A：对每次观测采集的目标场景原始回波数据进行二维成像，生成观测场景距离-方位平面的单视复图像；Step A: Perform two-dimensional imaging on the original echo data of the target scene collected for each observation, and generate a single-view complex image of the distance-azimuth plane of the observed scene; 步骤B：对各次观测生成的二维图像序列进行配准，以最低观测位置处得到的图像为主图像；Step B: Register the two-dimensional image sequences generated by each observation, and use the image obtained at the lowest observation position as the main image; 步骤C：对每幅图像进行相位补偿的解斜处理，相位调制因子由各次观测的位置决定；Step C: Perform phase compensation deskewing processing on each image, and the phase modulation factor is determined by the position of each observation; 步骤D：由解斜处理后得到的目标高度向观测采样数据和高程成像的运算算子矩阵，得到观测数据和目标高程图像之间的线性方程；Step D: Obtain the linear equation between the observation data and the target elevation image from the target height obtained after de-slanting processing to the observation sampling data and the operator matrix of elevation imaging; 步骤E：对矩阵向量形式的线性方程的系数矩阵使用QR分解方法进行求逆，得到目标沿高度方向的分辨率图像；Step E: Inverting the coefficient matrix of the linear equation in matrix-vector form using the QR decomposition method to obtain the resolution image of the target along the height direction; 步骤F：结合步骤A生成的目标场景二维图像，得到目标的距离-方位-高度三维分辨率图像；Step F: Combine the two-dimensional image of the target scene generated in step A to obtain a distance-azimuth-height three-dimensional resolution image of the target; 所述步骤D中高程成像的运算算子矩阵的构建公式为：The construction formula of the operator matrix of the elevation imaging in the step D is:
Figure FDA00003455361100021
Φ为N×M的矩阵，矩阵元素为
Figure FDA00003455361100021
Φ is an N×M matrix, and the matrix elements are
Figure FDA00003455361100022
Figure FDA00003455361100022
 其中，N为观测轨迹数目，M为目标高度向向量长度，n＝1，...，N，m＝1，...，M，j为虚数单位，exp为指数函数，λ为雷达波长，r’为目标斜距值，θ为合成孔径雷达的参考视角，
Figure FDA00003455361100023
为各次观测与水平方向的夹角，ln为第n次观测与参考观测位置之间的距离。Among them, N is the number of observation tracks, M is the length of the target height vector, n=1,..., N, m=1,..., M, j are imaginary units, exp is an exponential function, and λ is the radar wavelength , r' is the target slant distance value, θ is the reference angle of view of SAR,
Figure FDA00003455361100023
is the angle between each observation and the horizontal direction, l n is the distance between the nth observation and the reference observation position. 2.如权利要求1所述的合成孔径雷达三维成像的QR分解方法，其特征在于：所述步骤E中QR分解求解线性方程方法获取目标高程图像，包括如下步骤：2. the QR decomposition method of synthetic aperture radar three-dimensional imaging as claimed in claim 1, it is characterized in that: in the described step E, QR decomposition solution linear equation method obtains target height image, comprises the steps: 步骤E1：对高程成像的运算算子矩阵进行QR分解，分解为正交矩阵和上三角矩阵的乘积；Step E1: Perform QR decomposition on the operator matrix of the elevation imaging, and decompose it into the product of the orthogonal matrix and the upper triangular matrix; 步骤E2：对分解得到的正交矩阵求逆，其逆矩阵即为其共轭转置矩阵；Step E2: Invert the orthogonal matrix obtained by decomposing, and its inverse matrix is its conjugate transpose matrix; 步骤E3：由高度向观测采样数据和目标高程图像之间的线性方程，对方程两边分别左乘正交矩阵的逆矩阵，得到反演目标高程图像的上三角矩阵方程；Step E3: From the linear equation between the height observation sampling data and the target elevation image, the inverse matrix of the orthogonal matrix is multiplied to the left on both sides of the equation to obtain the upper triangular matrix equation of the inversion target elevation image; 步骤E4：求解上三角矩阵方程，得到目标的高程向图像。Step E4: Solve the upper triangular matrix equation to obtain the elevation image of the target.
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