XXII ISPRS Congress 2012: Technical Commission VII

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Multivolume work

Persistent identifier:: 1663813779

Title:: XXII ISPRS Congress 2012

Sub title:: Melbourne, Australia, 25 August-1 September 2012

Year of publication:: 2013

Place of publication:: Red Hook, NY

Publisher of the original:: Curran Associates, Inc.

Identifier (digital):: 1663813779

Language:: English

Additional Notes:: Kongress-Thema: Imaging a sustainable future

Corporations:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Adapter:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Founder of work:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Other corporate:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Document type:: Multivolume work

Volume

Persistent identifier:: 1663821976

Title:: Technical Commission VII

Scope:: 546 Seiten

Year of publication:: 2013

Place of publication:: Red Hook, NY

Publisher of the original:: Curran Associates, Inc.

Identifier (digital):: 1663821976

Illustration:: Illustrationen, Diagramme

Signature of the source:: ZS 312(39,B7)

Language:: English

Additional Notes:: Erscheinungsdatum des Originals ist ermittelt.; Literaturangaben

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Corporations:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Adapter:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Founder of work:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Other corporate:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2019

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: [VII/7: THEORY AND EXPERIMENTS IN RADAR AND LIDAR]

Document type:: Multivolume work

Structure type:: Chapter

Chapter

Title:: SPACEBORNE SAR IMAGERY STEREO POSITIONING BASED ON RANGE-COPLANARITY EQUATION C. Q. Cheng, J. X. Zhang, G. M. Huang,C. F. Luo

Document type:: Multivolume work

Structure type:: Chapter

the sensor; (2) The spatial range between sensor and ground points is equal to the range measured by radar wave. The Coplanarity equation is build according to the fact that radar beam plan is perpendicular to x' axes of satellite body coordinate system which is changing with attitude angles. Range-coplanarity condition is established by the following equations: R -|OP -OS | (1) i -(OP-OS)=0 i is the normal vector of the plane of radar beam center (the same as x' axis which is converted from x axis in the sensor coordinate system by rotating attitude angles), op.osare the position vectors of ground points and the radar antenna, respectively. R is the slant distance. P à x terrain Fig 1. Range-coplanarity imaging geometry for side-looking radar When the rotation of attitude angles of 9-x-« system is used, the expansion equation of imaging equation for radar image of planar scanning mode is correspondingly obtained as follow: (X — Xs)(cosp cos x) + (Y — Ys)sinx — (Z — Zs)(sin pcosx) = 0 (2) (X - Xsy! «(Y -Ysy! €(Z - Zsy. - (M, Ry In formula(2), (Xs, Ys,Zs) is sensor location coordinate, (X, Y,Z) is ground point coordinate, M, is the across-track resolution; Ro is nearest slant distance; y is the column coordinate of the pixel in the image. For satellite radar image, paper (Cheng,2012) has given two kinds of R-Cp model in ECR coordinate system, one is: i (X X) i (Y -3) -(Z - Z5) 20 (3) (X-X)Y «(Y -Ysy «(Z- 45 - GM, -Ry) -0 The other kind is explicit function of image coordinate (x,y) in ECR: pee AT f (4) y S[JCX — Xsy. (Y - Ysy +(Z —Zs} -RJ/ M, where , i =[i, iy ey =R"R,° [1 0 ol 2 RE R^ (o, Kk) are translate matrix special from orbit coordinate system to ECR coordinate system and from satellite body coordinate system to International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia orbit coordinate system. formula(4) is suitable for combined adjustment for multi-source data than formula(3). 2.2 The connection and difference between R-Cp model and R-D model The Range-Doppler (R-D) model is the most widely used physical sensor model for spaceborne SAR remote sensing system(Curlander and McDonough, 1991). In the R-D model, the geometric characteristics of SAR imaging procedure are rigorously described by two equations in azimuth and range (Curlander,1982): | ROT OS (5) fa = UVs -Vp)-(OP-OS)/(AR) where fp is the Doppler frequency, À is the radar wavelength, Vs and Vp represents velocity vectors of SAR sensor and target respectively. We can see from the range equation that it is the spatial point set, which the distance is R from ground points to sensor, and the geometric shape is range sphere; The doppler equation is a cone over the sensor; The coplanarity equation shows the ground points and the sensor in the same plane. On a sampling point, the geometry figure of R-D equation and R-Cp equation are shown in the left part of Figure (2). For any radar image pixel we can calculate the doppler frequency of corresponding ground point, the distance between ground point and sensor antenna of photography time and the attitude values, then the R-D and R-Cp model can be built, which together with Earth ellipsoid model and the ground elevation model could process the radar image direct positioning. The intersection of the Earth ellipsoid equation with range equation, coplanar equation, or doppler equation separately presented on ground are a circle, an arc/line, and a hyperbolic. Therefore, the hyperbolic and circle intersection point on earth surface is the solution of the R-D model positioning, the arc/line and circle intersection point is the solution of positioning point under the R-Cp model, the principles of two models shown in the right part of Figure (2). Figure 2 also shows the link and difference when the R-Cp model and R-D model positioning, and also concluded that different pixel points at the same image line for non side- looking radar image with one group attitude values but different doppler frequency values. For the real aperture radar, when the precision sensor attitudes and the doppler frequency are known, the positioning result of R-D and R-Cp model is same. But for SAR images, because of its variety of imaging modalities, yet not one rigorous positioning model is common to all the images. If SAR imagery has the same features of geometric deformation as that of the image shoot by the real aperture radar under the ideal motion state referenced by the motion compensation process, the real aperture radar-based R- Cp model established can still be useful to the SAR images. If

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