It is known that a push-broom image is the combination of lines captured by a linear camera, where the pixel shifts in the along-track direction can be derived from the cross-track pixel shifts. In other words, only to model the pixel shifts along the $x$-direction in the image plane is adequate under the assumption that the imaging platform is stable. Moreover, the relationship between the positioning error and the pixel shifts of three-line arrays can each be derived from the other since their relative positions are fixed. Therefore, according to Eqs. (3) and (4), the value of $xi$ can be decided by the arbitrary ground point ($X,Y,Z$) and the camera optical center ($Xsi,Ysi,Zsi$) in the object space coordinate, the camera attitude angles ($\phi i,\omega i,\kappa i$), and the focal length $f$. Thus, the pixel shifts can be expressed as follows: Display Formula
$xi=F(X,Y,Z,Xsi,Ysi,Zsi,\phi i,\omega i,\kappa i,f).$(5)