spacecraft 2 at the time of observation the los unit vector a pointing from the spacecraft 2 to the landmark of interest is therefore given by equ3 the mathematical model for the landmark scan angles is summarized below where e is the east west scan angle and n the north south scan angle of the imager instrument 10 when pointing to the landmark s is the line of sight unit vector from the spacecraft 2 to the landmark x b y b z b are the unit vectors of the spacecraft body coordinate system and u03b4e ma u03b4n ma are corrections to the respective scan angles due to the misalignment effect and are given by the following expressions the components of the line of sight unit vector in the body frame are related to the components in the orbital frame by the euler rotation matrix m e the euler matrix can be thought of as the product of three successive elementary rotations about each of the roll pitch and yaw axes the order of the elementary rotations is arbitrary and the inventors have adopted the 34 11 2 3 34 order i e first a rotation by u03c6 about the x direction followed by a rotation by u03b8 about the new body y direction and finally followed by a rotation by u03c8 about the new z direction with this ordering of elementary rotations the euler matrix takes the following form equ4 the unit vectors in the orbital frame are given in terms of the spacecraft 2 position and velocity vector equ5 the elements of the euler matrix m e are denoted by m ij and its three row vectors by m 1 m 2 m 3.