Georeferencing of Satellite Linear Array Stereo Images with Quaternion Attitude Kinematics Equation

Abstract

A quaternion method for georeferencing of satellite linear array stereo images is proposed in this paper. In this method, quaternion is used to describe the exterior orientation parameters (EOPs) of the satellite linear array stereo images, and gain the EOPs of any image line through quaternion attitude kinematics equation. Then the georeferencing results can be obtained after solving the collinearity equations with ground control points (GCPs). We validate this method through experiment with SPOT images. Experimental results indicate that quaternion attitude kinematics equation can be used for georeferencing of satellite linear array stereo images, the accuracy is as much as or even better than that of the conventional method, and the quaternion EOPs can overcome much of correlation. This method can successfully used in satellite linear array stereo images, and it can also effectively avoid a great deal of computation of trigonometric functions and the potential unstable factors. It provides another technique for georeferencing of satellite linear array stereo images. Quaternion algebra was invented by W.R.Hamilton in 1843, and it can be used to represent space orientation and rotations of space vectors very expediently. Quaternion can avoid the singularity may aroused by using Euler angles to describe attitude. So from the very beginning quaternion played a special role in the study of rotations in 3-dimensional vector spaces. For the pass few years, many photogrammetry scholars pay an attention to quaternion for their ascendant capability, and many photogrammetry algorithms are presented for processing close-range and aerial images. Jiang (2) proposed an algorithm of space resection based on unit quaternion; experiment indicated that this algorithm can obtain the EOPs independent on initial values. Wang (3) used Jiang's method in bundle block adjustment of aerial images. Guan (4) also presented a quaternion space resection which is similarity to triangular pyramid, and this method is not suit to block aerotriangulation. Liu (5) used quaternion to model the eccentric angle of IMU, and introduced it into the orientation image adjustment of airborne three-line CCD image supported by GPS/IMU. Experimental shows that the adjustment accuracy of quaternion is as much as or even better than that of the conventional method, and can avoid a great deal of computation of trigonometric functions. Zhao (6) presented a solution of 3D space similarity transformation model adjustment algorithm, which is based on quaternion rotation matrix. Some tests show that quaternion rotation matrix used in photogrammetry has a very clear superiority. Ji (7) detailedly studied the application of quaternion in aerial photogrammetry, and relative orientation and bundle block adjustment tests were done using actual aerial images. Peng (8) used quaternion for the general digital camera calibration, experimental results show that inner orientation and distortion parameters can be easily obtained using quaternion even when there were larger rotation angle between ground coordinate system and virtual photo coordinate. Tan (9) discussed the construction of rotation matrix in close- rang photogrammetry, and compared with Euler angle for the advantages and disadvantages. The test proved that the quaternion method needs fewer times in iteration and has steady result in calculation. Jiang (10) also tried to use quaternion in exterior orientation of linear array stereo images. All these show that quaternion can be used in photogrammetry very well.