Three Dimensional Positioning for Airborne Three-Line-Scanner Images
2. ORBIT ADJUSTMENT
The major works are the calculation of the position parameters and attitude data, followed by the
three-dimension positioning on ground. Two steps are included in this stage. The first step is to
define the imaging geometry of triplet. Then, the orientation parameters are calculated by space
resection using the triplets. The orientation parameters are expressed as low order polynomials
with respect of time (Gruen & Zhang, 2003). Finally, the conjugate points are used for
three-dimensional positioning by space intersection.
2.1 Definition of parameters
The orientation parameters , ö , ê , X c , Y c , Z c ) are expressed as second-order polynomials
function with respect to time .The dynamics is shown in eq.1.
Then, the collinearity equations are employed to relate the image coordinates(x, y) and the
object coordinates(X, Y, Z). Because three different images are used, the image coordinates have
to be defined with new parameters. The modified collinearity condition equations are used as
shown in eq.2. The x is a constant number, which are calculated by the focal length and the look
angle. The scale number is used to correct the image coordinate error in y direction. The . x and
. y are additional parameters for the compensation of systematic errors.
In addition to the 18 unknown orientation parameters, we include the additional parameters (x,
. y, scale) to compensate image coordinate for forward and backward images. The geometric
relation of the triplet images is shown in figure2.
Figure 2. Geometric relation of the triplet
2.2 Calculation of orientation parameters
We calculate orientation parameters and additional parameters by space resection. A least
squares adjustment is performed to determine the orientation parameters.
2.3 Space intersection
When the orientation parameters are determined, we use the tie points in three images to
calculate the ground coordinates. Then, error ellipses are calculated to analyze the precision.
