3. Precision Orientation Modeling
We will provide a procedure to model the precision orientation for monoscopic images. The procedures are stated as follows:
(1) Establishing the approximate orbital parameters using ephemeris data.
(2) Apply ground control points (GCPs) to determine the deviation between each observation vector and GCP, shown in fig.3 .
(3) Considering 3 or more GCPs, the orbital parameters are corrected according to the collinearity condition, as shown in eq.1.
Figure 3. Illustration of Orbit Correction
where
x ( t ) = x0 + a0 + a1 * t
y ( t ) = y0 + b0 + b1 * t
z ( t ) = z0 + c0 + c1 * t
(4) Applying Least Squares Filtering method to fine-tune the orbit, by eq. 2. We use Gaussian for covariance function in this study.
(5) Considering the extremely high correlation between orbital parameters and pitch and roll angles, we only correct yaw angle. Due to its very small field of view, i.e., about 1.5 degrees, the correlation between the orbit parameters [x(t), y(t)] and the attitude data(pitch, roll) are extremely high. This coupling phenomenon implies that systematic errors in pitch and roll will be compensated for by the orbit parameters x(t) and y(t), respectively. Accordingly, only the orbit parameters need to be considered in this investigation. However, the behavior of yaw is quite different. We observed that the yaw data does not significantly correlate to any other orientation parameters in the geometric reconstruction of the ROCSAT-2 images. Thus, corrections of yaw data must be taken into account.
Figure 4. Correction of Yaw Angle
Theoretically, having calibrated the orbital parameters, systematic errors in yaw angle would be reflected on the along-track component of the root-mean-square error (RMSE) for the GCPs. Thus, the RMSE could be used to fine-tune the yaw data. Referring to fig. 4(a), for any given yaw angle, we can get an along-track RMSE on the image plane for GCPs, then the RMSE derivative with respect to the angle in fig. 4(b). Therefore, the along-track RMSE and its derivative for GCPs may be expressed as functions of the yaw angle. Then, given a reasonable range of yaw angles, we can use a bisection method (Gerald and Wheatley 1994) to find the root of the derivative function and get the most probable value of the yaw angle that minimizes the along-track RMSE for the GCPs.
