**Liang-Chien Chen and Yi-Ying Wu **

Center for Space and Remote Sensing Research

National Central University

Chung-li, Taiwan

Tel: +886-3-4227151 ext. 7622 Fax: +886-3-4254908

E-mail:[email protected]

** Abstract**

The objective of this investigation is to propose a scheme to model the orientation parameters for ROCSAT-2 satellite. Due to the unavailability of the satellite imagery, a geometric simulation for ROCSAT-2 is also included. Four major components are included in the simulation procedure. The first is to perform the transformations between related coordinate systems. The second component establishes the satellite-flying model to describe the orbit and attitude variations. The third one is to form ROCSAT-2 images. Finally, we include systematic and random errors in the orbital and attitude data for simulating the ephemeris. In the orientation modeling, the ephemeris data with systematic and random errors are use to construct the approximate imaging geometry. Then ground control points are used to fine-tune the exterior orientation parameters. Experimental results indicate that the systematic errors may be mostly compensated while the random errors consistently influence the positioning accuracy.

** 1. Introduction **

ROCSAT-2 is a sun synchronous remote sensing satellite, which is scheduled to launch in early 2003. It flies 890km in height on a plane with 98.99o inclination angle. The off-nadir look angle may reach 45o in the along-track and cross-track directions [NSPO, 2000]. The pushbroom imager on board has 12,000 pixels per line, for panchromatic band each with 2m-ground coverage. Thus, the swath is 24km nadir and the FOV is about 1.5 o. The multi-spectral imager includes 4 bands namely blue, green, red, and near IR. The ground resolution for multi-spectral imagery is 8m nadir. In this investigation, we only use panchromatic imagery to validate the geometric simulation and processing.

Since the trend is to integrate remotely sensed information and other data in geographic information systems, geometric correction for satellite imagery is required. In addition, ROCSAT-2 has a capability of stereoscopic observation by collecting along-track or cross-track stereopairs. Thus, generation of digital terrain models (DTMs) is possible. No matte what in the generation of DTMs or performing orthorectification, a modeling for precision orientation parameters is always the first step [Chen & Chang, 1998]. The objective of this investigation is to propose a scheme to model precision orientation parameters.

The imagery of ROCSAT-2 is not available at the moment. Thus, we need to simulate ones for validation of the geometric process. Since the point is for the geometric processing, the radiometric unsoundness is not considered. In addition, we ignore the building effect during imaging due to the unavailability of digital building models.

** 2. Image Simulation **

The proposed procedures for image simulation are shown in fig.1. Given 6 elements for a satellite, namely right ascension, inclination (orbital plane with respect to equator), argument of perigee, semi-major axis and eccentricity of earth ellipsoid, and true anomaly, by assigning the initial time, we can determine the position of the satellite at a given instant [Tseng, 1983].

** Figure 1. Proposed Scheme for Image Simulation **

In order to simulate orientation parameters, transformations between following coordinate systems are considered:

(1) Attitude Reference System and Local Orbital Reference System

(2) Local Orbital Reference System and WGS84

(3) WGS84 and ECI (Earth Center Inertia)

(4) WGS84 and GRS67 (GRS67 is being replaced by WGS84 in Taiwan)

(5) GRS67 and Geographic System (Longitude, Latitude, Height)

(6) Map projection (Geographic System and 2 o Transverse Mercator)

When the satellite location is determined with respect to time, we may begin with image simulation for a target area. We need to calculate the attitude angle according to the target position with respect to satellite’s. Then an image simulation may be performed by Top-Down approach as shown in fig. 2. Two major steps are included:

(1) Calculation of observation vector for each CCD detector.

(2) Determination of the grey value for each CCD detector by corresponding the object point and image pixel using Top-Down ray tracing in an iteration way.

** Figure 2. Images Simulation by Ray Tracing **

Considering the errors of ephemeris data for ROCSAT-2, we include systematic and random errors to complete the simulation. The scale of the systematic error may be selected according to the satellite specification. On the other hand, random error is not well known at the moment. We consider the following factors: (1) random error are fully random and independent, (2) each component corresponds to half-pixel coverage on ground, i.e., 1m. ** 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.

** 4. Experimental Results **

We simulate two images based on the assumed orbit and orthorectified aerial images for the target area. The resolution of the orthoimage is 1m*1m(fig.5).A simulated DTM with 1m*1m is also prepared(fig.6).The orbit passes the Strait near Taiwan. The attitude angles for each of the images are:

Image1: roll=14.33125°, pitch=13.29759°, yaw=0°

Image2: roll=15.81852°, pitch=-10.50034°, yaw=0°

Fig.7 and fig.8 represent the two simulated images.

Figure 5. Target Image

Figure 6. Target DTM

Figure 7. Simulated Image1

Figure 8. Simulated Image2

Considering different combinations of systematic and random errors, the accuracy analyses for 5 GCPs are summarized in Table1. In which,121 checkpoints are analyzed. The systematic errors are not linear in terms of sampling time. The random errors are Gaussian distributed. It is observed that the systematic errors are well compensated. While random errors behave differently. This is what it reflects the characteristics of “Random”.

** Table1. Error Analyses by Checkpoints **

Error Inclusion | RMSE(m) | ||

Type | Quantity (each component) |
E | N |

Systematic position |
450m | 0.53 | 0.25 |

Systematic Attitude | 30″ | 0.13 | 0.20 |

Systematic Position + Attitude |
450m 30″ |
0.41 | 0.13 |

Random Position | 1m | 1.08 | 1.00 |

Random Attitude | 0.25″ | 1.34 | 1.28 |

Random Position + Attitude |
1m 0.25″ |
1.34 | 1.60 |

Systematic and Random(Position + Attitude) |
Systematic:450m 30″ Random:1m 0.25″ |
1.33 | 1.60 |

** 5. Conclusions **

We developed a scheme to simulated ROCSAT-2 Images. The scheme considers the satellite flying characteristics and imaging behaviors. Systematic and random errors are simulated in the scheme. A scheme for modeling precision orientation parameters is also established. Experimental results indicate that systematic errors may be compensated while random errors are still kept random. The RMSE from ground checkpoints reflects the random errors of inclusion consistently.

Only panchromatic images are simulated and tested. For multi-spectral images, the geometric behavior is expected to be similar. Because this investigation only concerns about the geometrical property, the simulated images do not consider the radiometric characteristics. Further investigation on radiometry is suggested.

** References**

- Chen, L.C., and Chang, L.Y., 1998, “Three-Dimensional Positioning Using SPOT Stereostrips with Sparse Control”, Journal of Surveying Engineering, ASCE, Vol.124, No.2., pp.63-72
- Gerald, C.F., and Wheatley,p.p.,1994,”Applied Numerical Analysis”, Addison -Wesley Publishing Co., Reading, Mass.
- NSPO, 2000,”ROCSAT-2 Satellite Property ” , welcome.htm
- Tseng, C.Y., 1983, “Remote Sensing of the Atmosphere: Principles and Applications “, Wen -Ying Qc871.T83, TAIWAN. (in Chinese)