4. Collinearity equation
The relationship between the satellite coordinates (x,y,z) and the ground coordinates (X,Y,Z) is expressed using the view vector in the satellite coordinates =( b_x, b_y, b_z,) the satellite position in the ground coordinates (X₀,Y₀,Z₀) and the transformation matrix (W) of both coordinates.


Finally, the collinearity equations can be introduced as follows (Hashimoto, 1997).


If the only alignments except other parameters like the satellite position, attitude and the ground coordinates are uncertain, they would be treated as unknown parameters. The collinearity equations are linearized by differentiating around unknown parameters.


5. Experiments and Results
The optimal alignments were corrected by the equation (6) utilizing GCPs. The OCTS images used here are LAC(Local Area Coverage) in Level 1B1 of which radiometric distortion and bands-to-bands registration error are corrected. The GCPs were collected manually from the images and TPC (Tactical Pilotage Chart) of 1:500,000.

The process needs the satellite position and attitude determined with high accuracy. The satellite position calculated by the bug-fixed software was verified with another independent determination using RIS (Retroreflector In Space) (Maeda,1996). The verification proved that the position could be determined in some ten meters. The satellite attitude data were not sufficiently correct as mentioned above. Only limited number of data could be processed with the new algorithm. In this research, two kinds of tactics were adopted; 1) to utilize a huge number of OCTS images without attitude data for mitigating attitude errors, 2) to utilize only OCTS images with the attitude data processed by new algorithm. Table 1 shows the OCTS images used in the experiment. In the table, ‘exist’ in attitude column means that the attitude data were processed with the new algorithm.

Table 1 OCTS images to be used

No.	observation time (GMT)	tilt angle(deg)	No. of GCP	attitude
1	1996.11.29 02:39:56-	0.00649	40	no
2	1996.11.29 02:52:40-	-9.9912	38	no
3	1996.12.30 02:13:31-	0.00375	32	no
4	1996.12.31 01:46:24-	0.00375	28	no
5	1997.04.14 02:54:26-	-9.4181	12	no
6	1997.04.14 02:11:19-	9.3175	11	no
7	1997.04.16 02:41:00-	-9.4177	9	no
8	1997.04.16 02:57:54-	9.3161	7	no
9	1997.04.25 01:58:28-	-9.4181	19	no
10	1997.05.09 02:23:31-	-9.4179	15	no
11	1996.12.12 01:51:04-	0.00363	38	exist
12	1996.12.12 02.23.31-	-9.9907	43	exist
13	1996.12.16 01:45:55-	0.00653	31	exist
14	1997.05.16 02:37:25-	-94168	17	exist
15	1997.06.17 01:57:45-	-9.4168	29	exist
16	1997.06.01 02:04:55-	-9.3612	41	exist
total No.1-10 : 211 No.11-15 : 158 No.1-15 : 369