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ORIGINAL HHTERER SEHSOR lisi 
  
-HIT DRESTELLUNG DER KURS- UND ZEITMARKEN 
Fig.9: Synchronous recorded interferometric and standard sonar image 
4.1 A geometrical-mathematical Model for Data Evaluation 
Side-Scan-Sonar is a dynamic imaging system and by that the definition of mathematical 
connections between image coordinates and space coordintes depend on the recording 
time. In this case each image line is recorded with an own geometric situation. This will 
be marked in the following expressions by the index j. 
According to Figure 10 four orthogonal coordinate systems will completely define geo- 
metry of imaging at time tj- 
xXx Y, Z0) "dynamic" sensor system. rotating around its origin due to 
1 1] l | time 
ur (Ut, Mv, wi "static" sensor system, defined with horizontal plane U.V 
in the same origin 
0. (U. V., WW.) ships coordinate system, parallel to the U: system with the U- 
] 3 4 ] axis in the ships course direction, origin irl ships centre 
R (Rh. H. Z) reference coordinate system 
The connections between these systems can be found easily: X; can be transformed to 
U' (both have the same origin) using a rotational matrix A; , wich contains functions 
of pitch, roll and yaw. Coordinates fixed in Uj'are transformed to U; with respect to 
translational parameters o;. 8; and d, using functions of them in the matrix Bi. At 
last a simple coordinate transformation from U; to R is necessary with respect to the 
measured positioning data of the ship. This is done in sequences between two positioning 
points Pg; and Pg;,, by the valid matrix Dj. In summary the equations for the determi- 
nation of space coordinates for discrete interference points are