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4 Task area “Recording the current situation” 
4.1 State identification 
4.1.1 Defining the reference systems and state variables 
In order to develop a clear description of the ship’s state variables, i.e. its position and movement, the 
reference systems and their position In relation to one another are defined. These definitions then serve 
as a reference for all further reference variables (e.g. ship dimensions, sensor positions). 
For the description of the system being considered here, the introduction of three reference systems is 
necessary (Figure 5). 
Figure 5: Reference systems 
Figure 5, only in schematic form, shows the differing Cartesian reference systems of ship (S), water (W) 
and bottom (B), the position of the coordinate origins being selected arbitrarily for the purpose of visuali 
sation. The reference system ‘ship’ has its origin at a fixed point in the ship hull (“reference point”). Its 
x-axis (xs) lies parallel with the longitudinal axis of the ship in the heading, its z-axis (z s ) being directed 
downwards parallel to the vertical axis of symmetry of the hull cross-section. The y-axis (y s ) is at right 
angles to the x-z plane and records positively to the right in the direction of travel. This reference sys 
tem “migrates” in tandem with all movements of the ship’s hull. 
The reference system ‘water 1 relates to the body of water surrounding the ship’s hull, which is assumed 
to be homogeneous in its motion over ground (bottom) in the vicinity of the ship’s hull. The origin of the 
system lies on the mean water surface, assumed to be level, in the vicinity of the ship’s hull. The z-axis 
(z w ) lies at right angles to this plane in the direction of the centre of the earth and Intersects the origin of 
the reference system ‘ship’ (by way of deviation from the representation in Figure 5). The x-axis (x w ) 
points to geographic north. The y-axis (y w ) is located orthogonally on the x-z plane and points towards 
geographic east. 
The reference system bottom is the geographical reference system with defined chart datum. The x- 
axis x B points towards geographic north, its y-axis y 0 to geographic east. The z-axis Zg is located verti 
cally on the x-y-axis and points in the direction of the centre of the earth. 
All three reference systems continue to possess three rotational axes a, (3 and y (see Figure 6).