Vessel Coordinate System (VCS)

Origo of the VCS is the vessel reference point. The VCS is defined according to the right hand rule, see figure 1.
x-axis pointing forward parallel to the vessel main axis.
y-axis pointing starboard parallel to the deck plane.
z-axis pointing down parallel to the mast.

Rotation of the vessel coordinate system around an axis is defined as positive in the clockwise direction, also according to the right hand rule.
Roll - rotation around the x-axis.
Pitch - rotation around the y-axis.
Heading - rotation around the z-axis. Heading as input in depth calculations is sensor data referred to true north.

Figure 1: The right hand rule coordinate system. Characters r, p and h denote roll, pitch and heading, respectively.

Array Coordinate System (ACS)

Origo of the ACS is at the centre of the array face. The ACS is defined according to the right hand rule.
x-axis pointing forward along the array (parallel to the vessel main axis).
y-axis pointing starboard along the array plane.
z-axis pointing down orthogonal to the array plane.

Surface Coordinate System (SCS)

Origo of the SCS is the vessel reference point at the time of transmission. The SCS is defined according to the right hand rule.
x-axis pointing forward along the horizontal projection of the vessel main axis.
y-axis pointing horizontally to starboard, orthogonal to the horizontal projection of the vessel main axis.
z-axis pointing down along the g-vector.
To move SCS into the waterline, use reference point height corrected for roll and pitch at the time of transmission.

Fixed Coordinate System (FCS)

Origo of the FCS is fixed somewhere in the nominal sea surface. The FCS is defined according to the right hand rule.
x-axis pointing north.
y-axis pointing east.
z-axis pointing down along the g-vector.