Transformations

The ADCP measures the water velocity in a number of beams (mostly four), in the direction of each beam. Internally these settings are transformed to a coordinate system as set by the user.

Transformation operations can be included in the pipeline to change the coordinate system in which the velocity data are output by the ADCP and/or apply corrections to the transformations that the ADCP has done internally. For example, if the output coordinate system is set to output velocities as a vector consisting of eastward, northward and upward velocities, but an analysis requires the velocities expressed relative to the platform that carries the ADCP, then the velocities need to be transformed accordingly. Another instance where transformations are required is when the ADCP is mounted with different angles than prescribed in the setup file. For example, if the ADCP is mounted with a slight roll angle, whereas the prescribed roll angle is zero, this can be corrected for by transforming the velocity data back to the coordinate system of the ADCP itself, using the same values as the ADCP has used internally, followed by the inverse transformation, using the corrected angles.

The rdi_transformation module defines the following coordinate systems:

BEAM	velocities as measured by the instrument in along beam direction
XYZ	velocities expressed in a coordinate system fixed to the ADCP
SFU	velocities expressed in ‘ship coordinates’, that is relative to the ship or platform (glider) that carries the ADCP. SFU is short for Forward, Starboard and Up.
ENU	velocities expressed in a earth referenced frame. ENU is short for Eastward, Northward and Up.

Both the BEAM and XYZ coordinate systems are bound to the ADCP only and require no external information to apply the transformation. To convert to the SFU coordinate system the mounting angles of the ADCP around the forward, starboard and up axis of the platform are required. To transform to the ENU coordinate system, in addition the attitude of the platform (pitch, heading and roll) is required.

The rdi_transforms module defines a number of classes to transform between two coordinate systems. Each transformation is a single step transformation. That is, only (bidrectional) transformations between BEAM and XYZ, XYZ and SFU, and SFU and ENU are implemented. An instance that transforms between other coordinate system combinations than those listed above, can be simply obtained by left multiplying instances of those single step transformations.

The transformation classes are all derived from an abstract transformation class Transform() which provides the machinery common to all transformation classes. The available transformation classes

TransformBEAM_XYZ()

TransformXYZ_SFU()

TransformSFU_ENU()

These transformation classes define transformations in the direction the ADCP applies them. This means that same sign convention applies to the angles of rotation used by these transformations as is used internally by the ADCP.

Inverse transformations can be defined by setting the optional parameter inverse = True when calling the constructor, or using the predefined classes (which are essentially short-hands for the transformation classes above with inverse = True set):

TransformXYZ_BEAM()

TransformSFU_XYZ()

TransformENU_SFU()

Note

The angles of rotation applied to the inverse transformations still comply to the sign conventions used in the forward rotations.

Example

Let’s assume the measurements are expressed in geodetic coordinates (ENU), and the ADCP was mounted to the platform frame with angles slightly deviating from what has been prescribed in the ADCP configuration file. This means we have to undo the transformations until the ADCP’s frame of reference (XYZ) and the redo the transformations using the correct mounting angles.

mounting_pitch_angle = 12*3.1415/180.
configured_mounting_pitch_angle = 11*3.1415/180.
# First undo last transformation step
t1 = TransformENU_SFU()
# then undo the second, using the mounting angle specified:
t2 = TransformSFU_XYZ(hdg=0, pitch=configured_mounting_pitch_angle,
                      roll=0)
# Now redo the transformation from XYZ to SFU using the correct
# mounting angle
t3 = TransformXYZ_SFU(hdg=0, pitch=mouting_pitch_angle, roll=0)
#and redo the transformation to geodetic coordinates
t4 = TransformSFU_ENU()

# the resulting transformation is given by left-multiplying the
#single transformation steps:
t_result = t4 * t3 * t2 * t1