Introduction
An ADCP deployed from a moving vessel measures both currents and vessel speed. The vessel speed must be subtracted from the measurements to obtain the current. This motion correction step uses speed over ground from the ADCP’s bottom-track. The bottom-track ping returns a strong signal from the sea bed which contains only the vessel speed since the current here is zero. Bottom-track data gaps are filled with speed over ground from the GNSS. The GNSS is typically mounted to a higher up on a vessel and subject to swaying from pitch and roll but also from heading in turns. These motions enter the corrected current and manifest as vertical ripples, see the figure below.
Lever arms
The ADCP, the GNSS, and the centroid of the boat are not co-located, and instrument motions must be removed before motion correction is applied. These adjustments require knowledge of the distance between the center of mass of the vessel and each instrument. The position vector that describes this distance is unknown and is referred to as the lever arm. It has ship coordinates of XYZ where x is the long axis of the vessel, y is the transverse axis, and z is up and down. Nortek has implemented an algorithm to solve for the lever arm and remove GNSS and ADCP oscillations from output. Time series plots of bottom track-corrected currents (BT), GNSS corrected-currents (GPS), and lever arm-corrected currents (LA) below illustrate the impact of the new algorithm. For this particular dataset, the LA corrected current magnitude shows even less vertical ripples than is present in the BT corrected currents. Note that BT correction does not require motion correction since current and bottom-track are recorded in the same reference frame. A reason for improvements in LA corrected results is likely due to timing errors, GNSS data was received at 10 Hz while BT was measured more than one second after currents were measured.
Corrections using angular velocities
Lever arm corrections are done in the Nortek VM software. The solution uses angular velocities to get a better estimate for the velocity of the GNSS by removing rotational components from the GNSS velocity. Angular velocities, as well as general velocities that include swaying motion are output by the GNSS. If we know the lever arm (R), we can calculate the velocities at the position of the GNSS due to rotations or angular velocities by multiplying the lever arm with the angular velocity tensor (Ω). The resulting vector (V) can then be subtracted from the velocities as measured by the GNSS to obtain velocities free of rotational motion.
The lever arm corrected GNSS velocities are more suitable for removing vessel motion from raw ADCP current data, resulting in less vertical ripples as shown in the previous section.
Automatic estimation of the lever arm
The Nortek VM Review software contains a feature to automatically calculate the lever arm offset. This is done by minimizing errors between bottom-track motion and GNSS motion using a least squares method. In a perfect system with correctly measured lever arms, the difference between motion measured by the bottom-track and the GNSS should be zero. In the real world this is generally not the case due to small errors in the measurements as well as timing errors. The automatic lever arm estimation algorithm is able to find good solutions however, especially when the dataset contains dynamic motion (pitch, roll and heading changes).
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