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velocityTrue = nan(3, n*p);
maxNumPosData = max([length(heading) length(pitch) length(roll)]);  % either 1 or p, the number of time stamps
for i = 1:maxNumPosData  
    % heading/pitch/roll matrices     
    % this rotation is from Nortek: http://www.nortek-as.com/lib/forum-attachments/coordinate-transformation/view
    % I considered various ways to get the index - pointers, use an eval, etc, but using 'min(length(heading),i)' is actually faster      
    hThis = (heading(min(length(heading),i)) - 90) * pi/180; % convert heading to yaw, the Nortek code doesn't have a '-' here, but the sine term is negated below
    pThis = pitch(min(length(pitch),i)) * pi/180;
    rThis = roll(min(length(roll),i)) * pi/180;
    H = [cos(hThis) sin(hThis) 0; -sin(hThis) cos(hThis) 0; 0 0 1];
    PR = [cos(pThis) -sin(pThis)*sin(rThis) -cos(rThis)*sin(pThis);...
        0             cos(rThis)          -sin(rThis);  ...
        sin(pThis) sin(rThis)*cos(pThis)  cos(pThis)*cos(rThis)];        
    % apply heading/pitch/roll rotations
    if maxNumPosData == 1
        velocityTrue = H * PR * T * beamReshape;
    else
        velocityTrue(:, (i-1)*n+1:1:i*n) = H * PR * T * beamReshape(:, (i-1)*n+1:i*n);
    end
end
% extract w values (u,v below) - use permute to ensure we don't lose singleton dimensions
velocityTrue = reshape(velocityTrue, [3 p n]);
ADCP.u = permute(velocityTrue(1,:,:), [3 2 1]);
ADCP.v = permute(velocityTrue(2,:,:), [3 2 1]);
ADCP.w = permute(velocityTrue(3,:,:), [3 2 1]);

Correction for Tilt: Bin-mapping

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In systems with four beams, the transformation from radial velocites to Earth co-ordinates velocities has redundant information; only three beams are needed to resolve currents in the three orthogonal directions, while the 4th beam effectively provides error estimation. In the case where exactly one bin out of of the four at any level is flagged and NaN'ed, then currents can still be calculated from the remaining three radial velocities, using the three-beam transformation solution. The screening steps that can flag the data 'NaN' prior to transformation include fish detection and correlation threshold, as well as any bin-mapping (particularly the RDI nearest vertical bin which can set many bins to NaN). The three-beam solution works by assigning the error velocity to be zero and then solving the transformation for the missing bin (for more details see Three Beam Solutions in adcp coordinate transformation_Jan08.pdf). With the missing data filled in, the normal transform from Beam to Instrument co-ordinate data is applied.

In cases where the data quality team has determined that an entire beam is bad, they can supply a device attribute specifying the bad beam number. That beam is then excluded in the processing from beam or instr co-ords and the values are filled in with the three-beam solution.

Once in Earth co-ordinates, the data can also be screened by the error velocity. Error velocity screening only applies to data with four valid beams (and non-zero error velocities). For further infromation on the screening steps, including algorithms, see adcp coordinate transformation_Jan08.pdf

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• If Instrument co-ordinate data, convert from Instrument to Beam co-ordinate data
• Exclude bad beams (RDI only, specified by device attribute, forces three-beam solutions to on)
• Apply correlation screening (RDI only, except for a fixed 50% screen on Nortek Signature55 data, applied to match Nortek's Signature Viewer software, option available)
• Apply fish detection screening (RDI only, if requested, tuneable)
• Apply bin-mapping (RDI default is 'nearest vertical bin', Nortek default is none, option available)
• Apply three-beam solutions (RDI only, if requested, option available)
• Transform from Beam co-ordinate data to to Instrument co-ordinate data
• Rotate Instrument data to true Earth (via a combination of fixed heading/pitch/roll, magnetic declination corrected compass heading and onboard pitch/roll data)
• Apply error velocity screening (RDI only, option available)
• Do ensemble averaging if requested (option available)

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