Each instrument has its own unique transformation matrix, based on the transducer geometry. It is used to transform raw data collected in BEAM coordinates to XYZ coordinates which is a cartesian coordinate system fixed to the instrument head.

For details on the coordinate system transformation, please see this FAQ: How is a coordinate transformation done?

Midlife / Gen1 instruments (Aquadopp, AWAC, Vector/Vectrino)

The transformation matrix T  can be found in the *.hdr file generated when performing a binary data conversion in the software. Each row of the matrix represents a component in the instrument’s XYZ coordinate system, starting with X at the top row. Each column represents a beam. The third and fourth rows of the Vectrino  transformation matrix represent the two estimates of vertical velocity (Z1 and Z2) produced by the instrument.

The instruments orientation needs to be taken into account for each deployment, when transforming to ENU. You can check the orientation of the instrument in the*.sen file (status bit, bit 0; 0 = up-looking, 1 = down-looking). If the instrument is pointing down, rows 2 and 3 of the matrix must change sign.

For the Vectrino Profiler: The transformation matrix for the Vectrino Profiler range cells is stored in Config.ProbeCalibration_calibrationMatrix, with one row per cell. To get the calibration matrix in a more usable form for transforms, this can be used:

(NB: Note the transpose of the matrix.)

(Some instruments, particularly if older then 2009, report the matrix in unscaled integer values (i.e. have a value of several thousand). In this case, T will have to be divided by 4096 to use for coordinate transformation. )

Gen2 instruments (Aquadopp, AWAC)

To access the transformation matrix and carry out coordinate transformations, the raw *.aqd / *.ad2cp files need to be transformed to either *.mat or *.csv using the File Conversion tool in Nortek Deployment.

If you have converted your raw data, then the transformation matrix can be found under Config.getxfavgM11, Config.getxfavgM12  etc.  in the *.mat file or in the String_Data.csv .

Alternatively, you can open the raw *.aqd / *.ad2cp file and navigate to the line that starts with GETFXBURST / GETFXAVG. The individual values represent the elements of the 3x3 matrix as shown in (2). These commands can equally be send to the instrument using the terminal which will return the same information.

The instruments orientation needs to be taken into account for each deployment, when transforming to ENU coordinates. If the instrument is pointing down, rows 2 and 3 of the matrix must change sign.

Signature

The transformation matrix T, which is used to transform collected velocities from the BEAM to XYZ coordinate system can be acquired in multiple ways from a Signature instrument.

If you have converted your raw data, then the transformation matrix can be found under Config.Average_Beam2xyz / Config.Burst_Beam2xyz in the *.mat / *.nc

Alternatively, you can open a raw .ad2cp file and navigate to the line that starts with GETFXBURST / GETFXAVG. The individual values represent the elements of the 4x4 matrix as shown in (1). These can commands can equally be send to the instrument using the terminal which will return the same information.

Example:

GETXFBURST,ROWS=4,COLS=4,M11=1.183,M12=0.000,M13=-1.183,M14=0.000,M21=0.000,M22=1.183,M23=0.000,M24=- 1.183,M31=0.552,M32=0.000,M33=0.552,M34=0.000,M41=0.000,M42=0.552,M 43=0.000,M44=0.552

The instruments orientation needs to be taken into account for each deployment, when transforming to ENU coordinates. If the instrument is pointing down, rows 2, 3 and 4 of the matrix must change sign.

!This is not necessary if an AHRS is installed!