xyz.to.enu.adp: Convert ADP from xyz coordinates to enu coordinates

Description

Convert ADP velocity components from a xyz-based coordinate system to an enu-based coordinate system, by using the instrument's recording of heading, pitch, and roll.

Usage

xyz.to.enu.adp(x, declination=0, debug=getOption("oce.debug"))

Arguments

an object of class "adp".

declination

magnetic declination to be added to the heading after "righting" (see below), to get ENU with N as "true" north.

debug

a flag that turns on debugging. Set to 1 to get a moderate amount of debugging information, or to 2 to get more.

Value

An object with data$ma$v[,,1:3] altered appropriately, and metadata$oce.orientation changed from xyz to enu.

Details

A single formula is used for different instruments and configuraitons, but its constituents are altered to fit each case. The first step is to convert the (x,y,z) velocity components (stored in the three columns of x$data$ma$v[,,1:3]) into what RDI (1998 pages 11 and 12) calls "ship", or "righted" components. For example, the z coordinate, which may point upwards or downwards depending on instrument orientation, is mapped onto a so-called "mast" coordinate that points more nearly upwards than downward (as for a righted ship). The other ship coordinates are called "starboard" and "forward", the meanings of which will be clear to a mariner. Once the (x,y,z) velocities are converted to ship/righted velocities, the detailed orientation of the instrument is extracted from heading, pitch, and roll vectors stored in x$data$ts. As in the previous step, these may be adjusted to account for instrument type and upward/downward orientation. The case-by-case details are as follows:

RDI pointed upward: values of heading, pitch and roll are used as stored in the object; "starboard" is taken as the negative of the "x" component, "forward" is taken as the "y" component, and "mast" is taken as the negative of the "z" component.
RDI pointed downward: (FILLIN)
nortek pointed upward: (FILLIN)
nortek pointed downward: (FILLIN)
sontek pointed upward: (FILLIN)
sontek pointed downward: (FILLIN)

After these steps, a standardized rotation matrix is used to convert to east-north-up coordinates. As is described in the RDI coordinate transformation manual (1998, pages 13 and 14), this matrix is based on sines and cosines of the attitude angles. Let CH and SH denote cosine and sine of heading (after adjusting for declination), with similar terms for pitch and roll using second letters P and R. Then, the rotation matrix is defined by

rbind(c( CH*CR + SH*SP*SR, SH*CP, CH*SR - SH*SP*CR), c(-SH*CR + CH*SP*SR, CH*CP, -SH*SR - CH*SP*CR), c( -CP*SR, SP, CP*CR))

This matrix is left-multiplied by a matrix with three rows, the top a vector of "starboard" values, the middle a vector of "forward" values, and the bottom a vector of "mast" values. Finally, the columns of data$ma$v[,,1:3] are filled in with the result of the matrix multiplication.

References