Coordinate transformation

File contents

% Transform.m is a Matlab script that shows how velocity data can be 
% transformed between beam coordinates and ENU coordinates. Beam 
% coordinates are defined as the velocity measured along the three 
% beams of the instrument.
% ENU coordinates are defined in an earth coordinate system, where
% E represents the East-West component, N represents the North-South
% component and U represents the Up-Down component.

% Note that the transformation matrix must be recalculated every time
% the orientation, heading, pitch or roll changes.

% Transformation matrix for beam to xyz coordinates,
% the values can be found from the header file that is generated in the
% conversion of data to ASCII format
% This example shows the transformation matrix for a standard Aquadopp head
T =[ 2896  2896    0 ;...
    -2896  2896    0 ;...
    -2896 -2896 5792  ];

T = T/4096;   % Scale the transformation matrix correctly to floating point numbers

T_org = T;

% If instrument is pointing down (bit 0 in status equal to 1)
% rows 2 and 3 must change sign
% NOTE: For the Vector the instrument is defined to be in 
%       the UP orientation when the communication cable 
%       end of the canister is on the top of the canister, ie when 
%       the probe is pointing down.
%       For the other instruments that are used vertically, the UP 
%       orientation is defined to be when the head is on the upper
%       side of the canister.


if statusbit0 == 1,
   T(2,:) = -T(2,:);   
   T(3,:) = -T(3,:);   
end

% heading, pitch and roll are the angles output in the data in degrees

hh = pi*(heading-90)/180;
pp = pi*pitch/180;
rr = pi*roll/180;

% Make heading matrix
H = [cos(hh) sin(hh) 0; -sin(hh) cos(hh) 0; 0 0 1]

% Make tilt matrix
P = [cos(pp) -sin(pp)*sin(rr) -cos(rr)*sin(pp);...
      0             cos(rr)          -sin(rr);  ...
      sin(pp) sin(rr)*cos(pp)  cos(pp)*cos(rr)]

% Make resulting transformation matrix
R = H*P*T;


% beam is beam coordinates, for example beam = [0.23 ; -0.52 ; 0.12]
% enu is ENU coordinates

% Given beam velocities, ENU coordinates are calculated as
enu = R*beam

% Given ENU velocities, beam coordinates are calculated as
beam = inv(R)*enu


% Transformation between beam and xyz coordinates are done using
% the original T matrix 
xyz = T_org*beam
beam = inv(T_org)*xyz

% Given ENU velocities, xyz coordinates are calculated as
xyz = T_org*inv(R)*enu