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Homework Help: Convert ENU velocity to ECEF

  1. Aug 21, 2011 #1
    1. The problem statement, all variables and given/known data
    This is not actually a homework problem, but it should be a fairly simple problem (hopefully). My apologies if this is better suited for the engineering forum.
    I have been given an aircraft heading and a set of velocities in the ENU coordinate system. I need to convert the velocities from ENU to ECEF and calculate the aircraft track. As far as I can tell I am doing the velocity conversions correctly, but I cannot get the aircraft heading and the aircraft track to agree within +/- 15 degrees.

    2. Relevant equations
    I am using the following direction cosine matrix, which I arrived at by starting with the DCM for converting from ECEF to NED, swapping the first and second rows, negating the third row and taking the transpose:

    CN2E = | -sin(lon) -sin(lat)*cos(lon) cos(lat)*cos(lon) |
    | cos(lon) -sin(lat)*sin(lon) cos(lat)*sin(lon) |
    | 0 cos(lat) sin(lat) |

    lat = 34.2547 %degrees
    lon = -96.6522 %degrees
    height = 3690 %meters
    velocity_ENU = [76.8213; -42.7113; 1.5302] %meters
    heading = 123.2568 %degrees

    3. The attempt at a solution
    Multiplying CN2E * vel_ENU yields:
    vel_x = 73.3726
    vel_y = -34.0346
    vel_z = -34.4414

    This gives an aircraft speed of approx 170 knots; i don't have our exact aircraft speed at the time the measurement was made, but that's in the ballpark.
    Finally, taking atan2(vel_y/vel_x) and converting to degrees yields an aircraft track of -24.8847 degrees, which is not even close to the heading of 123.2568 degrees.
    Can anyone see where I might have gone wrong?
  2. jcsd
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