Finding roll, pitch and yaw angles

[9988776655]

Homework Statement

I have three angles that relate the sensory body frame to the Earth centered Earth fixed frame:
roll_ecef, pitch_ecef, yaw_ecef
I have the longitude and latitude.
Find the roll, pitch and yaw angles that relate the sensor body frame to the local North East Down frame.

Homework Equations

The unit vectors in local north, east, and down directions, as expressed in ECEF Cartesian coordinates:
N = [- cos(lon)*sin(lat)
- sin(lon)*sin(lat)
cos(lat)];
E = [- sin(lon)
cos(lon)
0];
D = [- cos(lon)*cos(lat)
-sin(lon)*cos(lat)
- sin(lat)];

The Attempt at a Solution

I have no idea :(

 

[Dr. Courtney]

Draw a good diagram.