ECEF 6DOF block - position calculation

Hi all,

I am working with the ECEF 6DOF (Quaternion) block and am confused about the way in which it determines velocity/position based on accelerations.

The block appears to integrate the "inertial" (actually earth-fixed) acceleration once to determine velocity and again to determine the ECEF position. This works for a non-rotating earth (w_e = 0) but not for a rotating earth as the accelerations/velocities being integrated are with respect to a non-inertial (rotating) frame. The correct approach would appear to be a conversion of the fixed-frame acceleration to true inertial acceleration prior to integration to preserve the correct kinematics.

Is this an intentional aspect of this block and, if so, is it intended to be used with a nonzero rotation rate?

Answer 1

[Paul]

Hi Thomas,

As far as I can tell, the translational equations in the Algorithms section of the documentation page 6DOF ECEF (Quaternion) are correct. Whether or not those equations are as implemented in the block itself is another question, but it seemed to be the case after a quick check (though it was confusing because the notation in the block doesn't always match the doc and at least one block name was incorrect).

The block doesn't integrate acceleration to velocity to position, at least not without taking one detour along the way.

The key term is , which I would describe as the velocity (of the center-of-mass) relative to the ECEF frame resolved in the body frame.

Note that is first multiplied by DCM_fb to form , which is the velocity relative to ECEF resolved in ECEF, which is then integrated to , which is the position resolved in ECEF.

is called (which I can't describe in words), which can be integrated to . I believe that equation for is correct as well, despite yet another problem on the doc page that shows the components of all with subscipt b (and the last term should be w, not omega), but the components of do not use the subscript b. That doc page needs a lot of cleanup, as we previously discussed here.

Is there a specific concern about a specific equation or a simulation result that appears to be not correct?