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I just read this really nice paper "Quaternion kinematics for the error-state Kalman filter", according to this book "Principles-Multisensor-Integrated-Navigation-Applications" we have following coordinate frame for navigation:

  1. Earth-Centered Inertial Frame (ECIF) which is noted as $O^i$.
  2. Earth-Centered Earth-Fixed Frame (ECEF) which is noted as $O^e$.
  3. Local Navigation Frame which is noted as $O^n$.
  4. Body Frame which is noted as $O^b$.

In chapter 5.1-5.3 of the book following inertial navigation frame equiations are defined.

  1. Inertial-Frame Navigation Eq.
  2. Earth-Frame Navigation Eq.
  3. Local-Navigation-Frame Navigation Eq.

So my question is i am not realy sure, which of the above conventions are sued in the paper mentioned above? Even though i think it is the "Inertial-Frame Navigation Eq."!

Also i am intreseted to know, which one of the above equations is used for land-vehicle navigation?

Thanks

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