# Coordinate frame in IMU/GPS Error-state kalman filtering

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.