Publications Details
On The Jacobian of the ECEF J2 Gravitation Model
An Earth-centered, Earth-fixed (ECEF) inertial navigation system must compute the Jacobian of its employed gravitation model with respect to position while time-propagating the error covariance of the system. One commonly used gravitation model is the ‘J2 model’ which is a second-order truncation of the Earth’s spherical harmonic gravitation model. The J2 model is popular because it can quickly and efficiently be evaluated, and the truncation error is small: The ‘J3 term’ --- the third term in the spherical harmonic expansion --- is approximately 1000 times smaller than the J2 term.