50.6 ESKF prediction equations

Parents: [IMU index](imu index.md), 50.3 error-state-kalman-filter Source: Solà 2017 Quaternion kinematics for ESKF

Error state system equation becomes: where  (s.  IMU nominal-state and error-state kinematics  for an overview of the nonlinear kinematics equations)

State propagation (without considering noise) — produces a state estimate (a priori) Note: this always returns zero as the mean of the error  initialises to zero!

Covariance propagation (considers noise); a priori estimate

with the Jacobians (transition matrix approximated using first order Euler, more precise methods are available)

with the covariance matrices of the random impulses obtain the sigma values from the IMU datasheet or experimentally.