  The extended Kalman filter (EKF) is a common state estimation method for
discrete nonlinear systems. It recursively executes the propagation step as
time goes by and the update step when a set of measurements arrives. In the
update step, the EKF linearizes the measurement function only once. In
contrast, the iterated EKF (IEKF) refines the state in the update step by
iteratively solving a least squares problem. The IEKF has been extended to work
with state variables on manifolds which have differentiable $\boxplus$ and
$\boxminus$ operators, including Lie groups. However, existing descriptions are
often long, deep, and even with errors. This note provides a quick reference
for the IEKF on manifolds, using freshman-level matrix calculus. Besides the
bare-bone equations, we highlight the key steps in deriving them.
