  This paper presents the design and implementation of a Right Invariant
Extended Kalman Filter (RIEKF) for estimating the states of the kinematic base
of the Surena V humanoid robot. The state representation of the robot is
defined on the Lie group $SE_4(3)$, encompassing the position, velocity, and
orientation of the base, as well as the position of the left and right feet. In
addition, we incorporated IMU biases as concatenated states within the filter.
  The prediction step of the RIEKF utilizes IMU equations, while the update
step incorporates forward kinematics. To evaluate the performance of the RIEKF,
we conducted experiments using the Choreonoid dynamic simulation framework and
compared it against a Quaternion-based Extended Kalman Filter (QEKF). The
results of the analysis demonstrate that the RIEKF exhibits reduced drift in
localization and achieves estimation convergence in a shorter time compared to
the QEKF. These findings highlight the effectiveness of the proposed RIEKF for
accurate state estimation of the kinematic base in humanoid robotics.
