  Rigid body systems usually consider measurements of the pose of the body
using onboard cameras/LiDAR systems, that of linear acceleration using an
accelerometer and of angular velocity using an IMU. However, the measurements
of the linear acceleration and angular velocity are usually biased with an
unknown constant or slowly varying bias. We propose a measurement bias
estimator for such systems under assumption of boundedness of angular velocity.
We also provide continuous estimates to the state of the system, i.e. the pose,
linear velocity, and position of the body. These estimates are globally
exponentially convergent to the state of the rigid body system. We propose two
bias estimators designed with the estimate of the pose in the ambient Euclidean
space of the Special Euclidean group and show global exponential convergence of
the proposed observers to the state of the system. The first observer assumes
knowledge of bounds of the angular velocity, while the second observer uses a
Riccati observer to overcome this limitation. We show the convergence with an
example of a rigid body rotation and translation system on the special
Euclidean group. We show that the observer is able to estimate the bias using
data collected from an Intel Realsense camera.
