  Anytime a robot manipulator is controlled via visual feedback, the
transformation between the robot and camera frame must be known. However, in
the case where cameras can only capture a portion of the robot manipulator in
order to better perceive the environment being interacted with, there is
greater sensitivity to errors in calibration of the base-to-camera transform. A
secondary source of uncertainty during robotic control are inaccuracies in
joint angle measurements which can be caused by biases in positioning and
complex transmission effects such as backlash and cable stretch. In this work,
we bring together these two sets of unknown parameters into a unified problem
formulation when the kinematic chain is partially visible in the camera view.
We prove that these parameters are non-identifiable implying that explicit
estimation of them is infeasible. To overcome this, we derive a smaller set of
parameters we call Lumped Error since it lumps together the errors of
calibration and joint angle measurements. A particle filter method is presented
and tested in simulation and on two real world robots to estimate the Lumped
Error and show the efficiency of this parameter reduction.
