  The ability to accurately estimate the position of robotic agents relative to
one another, in possibly GPS-denied environments, is crucial to execute
collaborative tasks. Inter-agent range measurements are available at a low
cost, due to technologies such as ultra-wideband radio. However, the task of
three-dimensional relative position estimation using range measurements in
multi-agent systems suffers from unobservabilities. This letter presents a
sufficient condition for the observability of the relative positions, and
satisfies the condition using a simple framework with only range measurements,
an accelerometer, a rate gyro, and a magnetometer. The framework has been
tested in simulation and in experiments, where 40-50 cm positioning accuracy is
achieved using inexpensive off-the-shelf hardware.
