  Range-only (RO) pose estimation involves determining a robot's pose over time
by measuring the distance between multiple devices on the robot, known as tags,
and devices installed in the environment, known as anchors. The nonconvex
nature of the range measurement model results in a cost function with possible
local minima. In the absence of a good initialization, commonly used iterative
solvers can get stuck in these local minima resulting in poor trajectory
estimation accuracy. In this work, we propose convex relaxations to the
original nonconvex problem based on semidefinite programs (SDPs). Specifically,
we formulate computationally tractable SDP relaxations to obtain accurate
initial pose and trajectory estimates for RO trajectory estimation under static
and dynamic (i.e., constant-velocity motion) conditions. Through simulation and
real experiments, we demonstrate that our proposed initialization strategies
estimate the initial state accurately compared to iterative local solvers.
Additionally, the proposed relaxations recover global minima under moderate
range measurement noise levels.
