  A common approach to localize a mobile robot is by measuring distances to
points of known positions, called anchors. Locating a device from distance
measurements is typically posed as a non-convex optimization problem, stemming
from the nonlinearity of the measurement model. Non-convex optimization
problems may yield suboptimal solutions when local iterative solvers such as
Gauss-Newton are employed. In this paper, we design an optimality certificate
for continuous-time range-only localization. Our formulation allows for the
integration of a motion prior, which ensures smoothness of the solution and is
crucial for localizing from only a few distance measurements. The proposed
certificate comes at little additional cost since it has the same complexity as
the sparse local solver itself: linear in the number of positions. We show,
both in simulation and on real-world datasets, that the efficient local solver
often finds the globally optimal solution (confirmed by our certificate), but
it may converge to local solutions with high errors, which our certificate
correctly detects.
