  We propose hybrid methods for localization in wireless sensor networks fusing
noisy range measurements with angular information (extracted from video).
Compared with conventional methods that rely on a single sensed variable, this
may pave the way for improved localization accuracy and robustness. We address
both the single-source and network (i.e., cooperative multiple-source)
localization paradigms, solving them via optimization of a convex surrogate.
The formulations for hybrid localization are unified in the sense that we
propose a single nonlinear least-squares cost function, fusing both angular and
range measurements. We then relax the problem to obtain an estimate of the
optimal positions. This contrasts with other hybrid approaches that alternate
the execution of localization algorithms for each type of measurement
separately, to progressively refine the position estimates. Single-source
localization uses a semidefinite relaxation to obtain a one-shot matrix
solution from which the source position is derived via factorization. Network
localization uses a different approach where sensor coordinates are retained as
optimization variables, and the relaxed cost function is efficiently minimized
using fast iterations based on Nesterov's optimal method. Further, an automated
calibration procedure is developed to express range and angular information,
obtained by different devices, possibly deployed at different locations, in a
single consistent coordinate system. This drastically reduces the need for
manual calibration that would otherwise negatively impact the practical
usability of hybrid range/video localization systems. We develop and test, both
in simulation and experimentally, the new hybrid localization algorithms, which
not only overcome the limitations of previous fusing approaches but also
compare favorably to state-of-the-art methods, outperforming them in some
scenarios.
