  A reliable, accurate, and affordable positioning service is highly required
in wireless networks. In this paper, the novel Message Passing Hybrid
Localization (MPHL) algorithm is proposed to solve the problem of cooperative
distributed localization using distance and direction estimates. This hybrid
approach combines two sensing modalities to reduce the uncertainty in
localizing the network nodes. A statistical model is formulated for the
problem, and approximate minimum mean square error (MMSE) estimates of the node
locations are computed. The proposed MPHL is a distributed algorithm based on
belief propagation (BP) and Markov chain Monte Carlo (MCMC) sampling. It
improves the identifiability of the localization problem and reduces its
sensitivity to the anchor node geometry, compared to distance-only or
direction-only localization techniques. For example, the unknown location of a
node can be found if it has only a single neighbor; and a whole network can be
localized using only a single anchor node. Numerical results are presented
showing that the average localization error is significantly reduced in almost
every simulation scenario, about 50% in most cases, compared to the competing
algorithms.
