We propose a novel distributed expectation maximization (EM) method for non-cooperative RF device localization using a wireless sensor network. We consider the scenario where few or no sensors receive line-of-sight signals from the target. In the cas
e of non-line-of-sight signals, the signal path consists of a single reflection between the transmitter and receiver. Each sensor is able to measure the time difference of arrival of the targets signal with respect to a reference sensor, as well as the angle of arrival of the targets signal. We derive a distributed EM algorithm where each node makes use of its local information to compute summary statistics, and then shares these statistics with its neighbors to improve its estimate of the target localization. Since all the measurements need not be centralized at a single location, the spectrum usage can be significantly reduced. The distributed algorithm also allows for increased robustness of the sensor network in the case of node failures. We show that our distributed algorithm converges, and simulation results suggest that our method achieves an accuracy close to the centralized EM algorithm. We apply the distributed EM algorithm to a set of experimental measurements with a network of four nodes, which confirm that the algorithm is able to localize a RF target in a realistic non-line-of-sight scenario.
A graph $G(V,E)$ of order $|V|=p$ and size $|E|=q$ is called super edge-graceful if there is a bijection $f$ from $E$ to ${0,pm 1,pm 2,...,pm frac{q-1}{2}}$ when $q$ is odd and from $E$ to ${pm 1,pm 2,...,pm frac{q}{2}}$ when $q$ is even such that th
e induced vertex labeling $f^*$ defined by $f^*(x) = sum_{xyin E(G)}f(xy)$ over all edges $xy$ is a bijection from $V$ to ${0,pm 1,pm 2...,pm frac{p-1}{2}}$ when $p$ is odd and from $V$ to ${pm 1,pm 2,...,pm frac{p}{2}}$ when $p$ is even. indent We prove that all paths $P_n$ except $P_2$ and $P_4$ are super edge-graceful.
