A stochastic process model of the hop count distribution in wireless sensor networks

We consider target localization in randomly deployed multi-hop wireless sensor networks, where messages originating from a sensor node are broadcast by flooding and the node-to-node message delays are characterized by independent, exponential random variables. Using asymptotic results from first-passage percolation theory and a maximum entropy argument, we formulate a stochastic jump process to approximate the hop count of a message at distance rr from the source node. The resulting marginal distribution of the process has the form of a translated Poisson distribution which characterizes observations reasonably well and whose parameters can be learnt, for example by maximum likelihood estimation. This result is important in Bayesian target localization, where mobile or stationary sinks of known position use the hop count conditioned on the Euclidean distance, to estimate the position of a sensor node or event within the network, based solely on observations of the hop count. For the target localization problem, simulation results show that the proposed model provides reasonably good performance, especially for densely connected networks.