Modeling the hop count distribution in wireless sensor networks

We consider target localization in randomly deployed multihop wireless sensor networks, where messages originating from a source node are broadcast by flooding and the node-tonode message delays are characterized by random variables with a known probability distribution. Using asymptotic results from first-passage percolation theory and a maximum entropy argument, we formulate a stochastic jump process to approximate the hop count distribution of a message at a distance r from a source node. The resulting marginal distribution of the process has the form of a translated Poisson distribution which characterizes observations well and whose parameters can be learned, for example by maximum likelihood estimation. This result is important in Bayesian target localization, where mobile or stationary sinks of known positions use the hop count distribution conditioned on the Euclidean distance, to estimate the position of a sensor node within the network, based solely on observations of the hop count.