On optimal energy efficient convergecasting in unreliable sensor networks with applications to target tracking

In this paper, we develop a mathematical framework for studying the problem of maximizing the "information" received at the sink in a data gathering wireless sensor network. We explicitly account for unreliable links, energy constraints, and in-network computation. The network model is that of a sensor network arranged in the form of a tree topology, where the root corresponds to the sink node, and the rest of the network detects an event and transmits data to the sink over one or more hops. This problem of sending data from multiple sources to a common sink is often referred to as the convergecasting problem. We develop an integer optimization based framework for this problem, which allows for tackling link unreliability using general error-recovery schemes. Even though this framework has a non-linear objective function, and cannot be relaxed to a convex programming problem, we develop a low complexity, distributed solution. The solution involves finding a Maximum Weight Increasing Independent Set (MWIIS) in rectangle graphs over each hop of the network, and can be obtained in polynomial time. Further, we apply these techniques to a target tracking problem where we optimally select sensors to track a given target such that the information obtained is maximized subject to constraints on the per-node sensing and communication energy. We validate our algorithms through numerical evaluations, and illustrate the advantages of explicitly considering link unreliability in the optimization framework.