An approximate dynamic programming approach for communication constrained inference

Resource management in distributed sensor networks is a challenging problem. This can be attributed to the fundamental tradeoff between the value of information contained in a distributed set of measurements versus the energy costs of acquiring the measurements, fusing them into a model of uncertainty, and transmitting the resulting model. Communications is commonly the highest contributor among these costs, typically by orders of magnitude. Failure to consider this tradeoff can significantly reduce the operational lifetime of a sensor network. While a variety of methods have been proposed that treat a subset of these issues, the approaches are indirect and usually consider at most a single time step. In the context of target tracking with a distributed sensor network we propose an approximate dynamic programming approach which integrates the value of information and the cost of transmitting data over a rolling time horizon. Specifically, we consider tracking a single target and constrain the problem such that, at any time, a single sensor, referred to as the leader node, is activated to both sense and update the probabilistic model. The issue of selecting which sensor should be the leader at each time is of primary interest, as it directly impacts the trade-off between the estimation accuracy and the cost of communicating the probabilistic model from old leader node to new leader node. We formulate this trade-off as a dynamic program, and use an approximation based on a linearization of the sensor model about a nominal trajectory to find a tractable solution. Simulation results demonstrate that the resulting algorithm can provide similar estimation performance to that of the common most informative sensor election method at a fraction of the communication energy cost