Energy efficient sequential detection using feedback aided censoring

We consider a scenario where a sequential hypothesis test is performed in a wireless sensor network. A fusion center receives messages from remote sensors and needs to make a decision about the presence or absence of a phenomenon based on these data. Since the energy consumption of the sensors is one of the most critical factors in many networks, we design the sequential test not in order to minimize its average run-length, but to minimize the amount of energy spent at the nodes. We show that the design of an energy efficient sequential test can be formulated as an optimal stopping problem and be solved via dynamic programming. The resulting test strategy turns out to correspond to a well known censoring scheme, where only significant observations are transmitted to the fusion center, while insignificant ones are discarded. Apart from this, we show that censoring strategies employing feedback from the fusion center show some interesting characteristics and may considerably reduce the number of transmissions, compared to conventional censoring schemes. Our results are illustrated by a numerical toy example.