Optimal Sequential Detection with Stochastic Energy Constraint

The sequential detection problem in wireless sensors powered by energy harvested from the enviroment is considered. Assuming that a unit of energy arrives with probability p at each time instant, two different problem setups, namely minimizing the weighted sum of detection delay and error probabilities and minimizing the average detection delay subject to error probabilities constraints, are studied. Optimal decision rules including energy allocation, stopping rule and terminal decision rules are derived for both setups. For both setups, we show that the sensor will take samples immediately after energy arrives. However, the numbers of samples that the sensor will take for these two setups behave differently as p changes. For the first setup, the number of samples increases as p increase. For the second setup, the number of samples the sensor will take is the same for different values of p.