This paper investigates the sequential hypothesis testing problem with online sensor selection and sensor usage constraints. That is, in a sensor network, the fusion center sequentially acquires samples by selecting one 'most informative' sensor at each time until a reliable decision can be made. In particular, the sensor selection is carried out in the online fashion since it depends on all the previous samples at each time. Our goal is to develop the sequential test (i.e., stopping rule and decision function) and sensor selection strategy that minimize the expected sample size subject to the constraints on the error probabilities and sensor usages. To this end, we first recast the usage-constrained formulation into a Bayesian optimal stopping problem with different sampling costs for the usage-contrained sensors. The Bayesian problem is then studied under both finite- and infinite-horizon setups, based on which, the optimal solution to the original usage-constrained problem can be readily established. Moreover, by capitalizing on the structures of the optimal solution, a lower bound is obtained for the optimal expected sample size. In addition, we also propose algorithms to approximately evaluate the parameters in the optimal sequential test so that the sensor usage and error probability constraints are satisfied. Finally, numerical experiments are provided to illustrate the theoretical findings, and compare with the existing methods.
Bibliographical noteFunding Information:
Manuscript received January 5, 2016; revised September 11, 2017; accepted January 28, 2019. Date of publication April 11, 2019; date of current version June 14, 2019. S. Li was supported in part by the U.S. National Science Foundation (NSF) under Grant CIF1064575, and in part by the U.S. Office of Naval Research (ONR) under Grant N000141410667. X. Li was supported by NSF DMS-1712657. J. Liu was supported in part by NSF under Grant SES-1323977, Grant SES-1826540, and Grant IIS-1633360, and in part by the Army Research Office under Grant W911NF-15-1-0159. This paper was presented in part at the 2016 IEEE International Symposium on Information Theory (ISIT).
- Sequential hypothesis test
- dynamic programming
- online sensor selection
- sensor usages