The quickest change detection problem is to detect an abrupt change event as quickly as possible subject to constraints on false detection. Unlike the classical problem, where the decision maker can access only one sequence of observations, in this paper, the decision maker chooses one of two different sequences of observations at each time instant. The information quality and sampling cost of the two sequences of observations are different. We present an asymptotically optimal joint design of observation scheduling policy and stopping time such that the detection delay is minimized subject to constraints on both average run length to false alarm (ARLFA) and average cost per sample. The observation scheduling policy has a threshold structure and the detection scheme is a variant of the cumulative sum test where the detection statistic stochastically crosses the threshold that is used to switch observation modes. We further study the decentralized case in a multi-channel setting. We show that if each sensor uses the proposed observation scheduling policy locally and the fusion center uses the    $N_{\mathrm{sum}}$   algorithm, by which the center declares the change when the sum of the sensors' local detection statistics crosses a certain threshold, the detection delay is asymptotically minimized for any possible combination of the affected sensors subject to constraints on both global ARLFA and average cost per sample at each sensor node. Numerical examples are given to illustrate the main results.
['Xiaoqiang Ren', 'Karl Henrik Johansson', 'Ling Shi']
Quickest Change Detection With Observation Scheduling