Decentralized sequential change detection using physical layer fusion

The problem of decentralized sequential detection with conditionally independent observations is studied. The sensors form a star topology with a central node called fusion center as the hub. The sensors make noisy observations of a parameter that changes from an initial state to a final state at a random time where the random change time has a geometric distribution. The sensors amplify and forward the observations over a wireless Gaussian multiple access channel and operate under either a power constraint or an energy constraint. The optimal transmission strategy at each stage is shown to be the one that maximizes a certain Ali-Silvey distance between the distributions for the hypotheses before and after the change. Simulations demonstrate that the proposed analog technique has lower detection delays when compared with existing schemes. Simulations further demonstrate that the energy-constrained formulation enables better use of the total available energy than the power-constrained formulation in the change detection problem.Comment: 10 pages, two-column, 10 figures, revised based on feedback from reviewers, accepted for publication in IEEE Trans. on Wireless Communication

Change Detection via Affine and Quadratic Detectors

The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, "Hypothesis testing via affine detectors," Electronic Journal of Statistics 10:2204--2242, 2016. Namely, we consider the Change Detection problem as follows: given an evolving in time noisy observations of outputs of a discrete-time linear dynamical system, we intend to decide, in a sequential fashion, on the null hypothesis stating that the input to the system is a nuisance, vs. the alternative stating that the input is a "nontrivial signal," with both the nuisances and the nontrivial signals modeled as inputs belonging to finite unions of some given convex sets. Assuming the observation noises zero mean sub-Gaussian, we develop "computation-friendly" sequential decision rules and demonstrate that in our context these rules are provably near-optimal