Delay optimal event detection on ad hoc wireless sensor networks

The classical sequential change detection problem [1] aims at detecting a change in the state of a system from the normal state to the abnormal state at a random time T. The state of the system can not be observed directly and is observed only partially through the noisy observations X_k which are obtained at discrete time instants k = 1, 2, 3, ... . Given the state of the system, X_ks are conditionally i.i.d. (over time and across sensors) and the distribution of X_k before change is given by F₀ and that after change is given by F₁. At each time k, after having observed X_k, the decision maker (DM) has to make a decision to stop and raise an alarm or continue sampling at time k + 1. The problem is to obtain a detection-delay optimal stopping rule with respect to the sequence X₁, X₂, ... which stops at time τ that minimises the expected detection delay E [(τ - T)⁺] while the probability of false alarm P{τ <; T} does not exceed a desired quantity α. It is to be noted that at each time k, the DM has the knowledge of the observations X₁, X₂, ... ,X_k, the distribution functions F₀, F₁, and the distribution of the change time T.