An intermittent sensor versus a target that emits glimpses as a homogenous Poisson process

摘要

We consider a sensor that alternates randomly between working and broken versus a target that reluctantly gives away glimpses as a homogenous Poisson process. Over any interval of time, the sensor has a probability of detecting n glimpses, of detecting the kth glimpse, and of detecting the kth glimpse when there are n glimpses in that interval. The article provides closed-form approximations to the distributions for those probabilities, proves that the approximations become perfect as the time interval becomes infinitely long (asymptotic distributions, pointwise convergence), and compares the approximations with empirical results obtained from simulations.