The problem of online parameter identification for spatially distributed systems using a mobile sensor network is investigated in this brief. Inspired by the passive identifier developed for boundary control of partial differential equations (PDEs) using a static sensor network, we propose a distributed online passive identifier that is able to estimate the unknown diffusion coefficient of the advection-diffusion PDE using data collected by a mobile sensor network moving in the field. To enable the online passive identifier, we develop a distributed cooperative Kalman filter run by each sensing agent that provides state estimates of the field. Optimal trajectory for the mobile sensor network in the advection-diffusion field is found, and distributed control laws to control the mobile sensor network to estimate and follow the trajectory while keeping a desired formation are designed. We prove that the parameter estimation errors are bounded and achieve parameter consensus. In addition, by generating a persistence of excitation condition, we further verify the asymptotic parameter convergence. Numerical simulations for 2-D and 3-D cases demonstrate the effectiveness of the proposed online passive identifier.