Optimal Interlaced Mobile Sensor Motion Planning and Parameter Estimation for Distributed Parameter Systems

Using mobile sensors to perform optimal measurement and estimation of a distributed parameter system in a domain of interest is considered in this paper. Given parameters, how to optimally plan the motion trajectories of the mobile sensors has been known in the literature, where the purpose of mobile sensing is to best estimate the parameters. Clearly, there is a “chick-and-egg” problem regarding the optimal mobile sensor motion planning and parameter estimation for distributed parameter systems. For the first time, this paper solved this problem by the proposed optimal interlaced mobile sensor motion planning and parameter estimation. The problem formulation is given in detail with a numerical solution for generating and refining the mobile sensor motion trajectories for parameter estimation of the distributed parameter system. The basic idea is to use the finite horizon type of scheme. First, the optimal trajectories are computed in a finite time horizon based on the assumed parameter values. For the following time horizon, the parameters of the distributed parameter system are estimated using the measured data in the previous time horizon, and the optimal trajectories are updated accordingly based on these estimated parameters obtained. Simulations are offered to illustrate the advantages of the proposed interlaced method over the non-interlaced techniques. We call the proposed scheme “on-line” or “real-time” which offers practical solutions to optimal measurement and estimation of a distributed parameter system when mobile sensors are used.