Doptimal trajectory design of heterogeneous mobile sensors for parameter estimation of distributed systems

Abstract — An approach is proposed to joint optimization of trajecto-ries and measurement accuracies of mobile nodes in a sensor network collecting measurements for parameter estimation of a distributed parameter system. The problem is cast as maximization of the log-determinant of the information matrix associated with the estimated parameters over the set of all feasible information matrices, which yields a formulation in terms of convex optimization. This makes it possible to employ powerful tools of optimum experimental design theory to characterize the optimal solution and adapt the Wynn-Fedorov algorithm to construct its numerical approximation. As a crucial subtask in each iteration, a nontrivial optimal control problem must be solved, which is accomplished using the MATLAB PDE toolbox and the RIOTS 95 optimal control toolbox which handles various constraints imposed on the sensor motions. The effectiveness of the method is illustrated with a numerical example regarding a two-dimensional diffusion equation. I