D-optimal trajectory design of heterogeneous mobile sensors for parameter estimation of distributed systems

An approach is proposed to joint optimization of trajectories 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.