Path planning for moving sensors in parameter estimation of distributed systems

We develop an effective numerical procedure for optimizing trajectories of moving sensors which take measurements in a given spatial in order to find parameter estimates of a given distributed system. The global design criterion is the Frobenius condition number for the Hessian of the least-squares criterion. The approach converts the problem to an optimal control one in which both the control forces of the sensors and the initial sensor positions are optimized. Its solution is obtained by the use of a gradient algorithm which handles various constraints imposed on sensor motions. Among other things, the method copes efficiently with problems involving state constraints induced by collision-avoidance conditions or admissible distances between the sensors. A simple test problem is presented to illustrate the presented ideas.