Sensor Motion Planning in Distributed Parameter Systems Using Turing´s Measure of Conditioning

We present a technique for planning sensor motions in a specified two-dimensional spatial domain in such a way as to make the Hessian of the parameter estimation cost well conditioned. The framework is based on the use of Turing´s measure of conditioning, whose minimization yields the confidence regions for the parameters as spherical as possible. Since this does not necessarily guarantee a high information content in the measurements, an additional constraint is imposed on the D-efficiency of the solutions. Then 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. Numerical solutions are then obtained using the MATLAB PDE toolbox and the RIOTS_95 optimal control toolbox which handles various constraints imposed on the sensor motions