Two-dimensional optimal sensor placement

A method for determining the optimal two-dimensional spatial placement of multiple sensors participating in a robot perception task is introduced in this paper. This work is motivated by the fact that sensor data fusion is an effective means of reducing uncertainties in sensor observations, and that the combined uncertainty varies with the relative placement of the sensors with respect to each other. The problem of optimal sensor placement is formulated and a solution is presented in two dimensional space. The algebraic structure of the combined sensor uncertainty with respect to the placement of sensors is studied. A necessary condition for optimal placement is derived and this necessary condition is used to obtain an efficient closed-form solution for the global optimal placement. Numerical examples are provided to illustrate the effectiveness and efficiency of the solution