The author defines the problem of optimal sensor placement in two-dimensional space to address the issue of choosing a configuration of multiple sensors to minimize the uncertainty in the consensus estimate obtained by combining the sensor measurements. The algebraic structure of sensor errors with respect to sensor placement is studied, and a necessary condition for the optimal placement is derived. The solution to the problem is obtained by comparing sensor configurations that satisfy the necessary condition. The method does not assume specific sensor modality and is applicable to sensors of any type that are capable of providing position information. >