The problem of optimally locating a given number of Bensors for observing a general linear distributed parameter system is considered. Measurements at the sensors are assumed to be available continuously in time, and the design criterion is minimization of a scalar measure of the covariance of the estimate error in the optimal linear filter. Necessary conditions for optimality are derived based on the formulation of a distributed parameter matrix minimum principle. A computational algorithm is developed for determining the optimum set of measurement locations. The algorithm is applied to the problem of optimally locating temperature sensors in a solid undergoing transient heat conduction.