Optimal sensor placement for passive source localization

Estimating the position of a source given the signals received at a sensor array is a basic problem in the fields of acoustics and geophysics. Of interest is how to place the sensors so that the source can be most accurately localized. The Cramer-Rao bound is used as a gauge of the accuracy of source position estimators. A simple geometric interpretation of the Cramer-Rao bound is developed, and subject to geometric constraints, sensor arrangements minimizing bound variance are found. Carter's optimal arrays yielding minimum range, bearing, and position bound variance subject to the constraint that the sensors lie along a line segment are reproduced without tedious algebraic manipulations or computer-aided maximization. The bound variance of the optimal arrays is seen to be roughly a factor of three smaller than that of commonly used uniformly spaced arrays.<>