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