Optimal sensor placement for time difference of arrival localization

This paper addresses the problem of localizing a source from noisy time-of-arrival measurements. In particular, we are interested in the optimal placement of M planar sensors so as to yield the best expected source location estimate. The main result, on maximizing the expected determinant of the Fisher information matrix for truncated, radially-symmetric source distributions, shows two features not previously observed. First, the sensors should be placed as far from the expected source position as possible. Second, the sensors should be arranged in a splay configuration in which neighboring sensors are separated by equal angle increments. Specific examples are given for point, uniform, and truncated-Gaussian source density functions.