On the use of tight frames for optimal sensor placement in time-difference of arrival localization

In this paper we analyze the use of tight frames for the problem of localizing a source from noisy time-difference of arrival measurements. Based on the Fisher information matrix, we show that positioning the sensor network according to a tight frame that also obeys some internal symmetries provides the best average localization accuracy. We connect our result to previous approaches from the literature and show experimentally that near optimal accuracy can also be provided by random tight frames. We also make the assumption that the sensors are not fixed but placed on mobile units and we study the problem of bringing them to a tight configuration with the minimum energy consumption. Although our results hold for any dimension, for simplicity of exposition, the numerical experiments depicted are in the two dimensional case.