Performance Limits in 3D Localization via Molecular Diffusion

This paper investigates the performance limit of position estimation in a three dimensional (3D) molecular diffusion environment. Specifically, we consider a realistic molecular transmission process based on chemical-physical laws and a Poisson distribution of the received molecules. We derive a closed form expression of the Cramér-Rao Bound as a function of the system parameters, such as the number of molecules, the estimation time, the distance of the target, the constant reaction rate and the reagents concentration showing how they impact the localization estimation.