Distance Estimation from a Diffusive Process: Theoretical Limits and Experimental Results

Estimating the distance between the source of a diffusive process and a receiver has a variety of applications, ranging from gas source localization at the macro-scale to molecular communication at the micro-scale. Distance information can be extracted from features of the observed particle concentration, e.g. its peak. This paper derives the Cramér-Rao lower bound (CRB) for distance estimation given the advection-diffusion model for absorbing receivers, which is the fundamental limit of any distance estimator. Furthermore, CRBs are obtained for estimators using only information about the observed peak. A maximum-likelihood estimator using the entire signal and two estimators based on peak detection are deduced. The derived CRBs are used to study the effect of channel parameters on the estimation performance. Finally, the performance of the proposed estimators is verified by comparing the root mean squared errors with their theoretical bounds in a simulation, and preliminary experimental results are presented