  Accurate estimation of the distance between the transmitter (TX) and the
receiver (RX) in molecular communication (MC) systems can provide faster and
more reliable communication. Existing theoretical models in the literature are
not suitable for distance estimation in a practical scenario. Furthermore,
deriving an analytical model is not easy due to effects such as boundary
conditions in the diffusion process, the initial velocity of the molecules and
unsteady flows. Therefore, five different practical methods comprising three
novel data analysis based methods and two supervised machine learning (ML)
methods, Multivariate Linear Regression (MLR) and Neural Network Regression
(NNR), are proposed for distance estimation at the RX side. In order to apply
the ML methods, a macroscale practical MC system, which consists of an electric
sprayer without a fan, alcohol molecules, an alcohol sensor and a
microcontroller, is established, and the received signals are recorded. A
feature extraction algorithm is proposed to utilize the measured signals as the
inputs in ML methods. The numerical results show that the ML methods outperform
the data analysis based methods in the root mean square error sense with the
cost of complexity. Moreover, the peak time based estimation, which is one of
the proposed data analysis based methods, yields better results with respect to
the other proposed four methods, as the distance increases. Given the
experimental data and fluid dynamics theory, a possible trajectory of the
molecules between the TX and RX is given. Our findings show that distance
estimation performance is jointly affected by unsteady flows and the
non-linearity of the sensor. According to our findings based on fluid dynamics,
it is evaluated that fluid dynamics should be taken into account for more
accurate parameter estimation in practical macroscale MC systems.
