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. In addition, distance information can be used in determining the location of the molecular source in practical applications such as monitoring environmental pollution. Existing theoretical models in the literature are not suitable for distance estimation in a practical scenario. Furthermore, deriving an analytical model is a nontrivial problem, since the liquid in the TX is sprayed as droplets rather than molecules, these droplets move according to Newtonian mechanics, the size of the droplets change during their propagation and droplet-air interaction causes 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. The nearly equal performance of MLR and NNR shows that the input features such as peak time, peak concentration and the energy of the received signal have a highly linear relation with the distance. 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.

分子通信（MC）系统中发射器（TX）和接收器（RX）之间距离的准确估计可以提供更快，更可靠的通信。另外，在诸如监视环境污染的实际应用中，距离信息可用于确定分子源的位置。文献中的现有理论模型不适用于实际情况下的距离估计。此外，推导分析模型不是一个简单的问题，因为TX中的液体以液滴而不是分子的形式喷射，这些液滴根据牛顿力学运动，液滴的大小在其传播过程中发生变化，并且液滴与空气的相互作用导致流动不稳定。因此，针对RX端的距离估计，提出了五种不同的实用方法，包括三种基于新颖数据分析的方法和两种监督式机器学习（ML）方法，即多元线性回归（MLR）和神经网络回归（NNR）。为了应用ML方法，建立了一个大型的实际MC系统，该系统由不带风扇的电动喷雾器，酒精分子，酒精传感器和微控制器组成，并记录接收到的信号。提出了一种特征提取算法，利用测得的信号作为ML方法的输入。数值结果表明，在均方根误差意义上，机器学习方法优于基于数据分析的方法，但代价是复杂性高。MLR和NNR的性能几乎相等，这表明输入功能（例如峰值时间，峰值浓度和接收信号的能量与距离具有高度线性关系。此外，随着距离的增加，基于峰值时间的估计是提出的基于数据分析的方法之一，相对于其他提出的四种方法，产生了更好的结果。给定实验数据和流体动力学理论，给出了TX和RX之间分子的可能轨迹。我们的研究结果表明，距离估计性能受不稳定的流量和传感器的非线性共同影响。根据我们基于流体动力学的发现，我们评估了在实际的大型MC系统中应考虑流体动力学，以便更准确地估计参数。基于峰值时间的估计是提出的基于数据分析的方法之一，随着距离的增加，相对于其他提出的四种方法，可以获得更好的结果。给定实验数据和流体动力学理论，给出了TX和RX之间分子的可能轨迹。我们的研究结果表明，距离估计性能受不稳定的流量和传感器的非线性共同影响。根据我们基于流体动力学的发现，我们评估了在实际的大型MC系统中，应考虑流体动力学以进行更准确的参数估计。基于峰值时间的估计是提出的基于数据分析的方法之一，随着距离的增加，相对于其他提出的四种方法，可以获得更好的结果。给定实验数据和流体动力学理论，给出了TX和RX之间分子的可能轨迹。我们的研究结果表明，距离估计性能受不稳定的流量和传感器的非线性共同影响。根据我们基于流体动力学的发现，我们评估了在实际的大型MC系统中，应考虑流体动力学以进行更准确的参数估计。给定实验数据和流体动力学理论，给出了TX和RX之间分子的可能轨迹。我们的研究结果表明，距离估计性能受不稳定的流量和传感器的非线性共同影响。根据我们基于流体动力学的发现，我们评估了在实际的大型MC系统中，应考虑流体动力学以进行更准确的参数估计。给定实验数据和流体动力学理论，给出了TX和RX之间分子的可能轨迹。我们的研究结果表明，距离估计性能受不稳定的流量和传感器的非线性共同影响。根据我们基于流体动力学的发现，我们评估了在实际的大型MC系统中，应考虑流体动力学以进行更准确的参数估计。