Maximum-Likelihood Parameter Estimation for Detecting Local Concentration from a Carbon Nanotube-based Sensor

This paper proposes an optimal parameter estimation method for a stochastic process involving monomolecular adsorption and desorption occurring at the nano-scale. Recently, several carbon nanotube sensors that can selectively detect target molecules at a trace concentration level have been developed. These sensors make use of light intensity changes mediated by the adsorption or desorption phenomena on their surfaces. However, the molecular-level events are inherently stochastic, posing a challenge for optimal estimation. The stochastic behavior is modeled by the chemical master equation (CME), which contains a set of ordinary differential equations describing the time evolution of probabilities for the possible adsorption states. Given the inherent stochastic nature of the underlying phenomena, rigorous stochastic estimation based on the CME should outperform deterministic parameter estimation formulated based on the continuum model. Motivated by this expectation, we formulate the maximum likelihood estimation (MLE) based on an analytical solution of the relevant CME for both the constant and time-varying parameter cases. The performance of the MLE and the deterministic least squares are compared using data generated by kinetic Monte Carlo (KMC) simulations of the stochastic process.