(647a) Design of a Parameter and State Estimation Method for Detecting Local Concentration On the Surface of a Carbon-Nanotube Based Sensor

Carbon nanotube-based sensors have been developed by using the indirect detection of the adsorption and desorption of surrounding target molecules with light or electronic property changes. The adsorption and desorption phenomena can be modeled by the chemical master equation (CME), which is a system of stochastic ordinary differential equations (ODEs) describing the time evolution of the probability of each possible adsorption state. By discretizing the ODEs in CME with respect to time, standard linear parameter-varying (LPV) state-space system with Gaussian noises is obtained. In this work, an estimation algorithm with two optimization steps for estimating the sets of adsorption and desorption rate constant parameters and the probability states is proposed. The first step is the least-squares (LS) optimization for estimating the set of rate constant parameters, which changes the LPV system into a linear time-invariant (LTI) system. The second step is the full-information batch estimation method for estimating the probability distribution among the possible states in the LTI system. By iterating between the two optimization steps, both the parameter set and the probability states are converged to optimum values, which should closely track the true parameter and state values. The proposed combined parameter/state estimation method is shown to be more practical compared to the previous analytical method which has many limitations in terms of application to real systems.