State estimation for a carbon nanotube-based sensor array system

Abstract

This paper proposes state estimation methods for tracking a time-varying local concentration of target molecules from the carbon-nanotube (CNT)-based sensing system. The signals triggered by adsorption/desorption events of a trace of the proximate target molecules on the sensors show strongly stochastic behavior. The stochastic nature can be modelled by the chemical master equation (CME) describing the time evolution of the probabilities for all the possible numbers of adsorbed molecules. The adsorption rate on each sensor is proportional to the local concentration, thus connecting the sensor signal to it. At the macroscopic level, the concentration, which is the state, evolves according to the continuum equation represented by ordinary differential equations (ODEs). Various state estimation methods including the Kalman filter (KF), particle filter (PF), and moving horizon estimator (MHE) are designed for the system with highly stochastic, non-Gaussian measurements. Their performances are compared for single sensor as well as multiple sensors in the neighborhood that shares same concentration dynamics.