Nanomechanical Thermal Response Modeling for Optimal Signal Estimation via Kalman filtering

Abstract

We propose a thermal circuit model for nanomechanical infrared spectroscopy (NEMS-IR), suitable for model-based filtering techniques such as Kalman filtering. This model accounts for the resonator’s dual time constant response and its noise profiles, enabling optimal estimation of the absorbed input power by the nanomechanical resonator. System identification utilizes a step response (Figure 1a) and the power spectral density of the noise (Figure 1b). An adaptive Kalman filter, which increases in bandwidth upon resonator illumination, is employed for precise input estimation (Figure 1c and 1d). Reproducibility and linearity are evaluated by conducting five measurements across three power levels for both laser "on" and "off" transients (Figure 1e). Additionally, a staircase function is applied to demonstrate the resonator's immunity to the slower second time constant when the illuminating laser power is increased stepwise.