The authors present an adaptive algorithm based on a non-linear regression model for mitigating time-varying etalon drifts in line-scanned optical absorption spectrometers. By dynamically varying the etalon spectral background using physically realistic degrees of freedom, the authors’ dynamic etalon fitting-routine (DEF-R) significantly increases the spectral baseline recalibration interval as compared to conventional fringe subtraction models. They provide an empirical demonstration of the efficacy of DEF-R using an on-chip 10 cm silicon waveguide for near-infrared methane absorption spectroscopy at 6057 cm−1, which suffers significant etalon spectral noise due to reflections and multi-path interference from stochastic line-edge roughness imperfections. They demonstrate the corresponding improvement in both spectral clean-up and long-term stability via Allan-variance analysis. For the sensor presented here, application of DEF-R enables Gaussian-noise limited performance for more than 102 s and provides almost an order-of-magnitude improvement in stability time with respect to conventional baseline subtraction. Although DEF-R is applied here to an on-chip sensor embodiment, they envision their technique to be applicable to any absorption sensor limited by time-varying etalon drifts.