Fractional-order Savitzky–Golay filter for pre-treatment of on-line vis–NIR spectra to predict phosphorus in soil

Abstract

Visible and near infrared spectroscopy (vis-NIRS) has shown potential to predict soil phosphorous (P) with reasonable accuracy. However, spectra pre-treatment is essential in chemometric modelling. One of the most popular algorithms for spectral smoothing and differentiation is the integer-order Savitzky–Golay filter (IOSGF), which operates on a localised linear regression of several neighbouring points over a moving window. Herein, a modified Riemann–Liouville (RL) fractional-order Savitzky–Golay filter (MRLFOSGF) is presented based on the RL operators, as an extension of the conventional IOSGF. This filter was quantitatively analysed using power functions and Gaussian-type bands and were subsequently used to establish a partial least squares regression (PLSR) model for predicting P in soil. The results revealed that the MRLFOSGF offers significant flexibility with transition dynamics between integer-order SG derivatives and reduces baseline offsets and tilts. The PLSR model using the MRLFOSGF had a higher prediction accuracy than the corresponding PLSR model using the conventional IOSGF. This work demonstrates that the MRLFOSGF offers the advantage of wider applicability and better performance for predicting soil P than the conventional IOSGF.