Estimation of Available Phosphorus in Man Interference Zone Based on Fractional Derivative

Abstract

The fractional derivative has the advantages in terms of memory and globality, and it can overcome the shortcomings of the traditional integer differential algorithm. Moreover, the absorption characteristics of available phosphorus in soil in visible near-infrared bands are unclear, and the prediction model has a low precision. In this paper, we propose a novel method to improve the accuracy of the prediction model for available phosphorus content, which is based on the fractional derivative and stepwise multiple linear regression (SMLR). First, the relationship between the soil spectrum and the available phosphorus content under different fractional orders was studied. Secondly, spectrum dimensionality reduction based on sensitive bands was performed. Finally, the SMLR model was adopted to quantitatively predict the available phosphorus content, and the precision of different fractional order models was discussed. Simulation results revealed that the fractional derivative can describe the small differences in spectral data and increase the correlation between the soil spectrum and the available phosphorus content. The 1.4th-order model is the optimum fractional model. Thus, these results indicate that the fractional derivative could improve the accuracy of the estimation model for available phosphorus content.

Grassland Chlorophyll Content Estimation from Drone Hyperspectral Images Combined with Fractional-Order Derivative

“…It finds applications in various fields, such as system modeling, pattern recognition, signal filtering, and fractal theory. Fractional-order models often yield more accurate results compared to traditional integer-order models [28,29]. There are several approaches to define fractional order, including Riemann -Liouville, Caputo, and Grunwald-Letnikov approaches [30].…”