Data Fusion of XRF and Vis-NIR Using Outer Product Analysis, Granger–Ramanathan, and Least Squares for Prediction of Key Soil Attributes

Abstract

Visible-near-infrared (vis-NIR) and X-ray fluorescence (XRF) are key technologies becoming pervasive in proximal soil sensing (PSS), whose fusion holds promising potential to improve the estimation accuracy of soil attributes. In this paper, we examine different data fusion methods for the prediction of key soil fertility attributes including pH, organic carbon (OC), magnesium (Mg), and calcium (Ca). To this end, the vis-NIR and XRF spectra of 267 soil samples were collected from nine fields in Belgium, from which the soil samples of six fields were used for calibration of the single-sensor and data fusion models while the validation was performed on the remaining three fields. The first fusion method was the outer product analysis (OPA), for which the outer product (OP) of the two spectra is computed, flattened, and then subjected to partial least squares (PLS) regression model. Two versions of OPA were evaluated: (i) OPA-FS in which the full spectra were used as input; and (ii) OPA-SS in which selected spectral ranges were used as input. In addition, we examined the potential of least squares (LS) and Granger–Ramanathan (GR) analyses for the fusion of the predictions provided by the single-sensor PLS models. Results demonstrate that the prediction performance of the single-sensor PLS models is improved by GR in addition to the LS fusion method for all soil attributes since it accounts for residuals. Resorting to LS, the largest improvements compared to the single-sensor models were obtained, respectively, for Mg (residual prediction deviation (RPD) = 4.08, coefficient of determination (R2) = 0.94, ratio of performance of inter-quantile (RPIQ) = 1.64, root mean square error (RMSE) = 4.57 mg/100 g), OC (RPD = 1.79, R2 = 0.69, RPIQ = 2.82, RMSE = 0.16%), pH (RPD = 1.61, R2 = 0.61, RPIQ = 3.06, RMSE = 0.29), and Ca (RPD = 3.33, R2 = 0.91, RPIQ = 1, RMSE = 207.48 mg/100 g). OPA-FS and OPA-SS outperformed the individual, GR, and LS models for pH only, while OPA-FS was effective in improving the individual sensor models for Mg as well. The results of this study suggest LS as a robust fusion method in improving the prediction accuracy for all the studied soil attributes.