Optimizing Multi-Sensor Fusion Architectures: The Role of Non-Linear Meta-Learning in Predicting Soil Nitrogen and Phosphorus

Assessing soil macronutrients across diverse landscapes requires a transition from conventional, time-consuming, and labour-intensive wet chemistry analysis to rapid, low-cost, and non-destructive proximal sensing techniques. In this study, the individual performance as well as the synergistic potential of Portable X-ray Fluorescence Spectrometry (PXRF) and Visible–Near-Infrared (VisNIR; 350–2500 nm) diffuse reflectance spectroscopy were evaluated to enhance the prediction accuracy of soil available Nitrogen(N) and available Phosphorus(P). A total of 609 soil samples were collected from agricultural fields across West Bengal, India, representing a wide range of land-use patterns. Laboratory analysis of N and P served as the ground-truth data for evaluating several machine learning architectures. For individual sensor modelling, Linear Regression (LR), Random Forest (RF), Support Vector Regression (SVR), Partial Least Squares Regression (PLSR), and Extreme Gradient Boosting (XGBoost) models were independently developed for the PXRF and VisNIR datasets to assess their standalone predictive performance. In addition, Granger–Ramanathan Averaging (GRA) was implemented for multi-sensor data fusion using two strategies. The first was a linear approach in which Artificial Neural Networks (ANN) served as base learners with Ordinary Least Squares (OLS) as the meta-learner. The second was a non-linear approach in which RF replaced the linear meta-learner to capture complex data interactions. The results demonstrated that the prediction performance of the single-sensor models was poor but was improved through the GRA fusion framework. The GRA approach with OLS regression showed a slight improvement for P (R² = 0.45, RMSE = 63.20 Kg/ha, ratio of performance to interquartile distance (RPIQ) = 0.89) and N (R² = 0.17, RMSE = 68.86 Kg/ha, RPIQ = 0.96) compared with PXRF and VisNIR in isolation. However, GRA with a non-linear RF meta-learner significantly outperformed the linear strategies and markedly enhanced prediction accuracy for N (R² = 0.85, RMSE = 29.54 Kg/ha, RPIQ = 2.23) and P (R² = 0.87, RMSE = 31.18 Kg/ha, RPIQ = 1.80). These findings indicated that although multi-sensor fusion consistently outperformed single-sensor models, the relationship between sensor data and soil N and P concentrations was fundamentally non-linear. Consequently, these nutrients required the complex weighting capabilities of non-linear architectures, which traditional linear models failed to capture. This methodology offers a scalable solution for assessing soil health in tropical agroecosystems and encourages further exploration of digital mapping approaches for additional soil nutrients.