Uncertainty-aware decision-making increasingly relies on multimodal sensing pipelines that must fuse correlated measurements, propagate uncertainty, and trigger reliable control actions. This study develops a unified mathematical framework for multimodal data fusion and Bayesian decision-making under uncertainty. The approach integrates adaptive Covariance Intersection (aCI) for correlation-robust sensor fusion, a Gaussian state–space backbone with Kalman filtering, heteroskedastic Bayesian regression with full posterior sampling via an affine-invariant MCMC sampler, and a Bayesian likelihood-ratio test (LRT) coupled to a risk-sensitive proportional–derivative (PD) control law. Theoretical guarantees are provided by bounding the state covariance under stability conditions, establishing convexity of the aCI weight optimization on the simplex, and deriving a Bayes-risk-optimal decision threshold for the LRT under symmetric Gaussian likelihoods. A proof-of-concept agro-environmental decision-support application is considered, where heterogeneous data streams (IoT soil sensors, meteorological stations, and drone-derived vegetation indices) are fused to generate early-warning alarms for crop stress and to adapt irrigation and fertilization inputs. The proposed pipeline reduces predictive variance and sharpens posterior credible intervals (up to 34% narrower 95% intervals and 44% lower NLL/Brier score under heteroskedastic modeling), while a Bayesian uncertainty-aware controller achieves 14.2% lower water usage and 35.5% fewer false stress alarms compared to a rule-based strategy. The framework is mathematically grounded yet domain-independent, providing a probabilistic pipeline that propagates uncertainty from raw multimodal data to operational control actions, and can be transferred beyond agriculture to robotics, signal processing, and environmental monitoring applications.
Knights et al. (Tue,) studied this question.