We propose a Beidou-augmented Sparse Variational GNSS/INS Combined System (BSV-GIIS) to tackle the difficulties of high-accuracy positioning in intelligent sugarcane agriculture, where thick vegetation and multipath interference reduce the effectiveness of traditional tightly coupled Kalman filter (TCKF) approaches. The system introduces a hierarchical sparse approximate message passing (HSAMP) framework, which reformulates the fusion problem into a two-layer variational inference process with adaptive sparsity constraints, thereby capturing the inherent noise sparsity in agricultural environments. At the global scale, a mixture of sparse Gaussians approximates the posterior state distribution, whereas the local scale improves estimates by modeling Beidou-specific residuals with heavy-tailed distributions. In addition, a compact hybrid Kalman-variational filter (LHKVF) processes inertial data by means of selective Mahalanobis gating, which permits effective outlier rejection. The 5 cm accuracy is based on median performance at nominal conditions, while RMS errors in dense canopy environments are above 8 cm. This shows that although the median error values are within the 5 cm range for open and partial canopies, the RMS errors increase to 8.3 cm in dense canopies, thus proving the limitation of sparse assumptions in dense foliage occlusions. This shows that although the system attains centimeter-level accuracy in nominal situations, there is a performance degradation in dense foliage occlusions. Implemented on a Xilinx Versal ACAP, BSV-GIIS shows effective handling of sparse matrix computations and precise coordination between IMU and GNSS data flows. Experimental outcomes establish its advantage in accuracy and processing speed, which renders it a feasible option for embedded systems with limited resources in precision agriculture.
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