Real-Time Mass and Axle Load Estimation in Multi-Axle Trucks Through Fusion of TPMS Pressure and Vision-Derived Tire Deformation

This paper develops a theoretical framework and a numerical implementation for real-time estimation of the gross mass of heavy vehicles using only on-board signals: tire inflation pressure from the TPMS and radial deformation inferred from a monocular chassis camera. Each wheel is modeled as a single-degree-of-freedom radial oscillator with pressure-dependent stiffness kr(P) and damping cr(P). The contact patch geometry follows a compressed-arc approximation that maps radial deformation δ to contact length L(δ) and area S(δ). Two independent force surrogates are constructed—Fk=kr(P)δ and Fq=q(P)S(δ), where q(P) denotes the mean contact pressure—and fused by an adaptive Kalman filter operating at 30 Hz to recover per-wheel loads and total mass. Tuning the fusion weight λ yields a relative mass estimation error below 5% across 0.001≤δ≤0.20 m, and the maximum observed error is 4.99%. Numerical experiments using fixed-step RK4 and embedded RK45 methods confirm the accuracy and real-time feasibility on commodity hardware (runtime <33 ms per step). Uncertainty analysis based on Latin hypercube sampling, the PRCC, and Sobol indices shows robustness to parameter perturbations (±5% inflation, ±10% stiffness, ±15% damping, ±1° camera pitch, ±2 kPa TPMS bias). Observability analysis supports identifiability under the tested regimes. The estimator delivers wheel and axle loads for on-board alerts, telematics, V2X pre-screening for road user charging and weigh-in-motion technology, and friction-aware control.