Development of a Hybrid Deep-Learning Neural Network Using a Square-Root Sigma-Point Kalman Filter for Estimating Vehicle Mass and Road Grade

Abstract

Development of a Hybrid Deep-Learning Neural Network Using a Square-Root Sigma-Point Kalman Filter for Estimating Vehicle Mass and Road Grade

Hou Tianyu, Kulik A.A.

Incoming article date: 16.12.2025

The article presents a hybrid neural network for estimating the mass of a car and the longitudinal/transverse slopes of a road, combining a square-root sigma-point Kalman filter and a neural network model based on a transformer encoder using cross-attention to the evaluation residuals. The proposed approach combines the physical interpretability of the filter with the high approximation capability of the neural network. To ensure implementation on embedded electronic control units, the model was simplified by converting knowledge into a compact network of long-term short-term memory. The results of experiments in various scenarios showed a reduction in the average error by more than 25% with a computational delay of less than 0.3 ms.

Keywords: vehicle condition assessment, road slope assessment, vehicle mass assessment, transformer neural network, cross-focus, adaptive filtering, knowledge distillation, square-root sigma-dot Kalman filter, intelligent vehicles, sensor fusion