Robust Transformer-Enhanced Tire Force Estimation: Combining Model-Based Observer and Deep Learning
Bibliographic record
Abstract
This paper proposes a novel hybrid framework for estimating longitudinal tire forces by combining a model-based observer and a Transformer neural network architecture. A key advantage of the proposed approach is its independence from wheel torque measurements, which are commonly used in vehicle force estimation methods. The proposed framework first employs a model-based observer using the Pacejka tire model to generate preliminary estimates of longitudinal tire forces. These estimates are then refined by a neural network featuring an encoder-only Transformer architecture augmented with dilated convolutions, which effectively captures long-term temporal dependencies in sensor data while compensating for model inaccuracies. Additionally, our hybrid approach is able to estimate the longitudinal velocity and road friction coefficient, which are crucial for observer's preliminary force estimate in extreme road and driving conditions. Experimental validation on an electric Equinox vehicle under diverse driving scenarios-including highslip maneuvers on dry, wet, and icy roads-demonstrates the framework's superior performance compared to model-based and neural network-only approaches. The proposed method achieves robust estimation accuracy even under sensor faults (e.g., biased acceleration signals) and harsh driving conditions, indicating its potential for enhancing vehicle safety systems such as traction and stability control.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".