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arxiv: 2604.07939 · v1 · submitted 2026-04-09 · 💻 cs.RO

RAGE-XY: RADAR-Aided Longitudinal and Lateral Forces Estimation For Autonomous Race Cars

Davide Malvezzi , Nicola Musiu , Eugenio Mascaro , Francesco Iacovacci , Marko Bertogna This is my paper

Pith reviewed 2026-05-10 17:53 UTC · model grok-4.3

classification 💻 cs.RO
keywords force estimationautonomous race carsradarIMUvehicle dynamicstricycle modelsensor calibrationlongitudinal and lateral forces
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The pith

RAGE-XY adds online radar calibration and a tricycle model to estimate both lateral and longitudinal forces from IMU and radar data alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents RAGE-XY as an extension of an earlier real-time estimation framework for autonomous race cars. The method infers vehicle velocity, tire slip angles, and tire forces using only standard onboard IMU and radar sensors. It improves the prior version by adding an online radar calibration step that corrects for misalignment and by replacing the single-track model with a tricycle approximation that now captures rear longitudinal forces as well as lateral dynamics. Validation in high-fidelity simulations and on the EAV-24 autonomous race car shows gains in accuracy and robustness for both force directions. If the extensions hold, control systems for high-speed autonomous vehicles can rely on richer, sensor-light estimates of the forces that actually act on the tires.

Core claim

RAGE-XY incorporates an online RADAR calibration module to improve lateral velocity estimation despite sensor misalignment and extends the vehicle model from single-track to tricycle, which enables estimation of rear longitudinal tire forces in addition to lateral dynamics, validated through high-fidelity simulations and real-world experiments on the EAV-24 autonomous race car demonstrating improved accuracy and robustness.

What carries the argument

The RAGE-XY framework that fuses IMU and radar measurements through a tricycle vehicle model plus an online radar calibration module to compute velocity, slip angles, and tire forces simultaneously.

If this is right

  • Rear longitudinal tire forces can be estimated in real time alongside lateral forces without extra sensors.
  • Lateral velocity estimates become more accurate when radar sensors experience misalignment.
  • The framework maintains real-time operation suitable for direct use in vehicle control loops.
  • Both simulation and physical experiments on a full-scale autonomous race car confirm the accuracy gains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same sensor-light approach could support force-aware planning in other high-performance ground vehicles.
  • Force estimates might feed directly into predictive models of tire wear or chassis stress.
  • Calibration routines developed here may transfer to additional radar or lidar units on the same platform.

Load-bearing premise

The tricycle model captures the vehicle's essential dynamics and the online calibration fully removes radar misalignment errors without adding new inaccuracies from unmodeled effects or sensor drift.

What would settle it

A side-by-side comparison on the EAV-24 showing that estimated lateral and longitudinal forces diverge substantially from independent reference measurements during high-speed cornering or braking maneuvers.

Figures

Figures reproduced from arXiv: 2604.07939 by Davide Malvezzi, Eugenio Mascaro, Francesco Iacovacci, Marko Bertogna, Nicola Musiu.

Figure 1
Figure 1. Figure 1: Unimore Racing’s Dallara EAV-24 during the 2024 Abu Dhabi [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Estimator overview. wear, and thermal effects; • a lightweight model of a limited-slip differential, allowing a more accurate representation of rear-axle force distri￾bution. III. PRELIMINARIES In this paper, matrices are written in bold uppercase letters (e.g. R), while vectors are written as bold lowercase letters (e.g. v). A rigid-body transformation from frame B to frame A is represented as (RA B, t A … view at source ↗
Figure 3
Figure 3. Figure 3: Schematic representation of the hybrid tricycle model. For lateral [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Single-wheel model of vehicle. significant overestimation of the lateral velocity, as part of the longitudinal component is erroneously projected onto the lateral direction. To compensate for calibration inaccuracies and potential misalignment caused by vibrations, a ROLEQ estimator [31] is employed to estimate online the current RADAR rotation during straight-line driving. Under these conditions, the vehi… view at source ↗
Figure 5
Figure 5. Figure 5: Simulated results of the online auto-calibration method during [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

In this work, we present RAGE-XY, an extended version of RAGE, a real-time estimation framework that simultaneously infers vehicle velocity, tire slip angles, and the forces acting on the vehicle using only standard onboard sensors such as IMUs and RADARs. Compared to the original formulation, the proposed method incorporates an online RADAR calibration module, improving the accuracy of lateral velocity estimation in the presence of sensor misalignment. Furthermore, we extend the underlying vehicle model from a single-track approximation to a tricycle model, enabling the estimation of rear longitudinal tire forces in addition to lateral dynamics. We validate the proposed approach through both high-fidelity simulations and real-world experiments conducted on the EAV-24 autonomous race car, demonstrating improved accuracy and robustness in estimating both lateral and longitudinal vehicle dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper presents RAGE-XY, an extension of the RAGE real-time estimation framework that infers vehicle velocity, tire slip angles, and tire forces using only IMUs and RADARs. It adds an online RADAR calibration module for improved lateral velocity estimation under misalignment and extends the vehicle model from single-track to tricycle to enable rear longitudinal force estimation. Validation occurs via high-fidelity simulations and real-world experiments on the EAV-24 autonomous race car, with claims of improved accuracy and robustness for both lateral and longitudinal dynamics.

Significance. If the accuracy claims are substantiated, this work would advance sensor-efficient vehicle state estimation for autonomous racing applications, where minimizing hardware while maintaining real-time performance is valuable. The practical focus on standard onboard sensors, the model extension for longitudinal forces, and the combination of simulation with real-vehicle testing are strengths that could support better control algorithms in high-speed scenarios.

major comments (1)
  1. [Real-world experiments] Real-world experiments section: The central claim of improved accuracy and robustness in estimating lateral and longitudinal forces is supported only by indirect metrics (velocity consistency, slip angle estimates, and comparisons to baseline estimators), as the system uses solely IMUs and RADARs with no tire force sensors or dynamometers for direct ground truth. This indirect validation leaves open the possibility that observed improvements stem from the observer structure rather than genuine enhancements from the tricycle model or calibration module, undermining the force-specific contribution.
minor comments (2)
  1. [Abstract] The abstract states 'improved accuracy' without any quantitative metrics or error reductions; adding brief numerical results (e.g., RMSE values from simulations) would make the summary more informative.
  2. [Methods] Notation for forces (lateral/longitudinal) and slip angles should be introduced with a clear table or list early in the methods to prevent ambiguity when reading the model equations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback regarding the validation approach in the real-world experiments. We address the comment in detail below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Real-world experiments] Real-world experiments section: The central claim of improved accuracy and robustness in estimating lateral and longitudinal forces is supported only by indirect metrics (velocity consistency, slip angle estimates, and comparisons to baseline estimators), as the system uses solely IMUs and RADARs with no tire force sensors or dynamometers for direct ground truth. This indirect validation leaves open the possibility that observed improvements stem from the observer structure rather than genuine enhancements from the tricycle model or calibration module, undermining the force-specific contribution.

    Authors: We acknowledge that direct tire force measurements are unavailable in the real-world experiments on the EAV-24, which is equipped solely with IMUs and RADARs and lacks tire force sensors or dynamometers. This is an inherent constraint of field testing with standard onboard sensors. Our validation relies on indirect metrics such as velocity consistency across independent sources, slip angle estimates, and comparative performance against baselines. To better attribute improvements specifically to the online RADAR calibration and tricycle model extension rather than the observer structure alone, we will revise the real-world experiments section to include an ablation analysis comparing the full RAGE-XY framework against ablated variants (without calibration and using the single-track model). We will also more explicitly cross-reference the high-fidelity simulation results, where direct force ground truth is available from the simulator and demonstrates clear benefits from the proposed extensions. These changes will clarify the force-specific contributions while maintaining the practical focus on sensor-efficient estimation. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain; explicit model and sensor-driven estimation

full rationale

The paper extends an existing estimation framework with an online RADAR calibration module and a tricycle vehicle model to estimate velocities, slip angles, and tire forces from IMUs and RADARs. The core derivation applies standard observer techniques to this explicit model rather than defining outputs in terms of themselves or renaming fitted parameters as predictions. Validation occurs via independent high-fidelity simulations and real-world EAV-24 experiments, with no load-bearing step reducing by construction to prior inputs or self-citations. The reference to the original RAGE work provides context for the extension but does not carry the new claims.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so specific free parameters, axioms, or invented entities cannot be extracted; the work appears to rest on standard vehicle-dynamics assumptions and sensor models from prior literature.

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