💻 computer science

RAGE: A Tightly Coupled Radar-Aided Grip Estimator For Autonomous Race Cars

The paper introduces RAGE, a novel real-time estimator that utilizes standard IMU and RADAR sensors to accurately infer vehicle velocity, tire slip angles, and lateral forces for autonomous race cars, eliminating the need for costly specialized hardware while demonstrating high performance in both simulation and real-world testing.

Original authors: Davide Malvezzi, Nicola Musiu, Eugenio Mascaro, Francesco Iacovacci, Marko Bertogna

Published 2026-04-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Davide Malvezzi, Nicola Musiu, Eugenio Mascaro, Francesco Iacovacci, Marko Bertogna

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are driving a race car at 150 mph. You are pushing the car to its absolute limit, right on the edge of sliding off the track. The most important thing for the car's computer to know isn't just how fast it's going forward, but how much grip the tires actually have on the road right now.

If the tires lose grip (like stepping on a patch of ice), the car spins. If the computer knows exactly how much grip is left, it can adjust the steering and braking to keep the car safe and fast.

The problem? Measuring this "grip" usually requires expensive, fragile, high-tech sensors that cost thousands of dollars and are hard to install.

Enter RAGE (Radar-Aided Grip Estimator). Think of RAGE as a super-smart detective that figures out exactly how much grip the tires have using only the "standard" sensors already found on most modern cars: an IMU (like the accelerometer in your phone that knows when you tilt) and RADARs (like the ones in your car that warn you of obstacles).

Here is how RAGE works, broken down into simple concepts:

1. The "Ghost" Problem (Aliasing)

RADAR sensors are great at measuring speed, but they have a trick. Imagine a clock with only numbers 1 through 12. If the minute hand spins faster than the clock can count, it looks like it's spinning backward or stopping. This is called aliasing.

In a race car going 150 mph, the RADAR sees the speed "wrap around" and looks like the car is going much slower or even backward.

The RAGE Solution: RAGE acts like a time traveler. It looks at where the car should be based on its previous movement and "unwraps" the RADAR data to find the real speed, even if the sensor is confused. It's like realizing, "The clock says 1 o'clock, but I know I've been running for 2 hours, so it must actually be 3 o'clock."

2. The "Lag" Problem (Delay)

RADAR sensors take a tiny bit of time to process data. By the time the car gets the speed reading, the car has already moved. If the computer uses this old data to make a decision, it might steer too late.

The RAGE Solution: RAGE uses a technique called Moving Horizon Estimation (MHE). Imagine you are watching a movie, but you only see the last 10 seconds of the film at a time. Every time a new frame arrives, you rewind slightly, re-watch the last few seconds with the new information, and adjust your understanding of the plot. RAGE constantly rewinds its "mental movie" of the car's last 150 milliseconds to make sure the speed data matches the acceleration data perfectly, fixing the lag.

3. The "Magic Formula" (Learning the Tires)

Tires aren't static; they change based on heat, pressure, and how hard they are being pushed. A cold tire is slippery; a hot tire is grippy.

The RAGE Solution: Instead of using a fixed rulebook for how tires behave, RAGE learns on the fly. It uses a mathematical model (called the Pacejka Magic Formula) and constantly updates its own "rulebook" in real-time.
- Analogy: Imagine a chef tasting a soup while cooking. If it's too salty, they add water. If it's too bland, they add salt. RAGE is the chef tasting the "soup" of tire physics every 10 milliseconds, adjusting its internal recipe to match the current temperature and pressure of the tires.

4. The "Tight Couple" (Doing Everything at Once)

Usually, computers do things in a line: First, figure out the speed. Then, use that speed to figure out the slip angle. Then, use that to figure out the grip. If the first step is wrong, everything after it is wrong.

The RAGE Solution: RAGE does everything simultaneously. It estimates the speed, the slip angle, and the tire grip all in one giant, interconnected puzzle.
- Analogy: Think of a juggling act. If you try to juggle three balls one by one, you'll drop them. RAGE juggles all three balls (Speed, Slip, Grip) at the exact same time, keeping them all in the air. This makes the whole system much more stable and accurate.

The Results: Real-World Proof

The team tested this on a real autonomous race car (the EAV-24) at the Yas Marina F1 circuit in Abu Dhabi.

The Test: They drove at speeds up to 155 mph (70 m/s) and took corners with forces that would crush a normal car.
The Outcome: RAGE successfully tracked the car's movement and tire grip with incredible accuracy, matching the data from expensive, high-end optical sensors (which are usually the gold standard). It even figured out how the tires were heating up and cooling down during the race, adjusting its estimates automatically.

Why This Matters

This isn't just for race cars. If a self-driving car can figure out its own grip using cheap, standard RADAR sensors, it can:

Drive safer: It won't slide off the road in the rain because it knows exactly how slippery the road is.
Be cheaper: It doesn't need to buy expensive, custom sensors for every car.
Be scalable: This technology can be put into millions of cars, not just a few racing prototypes.

In short, RAGE turns a standard car's "eyes" (RADAR) and "inner ear" (IMU) into a super-sense that knows exactly how the tires are feeling, allowing autonomous cars to drive as fast and safely as a human professional racer.

1. Problem Statement

Accurate real-time estimation of vehicle-tire-road friction is critical for autonomous race cars to operate safely at their physical limits. Key quantities required for stability control and performance optimization include:

Lateral velocity ( $v_y$ ) and slip angles ( $\alpha$ ).
Lateral tire forces ( $F_y$ ).

Limitations of Current Approaches:

High-Cost Sensors: Traditional methods rely on expensive optical systems or high-precision inertial navigation systems, which are impractical for mass deployment.
Sensor Limitations: Existing low-cost alternatives (LiDAR, cameras) have drawbacks such as the need for textured surfaces, high computational loads for high frame rates, or failure in GNSS-denied environments.
RADAR Challenges: While RADAR is cost-effective and robust, it faces specific challenges in high-speed racing:
- Latency: Internal processing delays can cause inconsistencies between velocity corrections and acceleration measurements.
- Aliasing: Standard mmWave RADARs have a Nyquist velocity limit. At racing speeds (often exceeding this limit), Doppler measurements suffer from aliasing (wrapping), making raw data unusable without correction.
- Non-linearity: Linear approximations used in standard observers fail under the high lateral accelerations and non-linear tire dynamics of racing.

2. Methodology: The RAGE Framework

The authors propose RAGE (Radar-Aided Grip Estimator), a novel framework that fuses standard IMU and RADAR data to estimate vehicle states and tire parameters simultaneously.

Core Architecture

Estimator Type: Moving Horizon Estimation (MHE). Unlike standard Kalman Filters, MHE optimizes over a sliding time window, allowing it to handle delayed measurements and non-linear constraints effectively.
State Vector ( $X$ ): Includes longitudinal/lateral velocities ( $v_x, v_y$ ), yaw rate ( $r$ ), and IMU biases ( $b_x, b_y, b_r$ ).
Parameter Vector ( $P$ ): Includes Pacejka Magic Formula coefficients for front and rear axles ( $B, C, D, E, S_h, S_v$ ), which are estimated online to adapt to changing conditions.
Tightly Coupled Formulation: The system avoids sequential estimation (estimating velocity first, then forces). Instead, it jointly estimates states and tire model parameters to capture the strong interdependence between slip angles, lateral forces, and vehicle dynamics.

Key Technical Components

Motion Model:
- Uses a rigid-body model with curvilinear motion.
- Integrates IMU data (acceleration and yaw rate) using a forward Euler method.
- IMU Bias Initialization: Uses a Zero-Velocity Update (ZUPT) method when the car is stationary to calibrate biases.
RADAR Doppler Processing:
- De-aliasing: Addresses the Nyquist limit issue. The system predicts the expected Doppler velocity based on the current state estimate and uses this to determine the integer "wrap" count ( $n$ ) to recover the true velocity from the aliased measurement.
- Latency Compensation: The MHE formulation inserts states back in time corresponding to the actual RADAR capture timestamp, rather than the current time, to handle sensor processing delays (80–100 ms).
- Robustness: A Cauchy loss function is applied to RADAR residuals to mitigate the impact of outliers (e.g., ghost objects or moving dynamic obstacles).
Tire Dynamics (Pacejka Model):
- Uses the Pacejka Magic Formula to model the non-linear relationship between slip angle, vertical load, and lateral force.
- Online Fitting: The model coefficients are updated in real-time, allowing the system to adapt to thermal effects, tire pressure variations, and surface changes.
- Vertical Load Calculation: Accounts for static weight distribution, dynamic load transfer (due to longitudinal acceleration), and aerodynamic downforce.

3. Key Contributions

Novel Estimator: Introduction of RAGE, the first tightly coupled estimator for autonomous racing that simultaneously infers velocity, slip angles, and lateral forces using only standard IMU and RADAR sensors.
Solving RADAR Aliasing: Development of a practical de-aliasing algorithm adapted from meteorology, enabling the use of RADAR at speeds exceeding the sensor's Nyquist limit (up to 70 m/s).
Online Parameter Adaptation: The ability to estimate Pacejka tire model coefficients in real-time, removing the need for pre-calibrated, static tire models that fail under varying thermal and pressure conditions.
Handling Latency: A robust MHE formulation that explicitly accounts for asynchronous and delayed RADAR measurements without destabilizing the estimator.

4. Results and Validation

The method was validated through high-fidelity simulations and real-world experiments on the Unimore Racing Dallara EAV-24 at the Yas Marina F1 Circuit (Abu Dhabi Autonomous Racing League).

Simulation Results

Double-Lane Change (65 m/s): RAGE tracked lateral velocity with a max absolute error of 0.19 m/s and slip angles with 0.15° error, even during aggressive maneuvers.
Spin on Wet Asphalt: Successfully maintained state tracking during a 135° spin caused by loss of traction, demonstrating robustness in highly non-linear regimes.
Parameter Convergence: In a hot-lap simulation with randomized initial tire parameters, RAGE converged to accurate Pacejka coefficients within ~20 seconds, successfully tracking changing tire dynamics.
Force Estimation: Root Mean Square Error (RMSE) for lateral forces was < 500 N for both axles.

Real-World Experimental Results

High-Speed Performance: Validated on a full lap with speeds up to 70 m/s and lateral accelerations up to 28 m/s².
Correlation with Physics: The estimated tire cornering stiffness showed a clear inverse correlation with tire temperature and pressure (e.g., as rear tire temperature dropped, stiffness increased), confirming the physical validity of the online parameter estimation.
Spatial Awareness: Estimated stiffness variations were spatially correlated with track layout, showing constant values on straights and dynamic changes in corners.
Computational Efficiency: The system runs on a single CPU core (AMD EPYC) with an average optimization time of 2.287 ms, allowing for a 100 Hz update rate with significant performance margin.

5. Significance and Impact

Scalability: By relying on standard, low-cost sensors (IMU and RADAR) rather than specialized optical systems, RAGE offers a scalable solution for both autonomous racing and future production vehicles.
Safety and Performance: The ability to accurately estimate grip limits in real-time allows autonomous controllers to push vehicles closer to their physical limits safely, preventing loss of control.
Adaptability: The online adaptation of tire models makes the system resilient to environmental changes (rain, temperature) and tire degradation, addressing a major limitation of previous model-based approaches.
Benchmarking: This work provides a new benchmark for sensor fusion in high-speed autonomous driving, demonstrating that RADAR can be the primary source for lateral dynamics estimation when properly processed.

In conclusion, RAGE represents a significant step forward in autonomous vehicle state estimation, proving that tightly coupled, non-linear estimation with standard sensors can achieve the accuracy and robustness required for high-performance racing.