Radar-Inertial Online Temporal Calibration

Related docs: radar-inertial odometry, 4D imaging radar RIO and SLAM, radar-LiDAR-inertial fusion, sensor calibration and time synchronization, and robust multi-sensor localization.

Last updated: 2026-05-09

Executive Summary

Radar-inertial odometry is unusually sensitive to time alignment because radar Doppler measures velocity at the radar measurement time while the IMU propagates a high-rate trajectory. A few tens of milliseconds of radar-IMU offset can turn into biased velocity and pose updates during turns, acceleration, braking, and vibration.

Two recent lines are useful: EKF-RIO-TC estimates the radar-IMU time offset online inside an EKF radar-inertial odometry framework, and RIO-T estimates a temporal offset state in a factor graph with IMU and radar ego-velocity factors. Both highlight the same production lesson: hardware triggering helps, but it does not prove that radar measurements and IMU states are temporally aligned.

What It Adds

• Treats temporal offset as an estimated state, not a fixed assumption.
• Uses radar ego-velocity from a single scan as the measurement affected by time offset.
• Aligns radar and IMU updates to a common time stream.
• Demonstrates that online temporal calibration can reduce odometry error even without radar scan matching or target tracking.
• Provides public code for the EKF-RIO-TC variant.

Sensor and Factor Model

Sensor suite:

• Doppler-capable radar or 4D radar.
• IMU.
• Optional ground truth for calibration validation.

EKF-style abstraction:

x = [R, p, v, b_g, b_a, delta_t_RI]
z_radar_velocity(t_r) = h(x(t_r + delta_t_RI)) + noise

Factor-graph abstraction:

X* = arg min_X
      sum || r_imu ||^2
    + sum || r_radar_velocity(delta_t_RI) ||^2
    + sum || r_constant_time_offset ||^2

RIO-T adjusts the radar ego-velocity factor using recent IMU acceleration after bias and gravity correction, assuming locally constant acceleration around the relevant interval.

Observability and Motion Requirements

Temporal offset is easiest to observe when motion changes quickly:

• acceleration and braking,
• turns and yaw-rate changes,
• vibration or aggressive platform motion,
• radar velocity discrepancy that changes with offset.

Smooth constant-velocity motion can make the offset weakly observable. Calibration validation should therefore include intentional excitation rather than only straight, slow driving.

Dynamic and Degraded Scenes

Temporal calibration does not solve radar outliers. It should be combined with:

• static-return selection for Doppler ego-velocity,
• dynamic-object rejection,
• multipath gating,
• radar health metrics,
• IMU saturation checks.

The benefit is strongest in adverse weather or GNSS-denied environments where radar-inertial odometry becomes a primary fallback and time misalignment cannot be hidden by stronger LiDAR/camera/map factors.

Evaluation Guidance

Track:

• ATE/RPE with and without estimated time offset.
• Estimated offset convergence time.
• Sensitivity to injected artificial delays.
• Velocity RMSE during acceleration and turning.
• Radar ego-velocity residual before and after compensation.
• Robustness under hardware triggering, software timestamping, and replayed bags.

EKF-RIO-TC reports evaluation on simulated and real-world datasets, including a self-collected seven-sequence radar/IMU dataset with OptiTrack ground truth, plus ICINS2021 and ColoRadar. RIO-T reports real-world radar/IMU experiments focused on temporal delay impact.

Integration Readiness

The EKF-RIO-TC implementation is public and directly useful for radar-IMU timing studies. For production stacks, temporal calibration should be one part of a larger synchronization strategy: PTP/PPS where possible, driver timestamp audits, bag replay tests, temperature and boot-cycle checks, and runtime alarms if estimated offsets move outside calibrated bounds.

Limitations

• Online offset estimation needs excitation.
• A constant time offset model may be insufficient for variable driver latency or clock drift.
• Time calibration cannot compensate bad radar extrinsics.
• Radar ego-velocity still assumes enough static returns.
• Factor-graph or EKF tuning can overfit one radar model or motion profile.

Sources

• EKF-RIO-TC arXiv paper: https://arxiv.org/abs/2502.00661
• EKF-RIO-TC repository: https://github.com/spearwin/EKF-RIO-TC
• RIO-T project page: https://rio-online-t.github.io/
• RIO-T paper PDF: https://lamor.fer.hr/images/50050805/Impact_of_Temporal_Delay_on_Radar_Inertial_Odometry.pdf
• Classic camera-IMU online temporal calibration context: https://journals.sagepub.com/doi/pdf/10.1177/0278364913515286