Radar-Inertial Online Temporal and Spatio-Temporal Calibration

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

Last updated: 2026-05-23

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.

Three recent lines are useful. EKF-RIO-TC estimates the radar-IMU time offset online inside an EKF radar-inertial odometry framework. RIO-T estimates a temporal offset state in a factor graph with IMU and radar ego-velocity factors. LC-RIO-ET extends the hardening pattern to joint online extrinsic and temporal calibration with continuous-time IMU modeling.

The production lesson is broader than timestamps: hardware triggering helps, but it does not prove that radar measurements, IMU states, and radar-IMU extrinsics are mutually consistent. Online calibration should be treated as a monitored health and estimation function, not only an offline setup step.

What It Adds

• Treats temporal offset as an estimated state, not a fixed assumption.
• Treats radar-IMU extrinsics as estimated or monitored states when the method supports spatio-temporal calibration.
• 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.
• Uses continuous-time inertial models in LC-RIO-ET so radar factors can query acceleration and angular velocity at arbitrary measurement times.
• Demonstrates that online temporal calibration can reduce odometry error even without radar scan matching or target tracking.
• Provides public code for EKF-RIO-TC; LC-RIO-ET has a public project/repository shell, but the repository states code will be released after review.

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

Temporal 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

Spatio-temporal factor-graph abstraction:

X* = arg min_X
      sum || r_imu ||^2
    + sum rho(|| r_radar_velocity(T_RI, delta_t_RI) ||^2)
    + sum || r_constant_time_offset ||^2
    + sum || r_constant_extrinsic ||^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. LC-RIO-ET instead fits uniform cubic B-splines to raw acceleration and angular velocity over a sliding window, then evaluates the inertial signal at radar measurement times so temporal and extrinsic parameters can be optimized together.

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.

Spatial extrinsics add more observability requirements:

• yaw and lateral velocity excitation for radar mounting yaw,
• pitch/roll and vertical motion where the radar provides useful elevation structure,
• enough static radar returns across varied azimuth/elevation angles,
• repeated maneuvers that separate time delay from lever-arm error.

If the vehicle only drives slowly and straight, an online estimator can appear stable while converging to a biased offset or extrinsic.

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. LC-RIO-ET reports comparisons on the EKF-RIO-TC and ICINS datasets, with the strongest gains on unsynchronized sequences where joint extrinsic and temporal calibration can correct downstream radar-inertial estimators.

Integration Readiness

The EKF-RIO-TC implementation is public and directly useful for radar-IMU timing studies. LC-RIO-ET is currently better treated as primary-source method evidence because its GitHub repository says the implementation will be released after review.

For production stacks, temporal and extrinsic 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, calibration-bay replay, and runtime alarms if estimated offsets or extrinsics 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.
• Joint temporal/extrinsic estimation can converge to plausible but wrong parameters under weak motion excitation.
• Radar ego-velocity still assumes enough static returns.
• Factor-graph or EKF tuning can overfit one radar model or motion profile.
• A public repository shell is not the same as reusable code; check release status before planning implementation work around LC-RIO-ET.

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
• LC-RIO-ET project page: https://unizgfer-lamor.github.io/lc-rio-et/
• LC-RIO-ET arXiv paper: https://arxiv.org/abs/2603.19958
• LC-RIO-ET repository shell: https://github.com/StironjaVlaho/LC-RIO-ET
• Classic camera-IMU online temporal calibration context: https://journals.sagepub.com/doi/pdf/10.1177/0278364913515286