Impact of Temporal Delay on Radar-Inertial Odometry

TL;DR

The paper addresses robust ego-motion estimation under adverse perceptual conditions by fusing radar and IMU data in a factor-graph framework. It introduces RIO-T, which online estimates a temporal offset $t_{\mathrm{O},k}$ between radar and IMU measurements through a three-factor model (IMU, radar ego-velocity, and constant time offset) and IMU preintegration, using known IMU–radar extrinsics. Key contributions include the integration of online temporal offset calibration, thorough experimental validation on real data, and analysis of offset convergence and its impact on localization accuracy, showing significant gains in dynamic scenarios. The work demonstrates that accounting for time delays in radar–inertial fusion yields improved accuracy and robustness, with potential for extending to extrinsic online calibration and richer temporal models, thereby enhancing autonomous navigation in challenging environments.

Abstract

Accurate ego-motion estimation is a critical component of any autonomous system. Conventional ego-motion sensors, such as cameras and LiDARs, may be compromised in adverse environmental conditions, such as fog, heavy rain, or dust. Automotive radars, known for their robustness to such conditions, present themselves as complementary sensors or a promising alternative within the ego-motion estimation frameworks. In this paper we propose a novel Radar-Inertial Odometry (RIO) system that integrates an automotive radar and an inertial measurement unit. The key contribution is the integration of online temporal delay calibration within the factor graph optimization framework that compensates for potential time offsets between radar and IMU measurements. To validate the proposed approach we have conducted thorough experimental analysis on real-world radar and IMU data. The results show that, even without scan matching or target tracking, integration of online temporal calibration significantly reduces localization error compared to systems that disregard time synchronization, thus highlighting the important role of, often neglected, accurate temporal alignment in radar-based sensor fusion systems for autonomous navigation.

Figures (6)

• Figure 1: Absolute trajectory error (m) with origin alignment on the Mocap difficult sequence from the IRS dataset irs, comparing the loosely coupled factor graph-based radar-inertial odometry without our proposed modification and the same approach with our proposed modification of the factor graph structure. The results highlight the positive effects of integrating online temporal calibration and emphasize the overall importance of accurate temporal calibration for improved odometry performance.
• Figure 2: An illustration of a radar-inertial odometry system with unsynchronized measurements. We estimate the temporal offset between radar measurements and IMU measurements and optimize it within the factor graph framework. Radar ego-velocity measurements (red) indicate the time at which radar data is represented, while the red dashed line marks radar sequence timestamps. IMU measurements are shown in grey.
• Figure 3: Proposed factor graph structure. The factor graph consists of the IMU factor ($f_{IMU}$), the radar ego-velocity factor ($f_{R}$), and constant time offset factor ($f_{CT}$).
• Figure 4: Convergence of the temporal offset in the Gym sequence from the IRS dataset using the proposed method. The radar measurements were artificially shifted forward in time in steps of 2.5 ms to check whether the proposed method converges correctly to the expected offset values.
• Figure 5: Convergence of the temporal offset in the Mocap difficult sequence from the IRS dataset using the proposed method. The radar measurements were artificially shifted by 112.15 ms to simulate the time delay of a radar of 100 ms. We tested our method over three iterations to evaluate its convergence ability even with large temporal offsets.