Radar-Inertial Odometry with Online Spatio-Temporal Calibration via Continuous-Time IMU Modeling

Vlaho-Josip Štironja; Luka Petrović; Juraj Peršić; Ivan Marković; Ivan Petrović

cs.ROMar 20, 2026

Radar-Inertial Odometry with Online Spatio-Temporal Calibration via Continuous-Time IMU Modeling

Authors: Vlaho-Josip Štironja, Luka Petrović, Juraj Peršić, Ivan Marković, Ivan Petrović

Organizations: University of Zagreb Faculty of Electrical Engineering and Computing, Laboratory for Autonomous Systems and Mobile Robotics (LAMOR), Unska 3, HR-10000, Zagreb, Croatia · Calirad d.o.o., Augusta Harambašića 4, HR-10000, Zagreb, Croatia

Abstract

Radar-Inertial Odometry (RIO) has emerged as a robust alternative to vision- and LiDAR-based odometry in challenging conditions such as low light, fog, featureless environments, or in adverse weather. However, many existing RIO approaches assume known radar-IMU extrinsic calibration or rely on sufficient motion excitation for online extrinsic estimation, while temporal misalignment between sensors is often neglected or treated independently. In this work, we present a RIO framework that performs joint online spatial and temporal calibration within a factor-graph optimization formulation, based on continuous-time modeling of inertial measurements using uniform cubic B-splines. The proposed continuous-time representation of acceleration and angular velocity accurately captures the asynchronous nature of radar-IMU measurements, enabling reliable convergence of both the temporal offset and extrinsic calibration parameters, without relying on scan matching, target tracking, or environment-specific assumptions.

Figures & tables

Fig. 1 : Temporal misalignment between discrete radar ego-velocity measurements and the continuous-time motion estimated via a uniform cubic B-spline fit to IMU acceleration signals.

Fig. 2 : Factor graph architecture employed in this work. The graph comprises an IMU factor ( $f_{IMU}$ ), a radar ego-velocity factor ( $f_{R}$ ), and a constant time-offset ( $f_{CT}$ ) and constant extrinsic calibration factors ( $f_{CE}$ ).

Sequence	Method	APE Mean		RPE Mean
		Trans. (m)	Rot. ( ∘ )	Trans. (m)	Rot. ( ∘ )
1	EKF-RIO	0.583	2.997	0.354	2.707
1	EKF-RIO-TC	0.333	1.907	0.175	2.412
	RIO-T	0.435	2.102	0.183	2.618
	LC-RIO	0.411	1.915	0.196	2.992
	LC-RIO-E	0.586	1.794	0.224	3.081

TABLE I : Quantitative comparison on the EKF-RIO-TC dataset [ 15 ] .

Sequence	Method	APE Mean		RPE Mean
		Trans. (m)	Rot. ( ∘ )	Trans. (m)	Rot. ( ∘ )
carried 1	EKF-RIO	0.995	5.553	0.134	0.857
carried 1	EKF-RIO-TC	0.922	5.102	0.139	0.798
	RIO-T	0.754	4.098	0.126	0.641
	LC-RIO	0.745	4.037	0.128	0.655
	LC-RIO-E	0.863	5.228	0.141	0.687

TABLE II : Quantitative comparison on the ICINS dataset [ 13 ] .

Sequence	Method	APE Mean		RPE Mean
		Trans. (m)	Rot. ( ∘ )	Trans. (m)	Rot. ( ∘ )
5	EKF-RIO	1.311	6.122	0.386	3.391
5	EKF-RIO ∗	0.255	1.643	0.122	2.409
	LC-RIO	0.713	2.812	0.287	3.584
	LC-RIO ∗	0.293	1.607	0.140	2.276
flight 2	EKF-RIO	0.100	1.938	0.176	0.888

TABLE III : Impact of online spatio-temporal calibration: performance of EKF-RIO and LC-RIO when re-initialized with extrinsic and temporal parameters estimated by LC-RIO-ET (denoted by ∗ ). Best results per column in bold.

Fig. 3 : Trajectory visualization of EKF-RIO with original and estimated parameters on Sequence 5 from EKF-RIO-TC dataset [ 15 ] .

Panel of Figure 7 — Fig. 4 : Temporal offset estimation results. (a) Convergence under various initial values. (b) Comparison of LC-RIO-ET, EKF-RIO-TC, and RIO-T.

Radar-Inertial Odometry

Radar-inertial odometry fuses radar measurements and inertial sensing to estimate a robot’s motion when other sensors are unreliable.

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Inertial Odometry Equivariant Filtering Radar-Inertial Odometry

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Radar-Inertial Odometry (RIO) based on the Extended Kalman Filter (EKF) relies on accurate extrinsic calibration between the radar and the Inertial Measurement Unit (IMU) and is sensitive to disturbances, as large linearization errors can degrade performance or even cause divergence. To address these limitations, this letter proposes an Equivariant Filter (EqF) for RIO based on a Lie group symmetry that geometrically couples navigation states and IMU biases, extending it to incorporate radar-IMU extrinsic calibration and multi-state constraint updates. This equivariant formulation inherently preserves consistency and enhances robustness, enabling reliable state estimation even under poor or completely wrong initialization of calibration states. Real-world experiments on two different Uncrewed Aerial Vehicles (UAVs) show that the proposed EqF-RIO achieves state-of-the-art accuracy under correct extrinsic calibration and offers improved convergence under large calibration errors, where the conventional EKF-RIO fails. Evaluation code is open-sourced.

Abstract

Radar-Inertial Odometry

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