Organizations: Delft Center for Systems and Control, Delft University of Technology, 2628 CD Delft, the Netherlands · Department of Biomechanical Engineering, Delft University of Technology, 2628 CD Delft, the Netherlands
Recent magnetometer-free inertial measurement unit (IMU) methods can reduce drift in joint motion estimation using rigid-body constraints, but they typically require pre-calibrated sensor locations, assumptions of specific joint models (e.g., hinge joints) or limited motion types, or an external reference for global orientation. Furthermore, challenges related to high-frequency impacts (e.g. at foot strikes during gait) and numerical differentiation of noisy measurements have not been explicitly addressed. We propose an extended Kalman filter that estimates relative IMU orientation and sensor location simultaneously, requiring neither offline sensor location calibration nor a global orientation anchor. A systematic simulation study shows that the quality of the relative orientation and the sensor location estimates depends on different motion-intensity sources: the joint center acceleration and the relative angular velocity, respectively. A low-pass filter (LPF) is used to mitigate real-signal outliers before applying the rigid-body constraint. When applied to the OpenSense dataset with real IMU measurements across four subjects with three lower-body joint types during walking and complex tasks including various motion types, the proposed method achieves an overall relative orientation error of 2.61°, compared with 10.40° for a baseline using offline-estimated sensor locations and 7.43° for a baseline using marker-derived sensor locations. These results show that the proposed calibration-free estimation framework handles real IMU data effectively and achieves accurate relative orientation without offline sensor location calibration.
Figures & tables
Fig. 2: Left: Graphical illustration of the relative orientation qS1S2 and sensor location riSi . Right: Example of a subject equipped with IMUs and markers in the OpenSense dataset [ 14 ] .
Fig. 3: Alg.1 vs. Weygers-GT orientation error eq . Small dots are individual simulations for different intensity levels and diamond markers show the mean at each Iajc level encoded by color. The dashed line indicates equal performance between the two methods. To illustrate the trend around Iajc= 1.5 m/s 2 , we additionally show the mean eq at Iajc= 0.6 and 2.4 m/s 2 as diamond markers, omitting individual simulations for clarity.
Fig. 4: Alg.1 errors vs. motion intensity in simulation for (a) eq vs. Iajc and (b) er1 vs. Iω . Boxes show interquartile ranges with median lines. Red markers denote low- eq /high- er1 simulations ( eq<5∘ , er1>100mm ), and blue markers denote low- er1 / high- eq simulations ( er1<0.5mm , eq>30∘ ). The star and diamond markers represent simulations P1 and P2 as two examples.
Walking ( nsubject =4)
Complex Tasks ( nsubject =3)
Method
riSi source
Hip
Knee
Ankle
Avg
Hip
Knee
Ankle
Avg
Overall
Alg.1
IMU (Online)
2.55
1.99
1.72
2.09
4.20
2.91
2.79
3.30
2.61
Weygers [ 11 ]
IMU (pre-cal. [ 15 ] )
5.36
11.03
7.40
7.93
19.32
6.95
14.85
13.71
10.40
Weygers-Mrk
Marker (pre-cal.)
5.69
4.70
4.69
5.03
12.31
8.71
10.86
10.63
7.43
Weygers-Mrk-LPF
Marker (pre-cal.)
2.82
2.63
2.20
2.55
4.29
3.88
3.29
3.82
3.09
Alg.1-no-LPF
IMU (Online)
4.71
3.42
5.22
4.45
11.24
6.87
12.01
10.04
6.85
TABLE I: Relative orientation error eq in degrees after a 50 s convergence window. Values are means across all subjects. Overall denotes the mean across all joints, subjects, and motion types. The smallest (best) value in each column is bold.
Fig. 5: NIS over a 12-second walking segment (Subject 03, right knee). The zoomed window shows approximately one gait cycle.
Fig. 6: Sensor location error eri averaged over sensors i=1,2 , left/right sides, and subjects, for each joint and for both walking and complex tasks. The cross-hatched region on the Alg.1 knee bar indicates the error of the observable perpendicular component as described by [ 24 ] .
Fig. 7: Subject 04, right hip, complex motion. (a) Relative orientation error over the full trial, with the shaded intervals shown in the zoomed views. (b) Magnitudes of the estimated sensor location over the full trial, with the same zoomed views. Gray curves show the intensities.
Attitude estimation based on inertial sensing requires measurements of local angular velocities and local gravity via gyroscopes and accelerometers. However, during the motion of a mobile system the inertial measurement unit (IMU) will be subject to additional accelerations which skews the measurement of local gravity. This effect gets amplified the further away the IMU is from the base of the system. Many attitude estimation filters, such as "Madgwick" or "Mahony", account for this by relying more on gyroscope integration for periods of high angular velocity. However, this approach is prone to accumulate long term error especially around the gravity vector. In this work we utilize the gyroscope measurements to compensate the additional accelerations induced by the motion of the system, i.e., centripetal- and tangential-accelerations. Additionally, we introduce a calibration method that estimates intrinsic IMU parameters such as axes misalignment, bias, scale, as well as the extrinsic base-to-IMU vector without the necessity for additional external equipment. Our evaluation in simulation as well as in the real-world shows that this method improves any attitude filter that relies on the direction of gravity. Furthermore we demonstrate the effectivenes on highly dynamic systems, and systems that are unable to put the IMU at the center of rotation, using our real-world spherical mobile mapping system.
Inertial odometry (IO) using only Inertial Measurement Units (IMUs) provides a lightweight solution for human motion tracking in augmented reality (AR) and wearable devices. Recent learning-based IO methods have improved the generalizability of inertial localization through large-scale pretraining on human motion datasets. However, these approaches remain prone to drift and noise because they do not explicitly capture human motion dynamics, especially on daily activity datasets such as Nymeria. In this work, we propose to ground inertial odometry in human kinematics through a learned IMU-inferred pose prior, which promotes physically consistent motion constraints. We integrate this pose prior into existing IO architectures and reduce positional drift by up to 36% on the challenging Nymeria dataset, which is 5x larger than datasets used in prior work. We further improve long-term performance with a sensor-fusion framework that incorporates auxiliary signals from lightweight sensors already available on commercial AR glasses, including magnetometers, barometers, and secondary IMUs. With this fusion strategy, positional drift is reduced by up to 42%, improving robustness and generalization across diverse motion conditions. Together, our results introduce a new paradigm for inertial and lightweight odometry by unifying human motion kinematics with multimodal sensing, setting a new benchmark for accurate and robust camera-less human tracking. Our website is available at https://spice-lab.org/projects/MARIO/.
This paper addresses the problem of estimating the relative pose (position and orientation) and velocity of a vehicle with respect to a moving target, where both are equipped with Inertial Measurement Units (IMUs), assuming the availability of relative position or bearing measurements. The body-target relative dynamics are formulated on SE2(3) and recast into a linear time-varying (LTV) model in the ambient space R15, on which a deterministic Riccati observer is designed. We analyze the uniform observability (UO) conditions required to guarantee global exponential convergence of the estimation error in the ambient space for both measurement cases. In the case of relative position measurements, UO requires only a persistence-of-excitation condition on the target acceleration, whereas for bearing measurements, additional conditions are required. Building on this, a nonlinear complementary filter on SO(3) is designed to provide a smooth estimate of the orientation component of the state with almost global asymptotic stability. Finally, simulation results are provided to validate the proposed solution.
∗I3S-CNRS, Nice-Sophia Antipolis, France · ∗∗Department of Computer Science and Engineering, Universit´e du Qu´ebec en Outaouais (UQO), QC J8X 3X7, Canada · ∗∗∗Institut Universitaire de France, Nice-Sophia Antipolis, France