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Calibration-free IMU-based Relative Orientation Estimation under Dynamic Human Motion

Ruiyuan Li, Hassan Osman, Ajay Seth, Manon Kok

arXiv:2610.31156v1cs.ROcs.SYeess.SY

TL;DR

Existing magnetometer-free relative-orientation methods often require offline sensor-location calibration or have limited joint and motion coverage. This paper jointly estimates relative IMU orientation and sensor location with an EKF, achieving 2.61° overall relative orientation error on real OpenSense data, versus 10.40° and 7.43° for the reported baselines.

  • Problem

    Existing relative-orientation methods may require offline sensor-location calibration, assume specific joint types, or have limited motion coverage or real-data validation.

    Source: §I · p. 1

  • Method

    An EKF jointly estimates relative IMU orientation and sensor locations online, with low-pass filtering to mitigate real-signal outliers.

    Source: §IV · p. 3

  • Results

    2.61° overall relative orientation error for Alg.1, versus 10.40° for Weygers and 7.43° for Weygers-Mrk.

    Source: A. Relative orientation estimation… · p. 5

  • Takeaways & Limitations

    The method achieves accurate relative orientation on real IMU data across walking and complex tasks without offline sensor-location calibration.

    Source: A. Relative orientation estimation… · p. 5, §VII · p. 7

Abstract

from arXiv · show

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{\deg}, compared with 10.40{\deg} for a baseline using offline-estimated sensor locations and 7.43{\deg} 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.

I. INTRODUCTION

The paper targets magnetometer-free relative IMU orientation estimation without offline sensor-location calibration, while addressing limitations in prior methods’ joint assumptions, motion coverage, and validation. It estimates sensor locations online alongside relative orientation and models adjacent segments as connected by a 3D joint.

II. RELATED WORK

  • Prior relative-orientation methods relied on joint-type assumptions, offline calibration, or validation limited to simulation or walking, motivating evaluation across diverse human motions.Earlier approaches also included global-orientation anchoring or did not systematically address artifacts in real IMU measurements.Source: §I · p. 1, §II · p. 2

I. INTRODUCTION

  • The proposed approach jointly estimates relative sensor orientation and sensor locations online from acceleration and angular velocity, eliminating offline sensor-location calibration.The framework is intended for magnetometer-free estimation and is evaluated using real IMU measurements during diverse human motions.Source: §I · pp. 1–2

III. MODELING

  • The model treats two rigid body segments as connected by a 3D joint and estimates their relative sensor orientation using a connection constraint.Sensor locations are vectors from the joint center to each sensor, expressed in that sensor’s frame, and are estimated jointly with orientation.Source: §III · p. 2

A. Dynamic Model

The dynamic model propagates sensor orientation and treats sensor location as nearly constant. The measurement model uses the shared joint-center acceleration implied by the connected segments.

A. Dynamic Model

  • Sensor orientation dynamics use gyroscope measurements, while each sensor location is modeled as nearly constant.The orientation model includes zero-mean Gaussian gyroscope noise.Source: A. Dynamic Model · p. 2

B. Measurement Model

  • The connected-segment constraint equates joint-center acceleration computed from either sensor, using sensor acceleration, angular velocity, angular acceleration, and measurement-noise terms.Sensor acceleration is modeled from ideal specific force and accelerometer measurement noise.Source: B. Measurement Model · pp. 2–3

IV. METHOD

The EKF estimates relative orientation and sensor locations jointly, using the rigid-link measurement model. Before recursive updates, the method filters acceleration and gyroscope signals to reduce impact outliers and differentiation noise.

IV. METHOD

  • The EKF jointly estimates relative orientation and sensor-location vectors, deriving relative orientation from the estimated absolute sensor orientations.Sensor locations are modeled as approximately constant through their process-noise assumption.Source: §IV · p. 3
  • The EKF measurement update applies the joint-center acceleration constraint to update the joint state and covariance.The algorithm filters the input signals before recursive time and measurement updates, then outputs relative orientation and sensor-location estimates.Source: §IV · p. 3
  • A zero-phase fourth-order Butterworth low-pass filter is applied to acceleration to mitigate foot-strike transients that violate the EKF’s Gaussian measurement-noise assumption.The method also filters gyroscope measurements before five-point numerical differentiation to estimate angular acceleration.Source: §IV · p. 3

V. SYSTEMATIC SIMULATION STUDY

The simulation study evaluates how motion intensity relates to estimation accuracy and compares online sensor-location estimation with an adaptation using ground-truth locations.

V. SYSTEMATIC SIMULATION STUDY

  • The simulation compares Alg.1 with a [11] adaptation using ground-truth sensor locations to assess whether online location estimation degrades relative-orientation accuracy.The comparison uses the model described in Section III.Source: §V · p. 4
  • No low-pass filter is used in simulation because the simulated measurements approximately match the assumed Gaussian noise model.The study systematically evaluates estimation accuracy as a function of motion intensity.Source: §V · pp. 3–4

A. Simulation settings

The simulation study varied joint-center acceleration and relative angular velocity across 49 excitation scenarios. Each scenario comprised ten 50-second simulations at 100 Hz, with noisy IMU measurements and sensor-location vectors of fixed 200 mm magnitude.

A. Simulation settings

  • Relative angular-velocity excitation used seven levels from 0 to 3 rad/s, while sensor-location vectors had a fixed 200 mm magnitude and random directions.Initial orientations used three angles sampled from U(0, 2π).Source: A. Simulation settings · p. 4
  • Joint-center acceleration was generated as a 3D cubic spline scaled across seven levels from 0 to 10 m/s2.The passage lists levels 0, 0.05, 0.1, 0.5, 1, 2, and 10 m/s2.Source: A. Simulation settings · p. 4
  • Accelerometer and gyroscope signals included white Gaussian noise and sampled sensor biases.Noise standard deviations were 0.02 m/s2 and 0.2°/s; biases were sampled from U(−0.1, 0.1) m/s2 and U(−0.5, 0.5)°/s.Source: A. Simulation settings · p. 4
  • 490 simulations covered all 49 combinations of seven joint-center acceleration and seven relative-angular-velocity excitation levels.Each scenario contained 10 independent 50-second runs sampled at 100 Hz.Source: A. Simulation settings · p. 4

B. Evaluation settings and evaluation method

Evaluation measured relative-orientation accuracy and final sensor-location error, while motion intensity was characterized by joint-center acceleration and relative rotation. The filter used process-noise settings tied to the simulated gyroscope noise and nearly constant sensor locations.

B. Evaluation settings and evaluation method

  • Orientation accuracy was measured by RMSD angular distance from ground truth over each simulation’s final 10 seconds, and sensor-location error by Euclidean distance from ground truth at the final estimate.The final 10 seconds allowed time for convergence.Source: B. Evaluation settings and evaluation… · p. 4
  • Motion intensity was quantified using joint-center acceleration intensity Iajc and relative-rotation intensity Iω.The evaluation uses these two metrics to characterize system motion.Source: B. Evaluation settings and evaluation… · p. 4
  • The process covariance used simulated gyroscope noise for orientation and Σr = 10^-9I3 for nearly constant sensor locations.Weygers-GT used the same initial orientation and covariance as Alg. 1.Source: B. Evaluation settings and evaluation… · p. 4

C. Results

In simulation, Alg. 1’s orientation accuracy approached Weygers-GT as joint-center acceleration increased, while orientation and sensor-location errors were associated most strongly with different motion-intensity sources.

C. Results

  • At the three lowest joint-center intensity levels—0, 0.1, and 0.3 m/s2—both methods had large orientation errors because excitation was insufficient.Fig. 4 plots eq against Iajc and er1 against Iω using boxplots with interquartile ranges and median lines; red and blue markers identify the specified contrasting error regimes.Source: C. Results · p. 4, Figure 4 · p. 5
  • At Iajc = 1.5 m/s2, mean eq was 22.4° for Alg. 1 and 5.8° for Weygers-GT, while from 2.9 m/s2 onward both achieved approximately 5.4° or less.Fig. 3 also shows Alg. 1 mean eq falling to 2.5° at 5.9 m/s2 and 0.8° at 29.5 m/s2; online location estimation did not degrade orientation accuracy at sufficiently high Iajc.Source: Figure 3 · p. 4, C. Results · p. 4
  • Orientation error eq decreased as Iajc increased, while sensor-location error er1 decreased as Iω increased.For eq, R2 was 0.71 with Iajc versus 1.5 × 10^-2 with Iω; for er1, R2 was 0.90 with Iω versus 4.1 × 10^-5 with Iajc.Source: C. Results · p. 5, Figure 4 · p. 5

VI. EXPERIMENTS

The real-data evaluation used OpenSense lower-body IMU recordings during walking and complex tasks, with optical motion capture providing ground truth. Relative orientation was evaluated after a convergence window, alongside sensor-location error and motion-intensity measures.

VI. EXPERIMENTS

  • OpenSense data covered walking by subjects 02, 03, 04, and 07 and complex tasks by subjects 02, 03, and 04, using seven lower-body IMUs and synchronized 100 Hz IMU and Vicon recordings.Complex tasks included sitting, stair ascent and descent, side-stepping, and running; datasets were truncated to 600 seconds.Source: §VI · p. 5
  • Relative-orientation error was computed after a conservative 50-second convergence window, and sensor-location error was defined as the Euclidean distance from marker-based sensor locations.Marker-based locations used optical-marker centroids around each IMU and marker-based joint centers, then were time-averaged per dataset.Source: §VI · p. 5
  • The study quantified motion using joint-center acceleration and relative angular velocity, with joint-center acceleration approximated by twice differentiating marker-based joint-center locations.The Vicon ground-truth relative orientation was used to derive Iω.Source: §VI · p. 5
  • The low-pass filter cutoff was set to 6 Hz, and initial orientation used the first accelerometer sample for inclination with heading initialized to zero.The cutoff was selected as consistent with common human-gait filtering practices.Source: §VI · p. 5

A. Relative orientation estimation accuracy

Alg.1 achieves lower relative orientation error than both offline-calibrated and marker-location baselines. Across walking trials, greater joint-center acceleration coincides with lower orientation error.

A. Relative orientation estimation accuracy

  • 2.61° overall relative orientation error for Alg.1, versus 10.40° for Weygers and 7.43° for Weygers-Mrk.The overall mean is across joints, subjects, and motion types; Table I reports results after a 50 s convergence window.Source: A. Relative orientation estimation… · p. 5, Table I · p. 6
  • Alg.1’s 2.61° error is lower than Weygers-Mrk-LPF’s 3.09°, despite the latter using marker-based sensor locations.The marker-based locations were obtained through an offline procedure requiring an optical motion-capture system.Source: A. Relative orientation estimation… · pp. 5–6
  • Across walking trials, joint-center acceleration rises from 1.98 m/s2 at the hip to 5.21 m/s2 at the ankle as orientation error falls from 2.55° to 1.72°.The knee values are 3.88 m/s2 and 1.99°, respectively; every individual hip trial had lower acceleration and higher error than its ankle counterpart.Source: A. Relative orientation estimation… · p. 6

B. Effect of low-pass filtering

Low-pass filtering improves orientation and sensor-location estimates while suppressing foot-strike-related innovation spikes. Online location estimation has joint-dependent errors, with the knee’s hinge-axis component less observable.

B. Effect of low-pass filtering

  • Without LPF, foot-strike acceleration transients and differentiated angular-velocity noise produce periodic NIS spikes outside the expected χ2 range; Alg.1 suppresses them.Alg.1’s NIS remains mostly within the expected χ2 range.Source: B. Effect of low-pass filtering · p. 6
  • 2.61° overall orientation error for Alg.1, compared with 3.77° for Alg.1-NIS and 7.27° for Alg.1-SM.Fixed-threshold rejection may repeatedly reject valid measurements and require a recovery mechanism; state augmentation does not resolve the model inconsistency.Source: B. Effect of low-pass filtering · p. 6

C. Online sensor location estimation

  • Alg.1 reduces mean sensor-location error from 115 mm without LPF to 60 mm, versus 134 mm for Weygers’ fixed locations.The difference is most visible at the ankle, where the no-LPF and fixed-location errors both exceed 100 mm.Source: C. Online sensor location estimation · pp. 6–7
  • Mean sensor-location error is lowest at the ankle (50 mm walking, 47 mm complex tasks) and highest at the knee (about 71 mm for both).The knee’s hinge-like motion partly limits observability along the rotation axis; measuring only the perpendicular component gives 44 mm for walking and 41 mm for complex tasks.Source: Figure 6 · p. 6, C. Online sensor location estimation · p. 7
  • For the hip and ankle, errors are lower during complex tasks by 10.2 mm and 3.6 mm, respectively; the knee error is nearly unchanged at 70.9 versus 70.5 mm.Across the two 3D joints, the ankle has lower error and higher relative angular-velocity intensity than the hip in both motion types, consistent with the simulation pattern.Source: C. Online sensor location estimation · p. 7

D. Additional complex motion analysis

The complex-motion analysis relates orientation and sensor-location behavior to changing motion intensity. The conclusion reports overall orientation accuracy and identifies anatomical joint-angle estimation as future work.

D. Additional complex motion analysis

  • Orientation error remains large until sufficient joint-center acceleration appears; during sitting, near-zero acceleration makes the constraint uninformative and causes slow drift.The representative trial includes both low- and high-intensity intervals.Source: D. Additional complex motion analysis · p. 7
  • Orientation drift stops within seconds when sufficient joint-center acceleration resumes, suggesting recovery after low-intensity periods.Source: D. Additional complex motion analysis · p. 7
  • Sensor-location estimates settle as relative angular-velocity intensity increases, remain nearly unchanged at low intensity, and fluctuate modestly when intensity rises again.The method models sensor location as approximately constant while allowing small temporal variations; whether this flexibility improves orientation accuracy remains unresolved.Source: D. Additional complex motion analysis · p. 7

VII. CONCLUSION

  • 2.61° overall relative orientation error, 75% lower than the existing method using IMU-based offline sensor location calibration.The evaluation also covers walking and complex tasks.Source: §VII · pp. 7–8
  • Validation includes complex tasks, extending beyond the walking motions considered in previous studies.Source: §VII · p. 8
  • Future work will extend relative IMU orientation estimation to anatomical joint angles through automatic sensor-to-segment calibration.Source: §VII · p. 8
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