Selective orientation correction lowers VIO error without full-state UKF backend cost

A visual-inertial odometry backend that applied unscented inference only to orientation correction produced lower global trajectory errors than a conventional error-state Kalman filter in a controlled comparison, while its measured estimator-processing time remained close to the error-state baseline. The study tested three recursive architectures: an error-state Kalman filter, or ESKF; a Full UKF that propagated 31 sigma points across 15 local uncertainty dimensions; and a Hybrid ESKF–UKF that confined unscented processing to a nine-point quaternion orientation update. Across five EuRoC MAV Machine Hall sequences, the Hybrid recorded mean translational absolute trajectory error, ATE, of 0.123 metres and rotational ATE of 1.076 degrees, compared with 0.569 metres and 4.042 degrees for the ESKF and 0.140 metres and 3.155 degrees for the Full UKF. These controlled results used identical inertial measurements and paired, ground-truth-derived visual observations, isolating the behavior of the implemented backends rather than comparing complete navigation systems.

Visual-inertial odometry combines camera data with inertial measurements to estimate motion where satellite navigation may be unavailable, including indoors, in forests and among buildings. The three estimators represented the same 15-variable navigation state: orientation, position, velocity, gyroscope bias and accelerometer bias. The ESKF propagated uncertainty with first-order error-state equations, whereas the Full UKF used a scaled unscented transform to propagate 31 sigma points through nonlinear motion. The Hybrid retained the ESKF backbone for inertial propagation, velocity, position and visual-position correction, but maintained a separate four-dimensional quaternion-coordinate covariance and nine sigma points for visual-orientation correction. Because the quaternion covariance was not merged with the 15-dimensional ESKF covariance, the architecture did not perform complete fusion of two uncertainty models: it transferred a corrected nominal orientation while preserving ESKF-based translational estimation.

Global and local accuracy produced different winners. Over 30 paired trials on each EuRoC Machine Hall sequence, the Hybrid had the lowest translational ATE on four of five sequences and the lowest rotational ATE on all five. The Full UKF, however, had the lowest one-second translational relative pose error, RPE, on all five, while the ESKF had the lowest one-second rotational RPE on all five. ATE measures disagreement over an entire trajectory after one global rigid alignment and therefore captures accumulated deformation and drift; RPE measures relative-motion consistency over a one-second interval. The result shows that the estimator with the most globally accurate path was not necessarily the one with the sharpest short-term rotational motion. A matched Hybrid-LinearOri ablation used the same Hybrid backbone, observations, seeds and positional correction but replaced the unscented orientation branch with a linearized one. The Hybrid had lower translational ATE, rotational ATE and translational RPE on every EuRoC sequence, while the linearized version retained an advantage in rotational RPE.

Cross-dataset testing qualified the EuRoC result. The same estimator parameters were transferred without retuning to three TUM VI room sequences, with 30 paired trials per sequence. All 360 requested TUM VI runs completed, as did all 600 controlled EuRoC runs. The Hybrid achieved the lowest translational ATE on TUM VI room1 and room3, while the Full UKF led on room5. Rotational and short-horizon relative-motion results did not follow a consistent ordering across the three sequences. Across all eight controlled EuRoC and TUM VI sequences, the Hybrid had the lowest translational ATE in six. The study retained estimator failures as recorded outcomes rather than replacing them with reference states, although none occurred in these controlled benchmarks, and it reported means and sample standard deviations without applying inferential significance tests.

A second experiment replaced reference-derived observations with poses calculated by a common lightweight stereo visual-odometry frontend. The pipeline synchronized and rectified stereo images, extracted up to 2,000 ORB features per rectified image, matched them by Hamming distance, triangulated accepted correspondences and estimated relative motion with PnP-RANSAC. It contained no bundle adjustment, keyframe optimization, loop closure or global pose graph, and failed motion updates were not replaced with ground truth. All four estimators received the same image-derived observations. On EuRoC, the Hybrid had the lowest translational ATE and translational one-second RPE on all five sequences, and the lowest rotational ATE on four. Its translational ATE ranged from 3.726 to 4.297 metres, substantially above its controlled results, while the ESKF ranged from 4.505 to 5.453 metres and the Full UKF from 4.497 to 5.278 metres. Diagnostics showed that this comparison did not imply accurate visual observations: median PnP inlier ratios were 0.880–0.896, yet median frame-to-frame translation-direction errors remained 21.7–23.8 degrees.

The stereo results on TUM VI produced the lowest translational and rotational ATE for the Hybrid on all three room sequences, but exposed large orientation errors shared by every architecture. Depending on the estimator and sequence, rotational ATE ranged from about 73 to 141 degrees. The Hybrid’s translational one-second RPE was lowest on room3 and room5, yet it was not lowest for rotational RPE on any of the three sequences. These large values mean the TUM VI image experiment should be interpreted as a comparison of how the backends respond to a common, imperfect observation stream, not as evidence that any estimator achieved high absolute orientation accuracy. The discrepancy between controlled and image-derived results is central to the study: backend differences remained detectable with real images, but each final trajectory also reflected errors accumulated by the sequential visual frontend.

Two sensitivity studies separated observation quality from the confidence assigned to observations. In the first, injected position noise ranged from 0.075 to 0.30 metres and orientation noise from 0.25 to 1.00 degree, while estimator-assumed uncertainty remained fixed; all 5,400 runs completed. Among 45 sequence-noise conditions, the Hybrid had the lowest translational ATE in 31 and the lowest rotational ATE in all 45. The Full UKF led translational RPE in 30 conditions, and the ESKF led rotational RPE in 29. Across the tested position-noise range, the Hybrid’s mean translational RPE rose from approximately 0.072 to 0.226 metres; across the orientation-noise range, its mean rotational RPE increased from about 0.757 to 2.485 degrees. In the complementary analysis, stereo observations were held fixed while the estimators’ assumed position and orientation uncertainties were varied. The Hybrid then had the lowest translational ATE in 44 of 45 conditions and the lowest translational RPE in all 45, while rotational outcomes were more evenly divided.

Dedicated timing measurements showed the principal computational distinction among the backends. Across 1,346,350 measured updates per estimator, mean processing time was 0.005700 milliseconds for the ESKF, 0.017855 milliseconds for the Full UKF, 0.005533 milliseconds for Hybrid-LinearOri and 0.005371 milliseconds for the Hybrid. The Full UKF therefore required about 3.32 times the Hybrid’s mean backend time. At the 99th percentile, the respective times were 0.0230, 0.0647, 0.0215 and 0.0207 milliseconds; the Hybrid also had the lowest 95th-percentile time, at 0.007646 milliseconds, and the lowest mean. The timing pattern was consistent with the architectures: full-state unscented propagation required 31 points, whereas the Hybrid used nine points only during orientation correction. However, the measurements covered estimator backends, not image loading, feature extraction, stereo matching, triangulation, PnP-RANSAC, file operations or logging. They did not establish end-to-end latency, processor or memory demand, energy use, hard-real-time behavior or feasibility on an embedded UAV computer.

The findings support a targeted rather than universal advantage for nonlinear filtering. Within the tested implementations, observations and sequences, selective unscented orientation correction was associated with lower accumulated trajectory error without the typical backend cost of full-state sigma-point propagation. The benefit remained conditional on the metric, sequence and visual-observation quality. The Hybrid was not uniformly more accurate, and the ablation compared complete correction stages that also differed in covariance treatment, rather than isolating the unscented transform alone. The study used selected indoor EuRoC and TUM VI sequences, Gaussian perturbations, fixed covariance settings and a lightweight visual frontend. Outdoor flight, aggressive motion, illumination changes, motion blur, visually degraded scenes, non-Gaussian uncertainty, advanced frontends and onboard hardware remained untested. The supported conclusion is that selective unscented processing can improve global trajectory accuracy in these backends while avoiding the measured mean backend cost of full-state propagation, not that the Hybrid is a universally superior substitute for error-state or full-state filtering.

Subject of Research: Accuracy and estimator-backend processing trade-offs among ESKF, Full UKF and hybrid ESKF–UKF visual-inertial estimators

Article Title: Accuracy-efficiency trade-offs in visual-inertial odometry backends: Comparative evaluation of ESKF, UKF, and hybrid ESKF-UKF using real stereo-inertial data

Article References: Nigusie, A. T., Lin, B., & Teshome, F. B. (2026). Accuracy-efficiency trade-offs in visual-inertial odometry backends: Comparative evaluation of ESKF, UKF, and hybrid ESKF-UKF using real stereo-inertial data. Results in Engineering, 32, Article 113487. https://doi.org/10.1016/j.rineng.2026.113487

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113487

Keywords: visual-inertial odometry, error-state Kalman filter, unscented Kalman filter, hybrid filtering, trajectory accuracy, sigma-point propagation, stereo vision, robot navigation, EuRoC MAV, TUM VI, Accuracy-efficiency, trade-offs