How Are Visual-Inertial Odometry Errors Affected By Microsecond Timing Errors?

1. DAISCH Engineer’s Core Viewpoint

As a senior engineer at DAISCH (a world leading manufacturer of Inertial Measurement Unit (IMU)), I am often asked a seemingly extreme question, “Do microsecond timing errors of synchronization really have a practical impact on a Visual-Inertial Odometry (VIO) system?”

My answer is: Absolutely right. Especially in the high-speed or high-dynamics motion scenario, not only do these timing errors in microsecond-level have effects on the results, but also they may create significant and even systematic deviations in the pose estimation, which severely undermines the accuracy and robustness of the VIO system.

The list of core ideas is as follows:

The principle sensor synchronization on time is that the exact timestamp is attached to individual points of data from different sensors (such as IMU-camera fusion) under the same time frame. When the timing error Δt happens in microseconds time, this timing error gets “amplified” with the velocity v and angular velocity ω in high speed, which directly translates into position and attitude errors. This process is not a simple linear accumulation, but is propagated and coupled by geometric limitations by IMU pre integration and visual reprojection during the optimization process, eventually causing the trajectory drift.

The underlying geometric principle may be approximated as an intuitive way of saying that the non-coherent image was obtained is a snapshot of the system (the location of the point P_A, the time A), but because of the very short delay from the physical channel (i.e., the inductive coupling path), this snapshot (the point P_A , the time A) was “taken” at a later time A’, so small in the following time domain (the time delay Δt). In that instant, because of high speed motion, position and attitude of the carrier have already changed significantly. This mismatch causes the corruption of the basic data association on which VIO algorithms rely.

2. Timing Errors: A Problem from Macro to Micro

In a VIO system, a camera provides absolute spatial references (in terms of feature points) at a relative low frequency (at 30Hz for instance), whereas an IMU provides the increment of the motion (angular velocity and acceleration) at a high frequency (at 200Hz to 1000Hz). The key to VIO algorithms is the close integration of these two complementary sources of data. The key to this fusion is the high level of synchronization with respect to time^{1 2}.

2.1 Sources of Timing Error

The timing error Δt may come from several different parts of the system, from the hardware to the software, each one potentially causing microsecond and even millisecond delays or offset:

• Hardware Latency:
  • Internal Sensor Delay: The amount of time from the sensing of a physical quantity (such as a motion) to the conversion of the physical quantity into a digital quantity and a timestamp of the digital quantity. There are processing delays in this process of millisecond order³. For example, the level of internal timing control of the ADIS1657x series IMUs already gets to the nanosecond level.
  • Transmission Delay: Time, in which data takes in order to send to the processor through the buses ( such as SPI/I2C)
  • Trigger Delay: This is when using a hardware trigger signal, such as PPS pulse to achieve synchronization between different sensors, the signal transmission delay of the main circuit board.
• Software Latency:
  • Driver-Level Delay: Time delay between receiving the data on the user space application from the interrupt received by the OS kernels hardware device.
  • System Scheduling Delay: Uncertainty in the scheduling part of the operating system leads to the jitter of data processing.
  • The accuracy of software timestamps is far from the hardware timestamps and middleware such as ROS can add huge errors via software synchronization methods⁴.
• Clock Drift:
  • Different sensors use independent crystal oscillators, the frequency of which can be influenced slightly by a number of factors, such as temperature and voltage, meaning that their timestamps start to drift slightly with time^{5 6}. Although the modern IMUs systems can calibrate their local clocks using an external PPS signal (e.g. from GNSS), to achieve time accuracy down to the microseconds, some errors remain^{7
    8}.

Many of the high-end IMU systems, with the help of the hardware timestamping and precise trigger mechanism, can already control the accuracy of synchronization to the microsecond or even sub-microsecond⁹. For example, some systems have synchronisation accuracies of less than 2µs. However, even so, the leftover microsecond-level unaccuracy is under certain conditions still not negligible.

3. The Geometrical Effect of Microseconds Sensor Errors on VIO

In order to truly begin to understand the effect of these microsecond errors we need to look into the underlying geometry model. The fundamental effect occurs in two main region: IMU Pre-integration & Visual Reprojection Constraints.

3.1 Influence on IMU Pre-integration

IMU pre-integration In this method, all the IMU measurements that occur in the time between two consecutive camera frames are integrated to compute the relative pose transformation in the time between frames.

Ideal Case (No Timing Error):

IMU measurements (angular velocity, ω_m and acceleration a_m) are perfectly recorded at the instant t_m. In order to obtain the pose transformation from t_k to t_{k+1} this can be achieved through the integration of these measurements.

Case with Timing Error Δt:

Assume that the IMU timestamps have a constant offset Δt with respect to the camera timestamps (IMU timestamp = True timestamp + Δt). This means that the actual measurements of the IMU we integrate actually belong to a “shifted” time window.

Geometric Impact Analysis:

Consider a case of high speed rotation. Let the carrier’s angular velocity at true time t be ω(t).

• The system takes the IMU measurement omega ω(t_m) at time t_m.
• But due to the timing error Δt this measurement actually corresponds to the motion state at time t_m - Δt in the time frame of the camera.
• The VIO algorithm, however, wrongly assumes that the ω(t_m) occurred at time t_m and uses it to propagate the attitude.

When the angular velocity is changing at a high rate (high angular acceleration), it will be true that the angular velocities, ω(t_m) and ω(t_m - Δt) will be appreciably different. While this difference is miniscule when working with a single measurement, it adds up quickly when dealing with high frequency integration (e.g. 1000Hz).

A Simplified Geometric Model:

Assume that in time interval Δt, the angular velocity varies linearly, therefore,  ω(t) = ω_0 + αt where α is the angular acceleration.

• True angle increment: ∫[t, t+Δt] ω(τ) dτ
• As a result of the error in the timestamp, the algorithm acted with the value ω(t+Δt) for a duration Δt, and assumes that it had been acting for a time of Δt. Thus, the error in angle is roughly proportional to α * (Δt)^2.
• More directly the position error e can be approximated as e ≈ v * Δt¹⁰. By way of example, if a drone were to fly around at 30 meters per second (108km/h), a simple error in timing of only 100 microseconds (µs) would result in a direct error in position of 30 m/s * 100 * 10^-6 s = 3 mm. This mistake is injected directly to the next optimization process.

The following table compares the principles of the effects of timing error to the IMU pre-integration with different motion states as follows:

3.2 Effect on Visual Reprojection Constraints

The main point in VIO is reducing the “reprojection error” in a non-linear optimization process. Reprojection error is the distance in pixel between the 3D map point again projected on an image aspect (based on the current pose guess) and the actual observation of this point for the current images.

Geometric Impact Analysis:

1. Incorrect Pose Prior: Ultimately the errored IMU pre-integration result is used by the optimizer as the prior in the pose estimation. As mentioned this prior itself is “skewed.”
2. Erroneous Association of Feature Points and Pose: Assume that the exact time at which a camera takes photo of image I_k is t_k. Due to the time errorherent error, the system may register the time as t'_k = t_k + Δt.
   • The VIO algorithm is an algorithm which associates the feature point observations in image I_k to the pose P(t'_k) at time t'_k.
   • However, the image I_k is the reflection of the real world at time t_k. At high velocity of motion  P(t'_k) and P(t_k) are already significantly different.
   • Geometric Scenario: Suppose a car traveling at a high velocity of motion features a utility pole on the road, filming.
     • At time t_k, the pole is a point A in the image.
     • After Δt, at time t'_k, the car has moved forward by v*Δt, and possibly rotated slightly by ω*Δt. If it were to take another picture then, the pole would appear at point B in the picture.
     • The VIO algorithm commits the mistake of tying together the observation contained in time t_k (pole at A) with the pose contained in time t'_k. So this is equivalent to the statement to the optimizer which says: “When I was at position P(t'_k), I saw the pole at image point A”, which is contrary to the reality of geometrical optics.
3. Optimization does not Work or Converge to a Wrong Result:
   • Data fundamentals as a whole creates a challenging situation for the optimizer to compute a smaller reprojection error.
   • It may attempt to change the position of the cameras or 3D points to ignore this wrong constraint by force.
   • The resultant outcome is that the entire trajectory and the point cloud of the maps is “warped” to account for this systematic time offset causing the final estimated pose to become significantly drifted¹².

The following table compares the principles of the impact of timing errors on visual constraints:

4. Conclusion and Outlook

To summarize the information presented in the article, the microsecond-level timing errors in the VIO systems are far from being a negligible detail. They introduce systematic errors that are correlated with the motion state (in particular, the velocity and angular velocity) through the distortion of the basic data of the two core modules: IMU pre-integration and visible reprojection. In static or low-speed situations, this impact may be masked or to some extent corrected in the optimization capabilities of the VIO algorithm. However, in high-speed, high-dynamics applications (such as drones, autonomous vehicles, and fast-moving AR/VR headsets) the errors in the microseconds are amplified greatly and become a primary limiting characteristic that will limit the system accuracy.

This is the reason why a high-end IMU manufacturer such as DAISCH is dedicated not only to improve the uncorrected (raw) measurement accuracy of our sensors (e.g. noise and bias instability) but also to invest heavily in R&D activities to make the timing performance optimized. We offer hardware-level timestamping capabilities, low-latency data output capabilities and precise synchronous trigger interfaces. We do this because we have a deep understanding that for a high performing VIO system, “temporal purity” of data is just as important as its “measurement precision.”

Through future research on technologies for outdoor robotics, not only will there be online estimation and calibration of time offsets¹³, but robust VIO fusion algorithms, which are less sensitive to minor timing errors, will be developed too. But no matter what happens in the evolution of algorithms, uranium grade to minimize the timing errors in the hardware level always would be the path sure in building the high-precision motion-aware systems.

1. Zelin Zhou, and Hongzhou Yang. “State Covariance Based Spatio-Temporal Trajectory Alignment for VIO Systems.” P. 44, The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. XLVIII-M-8-2025, 46th Canadian Symposium on Remote Sensing (CSRS), 16–19 June 2025, Lethbridge, Canada, pp. 43–2025, https://doi.org/10.5194/isprs-archives-XLVIII-M-8-2025-43-2025.
2. Ivanna Dovbysh, Quadrotor UAV Attitude Estimation System. P. 22, Bachelor’s Thesis, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” 2025.
3. Weidong Ding. Optimal Integration of GPS with Inertial Sensors: Modelling and Implementation. P. 65, PhD Thesis, The University of New South Wales, 2008.
4. Henrik Senderud Storli, Timing and Time Synchronization within LiDAR- and IMU-Based Simultaneous Localization and Mapping (SLAM). P. 55, Master’s Thesis, Norwegian University of Science and Technology, 2023.
5. Brook Galna, et al. “Synchronisation of Multiple Unconnected Inertial Measurement Units Using Software Correction.” P. 3, Journal of Biomechanics, vol. 183, 2025, https://doi.org/10.1016/j.jbiomech.2025.112632.
6. Brook Galna, et al. “Synchronisation of Multiple Unconnected Inertial Measurement Units Using Software Correction.” P. 5, Journal of Biomechanics, vol. 183, 2025, https://doi.org/10.1016/j.jbiomech.2025.112632.
7. 唐海亮, 张全, 牛小骥, “新手入门系列4——MEMS IMU原始数据采集和时间同步的那些坑“, 2022
8. DS-IMU/GYRO Software User Manual. P. 40, Dewesoft, V24-3, 2025.
9. iSYNC: Accurate Time Stamping of IMU, GNSS Receiver, Cameras, Laserscanner, Odometer. iMAR Navigation GmbH, 2016.
10. Jonas Frey, “Boxi: Design Decisions in the Context of Algorithmic Performance for Robotics“, Robotics: Science and Systems 2025
11. Yonggen Ling, et al. “Modeling Varying Camera-IMU Time Offset in Optimization-Based Visual-Inertial Odometry.” P. 11, Proceedings of the European Conference on Computer Vision (ECCV), 2018, pp. 1–17.
12. Woosik Lee, et al. “Intermittent GPS-Aided VIO: Online Initialization and Calibration.” P. 6, Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 2020, pp. 1–10.
13. Chaoran Xiong, et al. “TON-VIO: Online Time Offset Modeling Networks for Robust Temporal Alignment in High Dynamic Motion VIO.” P. 7, arXiv preprint arXiv:2403.12504, 2024.