# Unleashing the Power of Discrete-Time State Representation: Ultrafast Target-based IMU-Camera Spatial-Temporal Calibration

arXiv: https://arxiv.org/abs/2509.12846 · HTML: https://mlsanity.com/paper/2509.12846/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 20 of 20)

- [Project Aria: A New Tool for Egocentric Multi-Modal AI Research](https://mlsanity.com/paper/2308.13561/) (2023)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [The TUM VI Benchmark for Evaluating Visual-Inertial Odometry](https://mlsanity.com/paper/1804.06120/) (2018)
- [On-Manifold Preintegration for Real-Time Visual-Inertial Odometry](https://mlsanity.com/paper/1512.02363/) (2015)
- [The Double Sphere Camera Model](https://mlsanity.com/paper/1807.08957/) (2018)
- [Visual-Inertial Mapping with Non-Linear Factor Recovery](https://mlsanity.com/paper/1904.06504/) (2019)
- [Autonomous Drone Racing: A Survey](https://mlsanity.com/paper/2301.01755/) (2023)
- [Efficient Derivative Computation for Cumulative B-Splines on Lie Groups](https://mlsanity.com/paper/1911.08860/) (2019)
- [Adaptive Robust Kernels for Non-Linear Least Squares Problems](https://mlsanity.com/paper/2004.14938/) (2020)
- [Continuous-Time vs. Discrete-Time Vision-based SLAM: A Comparative Study](https://mlsanity.com/paper/2202.08894/) (2022)
- [Continuous-Time State Estimation Methods in Robotics: A Survey](https://mlsanity.com/paper/2411.03951/) (2024)
- [Range-Visual-Inertial Odometry: Scale Observability Without Excitation](https://mlsanity.com/paper/2103.15215/) (2021)
- [The Monado SLAM Dataset for Egocentric Visual-Inertial Tracking](https://mlsanity.com/paper/2508.00088/) (2025)
- [On 'A Kalman Filter-Based Algorithm for IMU-Camera Calibration: Observability Analysis and Performance Evaluation'](https://mlsanity.com/paper/1311.4769/) (2013)
- [Hilti SLAM Challenge 2023: Benchmarking Single + Multi-session SLAM across Sensor Constellations in Construction](https://mlsanity.com/paper/2404.09765/) (2024)
- [High-Precision Online Markerless Stereo Extrinsic Calibration](https://mlsanity.com/paper/1903.10705/) (2019)
- [iKalibr: Unified Targetless Spatiotemporal Calibration for Resilient Integrated Inertial Systems](https://mlsanity.com/paper/2407.11420/) (2024)
- [Multi-Visual-Inertial System: Analysis, Calibration and Estimation](https://mlsanity.com/paper/2308.05303/) (2023)
- [Structure-Invariant Range-Visual-Inertial Odometry](https://mlsanity.com/paper/2409.04633/) (2024)
- [Equivariant IMU Preintegration with Biases: a Galilean Group Approach](https://mlsanity.com/paper/2411.05548/) (2024)

## Abstract (arXiv)

Visual-inertial fusion is crucial for a large amount of intelligent and autonomous applications, such as robot navigation and augmented reality. To bootstrap and achieve optimal state estimation, the spatial-temporal displacements between IMU and cameras must be calibrated in advance. Most existing calibration methods adopt continuous-time state representation, more specifically the B-spline. Despite these methods achieve precise spatial-temporal calibration, they suffer from high computational cost caused by continuous-time state representation. To this end, we propose a novel and extremely efficient calibration method that unleashes the power of discrete-time state representation. Moreover, the weakness of discrete-time state representation in temporal calibration is tackled in this paper. With the increasing production of drones, cellphones and other visual-inertial platforms, if one million devices need calibration around the world, saving one minute for the calibration of each device means saving 2083 work days in total. To benefit both the research and industry communities, the open-source implementation is released at https://github.com/JunlinSong/DT-VI-Calib.