# Continuous-Time Fixed-Lag Smoothing for LiDAR-Inertial-Camera SLAM

arXiv: https://arxiv.org/abs/2302.07456 · HTML: https://mlsanity.com/paper/2302.07456/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2023.

## Built on by (most cited first, 5 of 5)

- [Traj-LO: In Defense of LiDAR-Only Odometry Using an Effective Continuous-Time Trajectory](https://mlsanity.com/paper/2309.13842/) (2023)
- [Traj-LIO: A Resilient Multi-LiDAR Multi-IMU State Estimator Through Sparse Gaussian Process](https://mlsanity.com/paper/2402.09189/) (2024)
- [Radar and Event Camera Fusion for Agile Robot Ego-Motion Estimation](https://mlsanity.com/paper/2506.18443/) (2025)
- [MARVO: Marine-Adaptive Radiance-aware Visual Odometry](https://mlsanity.com/paper/2511.22860/) (2025)
- [Incremental Mapping with Measurement Synchronization & Compression](https://mlsanity.com/paper/2602.07901/) (2026)

## Abstract (arXiv)

Localization and mapping with heterogeneous multi-sensor fusion have been prevalent in recent years. To adequately fuse multi-modal sensor measurements received at different time instants and different frequencies, we estimate the continuous-time trajectory by fixed-lag smoothing within a factor-graph optimization framework. With the continuous-time formulation, we can query poses at any time instants corresponding to the sensor measurements. To bound the computation complexity of the continuous-time fixed-lag smoother, we maintain temporal and keyframe sliding windows with constant size, and probabilistically marginalize out control points of the trajectory and other states, which allows preserving prior information for future sliding-window optimization. Based on continuous-time fixed-lag smoothing, we design tightly-coupled multi-modal SLAM algorithms with a variety of sensor combinations, like the LiDAR-inertial and LiDAR-inertial-camera SLAM systems, in which online timeoffset calibration is also naturally supported. More importantly, benefiting from the marginalization and our derived analytical Jacobians for optimization, the proposed continuous-time SLAM systems can achieve real-time performance regardless of the high complexity of continuous-time formulation. The proposed multi-modal SLAM systems have been widely evaluated on three public datasets and self-collect datasets. The results demonstrate that the proposed continuous-time SLAM systems can achieve high-accuracy pose estimations and outperform existing state-of-the-art methods. To benefit the research community, we will open source our code at ~urlhttps://github.com/APRIL-ZJU/clic.