  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
~\url{https://github.com/APRIL-ZJU/clic}.
