Traj-LIO: A Resilient Multi-LiDAR Multi-IMU State Estimator Through
  Sparse Gaussian Process
Xin Zheng Jianke Zhu
Nowadays, sensor suits have been equipped with redundant LiDARs and IMUs to
mitigate the risks associated with sensor failure. It is challenging for the
previous discrete-time and IMU-driven kinematic systems to incorporate multiple
asynchronized sensors, which are susceptible to abnormal IMU data. To address
these limitations, we introduce a multi-LiDAR multi-IMU state estimator by
taking advantage of Gaussian Process (GP) that predicts a non-parametric
continuous-time trajectory to capture sensors' spatial-temporal movement with
limited control states. Since the kinematic model driven by three types of
linear time-invariant stochastic differential equations are independent of
external sensor measurements, our proposed approach is capable of handling
different sensor configurations and resilient to sensor failures. Moreover, we
replace the conventional $\mathrm{SE}(3)$ state representation with the
combination of $\mathrm{SO}(3)$ and vector space, which enables GP-based
LiDAR-inertial system to fulfill the real-time requirement. Extensive
experiments on the public datasets demonstrate the versatility and resilience
of our proposed multi-LiDAR multi-IMU state estimator. To contribute to the
community, we will make our source code publicly available.