ASRO-DIO: Active Subspace Random Optimization Based Depth Inertial Odometry

High-dimensional nonlinear state estimation is at the heart of inertial-aided navigation systems (INS). Traditional methods usually rely on good initialization and find difficulty in handling large interframe transformations due to fast camera motion. We opt to tackle these challenges by solving the depth inertial odometry (DIO) problem with random optimization. To address the exponentially increased amount of candidate states sampled for the high-dimensional state space, we propose a highly efficient variant of random optimization based on the idea of active subspace. Our method identifies the active dimensions, which contribute most significantly to the decrease of the cost function in each iteration, and samples candidate states only within the corresponding subspace. This allows us to efficiently explore the 18D state space of DIO and achieve good optimality by sampling and evaluating only thousands of candidate states. Experiments show that our method attains highly robust and accurate DIO under fast camera motions and low light conditions, without needing a slow-motion warm-up for initialization.