PC-SRIF: Preconditioned Cholesky-based Square Root Information Filter for Vision-aided Inertial Navigation

In this paper, we introduce a novel estimator for vision-aided inertial navigation systems (VINS), the Preconditioned Cholesky-based Square Root Information Filter (PC-SRIF). When solving linear systems, employing Cholesky decomposition offers superior efficiency but can compromise numerical stability. Due to this, existing VINS utilizing (Square Root) Information Filters often opt for QR decomposition on platforms where single precision is preferred, avoiding the numerical challenges associated with Cholesky decomposition. While these issues are often attributed to the ill-conditioned information matrix in VINS, our analysis reveals that this is not an inherent property of VINS but rather a consequence of specific parameterizations. We identify several factors that contribute to an ill-conditioned information matrix and propose a preconditioning technique to mitigate these conditioning issues. Building on this analysis, we present PC-SRIF, which exhibits remarkable stability in performing Cholesky decomposition in single precision when solving linear systems in VINS. Consequently, PC-SRIF achieves superior theoretical efficiency compared to alternative estimators. To validate the efficiency advantages and numerical stability of PC-SRIF based VINS, we have conducted well controlled experiments, which provide empirical evidence in support of our theoretical findings. Remarkably, in our VINS implementation, PC-SRIF's runtime is 41% faster than QR-based SRIF.

Learned Monocular Depth Priors in Visual-Inertial Initialization

Visual-inertial odometry (VIO) is the pose estimation backbone for most AR/VR and autonomous robotic systems today, in both academia and industry. However, these systems are highly sensitive to the initialization of key parameters such as sensor biases, gravity direction, and metric scale. In practical scenarios where high-parallax or variable acceleration assumptions are rarely met (e.g. hovering aerial robot, smartphone AR user not gesticulating with phone), classical visual-inertial initialization formulations often become ill-conditioned and/or fail to meaningfully converge. In this paper we target visual-inertial initialization specifically for these low-excitation scenarios critical to in-the-wild usage. We propose to circumvent the limitations of classical visual-inertial structure-from-motion (SfM) initialization by incorporating a new learning-based measurement as a higher-level input. We leverage learned monocular depth images (mono-depth) to constrain the relative depth of features, and upgrade the mono-depth to metric scale by jointly optimizing for its scale and shift. Our experiments show a significant improvement in problem conditioning compared to a classical formulation for visual-inertial initialization, and demonstrate significant accuracy and robustness improvements relative to the state-of-the-art on public benchmarks, particularly under motion-restricted scenarios. We further extend this improvement to implementation within an existing odometry system to illustrate the impact of our improved initialization method on resulting tracking trajectories.