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

2024-09-17

arXiv.org

AI Summary

In visual-inertial navigation systems (VINS), Cholesky decomposition suffers from numerical instability under single-precision arithmetic, while QR decomposition—though stable—incurs excessive computational overhead. Method: This paper proposes a Preconditioned Cholesky Square-Root Information Filter (PC-SRIF) for VINS backends. We first identify that the ill-conditioning of the VINS information matrix stems from parameterization design rather than intrinsic properties, and accordingly devise a tailored preconditioning strategy to enable numerically stable Cholesky decomposition in single precision. The method integrates preconditioning, Cholesky decomposition, and a tightly coupled visual–inertial estimation framework. Contribution/Results: PC-SRIF ensures robust numerical stability while significantly improving efficiency: it achieves a 41% speedup over QR-based SRIF implementations. This work establishes a new paradigm for efficient and robust VINS backend solving on resource-constrained embedded platforms.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Other Foundations of Computer Vision
• Machine Learning: Matrix & Tensor Methods

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Improves numerical stability in vision-aided inertial navigation systems.
• Addresses ill-conditioned information matrix issues in VINS.
• Enhances efficiency of Cholesky decomposition in single precision.

Innovation

• Preconditioned Cholesky-based Square Root Information Filter
• Mitigates ill-conditioned information matrix issues
• 41% faster runtime than QR-based SRIF