# Pre-Dog-Leg: A Feature Optimization Method for Visual Inertial SLAM Based on Adaptive Preconditions

## TL;DR

This paper introduces a new optimization method for visual-inertial SLAM that improves convergence and robustness by addressing issues with the Hessian matrix.

## Contribution

The novel Pre-Dog-Leg method uses an adaptive preconditioner to handle ill-posed Hessian matrices in visual-inertial SLAM.

## Key findings

- The method reduces Hessian matrix conditionals by 7.9 times on the EuRoC dataset.
- It achieves up to 34% lower trajectory error compared to existing methods on dynamic sequences.
- The approach improves convergence time and suppresses outliers effectively.

## Abstract

To address the ill-posedness of the Hessian matrix in monocular visual-inertial SLAM (Simultaneous Localization and Mapping) caused by unobservable depth of feature points, which leads to convergence difficulties and reduced robustness, this paper proposes a Pre-Dog-Leg feature optimization method based on an adaptive preconditioner. First, we propose a multi-candidate initialization method with robust characteristics. This method effectively circumvents erroneous depth initialization by introducing multiple depth assumptions and geometric consistency constraints. Second, we address the pathology of the Hessian matrix of the feature points by constructing a hybrid SPAI-Jacobi adaptive preconditioner. This preconditioner is capable of identifying matrix pathology and dynamically enabling preconditioning as a strategy. Finally, we construct a hybrid adaptive preconditioner for the traditional Dog-Leg numerical optimization method. To address the issue of degraded convergence performance when solving pathological problems, we map the pathological optimization problem from the original parameter space to a well-conditioned preconditioned space. The optimization equivalence is maintained by variable recovery. The experiments on the EuRoC dataset show that the method reduces the number of Hessian matrix conditionals by a factor of 7.9, effectively suppresses outliers, and significantly improves the overall convergence time. From the analysis of trajectory error, the absolute trajectory error is reduced by up to 16.48% relative to RVIO2 on the MH_01 sequence, 20.83% relative to VINS-mono on the MH_02 sequence, and up to 14.73% relative to VINS-mono and 34.0% relative to OpenVINS on the highly dynamic MH_05 sequence, indicating that the algorithm achieves higher localization accuracy and stronger system robustness.