To address the issues of insufficient robustness, large depth recovery errors, and poor scene adaptability currently present in the initialisation phase of event-based stereo visual inertial SLAM systems, we propose a global BA initialisation method based on an adaptive threshold robust kernel function, ES-ATRK. The algorithm first achieves spatio-temporal fusion of events and visual features. Event features are triangulated to obtain depth values that serve as the 3D map, whilst visual features provide 2D observations; both modalities jointly feed the Structure from Motion (SfM) pipeline, laying the foundation for global bundle adjustment (BA) optimisation. The core contribution lies in incorporating a robust kernel function into the global BA to suppress outlier interference and in designing an adaptive thresholding algorithm that dynamically determines the kernel threshold. Furthermore, the algorithm calculates an initial threshold based on the quantile distribution of residuals prior to BA optimisation, combined with validity checks and a multi-round iterative smoothing adjustment strategy, thereby achieving scene-adaptive thresholding. In over 85% of the test scenes on the VECtor dataset, its localisation accuracy improved by at least 10% compared to existing mainstream event-based SLAM methods, such as ESVIO and USLAM. In high-dynamic scenes, its ATE performance is approximately twice that of mainstream models such as ESIO, and it maintains excellent positioning accuracy and stability of three-axis errors in generalisation tests on the HKU and MVSEC datasets. Furthermore, in the large-scale outdoor testing scenarios of the DSEC dataset, ES-ATRK also demonstrates superior feature tracking and trajectory estimation performance. This method effectively enhances the robustness of initialisation and depth recovery performance in event-based stereo visual inertial SLAM systems, reduces overall positioning error, and offers greater adaptability in challenging scenarios such as low-texture, high-dynamic, and HDR environments.

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.