In this letter, we present a closed-form initialization method that recovers the full visual-inertial state without nonlinear optimization. Unlike previous approaches that rely on iterative solvers, our formulation yields analytical, easy-to-implement, and numerically stable solutions for reliable start-up. Our method builds on small-rotation and constant-velocity approximations, which keep the formulation compact while preserving the essential coupling between motion and inertial measurements. We further propose an observability-driven, two-stage initialization scheme that balances accuracy with initialization latency. Extensive experiments on the EuRoC dataset validate our assumptions: our method achieves 10-20% lower initialization error than optimization-based approaches, while using 4x shorter initialization windows and reducing computational cost by 5x.

翻译：本文提出一种闭式初始化方法，无需非线性优化即可恢复完整的视觉-惯性状态。与依赖迭代求解器的现有方法不同，我们的公式可导出解析、易于实现且数值稳定的解，确保可靠启动。该方法基于小旋转与恒定速度近似，在保持运动与惯性测量间本质耦合的同时维持公式紧凑性。我们进一步提出基于可观测性的两阶段初始化方案，在精度与初始化延迟间实现平衡。在EuRoC数据集上的大量实验验证了我们的假设：本方法相比基于优化的方法初始化误差降低10-20%，同时初始化窗口缩短4倍，计算成本减少5倍。