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：本文提出了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。与以往依赖迭代求解器的方法不同，我们的公式能够为可靠启动提供解析、易于实现且数值稳定的解。该方法基于小旋转和恒定速度近似，在保持运动与惯性测量之间本质耦合的同时，使公式保持紧凑。我们进一步提出了一种基于可观测性的两阶段初始化方案，以平衡精度与初始化延迟。在EuRoC数据集上的大量实验验证了我们的假设：与基于优化的方法相比，本方法实现了10-20%更低的初始化误差，同时使用4倍更短的初始化窗口，并将计算成本降低了5倍。