The essential of navigation, perception, and decision-making which are basic tasks for intelligent robots, is to estimate necessary system states. Among them, navigation is fundamental for other upper applications, providing precise position and orientation, by integrating measurements from multiple sensors. With observations of each sensor appropriately modelled, multi-sensor fusion tasks for navigation are reduced to the state estimation problem which can be solved by two approaches: optimization and filtering. Recent research has shown that optimization-based frameworks outperform filtering-based ones in terms of accuracy. However, both methods are based on maximum likelihood estimation (MLE) and should be theoretically equivalent with the same linearization points, observation model, measurements, and Gaussian noise assumption. In this paper, we deeply dig into the theories and existing strategies utilized in both optimization-based and filtering-based approaches. It is demonstrated that the two methods are equal theoretically, but this equivalence corrupts due to different strategies applied in real-time operation. By adjusting existing strategies of the filtering-based approaches, the Monte-Carlo simulation and vehicular ablation experiments based on visual odometry (VO) indicate that the strategy adjusted filtering strictly equals to optimization. Therefore, future research on sensor-fusion problems should concentrate on their own algorithms and strategies rather than state estimation approaches.

翻译：导航、感知与决策是智能机器人的基本任务，其核心在于对必要系统状态进行估计。其中，导航作为上层应用的基础，通过融合多传感器测量数据提供精确的位置与姿态信息。当各传感器的观测模型被合理建模后，面向导航的多传感器融合任务可简化为状态估计问题，该问题可通过优化与滤波两种方法求解。近年研究表明，基于优化的框架在精度上优于基于滤波的框架。然而，两种方法均基于最大似然估计，在相同的线性化点、观测模型、测量值及高斯噪声假设下，理论上应具有等价性。本文深入探究了优化与滤波方法所采用的理论与现有策略，证明两种方法在理论上等价，但这种等价性会因实时运行中采用的不同策略而失效。通过调整滤波方法的现有策略，基于视觉里程计的蒙特卡罗仿真与车载消融实验表明：调整后的滤波方法严格等价于优化方法。因此，未来传感器融合问题的研究应聚焦于算法与策略本身，而非状态估计方法的选择。