Accurate state estimation is critical for legged and aerial robots operating in dynamic, uncertain environments. A key challenge lies in specifying process and measurement noise covariances, which are typically unknown or manually tuned. In this work, we introduce a bi-level optimization framework that jointly calibrates covariance matrices and kinematic parameters in an estimator-in-the-loop manner. The upper level treats noise covariances and model parameters as optimization variables, while the lower level executes a full-information estimator. Differentiating through the estimator allows direct optimization of trajectory-level objectives, resulting in accurate and consistent state estimates. We validate our approach on quadrupedal and humanoid robots, demonstrating significantly improved estimation accuracy and uncertainty calibration compared to hand-tuned baselines. Our method unifies state estimation, sensor, and kinematics calibration into a principled, data-driven framework applicable across diverse robotic platforms.

翻译：精确的状态估计对于在动态不确定环境中运行的足式与空中机器人至关重要。一个核心挑战在于确定过程噪声与测量噪声的协方差矩阵，这些参数通常未知或依赖手动调节。本研究提出一种双层优化框架，以“估计器在环”的方式联合标定协方差矩阵与运动学参数。上层将噪声协方差与模型参数作为优化变量，下层执行全信息估计器。通过对估计器进行微分，能够直接优化轨迹级目标，从而获得准确且一致的状态估计结果。我们在四足机器人与仿人机器人上验证了所提方法，相较于手动调参基线，在估计精度与不确定性标定方面均展现出显著提升。本方法将状态估计、传感器标定与运动学标定统一为一个原则性的数据驱动框架，可广泛应用于各类机器人平台。