Simultaneous Calibration of Noise Covariance and Kinematics for State Estimation of Legged Robots via Bi-level Optimization
This work addresses the problem of accurate state estimation for legged and aerial robots in dynamic environments, offering a data-driven framework that unifies calibration tasks, though it is incremental as it builds on existing estimation methods.
The paper tackles the challenge of specifying unknown process and measurement noise covariances in state estimation for legged robots by introducing a bi-level optimization framework that jointly calibrates covariance matrices and kinematic parameters, resulting in significantly improved estimation accuracy and uncertainty calibration compared to hand-tuned baselines.
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.