We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference, these models are used to weigh different blocks of the Jacobian and error vector resulting from linearization and hence, additionally affect the stability and convergence of the non-linear system. We propose a gradient-based method to estimate well-conditioned covariance matrices by formulating the learning process as a constrained bilevel optimization problem over factor graphs. We evaluate our method against baselines across a range of simulated and real-world tasks and demonstrate that our technique converges to model estimates that lead to better solutions as evidenced by the improved tracking accuracy on unseen test trajectories.

翻译：我们考虑机器人状态估计中误差协方差矩阵的学习问题。状态估计器对机器人状态正确置信度的收敛依赖于噪声模型的适当调参。在推理过程中，这些模型被用于对线性化产生的雅可比矩阵和误差向量的不同块进行加权，从而进一步影响非线性系统的稳定性和收敛性。我们提出一种基于梯度的方法来估计良态协方差矩阵，将学习过程形式化为因子图上的约束双层优化问题。我们在模拟和真实世界的多种任务中与基线方法进行了比较，证明我们的方法能够收敛到更优的模型估计，表现为在未见测试轨迹上跟踪精度的提升。