Consistent state estimation is challenging, especially under the epistemic uncertainties arising from learned (nonlinear) dynamic and observation models. In this work, we develop a set-based estimation algorithm, that produces zonotopic state estimates that respect the epistemic uncertainties in the learned models, in addition to the aleatoric uncertainties. Our algorithm guarantees probabilistic consistency, in the sense that the true state is always bounded by the zonotopes, with a high probability. We formally relate our set-based approach with the corresponding probabilistic approach (GP-EKF) in the case of learned (nonlinear) models. In particular, when linearization errors and aleatoric uncertainties are omitted, and epistemic uncertainties are simplified, our set-based approach reduces to its probabilistic counterpart. Our method's improved consistency is empirically demonstrated in both a simulated pendulum domain and a real-world robot-assisted dressing domain, where the robot estimates the configuration of the human arm utilizing the force measurements at its end effector.
翻译:一致的状态估算具有挑战性, 特别是在从所学( 非线性) 动态和观察模型中产生的共认不确定性下。 在这项工作中, 我们开发了一个基于设定的估算算法, 产生基于设定的估算算法, 产生以尊重所学模型的共认不确定性为主的zonotiod 状态估算, 除了解析不确定性之外。 我们的算法保证了概率一致性, 也就是说, 真实状态总是受佐诺托普的束缚, 概率很高。 在所学( 非线性)模型中, 我们正式将基于设定的方法与相应的概率方法( GP- EKF ) 联系起来 。 特别是当线性错误和偏执不确定性被忽略, 缩略了, 我们基于设定的方法被归为概率的对应方。 我们的方法的改进一致性在实验上表现在模拟的支架域和真实世界的机器人辅助调料域, 机器人在其中估计了人体手臂在终端效果上使用力测量的配置 。