四旋翼飞行器的移动水平估计：一种 $\mathcal{L}_1$ 自适应优化器方法
Moving Horizon Estimation for Quadrotors: An $\mathcal{L}_1$ Adaptive Optimizer Approach
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中文总结 AI 辅助
本研究提出一种结合 $\mathcal{L}_1$ 自适应优化器的时变求解器，用于高效求解四旋翼的移动水平估计问题，在降低计算负担的同时提高估计精度。
中文摘要 AI 辅助
移动水平估计（MHE）是一种基于有限时域优化的状态估计方法，与基于卡尔曼滤波器的方法相比，它能以增加计算量为代价提供更高的精度。我们提出了一种线性平滑 MHE 公式，将其表述为稠密二次规划（QP），并设计了一种求解器，该求解器由连续时间牛顿法结合 $\mathcal{L}_1$ 自适应优化器（$\mathcal{L}_1$-AO）增强而成。虽然 MHE 本质上是时变的，但传统方法将其视为一系列独立的、时不变的问题，并在每个时间步采用迭代求解器，这既可能不准确，也可能计算负担沉重。相比之下，时变求解器通过利用问题的时间演化特性，以更少的迭代次数跟踪最优解，从而降低计算负担。在本研究中，我们通过一种时变求解器并辅以 $\mathcal{L}_1$-AO 增强来提升 MHE 的性能和效率，该增强用于补偿预测不准确性，这种不准确性在实践中很常见，原因在于传感器噪声和对系统缺乏先验知识。在四旋翼平台上的仿真结果表明，与基线时不变求解器相比，$\mathcal{L}_1$-AO 增强方法能更高效地求解 MHE 优化问题，并且在具有挑战性的条件下，与扩展卡尔曼滤波器和标准 MHE 相比，能实现更高的估计精度。
英文摘要
Moving Horizon Estimation (MHE) is a state estimation method based on finite-horizon optimization that can offer higher accuracy at the cost of increased computation compared to Kalman filter-based approaches. We present a linear smoothing MHE formulation as a dense Quadratic Program (QP), and a solver consisting of a continuous-time Newton's method augmented with the $\mathcal{L}_1$ Adaptive Optimizer ($\mathcal{L}_1$-AO). While MHE is inherently time-varying, conventional approaches treat it as a sequence of independent, time-invariant problems and employ iterative solvers at each time step, which can be both inaccurate and computationally burdensome. In contrast, time-varying solvers track the optimal solution with fewer iterations by exploiting the temporal evolution of the problem, thereby reducing the computational load. In this research, we enhance both the performance and efficiency of MHE through a time-varying solver with an $\mathcal{L}_1$-AO augmentation that compensates for the prediction inaccuracy, which is common in practice due to noisy sensors and the lack of prior knowledge of the system. Simulation results on a quadrotor platform show that the $\mathcal{L}_1$-AO-augmented approach solves the MHE optimization problem more efficiently than the baseline time-invariant solver and achieves higher estimation accuracy under challenging conditions, compared with both the Extended Kalman Filter and the standard MHE.
发表机构
- University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
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