提出新算法提升混合系统状态估计精度，尤其在撞击瞬间表现更优。
Hybrid Iterative Linear Quadratic Estimation: Optimal Estimation for Hybrid Systems
- 基于迭代线性二次优化，用盐度矩阵计算事件触发下的梯度信息。
- 在撞击时刻相比盐化卡尔曼滤波，状态估计误差最大降低63.55%。
- 适合需要高精度状态估计的机器人、跳跃系统等混合动力系统。
本文提出一种基于优化的离线状态估计算法——混合迭代线性二次估计（HiLQE），用于混合动力系统。该方法利用盐度矩阵（saltation matrix），即事件驱动混合跃迁的一阶变分近似，在迭代线性二次优化的反向传播中计算通过混合事件的梯度信息，从而实现每个时间步上价值函数的准确逼近。同时，前向传播通过滚动过程引入了混合动力学。采用参考扩展方法以处理不同撞击时间下状态比较时的反馈增益噪声计算问题。所提方法在带有位置测量的ASLIP跳跃系统上进行了验证。与盐化卡尔曼滤波（SKF）相比，该算法在撞击事件附近所有状态维度上的估计误差幅度最大降低了63.55%。
原文摘要 · Abstract (English)
In this paper we present Hybrid iterative Linear Quadratic Estimation (HiLQE), an optimization based offline state estimation algorithm for hybrid dynamical systems. We utilize the saltation matrix, a first order approximation of the variational update through an event driven hybrid transition, to calculate gradient information through hybrid events in the backward pass of an iterative linear quadratic optimization over state estimates. This enables accurate computation of the value function approximation at each timestep. Additionally, the forward pass in the iterative algorithm is augmented with hybrid dynamics in the rollout. A reference extension method is used to account for varying impact times when comparing states for the feedback gain in noise calculation. The proposed method is demonstrated on an ASLIP hopper system with position measurements. In comparison to the Salted Kalman Filter (SKF), the algorithm presented here achieves a maximum of 63.55% reduction in estimation error magnitude over all state dimensions near impact events.
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