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.

翻译：本文提出混合迭代线性二次估计（HiLQE），一种基于优化的离线状态估计算法，适用于混合动力系统。我们利用盐度矩阵——一种通过事件驱动混合跃迁的变分更新的一阶近似——在状态估计的迭代线性二次优化的反向传播过程中，计算跨越混合事件的梯度信息。这使得每个时间步的价值函数近似能够被精确计算。此外，迭代算法中的前向传播在推演过程中加入了混合动力学。在噪声计算中为反馈增益比较状态时，采用参考扩展方法来处理变化的冲击时间。所提方法在具有位置测量的ASLIP跳跃系统上进行了验证。与盐度卡尔曼滤波器（SKF）相比，该算法在冲击事件附近的所有状态维度上，估计误差幅值最大降低了63.55%。