Hybrid Iterative Linear Quadratic Estimation: Optimal Estimation for Hybrid Systems

TL;DR

This paper introduces HiLQE, an offline estimation algorithm for hybrid systems that improves accuracy by incorporating hybrid dynamics and the saltation matrix into an iterative linear quadratic framework, outperforming traditional filters.

Contribution

The paper presents a novel hybrid iterative Linear Quadratic Estimation method that effectively handles hybrid events using the saltation matrix, enhancing state estimation accuracy for hybrid dynamical systems.

Findings

Achieves up to 63.55% reduction in estimation error near impact events.

Demonstrated on an ASLIP hopper system with position measurements.

Outperforms Salted Kalman Filter in accuracy.

Abstract

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.