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In this letter 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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Augmented Physics-Based Models for High-Order Markov Filtering
Hybrid physics-based data-driven models, namely, augmented physics-based models (APBMs), are capable of learning complex state dynamics while maintaining some level of model interpretability that can be controlled through appropriate regularizations of the data-driven component. In this article, we extend the APBM formulation for high-order Markov models, where the state space is further augmented with past states (AG-APBM). Typically, state augmentation is a powerful method for state estimation for a high-order Markov model, but it requires the exact knowledge of the system dynamics. The proposed approach, however, does not require full knowledge of dynamics, especially the Markovity order. To mitigate the extra computational burden of such augmentation we propose an approximated-state APBM (AP-APBM) implementation leveraging summaries from past time steps. We demonstrate the performance of AG- and AP-APBMs in an autoregressive model and a target-tracking scenario based on the trajectory of a controlled aircraft with delay-feedback control. The experiments showed that both proposed strategies outperformed the standard APBM approach in terms of estimation error and that the AP-APBM only degraded slightly when compared to AG-APBM. For example, the autoregressive (AR) model simulation in our settings showed that AG-APBM and AP-APBM reduced the estimate error by 31.1% and 26.7%. The time cost and memory usage were reduced by 37.5% and 20% by AP-APBM compared to AG-APBM.
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- PAR ID:
- 10577565
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Sensors
- Volume:
- 24
- Issue:
- 18
- ISSN:
- 1424-8220
- Page Range / eLocation ID:
- 6132
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/s24186132
