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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.04551 |
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Table of Contents:
- State estimation refers to determining the states of a dynamical system that starts from a noisy initial condition and evolves under process noise, based on noisy measurements and a known system model. For linear dynamical systems with white Gaussian noises of known mean and variance, Kalman filtering is a well-known method that leads to stable error dynamics for detectable systems. There are some non-optimal extensions to nonlinear systems. Recent work has used neural networks to develop estimators for nonlinear systems that optimize a criterion. Stability of the error dynamics is even more important than optimality. Jordan recurrent neural networks (JRNs) have a structure that mimics that of a dynamical system and are thus appealing for estimator design. We show that a JRN performs better than an extended Kalman filter(EKF) and unscented Kalman filter(UKF) for several examples. The main contribution of this paper is an input-to-state stability analysis of the error dynamics of JRNs. The stability of the error dynamics of several examples is shown.