Stability of Jordan Recurrent Neural Network Estimator

TL;DR

This paper analyzes the stability of Jordan recurrent neural network estimators for nonlinear systems, demonstrating their superior performance over traditional Kalman filters through input-to-state stability analysis and empirical examples.

Contribution

It provides the first stability analysis of JRN-based estimators for nonlinear systems, showing their improved stability and performance over EKF and UKF.

Findings

JRN estimators outperform EKF and UKF in tested examples

Input-to-state stability of JRN error dynamics is established

JRN-based estimators show better stability and accuracy

Abstract

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.