Local observability of state variables and parameters in nonlinear modeling quantified by delay reconstruction

TL;DR

This paper investigates how the Jacobian matrix of delay coordinates can be used to assess the robustness of estimating states and parameters in nonlinear dynamical models from observed time series.

Contribution

It introduces a novel approach leveraging Jacobian features for quantifying the reliability of state and parameter estimation in nonlinear systems.

Findings

Effective in discrete and continuous systems

Applied to Hénon map and Rössler system

Provides insights into estimation robustness

Abstract

Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using an observed time series. Relevant concepts of this approach are introduced and illustrated for discrete and continuous time systems employing a filtered H\'enon map and a R\"ossler system.