Quantifying uncertainty in state and parameter estimation

TL;DR

This paper introduces a method to quantify the uncertainty in estimating states and parameters of dynamical systems from time series data, helping identify where accurate estimation is feasible.

Contribution

It presents a novel approach using the Jacobian of delay coordinates to measure uncertainty in state and parameter estimation, applicable to complex systems.

Findings

Effective in identifying estimable regions in state and parameter space

Demonstrated on the Ikeda map and Hindmarsh-Rose model

Provides a quantitative measure of estimation uncertainty

Abstract

Observability of state variables and parameters of a dynamical system from an observed time series is analyzed and quantified by means of the Jacobian matrix of the delay coordinates map. For each state variable and each parameter to be estimated a measure of uncertainty is introduced depending on the current state and parameter values, which allows us to identify regions in state and parameter space where the specific unknown quantity can (not) be estimated from a given time series. The method is demonstrated using the Ikeda map and the Hindmarsh-Rose model.