Quantifying uncertainty in state and parameter estimation

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.

5 pages, 6 figures

References in corpus (5)

• Using synchronization of chaos to identify the dynamics of unknown systems
• On Variational Data Assimilation in Continuous Time
• State and parameter estimation using Monte Carlo evaluation of path integrals
• Effective Actions for Ensemble Data Assimilation
• Nonlinear system identification employing automatic differentiation

Cited by in corpus (4)

• Local observability of state variables and parameters in nonlinear modeling quantified by delay reconstruction
• Data-assimilation by delay-coordinate nudging
• Inferring the dynamics of ionic currents from recursive piecewise data assimilation of approximate neuron models
• Basin structure of optimization based state and parameter estimation