A joint state and parameter estimation scheme for nonlinear dynamical systems

Smith, P. J. ORCID: https://orcid.org/0000-0003-4570-4127, Dance, S. L. ORCID: https://orcid.org/0000-0003-1690-3338 and Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220, (2014) A joint state and parameter estimation scheme for nonlinear dynamical systems. Report. Dept of Mathematics & Statistics, University of Reading pp24.

Abstract/Summary

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.