A joint state and parameter estimation scheme for nonlinear dynamical systems
Smith, P. J., Dance, S. L. and Nichols, N. K., (2014) A joint state and parameter estimation scheme for nonlinear dynamical systems. Technical Report. Dept of Mathematics & Statistics, University of Reading pp24.
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.