A Sensitivity Equation Framework for Parameter Estimation in Dynamical Systems

We present a new framework for understanding parameter estimation in dynamical systems. The approach is developed within the modeling approach of continuous data assimilation. We outline the basic assumptions that lead to our derivation. Under these assumptions we show that the parameter estimation turns into a finite dimensional nonlinear optimization problem. We show that our derivation reproduces and extends the algorithm originally developed in [9]. We then implement these methods in three example systems: the Lorenz '63 model, the two-layer Lorenz '96 model, and the Kuramoto Sivashinsky equation. So as to remain sufficiently general, our derivations are largely formal; we leave a more rigorous justification for future work.