Shadowing-Based Data Assimilation Method for Partially Observed Models

In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is on regularized Gauss-Newton method. We prove local convergence the solution manifold and provide lower bound algorithmic time step. use numerical experiments with Lorenz 63 96 models illustrate of show that results compare favourably variational (weak-constraint four-dimensional method) (pseudo-orbit assimilation). Numerical preconditioner chosen cost function allows find orbit dynamical system in vicinity true solution.