This work addresses the problem of trajectory planning for UAV sensors taking
measurements of a large nonlinear system to improve estimation and prediction of such a system. The lack of perfect knowledge of the global system state typically requires probabilistic state estimation. The goal is therefore to find trajectories such that the measurements along each trajectory minimize the expected error of the predicted state of the system some time into the future. The considerable nonlinearity of the dynamics governing these systems necessitates the use of com-putationally costly Monte-Carlo estimation techniques to update the state distri-bution over time. This computational burden renders planning infeasible, since the
search process must calculate the covariance of the posterior state estimate for each
candidate path. To resolve this challenge, this work proposes to replace the com-
putationally intensive numerical prediction process with an approximate model of
the covariance dynamics learned using nonlinear time-series regression. The use of
autoregressive (AR) time-series features with the regularized least squares (RLS)
algorithm enables the learning of accurate and ecient parametric models. The learned covariance dynamics are demonstrated to outperform other approximation strategies such as linearization and partial ensemble propagation when used for trajectory optimization, in both terms of accuracy and speed, with examples of simplified weather forecasting.