Learning covariance dynamics for path planning of UAV sensors in a large-scale dynamic environment

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 ofthe predicted state of the system some time into the future. The considerablenonlinearity 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 thesearch process must calculate the covariance of the posterior state estimate for eachcandidate path. To resolve this challenge, this work proposes to replace the com-putationally intensive numerical prediction process with an approximate model ofthe covariance dynamics learned using nonlinear time-series regression. The use ofautoregressive (AR) time-series features with the regularized least squares (RLS)algorithm enables the learning of accurate and efficient parametric models. Thelearned covariance dynamics are demonstrated to outperform other approximationstrategies such as linearization and partial ensemble propagation when used for trajectory optimization, in both terms of accuracy and speed, with examples of simpli ed weather forecasting.