Observability driven path planning for relative navigation of unmanned aerial systems

We consider the problem of relative navigation of two unmanned aerial systems (UAS) in GPS-denied environments. We design active path planning algorithms to maximize state observability defined in discrete time. We consider two definitions of the nonlinear observability matrix and establish their connections with Fisher information matrix and filtering Cramer-Rao lower bound, respectively. We also define a sensitivity function that correlates noise on control inputs to errors on the state estimate. We demonstrate using MonteCarlo simulations that by optimizing metrics from the state observability and sensitivity, we achieve significantly improved estimation performance over a nominal trajectory for relative navigation.