The goal of this paper is to increase the estimation performance of an Extended Kalman Filter for a nonlinear differentially flat system by planning trajectories able to maximize the amount of information gathered by onboard sensors in presence of both process and measurement noises. In a previous work, we presented an online gradient descent method for planning optimal trajectories along which the smallest eigenvalue of the Observability Gramian (OG) is maximized. As the smallest eigenvalue of the OG is inversely proportional to the maximum estimation uncertainty, its maximization reduces the maximum estimation uncertainty of any estimation algorithm employed during motion. However, the OG does not consider the process noise that, instead, in several applications is far from being negligible. For this reason, this paper proposes a novel solution able to cope with non-negligible process noise: this is achieved by minimizing the largest eigenvalue of the a posteriori covariance matrix obtained by solving the Continuous Riccati Equation as a measure of the total available information. This minimization is expected to maximize the information gathered by the outputs while, at the same time, limiting as much as possible the negative effects of the process noise. We apply our method to a unicycle robot. The comparison between the novel method and the one of our previous work (which did not consider process noise) shows significant improvements in the obtained estimation accuracy.

10acontinuous Riccati equation10acovariance matrices10aeigenvalues and eigenfunctions10aEstimation10aestimation algorithm10agradient methods10ainversely proportional10aKalman Filter10aKalman filters10alargest eigenvalue10amaximum estimation uncertainty10ameasurement noise10amobile robots10anoise measurement10anonlinear differentially flat system10anonlinear filters10anonnegligible process noise10aobservability10aobservability gramian10aOG10aonboard sensors10aonline gradient descent method10aoptimal active sensing10aoptimal trajectories10aoptimisation10apath planning10aposteriori covariance matrix10aRiccati equations10aRobot sensing systems10aTrajectory10atrajectory control10aunicycle robot1 aCognetti, M.1 aSalaris, P1 aGiordano, Robuffo uhttps://ieeexplore.ieee.org/document/8460476