|Optimal Active Sensing with Process and Measurement Noise
|Year of Publication
|2018 IEEE International Conference on Robotics and Automation (ICRA)
|Cognetti, M, Salaris, P, P. Giordano, R
|continuous Riccati equation, covariance matrices, eigenvalues and eigenfunctions, Estimation, estimation algorithm, gradient methods, inversely proportional, Kalman Filter, Kalman filters, largest eigenvalue, maximum estimation uncertainty, measurement noise, mobile robots, noise measurement, nonlinear differentially flat system, nonlinear filters, nonnegligible process noise, observability, observability gramian, OG, onboard sensors, online gradient descent method, optimal active sensing, optimal trajectories, optimisation, path planning, posteriori covariance matrix, Riccati equations, Robot sensing systems, Trajectory, trajectory control, unicycle robot
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.