Accurate Guaranteed State Estimation for Uncertain LPVs using Constrained Convex Generators

Guaranteed state estimation for autonomous vehicles in GPS-denied areas that resort to landmarks detection and onboard sensors requires set-membership techniques that are capable of representing heterogeneous bounds using hyperplanes and ellipsoids. Recently, in the literature, the concept of Convex Constrained Generators (CCGs) has been introduced for the case where the dynamical system can be represented by a Linear Parameter-Varying (LPV) model. However, in practical applications, dynamics have uncertain parameters caused by noise-corrupted measurements of quantities of interest such as mass or orientation angles. In this paper, we first explore a closed-form solution for the convex hull of polytopes to showcase the main challenges of guaranteed state estimation for uncertain LPVs. We then propose the use of CCGs to have low conservatism when in the presence of distance measurements and avoid the exponential growth of the generators used in the state representation by performing an approximation using ray-shooting. Simulations illustrate the ability of CCGs to accurately model distance measurements with the corresponding decrease in volume without adding additional constraints.