Unscented Kalman filter with stable embedding for simple, accurate, and computationally efficient state estimation of systems on manifolds in Euclidean space

Abstract

This article proposes a simple, accurate, and computationally efficient method to apply the ordinary unscented Kalman filter (UKF) developed in Euclidean space to systems whose dynamics evolve on manifolds. We use the mathematical theory called stable embedding to make a variant of UKF that keeps state estimates in close proximity to the manifold while exhibiting excellent estimation performance. We confirm the performance of our devised filter by applying it to the satellite system model and comparing the performance with other UKFs devised specifically for systems on manifolds. Our devised filter has a low estimation error, keeps the state estimates in close proximity to the manifold as expected, and consumes a minor amount of computation time. Also our devised filter is simple and easy to use because our filter directly employs the off-the-shelf standard UKF devised in Euclidean space without any particular manifold-structure-preserving discretization method or coordinate transformation.