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

TL;DR

This paper introduces a stable embedding-based unscented Kalman filter that accurately and efficiently estimates states on manifolds by leveraging standard Euclidean-space UKF without complex transformations.

Contribution

It presents a novel UKF variant using stable embedding to maintain estimates near manifolds, simplifying implementation and improving performance for systems on manifolds.

Findings

Low estimation error on satellite system model

Maintains state estimates close to the manifold

Consumes minimal computational resources

Abstract

This paper proposes a simple, accurate and computationally efficient method to apply the ordinary unscented Kalman filter developed in Euclidean space to systems whose dynamics evolve on manifolds.We use the mathematical theory called stable embedding to make a variant of unscented Kalman filter that keeps state estimates in closeproximity 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 unscented Kalman filters 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 unscented Kalman filter devised in Euclidean space without any particular manifold-structure-preserving discretization method or coordinate transformation.