A real-time unscented Kalman filter on manifolds for challenging AUV navigation

Abstract

We consider the problem of localization and navigation of Autonomous Underwater Vehicles (AUV) in the context of high performance subsea asset inspection missions in deep water. We propose a solution based on the recently introduced Unscented Kalman Filter on Manifolds (UKF-M) for onboard navigation to estimate the robot's location, attitude and velocity, using a precise round and rotating Earth navigation model. Our algorithm has the merit of seamlessly handling nonlinearity of attitude, and is far simpler to implement than the extended Kalman filter (EKF), which is widely used in the navigation industry. The unscented transform notably spares the user the computation of Jacobians and lends itself well to fast prototyping in the context of multi-sensor data fusion. Besides, we provide the community with feedback about implementation, and execution time is shown to be compatible with real-time. Realistic extensive Monte-Carlo simulations prove uncertainty is estimated with accuracy by the filter, and illustrate its convergence ability. Real experiments in the context of a 900m deep dive near Marseille (France) illustrate the relevance of the method.

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

“…Here, H 1 , H 2 , and H 3 are the Earth's magnetic field vector components in the orbit frame as a function of time given as where M e is the magnetic dipole moment of the Earth, 𝜖 is the magnetic dipole tilt, i is the orbit inclination, and 𝜔 e is the spin rate of the Earth. In (11), v mag,C ∈ R 3 is the magnetometer measurement noise which follows N(0, 𝜎 2 mag,C ⋅ I 3 ). The rate gyros measurement model is given as follows:…”

“…This is the stably embedded version (7) of the satellite system model (10), that is, S 3 × R 3 is an invariant manifold of the modified system and is exponentially stable for the modified system; refer to Lemma 1 in Ko et al's paper. 24 Then, we may apply the standard UKF derived in Euclidean space directly to the system model ( 13) and the measurement models given in (11) and (12). Since the satellite system in nature is a continuous-time system, we generate a continuous-time trajectory of the satellite using (10).…”

“…Brossard et al 10 used a similar framework of UKF on manifolds as Hauberg et al and made an open-source code that can be used for practitioners not being familiar with manifolds and Lie groups. Cantelobre et al 11 applied the method of Brossard et al on position estimation of autonomous underwater vehicles. Sjøberg and Egeland 12 developed an UKF for matrix Lie groups.…”

Evaluation of UKF-Based Fusion Strategies for Autonomous Underwater Vehicles Multisensor Navigation

“…The principal difficulty stems from the unavailability of the traditional global localization sensors, such as the global positioning system (GPS), due to the reduced propagation of radio frequency signals in the underwater domain. To reach a satisfactory navigation accuracy, most of the navigation filters for AUVs exploit Bayesian estimators, such as the Kalman filter (KF) or its variants applied to nonlinear systems, as the extended Kalman filter (EKF) [1] or the unscented Kalman filter (UKF) [2]. As reported in [3], three different categories can be defined to collect the navigation and localization techniques, as the dead reckoning (DR) strategies, the transponder-based strategies, or the geophysical data based strategies.…”