Related papers: $SE_2(3)$ based Extended Kalman Filtering and Smoo…
This paper proposes a equivariant filtering (EqF) framework for the inertial-integrated state estimation problem. As the kinematic system of the inertial-integrated navigation can be naturally modeling on the matrix Lie group $SE_2(3)$, the…
One of core advantages of the SE2(3) Lie group framework for navigation modeling lies in the autonomy of error propagation. Current research on Lie group based extended Kalman filters has demonstrated that error propagation autonomy holds…
Invariant extended Kalman filter (InEKF) possesses excellent trajectory-independent property and better consistency compared to conventional extended Kalman filter (EKF). However, when applied to scenarios involving both global-frame and…
In this paper, the spacecraft attitude estimation problem has been investigated making use of the concept of matrix Lie group. Through formulation of the attitude and gyroscope bias as elements of SE(3), the corresponding extended Kalman…
While many works exploiting an existing Lie group structure have been proposed for state estimation, in particular the Invariant Extended Kalman Filter (IEKF), few papers address the construction of a group structure that allows casting a…
One of the core advantages of SE2(3) Lie group framework for navigation modeling lies in the autonomy of error propagation. In the previous paper, the theoretical analysis of autonomy property of navigation model in inertial, earth and…
Inertial Navigation Systems (INS) are a key technology for autonomous vehicles applications. Recent advances in estimation and filter design for the INS problem have exploited geometry and symmetry to overcome limitations of the classical…
This paper investigates the problem of inertial navigation system (INS) filter design through the lens of symmetry. The extended Kalman filter (EKF) and its variants have been the staple of INS filtering for 50 years. However, recent…
The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The Invariant Extended Kalman Filter (IEKF) is a recent development of the EKF for the class of group-affine systems on…
This paper derives a contact-aided inertial navigation observer for a 3D bipedal robot using the theory of invariant observer design. Aided inertial navigation is fundamentally a nonlinear observer design problem; thus, current solutions…
We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the…
This paper derives the extended Kalman filter (EKF) for continuous-time systems on matrix Lie groups observed through discrete-time measurements. By modeling the system noise on the Lie algebra and adopting a Stratonovich interpretation for…
This work deals with error models for trident quaternion framework proposed in the companion paper (Part I) and further uses them to investigate the odometer-aided static/in-motion inertial navigation attitude alignment for land vehicles.…
An extended Kalman filter (EKF) is developed on the special Euclidean group, SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an extensive linearization on SE(3) to estimate the state of the quadrotor from noisy…
The Extended Kalman Filter (EKF) is both the historical algorithm for multi-sensor fusion and still state of the art in numerous industrial applications. However, it may prove inconsistent in the presence of unobservability under a group of…
The widely-used Extended Kalman Filter (EKF) provides a straightforward recipe to estimate the mean and covariance of the state given all past measurements in a causal and recursive fashion. For a wide variety of applications, the EKF is…
The traditional GNSS-aided inertial navigation system (INS) usually exploits the extended Kalman filter (EKF) for state estimation, and the initial attitude accuracy is key to the filtering performance. To spare the reliance on the initial…
Pose estimation is important for robotic perception, path planning, etc. Robot poses can be modeled on matrix Lie groups and are usually estimated via filter-based methods. In this paper, we establish the closed-form formula for the error…
Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and lighting conditions, or fusion of…
Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under…