Related papers: A Trident Quaternion Framework for Inertial-based …

The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution…

The Ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 [10] as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

Data assimilation has been applied to coastal hydrodynamic models to better estimate system states or parameters by incorporating observed data into the model. Kalman Filter (KF) is one of the most studied data assimilation methods whose…

This paper presents a solution for the state estimation and control problems for a class of unconventional vertical takeoff and landing (VTOL) UAVs operating in forward-flight conditions. A tightly-coupled state estimation approach is used…

This work presents new results and understanding of the Ensemble Kalman filter (EnKF) for inverse problems. In particular, using a Lagrangian dual perspective we show that EnKF can be derived from the sample average approximation (SAA) of…

Inertial navigation computation is to acquire the attitude, velocity and position information of a moving body by integrating inertial measurements from gyroscopes and accelerometers. Over half a century has witnessed great efforts in…

Inertial navigation applications are usually referenced to a rotating frame. Consideration of the navigation reference frame rotation in the inertial navigation algorithm design is an important but so far less seriously treated issue,…

Accurate structural response prediction forms a main driver for structural health monitoring and control applications. This often requires the proposed model to adequately capture the underlying dynamics of complex structural systems. In…

This paper presents a cost-effective inertial pedestrian dead reckoning method for the bipedal robot in the GPS-denied environment. Each time when the inertial measurement unit (IMU) is on the stance foot, a stationary pseudo-measurement…

Denavit and Hartenberg-based methods, such as Cardan, Fick, and Euler angles, describe the position and orientation of an end-effector in three-dimensional (3D) space. However, these methods have a significant drawback as they impose a…

This document describes standard approaches for filtering and estimation for quadrotors, created for the Udacity Flying Cars course. We assume previous knowledge of probability and some knowledge of linear algebra. We do not assume previous…

Respecting the geometry of the underlying system and exploiting its symmetry have been driving concepts in deriving modern geometric filters for inertial navigation systems (INSs). Despite their success, the explicit treatment of inertial…

This letter introduces two multi-sensor state estimation frameworks for quadruped robots, built on the Invariant Extended Kalman Filter (InEKF) and Invariant Smoother (IS). The proposed methods, named E-InEKF and E-IS, fuse kinematics, IMU,…

The kinematics of many control systems, especially in the robotics field, naturally live on smooth manifolds. Most classical state-estimation algorithms, including the extended Kalman filter, are posed on Euclidean space. Although any…

Autonomous proximity operations, such as active debris removal and on-orbit servicing, require high-fidelity relative navigation solutions that remain robust in the presence of parametric uncertainty. Standard estimation frameworks…

We propose a new type of the Ensemble Kalman Filter (EnKF), which uses the Fast Fourier Transform (FFT) for covariance estimation from a very small ensemble with automatic tapering, and for a fast computation of the analysis ensemble by…

This paper presents a novel Lagrangian approach to attitude tracking for rigid spacecraft using unit quaternions, where the motion equations of a spacecraft are described by a four degrees of freedom Lagrangian dynamics subject to a…

This letter re-visits the problem of visual-inertial navigation system (VINS) and presents a novel filter design we dub the multi state constraint equivariant filter (MSCEqF, in analogy to the well known MSCKF). We define a symmetry group…

Building upon the theory of Kalman Filtering on Lie Groups, this paper describes an Extended Kalman Filter and Smoother for Loosely Coupled Integration of GNSS/INS tailored for post-processing applications. The approach employs a dynamic…