Related papers: Quaternion kinematics for the error-state Kalman f…
The design of navigation observers able to simultaneously estimate the position, linear velocity and orientation of a vehicle in a three-dimensional space is crucial in many robotics and aerospace applications. This problem was mainly dealt…
This paper presents preliminary work on computing upper bounds on the estimation error covariance in the framework of the extended Kalman filter. The approach taken is using quadratic constraints to bound the dynamic nonlinearities and use…
Non-linear electrodynamics arising in the frames of field theories in noncommutative space-time is examined on the base of quaternion formalism. The problem of form-invariance of the corresponding nonlinear constitutive relations governed…
Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal…
This paper develops a geometric framework for invariant filtering of relative dynamics on Lie groups. We first revisit the notion of state trajectory independence, under which the estimation error evolves autonomously, and derive new…
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…
The miniaturization of inertial measurement units (IMUs) facilitates their widespread use in a growing number of application domains. Orientation estimation is a prerequisite for most further data processing steps in inertial motion…
Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…
Classical mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter or EKF, respectively), rely on…
In this paper, the intuitive idea of tilt is formalised into the rigorous concept of tilt rotations. This is motivated by the high relevance that pure tilt rotations have in the analysis of balancing bodies in 3D, and their applicability to…
A cooperative circumnavigation framework is proposed for multi-quadrotor systems to enclose and track a moving target without reliance on external localization systems. The distinct relationships between quadrotor-quadrotor and…
Kalman filtering is a classic state estimation technique used in application areas such as signal processing and autonomous control of vehicles. It is now being used to solve problems in computer systems such as controlling the voltage and…
Relying on the redefined vacuum state approach, and based on one-particle three-loop Feynman diagrams, partial third-order interelectronic corrections to the valence electron energy shift are investigated in Li-like ions. The idea is to…
The Kalman filter operates by storing a Gaussian description of the state estimate in the form of a mean and covariance. Instead of storing and manipulating the covariance matrix directly, a square-root Kalman filter only forms and updates…
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…
Magnetometer and inertial sensors are widely used for orientation estimation. Magnetometer usage is often troublesome, as it is prone to be interfered by onboard or ambient magnetic disturbance. The onboard soft-iron material distorts not…
From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through…
Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an…
Imitation learning techniques have been used as a way to transfer skills to robots. Among them, dynamic movement primitives (DMPs) have been widely exploited as an effective and an efficient technique to learn and reproduce complex discrete…
Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman…