Efficient motion estimation is central to observing and controlling dynamic legged locomotion. This paper considers a screw-theoretic (line-oriented) representation for this context and illustrates this on the attitude estimation subproblem. This is presented as part of an Extended Kalman Filter (EKF) based on inertial (gyroscopic) sensing in which each measurement axis is treated as an zeropit...

This paper presents a nonlinear numerical observer for accurate position, velocity and attitude (PVA) estimation including the accelerometer bias and gyro bias estimation. The Moving Horizon Observer (MHO) processes the accelerometer, gyroscope and magnetometer measurements from the Inertial Measurement Unit (IMU) and the position and velocity measurements from the Global Navigation Satellite S...

In this paper we present a quaternion-based Extended Kalman Filter (EKF) for estimating the three-dimensional orientation of a rigid body. The EKF exploits the measurements from an Inertial Measurement Unit (IMU) that is integrated with a tri-axial magnetic sensor. Magnetic disturbances and gyro bias errors are modeled and compensated by including them in the filter state vector. We employ the ...

Three-axis-magnetometers (TAMs) are widely utilized as a key component of attitude determination subsystems and as such are considered the corner stone of navigation for low Earth orbiting (LEO) space systems. Precise geomagnetic-based navigation demands accurate calibration of the magnetometers. In this regard, a complete online calibration process of TAM is developed in the current research t...

Many attitude estimation methods are based on an optimization problem posed in 1965 by Grace Wahba. All these methods will yield the same optimal estimate, except for inevitable computer roundoff errors. This note shows that Shuster’s Quaternion Estimator (QUEST) and Mortari’s Estimator of the Optimal Quaternion (ESOQ) are essentially identical even in the presence of computer roundoff errors. ...

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

The recently developed concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. In this paper, we will develop efficient algorithms for QFT, QCV, and quater...

In this project the possibility of using a network of magnetometers sensing a permanent magnet for tracking has been investigated. Both the orientation and the position of the magnet have been considered. A dipole approximation of the magnetic field is used to develop two models. One of the models parametrizes the orientation with the magnetic moment vector, while the other parametrizes the ori...

Obtaining precise attitude information is essential for aircraft navigation and control. This paper presents the results of the attitude determination using an in-house designed low-cost MEMS-based flight information measurement unit. This study proposes a quaternion-based extended Kalman filter to integrate the traditional quaternion and gravitational force decomposition methods for attitude d...