Quaternion-based extended Kalman filter for determining orientation by inertial and magnetic sensing

In this paper, a quaternion based extended Kalman filter (EKF) is developed for determining the orientation of a rigid body from the outputs of a sensor which is configured as the integration of a tri-axis gyro and an aiding system mechanized using a tri-axis accelerometer and a tri-axis magnetometer. The suggested applications are for studies in the field of human movement. In the proposed EKF, the quaternion associated with the body rotation is included in the state vector together with the bias of the aiding system sensors. Moreover, in addition to the in-line procedure of sensor bias compensation, the measurement noise covariance matrix is adapted, to guard against the effects which body motion and temporary magnetic disturbance may have on the reliability of measurements of gravity and earth's magnetic field, respectively. By computer simulations and experimental validation with human hand orientation motion signals, improvements in the accuracy of orientation estimates are demonstrated for the proposed EKF, as compared with filter implementations where either the in-line calibration procedure, the adaptive mechanism for weighting the measurements of the aiding system sensors, or both are not implemented.

Quaternion-based strap-down integration method for applications of inertial sensing to gait analysis

The proposed strap-down integration method exploits the cyclical nature of human gait: during the gait swing phase, the quaternion-based attitude representation is integrated using a gyroscope from initial conditions that are determined during stance by an accelerometer. Positioning requires double time integration of the gravity-compensated accelerometer signals during swing. An interpolation technique applied to attitude quaternions was developed to improve the accuracy of orientation and positioning estimates by accounting for the effect of sensor bias and scale factor drifts. A simulation environment was developed for the analysis and testing of the proposed algorithm on a synthetic movement trajectory. The aim was to define the true attitude and positioning used in the computation of estimation errors. By thermal modelling, the changes of bias and scale factor of the inertial sensors, calibrated at a single reference temperature, were analysed over a range of +/- 10 degrees C, for measurement noise standard deviations up to sigma(g) = 2.5 degrees s(-1) (gyroscope) and sigma(a) = 0.05 m s(-2) (accelerometer). The compensation technique reduced the maximum root mean square errors (RMSEs) to: RMSE(theta) = 14.6 degrees (orientation) and RMSE(d) = 17.7cm (positioning) for an integration interval of one gait cycle (an improvement of 3 degrees and 7 cm); RMSE(theta) = 14.8 degrees and RMSE(d) = 30.0 cm for an integration interval of two gait cycles (an improvement of 11 degrees and 262 cm).

A 3D Generic Inverse Dynamic Method using Wrench Notation and Quaternion Algebra

In the literature, conventional 3D inverse dynamic models are limited in three aspects related to inverse dynamic notation, body segment parameters and kinematic formalism. First, conventional notation yields separate computations of the forces and moments with successive coordinate system transformations. Secondly, the way conventional body segment parameters are defined is based on the assumption that the inertia tensor is principal and the centre of mass is located between the proximal and distal ends. Thirdly, the conventional kinematic formalism uses Euler or Cardanic angles that are sequence-dependent and suffer from singularities. In order to overcome these limitations, this paper presents a new generic method for inverse dynamics. This generic method is based on wrench notation for inverse dynamics, a general definition of body segment parameters and quaternion algebra for the kinematic formalism.

A modular software system for computer-aided surgery and its first application in oral implantology

Development of complex software applications in image guided therapy (IGT) is often complicated by the fact that providing basic functionality for image processing and user interaction from a graphical user interfaces (GUI) requires considerable manpower for software development. We present a programming environment that combines the high-level image processing library AVW, in-house developed patient-to-image registration procedures, and an interface to position measurement hardware. A specific application can be developed by using Tcl/Tk, a simple platform-independent scripting language, for GUI development. This environment was applied to developing VISIT, a navigation system for computer-aided implant dentistry. VISIT is presented as a result of this paper. Parts of the development environment were made accessible to the public. Future work includes the implementation of video input for connecting ultrasound or fluoroscopy units. We conclude that our approach is well suited to accelerate the development of exploratory new applications of IGT.

Multilayer Perceptrons to Approximate Quaternion Valued Functions

In this paper a new type of multilayer feedforward neural network is introduced. Such a structure, called hypercomplex multilayer perceptron (HMLP), is developed in quaternion algebra and allows quaternionic input and output signals to be dealt with, requiring a lower number of neurons than the real MLP, thus providing a reduced computational complexity. The structure introduced represents a generalization of the multilayer perceptron in the complex space (CMLP) reported in the literature. The fundamental result reported in the paper is a new density theorem which makes HMLPs universal interpolators of quaternion valued continuous functions. Moreover the proof of the density theorem can be restricted in order to formulate a density theorem in the complex space. Due to the identity between the quaternion and the four-dimensional real space, such a structure is also useful to approximate multidimensional real valued functions with a lower number of real parameters, decreasing the probability of being trapped in local minima during the learning phase. A numerical example is also reported in order to show the efficiency of the proposed structure. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.