Application of Fractional Sensor Fusion Algorithms for Inertial Mems Sensing

Abstract

The work presents an extension of the conventional Kalman filtering concept for systems of fractional order (FOS). Modifications are introduced using the Grünwald-Letnikov (GL) definition of the fractional derivative (FD) and corresponding truncation of the history length. Two versions of the fractional Kalman filter (FKF) are shown, where the FD is calculated directly or by augmenting the state vector with the estimate of the FD. The filters are compared to conventional integer order (IO) Position (P-KF) and Position-Velocity (PV-KF) Kalman filters as well as to an adaptive Interacting Multiple-Model Kalman Filter (IMM-KF).The performance of the filters is assessed based on a hand and a head motion data set. The feasibility of the given approach is shown.

Exoskeleton Hand Control by Fractional Order Models

“…The polar plot of cT(jωI−A1)−1b is shown in Figure 6. The closed-loop system satisfies the frequential criterion (Equation (17)), condition (18) is verified for ||Q||=14.5, ρ=2.17, MATLAB/SIMULINK and techniques based on the Mittag-Leffler functions are used for the simulation [1,2]. Figure 7 shows the trajectories of fractional order variables.…”

“…The idea is supported by the evidence of sβ dynamics in muscles and joint tissues throughout human musculo-skeletal system [2,3]. Interaction and dependence between biological systems and associated mechanical components was analyzed in [4,5,6].…”

Fractional Order Estimation Schemes for Fractional and Integer Order Systems with Constant and Variable Fractional Order Colored Noise

“…Similar algorithm to FKF was also used in [4] for R-wave detection in electrocardiogram signal. Moreover, Fractional Kalman-like algorithm also has been used to improve measurement results from MEMS sensors [22]. One of the most interesting and useful generalizations of the KF algorithm is the one for the case, where the noise is dynamically correlated [6].…”

Duality of variable fractional order difference operators and its application in identification

“…An algorithm similar to FKF was also used [29] for R-wave detection in electrocardiogram signal. Fractional Kalman-like algorithm has also been used to improve measurement results from microelectromechanical sensors [30].…”