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.

Key words:

• Kalman filter
• fractional‐order system,fractional filtering
• sensor fusion
• Grünwald‐Letnikov derivative