An Extended Kalman Filter for Time Delays Inspired by a Fractional Order Model

In this paper a method to estimate time delays between two periodic signals using Extended Kalman Filters (EKF) is presented. Fractional Derivatives were used as an inspiration in the underlying EKF system model of the time delay to improve the approximation of the time delay transfer function by a truncated Taylor polynomial. This method results to reduce estimation offsets. The approach is based on the assumption that, apart from some noise and the time delay to be estimated, there is no difference between the two signals. Simulations confirm that this method works well for Gaussian bell curve-like signals with a period that is one order of magnitude greater than the time delay.

[1]  Yan Zhou,et al.  Non-fragile Observer Design for Fractional-order One-sided Lipschitz Nonlinear Systems , 2013, Int. J. Autom. Comput..

[2]  Paolo Mercorelli,et al.  Friction hysteresis compensation using phase correction of periodic trajectories , 2017, 2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR).

[3]  Li Chunlin,et al.  Observer-based robust stabilisation of a class of non-linear fractional-order uncertain systems: an linear matrix inequalitie approach , 2012 .

[4]  Paolo Mercorelli.  Combining flatness based feedforward action with a fractional PI regulator to control the intake valve engine , 2017, 2017 18th International Carpathian Control Conference (ICCC).

[5]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[6]  I. Podlubny.  Fractional differential equations , 1998 .

[7]  Jean Lévine,et al.  Flatness for linear fractional systems with application to a thermal system , 2013, Autom..

[8]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order $\alpha$: The $0≪\alpha≪1$ Case , 2010, IEEE Transactions on Automatic Control.

[9]  Jun-Guo Lu,et al.  Stability Analysis of a Class of Nonlinear Fractional-Order Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Xuefeng Zhang,et al.  Observer-based robust control of ( 0 < α < 1 ) fractional-order linear uncertain control systems , 2016 .

[11]  J. Machado.  Analysis and design of fractional-order digital control systems , 1997 .

[12]  Paolo Mercorelli.  A discrete-time fractional order PI controller for a three phase synchronous motor using an optimal loop shaping approach , 2017 .

[13]  Salim Ibrir,et al.  New sufficient conditions for observer-based control of fractional-order uncertain systems , 2015, Autom..

[14]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .