Fusion Kalman/UFIR Filter for State Estimation With Uncertain Parameters and Noise Statistics

In this paper, we fuse the Kalman filter (KF) that is optimal but not robust with the unbiased finite-impulse response (UFIR) filter which is more robust than KF but not optimal. The fusion filter employs the KF and UFIR filter as subfilters and produces smaller errors under the industrial conditions. In order to provide the best fusion effect, the operation point where UFIR meets Kalman is determined by applying probabilistic weights to each subfilter. Extensive simulations of the three degree of freedom (3-DOF) hover system have shown that the fusion filter output tends to range close to that by the best subfilter. Experimental verification provided for a 1-DOF torsion system has confirmed validity of simulation.

[1]  Henry Cox,et al.  On the estimation of state variables and parameters for noisy dynamic systems , 1964 .

[2]  Kiyoshi Ohishi,et al.  Kalman-Filter-Based Sensor Integration of Variable Power Assist Control Based on Human Stiffness Estimation , 2009, IEEE Transactions on Industrial Electronics.

[3]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[4]  Yuriy S. Shmaliy,et al.  Time‐variant linear optimal finite impulse response estimator for discrete state‐space models , 2012 .

[5]  Seong Yun Cho,et al.  Adaptive IIR/FIR fusion filter and its application to the INS/GPS integrated system , 2008, Autom..

[6]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[7]  Fei Liu,et al.  Fast Kalman-Like Optimal Unbiased FIR Filtering With Applications , 2016, IEEE Transactions on Signal Processing.

[8]  Dan Simon,et al.  Unified forms for Kalman and finite impulse response filtering and smoothing , 2013, Autom..

[9]  B. Anderson,et al.  Detectability and Stabilizability of Time-Varying Discrete-Time Linear Systems , 1981 .

[10]  Josep M. Guerrero,et al.  Introduction to the Special Section on Industrial Applications and Implementation Issues of the Kalman Filter , 2012, IEEE Trans. Ind. Electron..

[11]  Ali H. Sayed,et al.  A framework for state-space estimation with uncertain models , 2001, IEEE Trans. Autom. Control..

[12]  Fei Liu,et al.  Minimum variance unbiased FIR filter for discrete time-variant systems , 2015, Autom..

[13]  Farid Golnaraghi,et al.  A Fastening Tool Tracking System Using an IMU and a Position Sensor With Kalman Filters and a Fuzzy Expert System , 2009, IEEE Transactions on Industrial Electronics.

[14]  Jae Weon Choi,et al.  Localization of a mobile robot using the image of a moving object , 2003, IEEE Trans. Ind. Electron..

[15]  Yuriy S. Shmaliy,et al.  An Iterative Kalman-Like Algorithm Ignoring Noise and Initial Conditions , 2011, IEEE Transactions on Signal Processing.

[16]  Yuriy S. Shmaliy,et al.  Optimal Memory for Discrete-Time FIR Filters in State-Space , 2014, IEEE Trans. Signal Process..

[17]  Kouhei Ohnishi,et al.  Implementation of Bilateral Control System Based on Acceleration Control Using FPGA for Multi-DOF Haptic Endoscopic Surgery Robot , 2009, IEEE Transactions on Industrial Electronics.

[18]  Yong Zhou,et al.  Speed Estimation and Nonmatched Time-Varying Parameter Identification for a DC Motor With Hybrid Sliding-Mode Observer , 2013, IEEE Transactions on Industrial Electronics.

[19]  Josep M. Guerrero,et al.  Industrial Applications of the Kalman Filter: A Review , 2013, IEEE Transactions on Industrial Electronics.

[20]  Georg Fuchs,et al.  Application of the Modern Taylor Series Method to a multi-torsion chain , 2013, Simul. Model. Pract. Theory.

[21]  Yuriy S. Shmaliy.  GPS-Based Optimal FIR Filtering of Clock Models , 2013 .

[22]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[23]  Roberto Oboe,et al.  Acceleration Measurement Drift Rejection in Motion Control Systems by Augmented-State Kinematic Kalman Filter , 2016, IEEE Transactions on Industrial Electronics.

[24]  A. Jazwinski.  Limited memory optimal filtering , 1968 .

[25]  Fei Liu,et al.  Fast Computation of Discrete Optimal FIR Estimates in White Gaussian Noise , 2015, IEEE Signal Processing Letters.

[26]  Fan-Tien Cheng,et al.  Study and resolution of singularities for a 7-DOF redundant manipulator , 1997, Proceedings of the IECON'97 23rd International Conference on Industrial Electronics, Control, and Instrumentation (Cat. No.97CH36066).

[27]  Václav Smídl,et al.  Variational Bayesian Filtering , 2008, IEEE Transactions on Signal Processing.

[28]  W. Kwon,et al.  Receding Horizon Control: Model Predictive Control for State Models , 2005 .

[29]  Ian R. Petersen,et al.  Robust Kalman Filtering for Signals and Systems with Large Uncertainties , 1999 .

[30]  Yuriy S. Shmaliy,et al.  Optimal horizons for a one-parameter family of unbiased FIR filters , 2008, Digit. Signal Process..

[31]  Pedro Albertos,et al.  A new dead-time compensator to control stable and integrating processes with long dead-time , 2008, Autom..

[32]  Kouhei Ohnishi,et al.  Multi-DOF Micro-Macro Bilateral Controller Using Oblique Coordinate Control , 2011, IEEE Transactions on Industrial Informatics.

[33]  Yuriy S. Shmaliy,et al.  Linear Optimal FIR Estimation of Discrete Time-Invariant State-Space Models , 2010, IEEE Transactions on Signal Processing.