Fast Kalman-like optimal FIR filter for time-variant systems with improved robustness.

In this paper, a fast Kalman-like iterative OFIR algorithm is proposed for discrete-time filtering of linear time-varying dynamic systems. The batch OFIR filter is re-derived in an alternative way to show that this filter is unique for such systems. A computationally efficient fast iterative form is found for the OFIR filter using recursions. It is shown that each recursion has the Kalman filter (KF) predictor/corrector format with initial conditions specified via measurements on a horizon of N nearest past points. In this regard, the KF is considered as a special case of the iterative OFIR filtering algorithm when N goes to infinity. Applications are given for the 3-state target tracking and three-degree-of-freedom (DOF) hover system. It has been shown experimentally that the proposed iterative OFIR algorithm operates much faster than the batch OFIR filter and has the computational complexity acceptable for real-time applications. It has also been demonstrated by simulations that an increase in the number of the states results in better robustness of the OFIR filter against temporary model uncertainties and in higher immunity against errors in the noise statistics.

[1]  FU Jinbin,et al.  Maneuvering target tracking with modified unbiased FIR filter , 2015 .

[2]  Ji-Woong Choi,et al.  An FIR Channel Estimation Filter with Robustness to Channel Mismatch Condition , 2008, IEEE Transactions on Broadcasting.

[3]  Wook Hyun Kwon,et al.  A receding horizon Kalman FIR filter for discrete time-invariant systems , 1999, IEEE Trans. Autom. Control..

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

[5]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[6]  Feng Ding,et al.  Combined state and least squares parameter estimation algorithms for dynamic systems , 2014 .

[7]  Yuriy S. Shmaliy,et al.  Unbiased FIR Filtering of Discrete-Time Polynomial State-Space Models , 2009, IEEE Transactions on Signal Processing.

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

[9]  Yu Yao,et al.  A novel method for estimating the track-soil parameters based on Kalman and improved strong tracking filters. , 2015, ISA transactions.

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

[11]  Feng Ding,et al.  Iterative identification algorithms for bilinear-in-parameter systems with autoregressive moving average noise , 2017, J. Frankl. Inst..

[12]  G. Goodwin,et al.  Riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices , 1986 .

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

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

[15]  H.A.P. Blom,et al.  Exact Bayesian and particle filtering of stochastic hybrid systems , 2007, IEEE Transactions on Aerospace and Electronic Systems.

[16]  Wook Hyun Kwon,et al.  FIR filters and recursive forms for discrete-time state-space models , 1987, Autom..

[17]  Peter Willett,et al.  A Low-Complexity Sliding-Window Kalman FIR Smoother for Discrete-Time Models , 2010, IEEE Signal Processing Letters.

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

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

[20]  Wook Hyun Kwon,et al.  Minimum Variance FIR Smoothers for Discrete-Time State Space Models , 2007, IEEE Signal Processing Letters.

[21]  Meng Zhang,et al.  Low-cost precise measurement of oscillator frequency instability based on GNSS carrier observation , 2013 .

[22]  C. Ahn,et al.  Unbiased Finite Impluse Response Filtering: An Iterative Alternative to Kalman Filtering Ignoring Noise and Initial Conditions , 2017, IEEE Control Systems.

[23]  C. Desoer,et al.  Linear System Theory , 1963 .

[24]  Andrey V. Savkin,et al.  Real-time navigation of mobile robots in problems of border patrolling and avoiding collisions with moving and deforming obstacles , 2012, Robotics Auton. Syst..

[25]  Jay A. Farrell,et al.  Real-Time Computer Vision/DGPS-Aided Inertial Navigation System for Lane-Level Vehicle Navigation , 2012, IEEE Transactions on Intelligent Transportation Systems.

[26]  Leonid Mirkin,et al.  L2 Optimization in Discrete FIR Estimation: Exploiting State-Space Structure , 2013, SIAM J. Control. Optim..

[27]  Panos J. Antsaklis,et al.  Control and Communication Challenges in Networked Real-Time Systems , 2007, Proceedings of the IEEE.

[28]  Yaguo Lei,et al.  A data-driven multiplicative fault diagnosis approach for automation processes. , 2014, ISA transactions.

[29]  Ce Liu,et al.  A simple recursive method for stationary receiver position estimation using GPS difference measurements. , 2007, ISA transactions.

[30]  Gibson,et al.  A steady-state optimal control problem , 1976 .

[31]  Pyung-Soo Kim,et al.  A New FIR Filter for State Estimation and Its Application , 2007, Journal of Computer Science and Technology.

[32]  Fei Liu,et al.  Linear Optimal Unbiased Filter for Time-Variant Systems Without Apriori Information on Initial Conditions , 2017, IEEE Transactions on Automatic Control.

[33]  Feng Ding,et al.  Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering , 2017, Digit. Signal Process..

[34]  Wook Hyun Kwon,et al.  A receding horizon unbiased FIR filter for discrete-time state space models , 2002, Autom..

[35]  Wang Honglun,et al.  Sliding mode based trajectory linearization control for hypersonic reentry vehicle via extended disturbance observer. , 2014, ISA transactions.

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

[37]  Feng Ding,et al.  Kalman state filtering based least squares iterative parameter estimation for observer canonical state space systems using decomposition , 2016, J. Comput. Appl. Math..

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

[39]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[40]  Keck Voon Ling,et al.  Receding horizon recursive state estimation , 1999, IEEE Trans. Autom. Control..

[41]  Choon Ki Ahn,et al.  A new solution to the induced l∞ finite impulse response filtering problem based on two matrix inequalities , 2014, Int. J. Control.

[42]  Yuriy S. Shmaliy,et al.  Suboptimal FIR Filtering of Nonlinear Models in Additive White Gaussian Noise , 2012, IEEE Transactions on Signal Processing.

[43]  Visa Koivunen,et al.  Detection and Tracking of MIMO Propagation Path Parameters Using State-Space Approach , 2009, IEEE Transactions on Signal Processing.

[44]  Choon Ki Ahn,et al.  Fixed-lag maximum likelihood FIR smoother for state-space models , 2008, IEICE Electron. Express.

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

[46]  Choon Ki Ahn,et al.  Strictly passive FIR filtering for state-space models with external disturbance , 2012 .

[47]  Feng Ding,et al.  Some new results of designing an IIR filter with colored noise for signal processing , 2018, Digit. Signal Process..

[48]  Dan Simon,et al.  Iterative unbiased FIR state estimation: a review of algorithms , 2013, EURASIP J. Adv. Signal Process..

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

[50]  Peng Shi,et al.  Fusion Kalman/UFIR Filter for State Estimation With Uncertain Parameters and Noise Statistics , 2017, IEEE Transactions on Industrial Electronics.