Kalman state filtering based least squares iterative parameter estimation for observer canonical state space systems using decomposition

This paper focuses on the parameter and state estimation problems for observer canonical state space systems from measurement information, derives a Kalman filter based least squares iterative (KF-LSI) algorithm to estimate the parameters and states, and a model decomposition based KF-LSI algorithm to enhance computational efficiency. An example is provided to confirm the effectiveness of the proposed algorithms.

[1]  Tao Tang,et al.  Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems , 2014, Appl. Math. Lett..

[2]  Feng Ding,et al.  Hierarchical gradient parameter estimation algorithm for Hammerstein nonlinear systems using the key term separation principle , 2014, Appl. Math. Comput..

[3]  Feng Ding,et al.  Highly Efficient Identification Methods for Dual-Rate Hammerstein Systems , 2015, IEEE Transactions on Control Systems Technology.

[4]  Feng Ding,et al.  Recursive and iterative least squares parameter estimation algorithms for observability canonical state space systems , 2015, J. Frankl. Inst..

[5]  Mehdi Dehghan,et al.  Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices , 2014 .

[6]  Feng Ding,et al.  Decomposition Based Newton Iterative Identification Method for a Hammerstein Nonlinear FIR System with ARMA Noise , 2014, Circuits Syst. Signal Process..

[7]  Junhong Li,et al.  Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration , 2013, Appl. Math. Lett..

[8]  Tülay Adali,et al.  Unbiased Recursive Least-Squares Estimation Utilizing Dichotomous Coordinate-Descent Iterations , 2014, IEEE Transactions on Signal Processing.

[9]  Rik Pintelon,et al.  Identification of a Wiener–Hammerstein system using the polynomial nonlinear state space approach , 2009 .

[10]  Feng Ding,et al.  Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle , 2015, Signal Process..

[11]  Masoud Hajarian,et al.  Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations , 2013, J. Frankl. Inst..

[12]  Huazhen Fang,et al.  Kalman filter-based identification for systems with randomly missing measurements in a network environment , 2010, Int. J. Control.

[13]  Spilios D. Fassois,et al.  Adaptable functional series TARMA models for non-stationary signal representation and their application to mechanical random vibration modeling , 2014, Signal Process..

[14]  Feng Ding,et al.  Transformations between some special matrices , 2010, Comput. Math. Appl..

[15]  Jie Ding,et al.  Modified Subspace Identification for Periodically Non-uniformly Sampled Systems by Using the Lifting Technique , 2013, Circuits, Systems, and Signal Processing.

[16]  Mehdi Dehghan,et al.  Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations , 2011, Appl. Math. Lett..

[17]  Hazem N. Nounou,et al.  State and parameter estimation for nonlinear biological phenomena modeled by S-systems , 2014, Digit. Signal Process..

[18]  Johan Schoukens,et al.  Identification of systems with localised nonlinearity: From state-space to block-structured models , 2013, Autom..

[19]  F. Ding,et al.  Least squares algorithm for an input nonlinear system with a dynamic subspace state space model , 2014 .

[20]  Bo Yu,et al.  Robust mixed H2/H∞ control of networked control systems with random time delays in both forward and backward communication links , 2011, Autom..

[21]  Ximei Liu,et al.  New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems , 2014, Nonlinear Dynamics.

[22]  Fernando Jiménez Torres,et al.  Estimation of parameters of the shifted Gompertz distribution using least squares, maximum likelihood and moments methods , 2014, J. Comput. Appl. Math..

[23]  Mehdi Dehghan,et al.  Results concerning interval linear systems with multiple right-hand sides and the interval matrix equation AX=B , 2011, J. Comput. Appl. Math..

[24]  Hao Shen,et al.  Averaging complex subspaces via a Karcher mean approach , 2012, Signal Process..

[25]  Feng Ding,et al.  Gradient-Based Parameter Identification Algorithms for Observer Canonical State Space Systems Using State Estimates , 2015, Circuits Syst. Signal Process..

[26]  Yuanbiao Hu,et al.  Iterative and recursive least squares estimation algorithms for moving average systems , 2013, Simul. Model. Pract. Theory.

[27]  Fatemeh Panjeh Ali Beik,et al.  Preconditioned generalized mixed-type splitting iterative method for solving weighted least-squares problems† , 2014, Int. J. Comput. Math..

[28]  M. Dehghan,et al.  On the generalized reflexive and anti-reflexive solutions to a system of matrix equations , 2012 .

[29]  Ling Xu,et al.  The damping iterative parameter identification method for dynamical systems based on the sine signal measurement , 2016, Signal Process..

[30]  Feng Ding,et al.  Joint Estimation of States and Parameters for an Input Nonlinear State-Space System with Colored Noise Using the Filtering Technique , 2016, Circuits Syst. Signal Process..

[31]  Ling Xu,et al.  Application of the Newton iteration algorithm to the parameter estimation for dynamical systems , 2015, J. Comput. Appl. Math..

[32]  Mehdi Dehghan,et al.  A Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems , 2013 .

[33]  Yan Ji,et al.  Unified Synchronization Criteria for Hybrid Switching-Impulsive Dynamical Networks , 2015, Circuits Syst. Signal Process..

[34]  Wei Zhang,et al.  Improved least squares identification algorithm for multivariable Hammerstein systems , 2015, J. Frankl. Inst..

[35]  Mehdi Dehghan,et al.  Generalized solution sets of the interval generalized Sylvester matrix equation ∑i=1pAiXi + ∑j=1qYjBj = C and some approaches for inner and outer estimations , 2014, Comput. Math. Appl..

[36]  Feng Ding,et al.  Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model , 2015, Digit. Signal Process..

[37]  Joon-Hyuk Chang,et al.  Shrinkage estimation-based source localization with minimum mean squared error criterion and minimum bias criterion , 2014, Digit. Signal Process..

[38]  Dongqing Wang,et al.  Recursive maximum likelihood identification method for a multivariable controlled autoregressive moving average system , 2016, IMA J. Math. Control. Inf..

[39]  Feng Ding,et al.  Computation of matrix exponentials of special matrices , 2013, Appl. Math. Comput..

[40]  Ling Xu,et al.  Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration , 2015 .

[41]  Feng Ding,et al.  Recursive Least Squares Parameter Estimation for a Class of Output Nonlinear Systems Based on the Model Decomposition , 2016, Circuits Syst. Signal Process..

[42]  Ling Xu,et al.  A proportional differential control method for a time-delay system using the Taylor expansion approximation , 2014, Appl. Math. Comput..

[43]  Mehdi Dehghan,et al.  The interval Lyapunov matrix equation: Analytical results and an efficient numerical technique for outer estimation of the united solution set , 2012, Math. Comput. Model..

[44]  Feng Ding,et al.  Hierarchical gradient based and hierarchical least squares based iterative parameter identification for CARARMA systems , 2014, Signal Process..

[45]  Jie Ding,et al.  Auxiliary model based parameter estimation for dual-rate output error systems with colored noise ☆ , 2013 .