EM-based identification of continuous-time ARMA Models from irregularly sampled data

Abstract In this paper we present a novel algorithm for identifying continuous-time autoregressive moving-average models utilizing irregularly sampled data. The proposed algorithm is based on the expectation–maximization algorithm and obtains maximum-likelihood estimates. The proposed algorithm shows a fast convergence rate, good robustness to initial values, and desirable estimation accuracy. Comparisons are made with other algorithms in the literature via numerical examples.

[1]  N. Shephard,et al.  Likelihood INference for Discretely Observed Non-linear Diffusions , 2001 .

[2]  M. Gevers,et al.  A personal view of the development of system identification: A 30-year journey through an exciting field , 2006, IEEE Control Systems.

[3]  G. Goodwin,et al.  Sampling and Sampled-Data Models: The Interface Between the Continuous World and Digital Algorithms , 2013, IEEE Control Systems.

[4]  Lennart Ljung,et al.  Issues in sampling and estimating continuous-time models with stochastic disturbances , 2010, Autom..

[5]  A. Dembo,et al.  Parameter estimation of partially observed continuous time stochastic processes via the EM algorithm , 1992 .

[6]  Torsten Söderström,et al.  Identification of Continuous-Time ARX Models From Irregularly Sampled Data , 2007, IEEE Transactions on Automatic Control.

[7]  Boris I. Godoy,et al.  Identification of Continuous-time Transfer Function Models from Non-uniformly Sampled Data in Presence of Colored Noise , 2014 .

[8]  Torsten Söderström,et al.  Discrete-time Stochastic Systems , 2002 .

[9]  Henghsiu Tsai,et al.  Quasi‐Maximum Likelihood Estimation for a Class of Continuous‐time Long‐memory Processes , 2005 .

[10]  C. Charalambous,et al.  Exact filters for Newton–Raphson parameter estimation algorithms for continuous-time partially observed stochastic systems☆ , 2001 .

[11]  Graham C. Goodwin,et al.  Dual time-frequency domain system identification , 2012, Autom..

[12]  Magnus Mossberg,et al.  Estimation of Continuous-Time Stochastic Signals From Sample Covariances , 2008, IEEE Transactions on Signal Processing.

[13]  Tomas McKelvey,et al.  State-space parametrizations of multivariable linear systems using tridiagonal matrix forms , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[14]  N. Sinha,et al.  Identification of Continuous-Time Systems: Methodology and Computer Implementation , 1991 .

[15]  Michael Unser,et al.  A Sampling Theory Approach for Continuous ARMA Identification , 2011, IEEE Transactions on Signal Processing.

[16]  Graham C. Goodwin,et al.  Sampling and sampled-data models , 2010, Proceedings of the 2010 American Control Conference.

[17]  R. Engle,et al.  Alternative Algorithms for the Estimation of Dynamic Factor , 1983 .

[18]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[19]  T. Söderström,et al.  Estimation of Continuous-time Stochastic System Parameters , 2008 .

[20]  G. Goodwin,et al.  Identification of continuous-time state-space models from non-uniform fast-sampled data , 2011 .

[21]  Brett Ninness,et al.  Robust maximum-likelihood estimation of multivariable dynamic systems , 2005, Autom..

[22]  J. Brewer.  The derivative of the exponential matrix with respect to a matrix , 1977 .

[23]  Thomas B. Schön,et al.  System identification of nonlinear state-space models , 2011, Autom..

[24]  Adrian Wills,et al.  Issues in sampling and estimating continuous-time models with stochastic disturbances , 2008 .

[25]  K. Chan,et al.  COMPARISON OF TWO DISCRETIZATION METHODS FOR ESTIMATING CONTINUOUS-TIME AUTOREGRESSIVE MODELS , 2000 .

[26]  Boris I. Godoy,et al.  An EM-based identification algorithm for a class of hybrid systems with application to power electronics , 2014, Int. J. Control.

[27]  R. Shumway,et al.  AN APPROACH TO TIME SERIES SMOOTHING AND FORECASTING USING THE EM ALGORITHM , 1982 .

[28]  Liuping Wang,et al.  Identification of Continuous-time Models from Sampled Data , 2008 .

[29]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[30]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[31]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[32]  G.C. Goodwin,et al.  Approximate EM Algorithms for Parameter and State Estimation in Nonlinear Stochastic Models , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[33]  Feng Ding,et al.  Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems , 2009, Autom..