High-Accuracy Instrumental Variable Identification of Continuous-Time Autoregressive Processes From Irregularly Sampled Noisy Data

A computationally efficient estimator of continuous-time autoregressive (AR) process parameters from irregularly sampled data affected by discrete-time white measurement noise is presented. It is described how an instrumental variable approach can be used for estimating the AR process parameters with high accuracy. Possible estimators of the incremental variance of the driving continuous-time white noise source and of the variance of the discrete-time white measurement noise are also discussed.

[1]  Karl Johan Åström Maximum likelihood and prediction error methods , 1980, Autom..

[2]  harald Cramer,et al.  Stationary And Related Stochastic Processes , 1967 .

[3]  Arnaud Rivoira,et al.  Real time Continuous AR parameter estimation from randomly sampled observations , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  Erik G. Larsson,et al.  The CRB for parameter estimation in irregularly sampled continuous-time ARMA systems , 2003, IEEE Signal Processing Letters.

[5]  Erik Larsson Identification of Stochastic Continuous-time Systems : Algorithms, Irregular Sampling and Cramér-Rao Bounds , 2003 .

[6]  S. Berman Stationary and Related Stochastic Processes , 1967 .

[7]  M. Mossberg,et al.  Instrumental variable identification of fading channel models from irregularly sampled noisy data , 2008, 2008 American Control Conference.

[8]  Dinh-Tuan Pham Estimation of continuous-time autoregressive model from finely sampled data , 2000, IEEE Trans. Signal Process..

[9]  Karl Johan Åström,et al.  On the choice of sampling rates in parametric identification of time series , 1969, Inf. Sci..

[10]  Bengt Carlsson,et al.  Estimation of continuous-time AR process parameters from discrete-time data , 1999, IEEE Trans. Signal Process..

[11]  W. Donoghue Monotone Matrix Functions and Analytic Continuation , 1974 .

[12]  Magnus Mossberg,et al.  Fast estimators for large-scale fading channels from irregularly sampled data , 2006, IEEE Transactions on Signal Processing.

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

[14]  T. Söderström,et al.  An IV-Scheme for Estimating Continuous-Time Stochastic Models from Discrete-Time Data , 1994 .

[15]  M. Mossberg Identification of Local Oscillator Noise in Sampling Mixers , 2006, 2006 IEEE 12th Digital Signal Processing Workshop & 4th IEEE Signal Processing Education Workshop.

[16]  T. Söderström,et al.  Least squares parameter estimation of continuous-time ARX models from discrete-time data , 1997, IEEE Trans. Autom. Control..

[17]  Torsten Söderström,et al.  Identification of continuous-time AR processes from unevenly sampled data , 2002, Autom..

[18]  Simon J. Godsill,et al.  Estimation of CAR processes observed in noise using Bayesian inference , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[19]  F. Marvasti Nonuniform sampling : theory and practice , 2001 .