Abstract:
The standard discrete-time autoregressive model is poorly suited for modeling series obtained by sampling continuous-time processes at fairly rapid rates. Large computati...Show MoreMetadata
Abstract:
The standard discrete-time autoregressive model is poorly suited for modeling series obtained by sampling continuous-time processes at fairly rapid rates. Large computational errors can occur when the Levinson algorithm is used to estimate the parameters of this model, because the Toeplitz covariance matrix is ill-suited for inversion. An alternative model is developed based on an incremental difference operator, rather than the shift operator. It is shown that, as the sampling period goes to zero, unlike the standard autoregressive parameters, the coefficients of this model converge to certain parameters that depend directly on the statistics of the continuous-time process. A Levinson-type algorithm for efficiently estimating the parameters of this model is derived. Numerical examples are given to show that when the sampling interval is small this algorithm is considerably less sensitivity to arithmetic roundoff errors than the Levinson algorithm.<>
Published in: IEEE Transactions on Automatic Control ( Volume: 36, Issue: 3, March 1991)
DOI: 10.1109/9.73564
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Cites in Papers - IEEE (35)
Select All
1.
Manuel Duarte Ortigueira, J.A. Tenreiro Machado, "The 21st Century Systems: An Updated Vision of Discrete-Time Fractional Models", IEEE Circuits and Systems Magazine, vol.22, no.3, pp.6-21, 2022.
2.
Chen Qin, Zhengrong Xiang, Hamid Reza Karimi, "Robust fault detection for switched systems with time-varying delay using delta operator approach", 2014 UKACC International Conference on Control (CONTROL), pp.145-150, 2014.
3.
B. Bandyopadhyay, P. S. Lal Priya, "Periodic output feedback control for Delta operator systems", 2013 International Conference on Control Communication and Computing (ICCC), pp.45-50, 2013.
4.
Xiaoming Su, Xiaoqi Kang, Haopeng Li, "Robust stabilization problem for a class of nonlinear singular systems with uncertainty", 2009 Chinese Control and Decision Conference, pp.4138-4142, 2009.
5.
Li Wen, P.J. Sherman, "On the influence of sampling and observation times on estimation of the bandwidth parameter of a Gauss-Markov process", IEEE Transactions on Signal Processing, vol.54, no.1, pp.127-137, 2006.
6.
P. De, H.H. Fan, "A delta least squares lattice algorithm for fast sampling", IEEE Transactions on Signal Processing, vol.47, no.9, pp.2396-2406, 1999.
7.
H. Fan, T. Soderstrom, M. Mossberg, B. Carlsson, Yuanjie Zou, "Estimation of continuous-time AR process parameters from discrete-time data", IEEE Transactions on Signal Processing, vol.47, no.5, pp.1232-1244, 1999.
8.
P. De, H.H. Fan, "Stable lattice filters and their continuous-time limits", IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.46, no.2, pp.149-164, 1999.
9.
H. Fan, "On delta-operator Schur-Cohn zero-location tests for fast sampling", IEEE Transactions on Signal Processing, vol.46, no.7, pp.1851-1860, 1998.
10.
H. Fan, T. Soderstrom, M. Mossberg, B. Carlsson, Y. Zon, "Continuous-time AR process parameter estimation from discrete-time data", Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), vol.4, pp.2333-2336 vol.4, 1998.
11.
P. De, H. Fan, "A delta least squares lattice algorithm for fast sampling", Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), vol.3, pp.1373-1376 vol.3, 1998.
12.
H.V. Poor, "Delta-operator based signal processing: fast algorithms for rapidly sampled data", Proceedings of the 36th IEEE Conference on Decision and Control, vol.1, pp.872-877 vol.1, 1997.
13.
H. Fan, "Efficient stability tests: unifying theory and further results using the delta operator", Proceedings of the 36th IEEE Conference on Decision and Control, vol.1, pp.896-901 vol.1, 1997.
14.
H. Fan, "A normalized Schur-Cohn stability test for the delta-operator-based polynomials", IEEE Transactions on Automatic Control, vol.42, no.11, pp.1606-1612, 1997.
15.
Qiang Li, H. Fan, "On properties of information matrices of delta-operator based adaptive signal processing algorithms", IEEE Transactions on Signal Processing, vol.45, no.10, pp.2454-2467, 1997.
16.
H. Fan, "Delta-operator based efficient stability tests", Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), vol.4, pp.2508-2512 vol.4, 1997.
17.
H.H. Fan, "Efficient zero location tests for delta-operator-based polynomials", IEEE Transactions on Automatic Control, vol.42, no.5, pp.722-727, 1997.
18.
T. Soderstrom, H. Fan, B. Carlsson, S. Bigi, "Least squares parameter estimation of continuous-time ARX models from discrete-time data", IEEE Transactions on Automatic Control, vol.42, no.5, pp.659-673, 1997.
19.
P. De, H. Fan, "A modified normalized lattice adaptive filter for fast sampling", 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, vol.3, pp.1941-1944 vol.3, 1997.
20.
Qiang Li, H. Fan, E. Karlsson, "A delta MYWE algorithm for parameter estimation of noisy AR processes", IEEE Transactions on Signal Processing, vol.44, no.5, pp.1300-1303, 1996.
21.
T. Soderstrom, H. Fan, S. Bigi, B. Carlsson, "Can a least-squares fit be feasible for modelling", Proceedings of 1995 34th IEEE Conference on Decision and Control, vol.2, pp.1795-1800 vol.2, 1995.
22.
A.D. Back, Ah Chung Tsoi, "Constrained pole-zero filters as discrete-time operators for system approximation", Proceedings of 1995 IEEE Workshop on Neural Networks for Signal Processing, pp.191-200, 1995.
23.
H.V. Poor, "Differential encoding of high-resolution data", 1995 International Geoscience and Remote Sensing Symposium, IGARSS '95. Quantitative Remote Sensing for Science and Applications, vol.3, pp.1675-1677 vol.3, 1995.
24.
Xiaqi Liu, H. Fan, "Unequal-length multichannel /spl delta//sub b/-Levinson and Schur type RLS algorithms", IEEE Transactions on Signal Processing, vol.43, no.1, pp.336-341, 1995.
25.
A.D. Back, Ah Chung Tsoi, "Alternative discrete-time operators in neural networks for nonlinear prediction", Proceedings of ANZIIS '94 - Australian New Zealnd Intelligent Information Systems Conference, pp.14-17, 1994.
26.
H. Fan, Xiaqi Liu, "Delta Levinson and Schur-type RLS algorithms for adaptive signal processing", IEEE Transactions on Signal Processing, vol.42, no.7, pp.1629-1639, 1994.
27.
K. Premaratne, R. Salvi, N.R. Habib, J.P. LeGall, "Delta-operator formulated discrete-time approximations of continuous-time systems", IEEE Transactions on Automatic Control, vol.39, no.3, pp.581-585, 1994.
28.
S.R. Weller, A. Feuer, G.C. Goodwin, H.V. Poor, "Interrelations between continuous and discrete lattice filter structures", IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.40, no.11, pp.705-713, 1993.
29.
C.J. Zarowski, "A QR-type algorithm for fitting the delta AR model to autocorrelation windowed data", IEEE Transactions on Signal Processing, vol.41, no.4, pp.1728-1730, 1993.
30.
H. Fan, "A structural view of asymptotic convergence speed of adaptive IIR filtering algorithms. I. Infinite precision implementation", IEEE Transactions on Signal Processing, vol.41, no.4, pp.1493-1517, 1993.
Cites in Papers - Other Publishers (24)
1.
P.S. Lal Priya, B. Bandyopadhyay, "Discrete time sliding mode control for uncertain Delta operator systems with infrequent output measurements", European Journal of Control, 2016.
2.
Chen Qin, Zhengrong Xiang, Hamid Reza Karimi, "Robust H? reliable control for delta operator switched systems with time-varying delays under asynchronous switching", Transactions of the Institute of Measurement and Control, vol.37, no.2, pp.219, 2015.
3.
Manuel D. Ortigueira, Fernando J.V. Coito, Juan J. Trujillo, "Discrete-time differential systems", Signal Processing, vol.107, pp.198, 2015.
4.
Chen Qin, Zhengrong Xiang, Hamid Reza Karimi, "Finite-time H ? control for switched systems with time-varying delay using delta operator approach", International Journal of Control, Automation and Systems, vol.12, no.6, pp.1150, 2014.
5.
Chen Qin, Zhengrong Xiang, Hamid Reza Karimi, "Robust Stability and Stabilization of Switched Systems with Time-Varying Delays Using Delta Operator Approach", Mathematical Problems in Engineering, vol.2013, pp.1, 2013.
6.
JÉRÔME HŒPFFNER, YOSHITSUGU NAKA, KOJI FUKAGATA, "Realizing turbulent statistics", Journal of Fluid Mechanics, vol.676, pp.54, 2011.
7.
JÉRÔME HŒPFFNER, YOSHITSUGU NAKA, KOJI FUKAGATA, "Realizing turbulent statistics", Journal of Fluid Mechanics, pp.1, 2011.
8.
H.Howard Fan, Parthapratim De, "High Speed Adaptive Signal Progressing Using the Delta Operator", Digital Signal Processing, vol.11, no.1, pp.3, 2001.
9.
P. Suchomski, "Numerical conditioning of delta-domain Lyapunov and Riccati equations", IEE Proceedings - Control Theory and Applications, vol.148, no.6, pp.497-501, 2001.
10.
Lih-Huah Yiin, H. Vincent Poor, "Linear interpolation models for rapidly-sampled data", Communications in Statistics. Stochastic Models, vol.14, no.4, pp.867, 1998.
11.
H.(Howard) Fan, "An efficient order recursive algorithm with a lattice structure for estimating continuous-time AR process parameters", Automatica, vol.33, no.3, pp.305, 1997.
12.
T. Söderström, H. Fan, M. Mossberg, B. Carlsson, "A Bias-Compensation Scheme for Estimating Continuous Time AR Process Parameters 1", IFAC Proceedings Volumes, vol.30, no.11, pp.1287, 1997.
13.
R. Vijayan, H.V. Poor, "Lattice filters based on the delta operator", IEE Proceedings - Vision, Image and Signal Processing, vol.144, no.3, pp.125-128, 1997.
14.
Kathleen E. Cullen, Claudio G. Rey, Daniel Guitton, Henrietta L. Galiana, "The use of system identification techniques in the analysis of oculomotor burst neuron spike train dynamics", Journal of Computational Neuroscience, vol.3, no.4, pp.347, 1996.
15.
M Mrabti, M Benseddik, "Unified type non-stationary Lyapunov matrix equation — Simultaneous eigenvalue bounds", Systems & Control Letters, vol.24, no.1, pp.53, 1995.
16.
Ah Chung Tsoi, Andrew Back, "Static and dynamic preprocessing methods in neural networks", Engineering Applications of Artificial Intelligence, vol.8, no.6, pp.633, 1995.
17.
Kamal Premaratne, A. S. Boujarwah, "An algorithm for stability determination of two-dimensional delta-operator formulated discrete-time systems", Multidimensional Systems and Signal Processing, vol.6, no.4, pp.287, 1995.
18.
Ah Chung Tsoi, Andrew Back, Safety, Reliability and Applications of Emerging Intelligent Control Technologies, pp.153, 1995.
19.
Ah Chung Tsoi, Andrew Back, "Static and Dynamic Preprocessing Methods in Neural Networks", IFAC Proceedings Volumes, vol.27, no.16, pp.153, 1994.
20.
C. G. Rey, H. L. Galiana, "Transient analysis of vestibular nystagmus", Biological Cybernetics, vol.69, no.5-6, pp.395, 1993.
21.
C. G. Rey, H. L. Galiana, "Transient analysis of vestibular nystagmus", Biological Cybernetics, vol.69, no.5-6, pp.395, 1993.
22.
Rajiv Vijayan, H. Vincent Poor, "Fast Triangular Factorization of Covariance Matrices of Differenced Time Series", SIAM Journal on Matrix Analysis and Applications, vol.14, no.4, pp.1096, 1993.
23.
Alain Le Breton, Dinh Tuan Pham, "Maximum likelihood estimation for continuous-time autoregressive models by relaxation on residual variances ratio parameters", Mathematics of Control, Signals and Systems, vol.6, no.1, pp.62, 1993.
24.
H. V. Poor, Adaptive Signal Processing, pp.173, 1991.