Evaluation of the ANN Based Nonlinear System Models in the MSE and CRLB Senses
The System Identification problem looks for a
suitably parameterized model, representing a given process. The
parameters of the model are adjusted to optimize a performance
function based on error between the given process output and
identified process output. The linear system identification field is
well established with many classical approaches whereas most of
those methods cannot be applied for nonlinear systems. The problem
becomes tougher if the system is completely unknown with only the
output time series is available. It has been reported that the
capability of Artificial Neural Network to approximate all linear and
nonlinear input-output maps makes it predominantly suitable for the
identification of nonlinear systems, where only the output time series
is available. [1][2][4][5]. The work reported here is an attempt to
implement few of the well known algorithms in the context of
modeling of nonlinear systems, and to make a performance
comparison to establish the relative merits and demerits.
[1] N.K Sinha and B Kuszta, Modeling and Identification of Dynamic
systems,Van Nostrand Reinhold Company, New York,1983.
[2] Simon Haykin, Neural Networks a comprehensive Foundation,
Prentice Hall International Editions, 1999.
[3] A.V. Balakrishnan, Kalman Filtering Theory, Optimization
Software Inc. Publications Division, Newyork,1992
[4] Fa-Long Luo and Rolf Unbehauen, Applied Neural Networks for
Signal Processing, Cambridge University Press, 1997.
[5] Yaakov Bar-Shalaom and Xiao-Rong Li, Estimation and Tracking:
Principles, Techniques and Software. Artech House, Boston,
London, 1993.
[6] G.V. Puskorius and L.A Feldkamp, " Neuro Control of nonlinear
dynamical systems with Kalman Filter trained recurrent networks"
IEEE Transactions on neural networks, Vol 5, No.2, pp 279-297,
1994.
[7] K.S. Narendra and K Parthasarathy, "Identification and control of
Dynamical systems using neural networks", IEEE Transactions on
Neural Networks, Vol 1, No.2, pp 4-27, March 1990
[8] Shuhi Li, "Comparative Analysis of back propagation and
Extended Kalman filter in Pattern and Batch forms for training
Neural Networks", IEEE Transactions on Neural Network, Vol 2,
No.1, pp144-149, 2001
[9] M.S. Grewal and A.P Andrews, Kalman Filtering Theory and
Practice, Prentice Hall, Englewood Cliffs, 1993.
[10] Y. Linguni, H. Sakai, H. Tokumaru, "A Real Time Learning
Algorithm for Multilayered Neural Network based on the Extended
Kalman Filter", IEEE Transactions on Signal Processing, Vol 40,
No.4, pp 959-966,1992.
[11] Joost H. de Vlieger and Robert H.J. Gmelig Meyling , "Maximum
Likelihood Estimation for Long Range Target Tracking Using
Passive Sonar Measurements", IEEE transactions on Signal
Processing, Vol. 40, No.5, pp 1216-1225,May 1992
[12] Ivan Petrovic, Mato Baotic, Nedjeljko Peric "Model structure
selection for nonlinear system identification using feed forward
neural networks" ,Department of Control and Computer
Engineering in Automation, Unska 3, HR - 10 000 Zagreb,
Croatia.
[13] Simon Haykin, Adaptive Filter Theory, Prentice Hall International
editions, 1986
[14] Anders Forsgren and Robert Kling "Implementation of Recurrent
Neural Networks for Prediction and control of Nonlinear Dynamic
Systems", Lulea University of Technology, Lulea, Sweden
[15] Ben James, Brian D.O, Anderson, and Robert . C. Williamson
"Conditional Mean and Maximum Likelihood approaches to Multi
harmonic frequency estimation.", IEEE Transactions on Signal
Processing, Vol 42, No.6, pp 1366-1375, June 1994.
[16] Langford B White, "Robust Approximate likelihood ratio Tests for
Nonlinear dynamic systems", IEEE Transactions on Signal
Processing, Vol 43, No.8, pp 2028-2031, August 1995.
[1] N.K Sinha and B Kuszta, Modeling and Identification of Dynamic
systems,Van Nostrand Reinhold Company, New York,1983.
[2] Simon Haykin, Neural Networks a comprehensive Foundation,
Prentice Hall International Editions, 1999.
[3] A.V. Balakrishnan, Kalman Filtering Theory, Optimization
Software Inc. Publications Division, Newyork,1992
[4] Fa-Long Luo and Rolf Unbehauen, Applied Neural Networks for
Signal Processing, Cambridge University Press, 1997.
[5] Yaakov Bar-Shalaom and Xiao-Rong Li, Estimation and Tracking:
Principles, Techniques and Software. Artech House, Boston,
London, 1993.
[6] G.V. Puskorius and L.A Feldkamp, " Neuro Control of nonlinear
dynamical systems with Kalman Filter trained recurrent networks"
IEEE Transactions on neural networks, Vol 5, No.2, pp 279-297,
1994.
[7] K.S. Narendra and K Parthasarathy, "Identification and control of
Dynamical systems using neural networks", IEEE Transactions on
Neural Networks, Vol 1, No.2, pp 4-27, March 1990
[8] Shuhi Li, "Comparative Analysis of back propagation and
Extended Kalman filter in Pattern and Batch forms for training
Neural Networks", IEEE Transactions on Neural Network, Vol 2,
No.1, pp144-149, 2001
[9] M.S. Grewal and A.P Andrews, Kalman Filtering Theory and
Practice, Prentice Hall, Englewood Cliffs, 1993.
[10] Y. Linguni, H. Sakai, H. Tokumaru, "A Real Time Learning
Algorithm for Multilayered Neural Network based on the Extended
Kalman Filter", IEEE Transactions on Signal Processing, Vol 40,
No.4, pp 959-966,1992.
[11] Joost H. de Vlieger and Robert H.J. Gmelig Meyling , "Maximum
Likelihood Estimation for Long Range Target Tracking Using
Passive Sonar Measurements", IEEE transactions on Signal
Processing, Vol. 40, No.5, pp 1216-1225,May 1992
[12] Ivan Petrovic, Mato Baotic, Nedjeljko Peric "Model structure
selection for nonlinear system identification using feed forward
neural networks" ,Department of Control and Computer
Engineering in Automation, Unska 3, HR - 10 000 Zagreb,
Croatia.
[13] Simon Haykin, Adaptive Filter Theory, Prentice Hall International
editions, 1986
[14] Anders Forsgren and Robert Kling "Implementation of Recurrent
Neural Networks for Prediction and control of Nonlinear Dynamic
Systems", Lulea University of Technology, Lulea, Sweden
[15] Ben James, Brian D.O, Anderson, and Robert . C. Williamson
"Conditional Mean and Maximum Likelihood approaches to Multi
harmonic frequency estimation.", IEEE Transactions on Signal
Processing, Vol 42, No.6, pp 1366-1375, June 1994.
[16] Langford B White, "Robust Approximate likelihood ratio Tests for
Nonlinear dynamic systems", IEEE Transactions on Signal
Processing, Vol 43, No.8, pp 2028-2031, August 1995.
@article{"International Journal of Electrical, Electronic and Communication Sciences:59025", author = "M.V Rajesh and Archana R and A Unnikrishnan and R Gopikakumari and Jeevamma Jacob", title = "Evaluation of the ANN Based Nonlinear System Models in the MSE and CRLB Senses", abstract = "The System Identification problem looks for a
suitably parameterized model, representing a given process. The
parameters of the model are adjusted to optimize a performance
function based on error between the given process output and
identified process output. The linear system identification field is
well established with many classical approaches whereas most of
those methods cannot be applied for nonlinear systems. The problem
becomes tougher if the system is completely unknown with only the
output time series is available. It has been reported that the
capability of Artificial Neural Network to approximate all linear and
nonlinear input-output maps makes it predominantly suitable for the
identification of nonlinear systems, where only the output time series
is available. [1][2][4][5]. The work reported here is an attempt to
implement few of the well known algorithms in the context of
modeling of nonlinear systems, and to make a performance
comparison to establish the relative merits and demerits.", keywords = "Multilayer neural networks, Radial Basis Functions,Clustering algorithm, Back Propagation training, Extended Kalmanfiltering, Mean Square Error, Nonlinear Modeling, Cramer RaoLower Bound.", volume = "2", number = "12", pages = "2781-5", }