The problem of approximate realisation is described and various methods are discussed. A new method is then given which directly identifies the system poles from pulse response data by finding the local minima of a real function of a complex variable. These estimates of the poles are then refined using a new iterative nonlinear least-squares algorithm. Finally, these methods are applied to a ‘seismic wavelet’, and are shown to give good qualitative and quantitative information on the system being modelled.
Inspec keywords: seismology; poles and zeros; geophysics computing; geophysical techniques; signal processing; data reduction and analysis
Other keywords:
Subjects: Numerical approximation and analysis; Civil and mechanical engineering computing; Seismic waves; Geophysics computing; Function theory, analysis; Instrumentation and techniques for geophysical, hydrospheric and lower atmosphere research; Simulation, modelling and identification
References
-
-
1)
- J.M. Mendel . (1973) , Discrete techniques of parameter estimation: the equation error formulation.
-
2)
- P.E. Gill , W. Murray . Algorithms for the solution of the non-linear least squares problem. SIAM J. Num. Anal. , 977 - 992
-
3)
- J.C. Willems . Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans. , 621 - 634
-
4)
- M.R. Chidambara , E.J. Davison . On a method for simplifying linear dynamical systems. IEEE Trans. , 119 - 121
-
5)
- M. Decoster , A.R. van Cauwenberghe . A comparative study of different reduction methods (Part 1 and 2). J. A , 2
-
6)
- J.M. Mendel . White noise estimators for seismic data processing in oil exploration. IEEE Trans. , 694 - 706
-
7)
- N.K. Gupta . Efficient computation of gradient and hessian of likelihood function in linear dynamic systems. IEEE Trans. , 781 - 783
-
8)
- P.C. Young . (1979) , Refined instrumental variable methods of recursive time series analysis parts 1 and 2.
-
9)
- Soderstrom, T., Ljung, L., Gustavsson, I.: `A comparative study of recursive identification methods', Report 7427, 1974.
-
10)
- R.W. Brockett . (1970) , Finite dimensional linear systems.
-
11)
- Glover, K.: `An approximate realisation algorithm which directly identifies the system poles', Paper 43A.3, IFAC World Congress, 1978, Helsinki.
-
12)
- G.R. Gavalas . A new method of parameter estimation in linear systems. A.I. Chem. E.J. , 214 - 222
-
13)
- Pinguet, P.J.M.: `State space formulation of a class of model reduction methods', 1978, M.Phil. dissertation, University of Cambridge, Department of Engineering.
-
14)
- N.K. Gupta , R.K. Mehra . Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations. IEEE Trans. , 774 - 783
-
15)
- de Jong, L.S.: `Numerical aspects of realisation algorithms in linear systems theory', 1975, Ph.D. dissertation, University of Eidnhoven, The Netherlands.
-
16)
- M.F. Hutton , B. Friedland . Routh approximations for reducing order of linear time-invariant systems. IEEE Trans. , 329 - 337
-
17)
- A.J. Tether . Construction of minimal linear state variable models from finite input - output data. IEEE Trans. , 427 - 436
-
18)
- L.M. Silverman . Realisation of linear dynamical systems. IEEE Trans. , 554 - 567
-
19)
- L. Meier , D.G. Luenberger . Approximation of linear constant systems. IEEE Trans. , 585 - 588
-
1)
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