Multi-state Dependent Parameter Model Identification and Estimation

  • Włodek Tych
  • Jafar Sadeghi
  • Paul J. Smith
  • Arun Chotai
  • C. James Taylor


This chapter describes an important generalisation of the State Dependent Parameter (SDP) approach to the modelling of nonlinear dynamic systems to include Multi-State Dependent Parameter (MSDP) nonlinearities. The recursive estimation of the MSDP model parameters in a multivariable state space occurs along a multi-path trajectory, employing the Kalman Filter and Fixed Interval Smoothing algorithms. The novelty of the method lies in redefining the concepts of sequence (predecessor, successor), allowing for its use in a multi-state dependent context, so producing efficient parameterisation for a fairly wide class of non-linear, stochastic dynamic systems. The format of the estimated model allows its direct use in control system design. Two worked examples in Matlab are included.


Kalman Filter Linear Dynamic System Time Vary Parameter Ensemble Kalman Filter Sample Time Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Peter Young’s help and advice was invaluable in the development of the project, built largely upon his ideas and philosophy. It is a great satisfaction and an honour to contribute to this volume.

This generalisation of SDP has been developed at Lancaster University during Jafar Sadeghi’s Ph.D. studentship funded by the Iranian Government between 2003–2006.

Thanks are also due to Katarzyna M. Tych of Leeds University for comments and suggestions on data and results visualisation.


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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Włodek Tych
    • 1
  • Jafar Sadeghi
    • 1
  • Paul J. Smith
    • 1
  • Arun Chotai
    • 1
  • C. James Taylor
    • 2
  1. 1.Lancaster Environment CentreLancaster UniversityLancasterUK
  2. 2.Engineering DepartmentLancaster UniversityLancasterUK

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