State Inference and Bayesian Identification of Non-linear State-space Models

• Author / Creator

  Tulsyan, Aditya

• State inference and identification of discrete-time, non-linear, stochastic state-space models (SSMs) are considered here. A novel sequential Monte Carlo (SMC) based Bayesian method for simultaneous on-line state inference and identification of non-linear SSMs is proposed. Extension of the method to handle missing measurements in real-time is also provided. Using posterior Cramer-Rao lower bound (PCRLB), a minimum mean square error (MMSE) simultaneous state inferencing and identification strategy is developed for general non-linear systems. The PCRLB used here is derived for discrete-time, stochastic non-linear SSMs with unknown model parameters. It is shown that under some conditions, performing simultaneous state inferencing and identification according to the developed PCRLB based strategy yields a minimum mean square error state and parameter estimates. A PCRLB based tool is developed to assess the quality of the parameter estimates. A distinct advantage of the developed tool is that it is general, and can be used to perform error analysis for an entire class of on-line Bayesian identification methods. The problems of input design and prior design are also considered. The input design problem helps to design optimal inputs for Bayesian identification, while the prior design problem helps to effectively organize a priori process information. In this thesis, the problem of prior design is only considered in the context of designing optimal inputs for Bayesian identification. For state inferencing in non-linear SSMs, a PCRLB based performance assessment and diagnosis tool is proposed for different non-linear state filters. The proposed assessment and diagnosis tool makes use of the PCRLB, derived for discrete-time, stochastic non-linear SSMs with known model parameters. Its utility in devising an optimal state inferencing strategy for non-linear systems is also provided. To avoid using the true states in the computation of the PCRLB, an SMC based method is also developed to allow computation of the PCRLB in absence of true state information. Finally, it is illustrated how the tools developed in this thesis can be put together into a unified framework to allow for efficient state inferencing and Bayesian identification of non-linear dynamical systems.

• Subjects / Keywords

  • State inference
  • Bayesian methods
  • Identification
  • State-space models

• Graduation date

  Fall 2013

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3TT4G44M

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.