On the state and parameter estimation of stochastic bilinear systems : a sub-optimal filtering approach Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/wd375z603

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  • Bilinear systems due to their variable structure properties offer more versatility in modelling of nonlinear processes than linear systems. The state estimation problem for a continuous bilinear system with a continuous observation model is studied and the results are extended to the case where the observations are of a discrete nature. It is shown that the optimal filter is of infinite dimension and a suboptimal solution based on the use of the conditional best estimate of the state in the multiplicative term, rather than the actual state, is proposed. The filter dimension is reduced to two and the mean and the variance equations are provided. A recursive maximum likelihood procedure operating on the proposed filter is used for the parameter identification. Both the likelihood functional and the gradient equations are provided. Computation of the gradient is dependent on computing the partial derivatives of the proposed filter equations with respect to the parameters. Simulation of the sample functions of bilinear systems using closed form solutions is discussed and a complete solution for the scalar case is provided. Parametric conditions for obtaining closed form solutions to the vector cases are supplied. A number of numerical examples illustrating the feasibility and performance of the proposed filter and parameter identification schemes are included. Both scalar and multivariable computational examples are considered.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2013-10-21T16:36:18Z (GMT) No. of bitstreams: 1 ShadmanValaviAli1978.pdf: 1074536 bytes, checksum: 8884a3b9fabdc61e5cf65fa7392b2917 (MD5)
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  • description.provenance : Approved for entry into archive by Kirsten Clark(kcscannerosu@gmail.com) on 2013-10-24T19:27:16Z (GMT) No. of bitstreams: 1 ShadmanValaviAli1978.pdf: 1074536 bytes, checksum: 8884a3b9fabdc61e5cf65fa7392b2917 (MD5)

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