Exact filters for Newton-Raphson parameter estimation algorithms for continuous-time partially observed stochastic systems
AuthorCharalambous, Charalambos D.
Hibey, Joseph L.
SourceProceedings of the IEEE Conference on Decision and Control
Proceedings of the IEEE Conference on Decision and Control
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This paper presents explicit finite-dimensional filters for implementing Newton-Raphson (NR) parameter estimation algorithms. The models which exhibit nonlinear parameter dependence are stochastic, continuous-time and partially observed. The implementation of the NR algorithm requires evaluation of the log-likelihood gradient and the Fisher information matrix. Fisher information matrices are important in bounding the estimation error from below, via the Cramer-Rao bound. The derivations are based on relations between incomplete and complete data, likelihood, gradient and Hessian likelihood functions, which are derived using Girsanov's measure transformations.