Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 219, Issue 17, Pages 9033-9042Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2013.03.019
Keywords
Sequential parameter estimation; Nonlinear systems; Unscented Kalman filter; Continuous-discrete state space; Estimation of uncorrelated states; Volatility estimation
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Many nonlinear extensions of the Kalman filter, e. g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, these filters only estimate states that are correlated with the observation. Therefore, sequential estimation of diffusion parameters, e. g., volatility, which are not correlated with the observations is not possible. While other filters overcome this problem with simulations, we extend the measurement update of the Gaussian two-moment filters by a higher order correlation measurement update. We explicitly state formulas for a higher order unscented Kalman filter within a continuous-discrete state space. We demonstrate the filter in the context of parameter estimation of an Ornstein-Uhlenbeck process. (C) 2013 Elsevier Inc. All rights reserved.
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