Estimation Theory with Fractional Gaussian Noise.
NAVAL SURFACE WARFARE CENTER DAHLGREN DIV VA
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Physical processes often cannot be accurately modeled as purely deterministic mathematical processes because of the random aspects of their behavior. This unpredictable aspect is often statistically modeled as Gaussian white noise. This research developed an optimal estimator for parameters and states of systems driven by another type of noise, known as fractional Gaussian noise FON processes. These stochastic processes can model systems containing long-term, slowly decreasing time-correlated random disturbances. Examples of processes that behave as fractional Gaussian noise processes are given. This report examines an estimator for an unknown parameter in a model represented by a form of FGN driven stochastic differential equation. This parameter determines which equation out of a family of differential equations best fits the physical phenomena being modeled. A simulation of fractional Brownian motion FBM process and a state model driven by FGN was also developed for the purpose of testing the estimator. Their correspondence is discussed. The estimator was tested, using the simulations of FEM and the state model driven by FGN. The simulator has potential for applications for studying a physical process that cannot be replicated in a laboratory, although its behavior needs to be simulated for examination. An alternate estimator was also derived that was shown to possess the property of strong consistency.
- Statistics and Probability