NSF Research Statement

of a system in an information deficient environment. Many systems have unobservable or hidden states, which implies that any observations of the system will be unable to contribute to a unique determination of its full state. In other cases, several observations are required before the state can be determined. In the most basic sense, this leads to a system in which there are more unknowns than constraints. Thus, there exists a continuum of possible true system states, making a unique state estimate difficult to obtain. With this in mind, how can an optimal estimation of the state be obtained with the limited information available to the observer? Hypothesis: Measurement uncertainties can be incorporated in the admissible region method to provide a better approximation of the initial probability distribution over the possible true system states. The initial distributions can then be used to start an estimator, providing better state estimates with limited information. Research Plan: An admissible region is a set of the possible true states of a system based bounded by a given constraint of the system [?]. The region itself represents a probability distribution over the solutions meeting the constraints. The admissibl