On Robust Continuous-Time Discrimination
MARYLAND UNIV COLLEGE PARK SYSTEMS RESEARCH CENTER
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Target discrimination problems are modeled as the testing of binary hypotheses characterized by continuous-time observations which i consist of distinct signals in additive white Gaussian noise, or ii are the output of stochastic dynamical systems driven by white Gaussian noise, and in both cases have paflially known statistics. In particular, the signals in the first model, the parameters of the dynamical systems in the second model, and the autocorrelation functions of the noise in both models belong to one of the following distinct uncertainty classes classes determined by 2-alternating capacities and classes with minimum or maximum elements. Robust discrimination tests with a fixed observation interval and sequential tests are derived whose likelihood ratios depend on the least-favorable palrs of parameters in the aforementioned uncertainty classes and are shown to have an acceptable level of performance despite the uncertainty. For tests with a fixed observation interval the performance measures considered are the actual error probabilities and the chernoff upper bounds on them the latter are shown to preserve their desirable asymptotic properties in the presence of the unceflainties. For sequential tests the performance measures are the error probabilities and the average required length of the observation interval under each hypothesis.
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