Any regular stationary random processes can be represented as the sum of a purely indeterministic process and a deterministic one. This paper considers the achievable accuracy in the joint estimation of the parameters of these two components, from a single observed realization of the process. An exact form of the Cramer-Rao bound (CRB) is derived, as well as a conditional CRB. The relationships between these bounds, and their relations to the previously derived asymptotic bound, are explored by analysis and numerical examples.
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