Joint statistical signal detection and estimation. Part I: Theoretical aspects of the problem

Abstract It is known that the problem of binary (or M-ary) hypothesis testing can be addressed in terms of the estimation of one (or M−1) discrete parameters which can assume the values 0 and 1. In the same fashion, the problem of composite hypothesis testing and parameter estimation can be seen as the joint estimation of a set of mixed discrete and continuous parameters, which can be modelled as random variables. In this paper, a comparison between serial and joint detection and parameter estimation schemes is carried out. The mathematical formulation is set up for the case of maximum a posteriori detectors and estimators; analytical results are derived for a meaningful case study, which permit to deeply understand the different mechanisms which govern the two schemes. The obtained results show that, although in quite different fashions, both schemes achieve the optimum average performance for a given amount of a priori information.

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