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

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 (C) and i. In the same fashion, the problem of composite hypothesis testing and parameter estimation can be seen as the j oint estimation of a set of mixed discrete and continuous parameters, which can be modelled as random variables. In this paper, a comparison between s erial 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 whic h govern the two schemes. The obtained results show that, although in quite different fashions, both schemes achieve the optimum average performance f or a given amount of a priori information. (C) 2000 Elsevier Science B.V. A ll rights reserved.