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Threshold parameter estimation in nonadditive non-Gaussian noise

Threshold or weak-signal locally optimum Bayes estimators (LOBEs) of signal parameters, where the observations are an arbitrary mixture of signal and noise, the latter being independent, are first derived for "simple" as well as quadratic cost functions under the assumption that the signal is present a priori. It is shown that the desired LOBEs are either a linear (simple cost function) or a nonlinear (quadratic cost function) functional of an associated locally optimum and asymptotically optimum Bayes detector. Second, explicit classes of (threshold) optimum estimators are obtained for both cost functions in the coherent as well as in the incoherent reception modes. Third, the general results are applied to amplitude estimation, where two examples are considered: (1) coherent amplitude estimation in multiplicative noise with simple cost function (SCF) and (2) incoherent amplitude estimation with quadratic cost function (QFC) of a narrowband signal arbitrarily mixed with noise. Moreover, explicit estimator structures are given together with desired properties (i.e. efficiency of the unconditional maximum likelihood (ML) estimator) and Bayes' risks. These properties are obtained by employing contiguity-a powerful concept in modern statistics-implied by the locally asymptotically normal character of the detection algorithms.