  Simultaneous detection and estimation is important in many engineering
applications. In particular, there are many applications where it is important
to perform signal detection and Signal-to-Noise-Ratio (SNR) estimation jointly.
Application of existing frameworks in the literature that handle simultaneous
detection and estimation is not straightforward for this class of application.
This paper therefore aims at bridging the gap between an existing framework,
specifically the work by Middleton et al., and the mentioned application class
by presenting a jointly optimal detector and signal and noise power estimators.
The detector and estimators are given for the Gaussian observation model with
appropriate conjugate priors on the signal and noise power. Simulation results
affirm the superior performance of the optimal solution compared to the
separate detection and estimation approaches.
