  The problem of detection and possible estimation of a signal generated by a
dynamic system when a variable number of noisy measurements can be taken is
here considered. Assuming a Markov evolution of the system (in particular, the
pair signal-observation forms a hidden Markov model), a sequential procedure is
proposed, wherein the detection part is a sequential probability ratio test
(SPRT) and the estimation part relies upon a maximum-a-posteriori (MAP)
criterion, gated by the detection stage (the parameter to be estimated is the
trajectory of the state evolution of the system itself). A thorough analysis of
the asymptotic behaviour of the test in this new scenario is given, and
sufficient conditions for its asymptotic optimality are stated, i.e. for almost
sure minimization of the stopping time and for (first-order) minimization of
any moment of its distribution. An application to radar surveillance problems
is also examined.
