We consider the problem of sequential estimation of a random parameter under a controlled setting. Unlike traditional estimation problems, the collected observations depend on the used actions, which control the quality of the sensing process. At each time step, the decision maker chooses a control from a finite set of controls or decides to stop collecting measurements.  The goal is to design an efficient causal control policy and a stopping rule and the efficiency is captured using the notion of asymptotic pointwise optimality (APO). We propose a procedure consisting of a control policy and a stopping rule, which is shown to be APO.