This paper deals with a class of linear-quadratic Gaussian control problems where there exist parameter uncertainties in both the state and observation equations. An active dual control law is derived by using a variance minimization approach while an embedding scheme is proposed to overcome nonseparability in variance minimization. In order to solve the resulting auxiliary parametic problem, a solution method is adopted to treat the true system with uncertain parameters as a composition of multiple fictitious systems with completely known parameters, while the amount of contribution from the state of each fictitious system to the overall performance index at each stage is determined by the current posterior probability.