This paper presents the duality property of a Modified State-Dependent Riccati Equation MSDRE approach in optimal estimation and control. A nonlinear controller using the MSDRE is developed through a pseudo-linearization of spacecraft augmented nonlinear dynamics and kinematics. Based on the duality property of the MSDRE, the full-state information required for the controller is provided by a MSDRE estimator for spacecraft three-axis attitude and rate estimation based on the magnetometer measurements and their time derivatives. The spacecraft is controlled via magnetic actuation only using magnetorquers in a momentum bias system. The stability of the controller/estimator is investigated through Lyapunov function analysis. The presented approach has shown the capability of estimating the attitude better than 5 deg and rate of order 0.03 deg/s while, keeping the pointing accuracy within 5 deg with pointing stability of less than 0.05 deg/s in each axis.