A major advance of using the quaternion to describe body orientation is that the kinematics equation is linear and the quaternion is also globally nonsingular. However, the algebraic constraint of unit norm needs to be maintained. An improved nonlinear constrained filter algorithm is proposed for the spacecraft attitude estimation problem subject to a unit quaternion norm constraint. First,by comparing the quaternion norm of a priori and a posteriori estimate, it is proved that the Multiplicative Extended Kalman filter can not gain the optimal solution under nonlinear constraint. Then, a generalized quadratically constrained optimization object function is developed by effective combination of QUEST algorithm and Multiplicative Kalman filter. During the predicting state, the attitude and its covariance propagation models are used to modify the cost function. During the measurement update phase, the quaternion normalization is explicitly maintained in a globally optimal manner by solving the eigenvalue-eigenvector problem and therefore the local linearization is avoided. Compared with the Multiplicative Extended Kalman filter, numerical simulation result demonstrates the precision, stability and convergence of the presented algorithm.