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In attitude determination using the unit quaternion representation, the unit norm constraint results in singularity of the covariance matrix using classical filtering methods. To cope with this problem, a constrained filtering method is developed. In this method, the constraint equations and the state equations are treated as pseudo-measurement equations, so that they can be processed simultaneously with the real measurement equations. To illustrate the application of the proposed scheme, a scenario using GPS and gyro to perform attitude determination is considered. Software simulations show that the proposed scheme is sound, effective, and superior to existing methods.