Constrained filtering method for attitude determination using GPS and gyro

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.