Maximum-likelihood attitude estimation using GPS signals

The maximum likelihood estimator (MLE) for a vehicle's attitude using signals received from GPS satellites is derived in this paper. A statistical model of the measured phase double-differences is developed to form the likelihood function. The attitude is represented by a rotation matrix, a member of the group of 3×3 special orthogonal matrices. A steepest descent-like maximization algorithm is derived, that guarantees that the estimates belong to this manifold. Experimental results illustrate the performance and the importance of considering the right correlation between measurements.