Maximum-likelihood-based filtering for attitude determination via GPS carrier phase

A maximum-likelihood-based (ML-based) filter is proposed for attitude determination via the GPS carrier phase observables. The quaternion representation is adopted here to describe the attitude. Hence, the norm constraint on the quaternion should be considered. The ML estimation with Lagrange multipliers can be used to consider simultaneously the evolution equation and the constraint, and to minimize the error covariance matrix. The attitude determination via GPS carrier phase observables is fulfilled in two steps. The first step is the GPS carrier phase ambiguity resolution. After the integer ambiguities being fixed, the ML-based filter is used to determine the optimal attitude. The advantage of adopting the quaternion as the state vector to describe the kinematic behavior is that no singular problems arise. To verify our algorithm, the simulation has been conducted. In the simulation, the white noises are added on the carrier phase observables to assess the performance of the proposed method. The body frame is formed by three non-colinear GPS antennae which are mounted on a platform with two aluminum bars representing the baseline vectors. According to the simulation, our method is sound and effective.