Batch Algorithm for Global-Positioning-System Attitude Determination and Integer Ambiguity Resolution

A new algorithm has been developed for simultaneous determination of attitude and carrier phase integer ambiguities based on data from an array of global-positioning-system (GPS) antennas. The purpose of the algorithm is to reduce the required number of tracked GPS satellites and antenna baselines needed to correctly resolve the ambiguities. This new motion-based method relies on data from several sample times. The vehicle must rotate about one or more axes among the samples. The solution algorithm works in two stages. It first solves a nonlinear least-squares problem in which the single-differenced carrier-phase ambiguities are allowed to vary as continuous real numbers. The second stage solves a nonlinear least-squares problem that restricts the ambiguities to be integers. This latter algorithm uses a combined Newton/Levenberg‐Marquardt method to deal with attitude quaternion nonlinearities, and it uses the least-squares ambiguity decorrelation adjustment method to deal with the integers. The second-stage algorithm is very accurate, but it needs to use initial guesses generated from first-stage algorithm solutions to find the global optimum. If the maneuver is large enough, then this new method can reliably solve difficult attitude/ambiguity-resolution problems. This capability has been demonstrated using Monte Carlo simulation. In one set of cases, the new algorithm correctly resolves ambiguities and achieves an accuracy of 4 deg or better when using two GPS satellite signals received by three antennas that are arrayed along 1-m baselines.