A semi-analytical solution to the global navigation satellite system attitude determination problem

Global navigation satellite system attitude determination based on carrier phase differencing technique is studied. A realistic stochastic model is followed to fully consider the correlations among different measurements in the least-squares problem formulation. A prior-free, computation-fixed, and averagely optimal solution is proposed suitable for real-time and high-dynamic situations. The prior-free property is achieved by developing an analytical sub-optimal solution. This solution follows first transforming the original problem into one with vector measurements and then further approximating it with a general Wahba's problem. The fixed computation is guaranteed by performing only one or two rounds of correction of the analytical solution. Every single round follows a linearization-estimation-correction process. The process also provides an error or covariance analysis for the estimate. The average optimality in terms of the root mean squared errors is brought about by the relatively good quality of the analytical solution and the fast convergence of the correction processes. The numerical experiments, with three 4 m long baselines and 5 mm (standard deviation) carrier phase errors, show that the estimation errors (in magnitude) for all three channels are well below 0.4 degrees for almost all epochs and within 0.2 degrees for most epochs.