Enhancing the Time-To-Fix for the unaided single-frequency integer ambiguity resolution in GNSS attitude determination applications

GNSS-based attitude determination is a viable technique with a large spectrum of applications. Attitude determination requires an accurate relative positioning solution, that can be provided by the very precise GNSS carrier phase observables. The phase observables are, however, biased by unknown integer ambiguities, that must be resolved in order to fully exploit their higher precision. By applying the optimal integer least-squares (ILS) principle and introducing a nontrivial modification of the popular LAMBDA method, a set of geometrical nonlinear constraints given by the known antennas placement on the platform is embedded in the ambiguity search method. The multivariate constrained LAMBDA method is described and tested: the large improvement in fixing the correct set of integer ambiguities from single-frequency, single-epoch observations is stressed, as this is the most challenging scenario for ambiguity resolution. The method is tested by processing and analyzing actual GNSS data, collected on both static and dynamic platforms. The experimental results show the enormous improvement obtained when applying the nonlinearly constrained, mixed integer GNSS attitude model, resulting in a very strong reduction in the Time-To-Fix.