Four-Element Array for GNSS Attitude Determination Using IRLS: An Improved Rounding of Long-Short Baseline Approach

Integer ambiguity resolution (AR) is the key to high-precision attitude determination with carrier phases. Traditional search-based AR methods require considerable computational power that is extremely challenging for high-rate and single-epoch implementations. Whereas, search-free AR methods via direct rounding suffer from the difficult deployment of short baseline and increased measurement noise. In this paper, an improved rounding strategy without any exhaustive search is proposed for properly designed four-element arrays to overcome the deployment issues and improve the AR success rate simultaneously. First, the novel four-element array is proposed to reduce the measurement noise of the virtual baseline, thus improve the AR success rate. The fourth antenna brings another virtual short baseline, such that the measurement quality can be improved by averaging. Second, the average operation is realized after detecting the integer ambiguity parity of each satellite. With a rounding scheme, the detection is performed on an epoch-by-epoch basis. Third, the success rate of AR in the long-short baseline method with a bias term is derived. Fourth, an improved rounding strategy is proposed by resolving the ambiguities sequentially. It is abbreviated as the Improved Rounding of Long-Short baseline (IRLS) approach. The least-squares method with quadratic equality constraints is further incorporated into IRLS to improve the accuracy of baseline estimation, namely QC-IRLS. Last, numerical simulations and field tests are carried out to verify the proposed array geometry and AR approach. In the field test, the proposed array reduces the standard deviation of short baseline estimation by up to two times, wherein all the ambiguities of 1886 valid epochs are successfully resolved.