Attitude Determination with GPS L1/Galileo E1 Observations from Common-Clock Receiver: A Comparison of Four Different Models

The development of the commercial multi global navigation satellite system (GNSS) dual (multi)-antenna common-clock receiver that uses time-synchronization technology has brought new opportunities for high-precision GNSS-based attitude determination. In this article, for the first time, we present a performance comparison of global positioning system (GPS) L1/Galileo navigation satellite system (Galileo) E1 attitude determination with a common-clock receiver using four different models, i.e., the loosely combined single-differenced (SD-LC) model, the tightly combined single-differenced (SD-TC) model, the loosely combined double-differenced (DD-LC) model, and the tightly combined double-differenced (DD-TC) model. We first introduce the SD-LC, SD-TC, DD-LC, and DD-TC relative positioning models with GPS L1/Galileo E1 observations from a common-clock receiver. Then, we present a performance comparison of the four models in both single-epoch and multi-epoch modes using static data collected with a Trimble BD992 common-clock receiver in terms of the ambiguity dilution of precision (ADOP), the ambiguity resolution (AR) success and failure rates, and the positioning and attitude determination accuracy. In the case of the single-epoch mode, the experimental results revealed that the results of the single-differenced (SD) models were identical to those of double-differenced (DD) models, i.e., the results of SD-LC and SD-TC models were identical to DD-LC and DD-TC models, respectively. Moreover, compared with the loosely combined model (SD-LC/DD-LC), the tightly combined model (SD-TC/DD-TC) delivered a much higher AR success rate and a lower AR failure rate, especially under a high elevation cutoff angle. The AR success rate increased by approximately 35.1% under a 40° elevation cutoff angle, while the AR failure rate decreased by approximately 4.3%. In the case of the multi-epoch mode, the experimental results confirmed the advantages of the tightly combined model over the loosely combined model as well as the SD model over the DD model. Compared with the DD-LC and SD-LC models, the AR success rates of the DD-TC and SD-TC models were improved by approximately 16.7% and 0.6% under a 45° elevation cutoff angle, respectively. The AR failure rates were reduced by approximately 12.4% and 0.3%, respectively. Moreover, compared with the DD-LC and DD-TC models, the AR success rates of the SD-LC and SD-TC models under a 45° elevation cutoff angle were improved by approximat