Abstract
A global navigation satellite system (GNSS) receiver with multi-antenna using clock synchronization technology is a powerful piece of equipment for precise attitude determination and reducing costs. The single-difference (SD) can eliminate both the satellites and receiver clock errors with the common clock between antennas, which benefits the GNSS short-baseline attitude determination due to its lower noise, higher redundancy and stronger function model strength. However, the existence of uncalibrated phase delay (UPD) makes it difficult to obtain fixed SD attitude solutions. Therefore, the key problem for the fixed SD attitude solutions is to separate the SD UPD and fix the SD ambiguities into integers between antennas. This article introduces the one-step ambiguity substitution approach to separate the SD UPD, through which we merge the SD UPD parameter with the SD ambiguity of the reference satellite ambiguity as the new SD UPD parameter. Reconstructing the other SD ambiguities, the rank deficiency can be remedied by nature, and the new SD ambiguities can have a natural integer feature. Finally, the fixed SD baseline and attitude solutions are obtained by combining the ambiguity substitution approach with integer ambiguity resolution (IAR). To verify the effect of the ambiguity substitution approach and the advantages of the SD observables with a common clock in practical applications, we conducted static, kinematic, and vehicle experiments. In static experiments, the root mean squared errors (RMSEs) of the yaw and pitch angles obtained by the SD observables with a common clock were improved by approximately 80% and 93%, respectively, compared to double-difference (DD) observables with a common clock in multi-day attitude solutions. The kinematic results show that the dispersion of the SD-Fix in the pitch angle is two times less that of the DD-Fix, and the standard deviations (STDs) of the pitch angle for SD-Fix can reach 0.02°. Based on the feasibility, five bridges with low pitch angles in the vehicle experiment environment, which the DD observables cannot detect, were detected by the SD observables with a common clock. The attitude angles obtained by the SD observables were also consistent with the fiber optic gyroscope (FOG) inertial navigation system (INS). This research on the SD observables with a common clock provides higher accuracy.
Highlights
Complementary to inertial navigation systems (INSs), attitude determination based on global navigation satellite system (GNSS) short-baseline technology demonstrates its advantages of low cost and immunity to error accumulations [1]
Besides the saving of product cost and volume owing to sharing a common clock between two original equipment manufacturer (OEM) boards or between two antennas, its significant advantage is that using the convenience provided by a common clock the between-antenna (BA) single-difference (SD) observables can eliminate the errors of both the satellite and receiver clocks, improving the redundancy of the observation equation and the success rate of ambiguity resolution [5]
Satellite be received the horizontal direction during the obserHowever, in the vertical direction satellites signals can only be received from the upper vation
Summary
Complementary to inertial navigation systems (INSs), attitude determination based on global navigation satellite system (GNSS) short-baseline technology demonstrates its advantages of low cost and immunity to error accumulations [1]. Theoretical studies indicated that the BA SD (hereafter SD) and double-difference (DD) observables were no longer equivalent for the multi-antenna receiver with a common clock. The asymptotic analysis further demonstrated that using this multi-antenna GNSS receiver with a common clock, the pitch solutions of the SD algorithm were significantly superior to that of the DD algorithm. The dispersions of the pitch solutions from the SD algorithm were five times smaller than that from the DD algorithm [7] These advantages allow using SD observables for attitude determination and research in other fields such as multipath [8] and stochastic models [9]
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