Abstract
With multi-antenna synchronized global navigation satellite system (GNSS) receivers, the single difference (SD) between two antennas is able to eliminate both satellite and receiver clock error, thus it becomes necessary to reconsider the equivalency problem between the SD and double difference (DD) models. In this paper, we quantitatively compared the formal uncertainties and dispersions between multiple SD models and the DD model, and also carried out static and kinematic short baseline experiments. The theoretical and experimental results show that under a non-common clock scheme the SD and DD model are equivalent. Under a common clock scheme, if we estimate stochastic uncalibrated phase delay (UPD) parameters every epoch, this SD model is still equivalent to the DD model, but if we estimate only one UPD parameter for all epochs or take it as a known constant, the SD (here called SD2) and DD models are no longer equivalent. For the vertical component of baseline solutions, the formal uncertainties of the SD2 model are two times smaller than those of the DD model, and the dispersions of the SD2 model are even more than twice smaller than those of the DD model. In addition, to obtain baseline solutions, the SD2 model requires a minimum of three satellites, while the DD model requires a minimum of four satellites, which makes the SD2 more advantageous in attitude determination under sheltered environments.
Highlights
Attitude determination (AD) is an important branch in navigation for both ground-based and space-based platforms
Note that the double difference (DD) and SD1 models require a minimum of four satellites to obtain the baseline baseline solutions and the SD2 model requires a minimum of three satellites
The emerging multi-antenna synchronized global navigation satellite system (GNSS) receiver uses a common clock for the multiple antennas
Summary
Attitude determination (AD) is an important branch in navigation for both ground-based and space-based platforms. It has been proved theoretically that the non-common clock SD and DD models are equivalent in the sense of deriving exactly the same position and baseline solutions with same formal uncertainties [20], the emerging multi-antenna synchronized GNSS receiver (using a common clock) has prompted scientists to reconsider the equivalence problem, in particular for AD [20,21] With this device, the SD between two antennas is able to eliminate both satellite and receiver clock errors simultaneously, and the estimation parameters of the SD observation equation are reduced by omitting the receiver clock term. Reference [20] performed a theoretical investigation on AD for single epoch solutions They proved that for a traditional GNSS receiver the SD model still estimated receiver clock parameters. Both static and kinematic short baseline experiments are carried out
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