title: Formal Uncertainty and Dispersion of Single and Double Difference Models for GNSS-Based Attitude Determination.
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.
authors.affiliation: Engineering Center of SHMEC for Space Information and GNSS, East China Normal University, Shanghai 200241, China. wchen@sist.ecnu.edu.cn.|Key Laboratory of Geographic Information Science, Ministry of Education, East China Normal University, Shanghai 200241, China. wchen@sist.ecnu.edu.cn.|Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai 200241, China. wchen@sist.ecnu.edu.cn.
authors.forename: Wen
authors.initials: W
authors.lastname: Chen
authors.affiliation: Engineering Center of SHMEC for Space Information and GNSS, East China Normal University, Shanghai 200241, China. cyu@sist.ecnu.edu.cn.|Key Laboratory of Geographic Information Science, Ministry of Education, East China Normal University, Shanghai 200241, China. cyu@sist.ecnu.edu.cn.|Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai 200241, China. cyu@sist.ecnu.edu.cn.
authors.forename: Chao
authors.initials: C
authors.lastname: Yu
authors.affiliation: Engineering Center of SHMEC for Space Information and GNSS, East China Normal University, Shanghai 200241, China. dndong@cs.ecnu.edu.cn.|Key Laboratory of Geographic Information Science, Ministry of Education, East China Normal University, Shanghai 200241, China. dndong@cs.ecnu.edu.cn.|Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai 200241, China. dndong@cs.ecnu.edu.cn.
authors.forename: Danan
authors.initials: D
authors.lastname: Dong
authors.affiliation: Engineering Center of SHMEC for Space Information and GNSS, East China Normal University, Shanghai 200241, China. mmcai@outlook.com.
authors.forename: Miaomiao
authors.initials: M
authors.lastname: Cai
authors.affiliation: Engineering Center of SHMEC for Space Information and GNSS, East China Normal University, Shanghai 200241, China. zhoufecnu@163.com.
authors.forename: Feng
authors.initials: F
authors.lastname: Zhou
authors.affiliation: Engineering Center of SHMEC for Space Information and GNSS, East China Normal University, Shanghai 200241, China. wangwangzhiren@163.com.
authors.forename: Zhiren
authors.initials: Z
authors.lastname: Wang
authors.affiliation: Engineering Center of SHMEC for Space Information and GNSS, East China Normal University, Shanghai 200241, China. lzhang@cs.ecnu.edu.cn.|Key Laboratory of Geographic Information Science, Ministry of Education, East China Normal University, Shanghai 200241, China. lzhang@cs.ecnu.edu.cn.|Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai 200241, China. lzhang@cs.ecnu.edu.cn.
authors.forename: Lei
authors.initials: L
authors.lastname: Zhang
authors.affiliation: Engineering Center of SHMEC for Space Information and GNSS, East China Normal University, Shanghai 200241, China. zqzheng@ee.ecnu.edu.cn.|Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai 200241, China. zqzheng@ee.ecnu.edu.cn.
authors.forename: Zhengqi
authors.initials: Z
authors.lastname: Zheng
keywords: GNSS; common clock; dispersion; double difference; formal uncertainty; single difference