The Statistical Property of the GNSS carrier Phase Observations and its Effects on the Hy-pothesis Testing of the Related Estimators

Jianqing Cai, Erik W. Grafarend and Congwei Hu

Abstract:	Although the GNSS carrier phase measurements are the basic observables for the high precision GPS geodesy and navigation. Their statistical properties have not yet been paid attention to in details. Until now they are applied more or less with having a Gauss-Laplace normal distribution. Ever since von Mises (1918) introduced the von Mises normal distribution on the circle, its importance has not been recognized by the data analysts. Actually von Mises developed the normal distribution for the circular (directional, angular) random variable by the investigation of the distribution of the fractional parts of the atomic weights, which is just appropriate to the GPS carrier phase observables, the measurements of the fractional phase. Recently, Gao, Cai and Grafarend (2001), Grafarend (2006) and Cai and Grafarend (2006) have discussed this kind of problem in the opinion of geodesists. Here the statistical properties of double difference GPS phase observations are validated as von Mises normal distribution by applying series analyses with the Test of Uniformity, Test of Goodness-of Fit and Tests on von Mises distributions. Under the von Mises normal distribution property of carrier phase observations, proper hypothesis tests on these parameters and their variance-covariances are discussed and proposed.
Published in:	Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007) September 25 - 28, 2007 Fort Worth Convention Center Fort Worth, TX
Pages:	331 - 338
Cite this article:	Cai, Jianqing, Grafarend, Erik W., Hu, Congwei, "The Statistical Property of the GNSS carrier Phase Observations and its Effects on the Hy-pothesis Testing of the Related Estimators," Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, September 2007, pp. 331-338.
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