Characteristics of GPS positioning error with non-uniform pseudorange error |
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| Authors: | Jiangtao Fan Guanyi Ma |
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| Institution: | 1. National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China
2. University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, China
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| Abstract: | We study the characteristics of the random GPS positioning errors when the pseudorange errors differ for each satellite. A concise, explicit, analytical formula is derived for the covariance of the positioning error by using singular value decomposition. It is composed of a uniform error covariance together with additional contributions from those satellites with larger pseudorange errors. The eigenvectors of the uniform error covariance define the principal directions of the 4-dimensional error ellipsoid, and the eigenvalues are the squares of the semi-axes. The additional part from individual satellites has only one eigenvector and one eigenvalue. This makes the error ellipsoid enlarge mainly along a direction related to both the overall satellite geometry and the position of the specific satellites. The theory is validated by simulating the GPS constellation and pseudorange measurements. The random positioning error is examined while any one or more pseudorange errors are increased. Horizontal positioning error distributions are presented to demonstrate the variations of the orientation and size of the error ellipses with the pseudorange error of a specific satellite. The results show that the analytical formula describes the positioning error accurately. |
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