Helmert transformation with mixed geodetic and Cartesian coordinates. Issue 9 (1st May 2019)

• Record Type: Journal Article
• Authors: Lin, Peng; Chang, Guobin; Gao, Jingxiang; Wang, Qianxin; Bian, Hefang
• Is Part Of: Advances in space research. Volume 63:Issue 9(2019)
• Page Start: 2964
• Page End: 2971
• Publication Date: 2019-05-01
• Subjects: Helmert transformation -- Geodetic coordinates -- Cartesian coordinates -- Weighted least-squares; Space sciences -- Periodicals; Astronautics -- Periodicals; Geophysics -- Periodicals; 500.505
• DOI: 10.1016/j.asr.2017.11.029
• Languages: English
• ISSNs: 0273-1177

Abstract

Abstract: It is common in geodetic practice that station geodetic coordinates in an old frame are measured/estimated by adjusting conventional leveling and vertical networks (together with a vertical datum), whereas their Cartesian coordinates in a new frame are measured/estimated by adjusting modern 3D Global Navigation Satellite System (GNSS) networks. To estimate Helmert transformation parameters between the two frames, one can simply convert the geodetic coordinates to their Cartesian counterparts in the same frame, and then perform a least-squares transformation with Cartesian coordinates in both frames. This stepwise approach is not optimal because of nonlinearity in the first step. In this work, a direct transformation is conducted. A functional model with mixed geodetic and Cartesian measurements is followed, and a realistic stochastic model considering measurement errors in both frames is adopted. Correlations between common and non-common stations are also taken into account. Weighted least-squares estimates of the transformation parameters and transformed/adjusted coordinates in the new frame are derived in detail, the latter representing the enlarged network of the new frame. Simulations are conducted, and the results validate the superiority of the proposed method compared with the stepwise method.