Orthometric height connection across sea with ship-borne gravimetry and GNSS measurement along the ship route

A new method is proposed to connect the orthometric height datum of island far from mainland with measurements of both ship-borne gravimetry and GNSS along the ship route connecting these datums. The methodology of route height datum connection is based on the astronomical leveling principle. The effect of the deflection of the vertical (DOV) error and the ellipsoidal height difference error are major factors on the precision of the orthometric height connection. To improve the computational accuracy of DOVs along the ship route, the collinear adjustment is used to improve the accuracy of the gravity measurements and GNSS ellipsoidal heights. The remove-restore technique in conjunction with the measured DOVs on the mainland and island is used to improve the estimation accuracy of the DOVs along the ship route. The least squares collocation method is used to estimate the residual DOVs. The covariance of gravity anomalies and cross-covariance function between gravity anomalies and DOVs are derived from the disturbing potential spherical harmonic expansion. The optimal partition number is also studied for the high precision orthometric height connection across sea. Finally, we use the proposed method to connect the orthometric height datum point on Qingdao coast in Shandong Province of China with the datum point on Caoyu coast in Fujian Province of China.