The ocean real-time kinematic (ORTK) technique was proposed to realize high-precision GNSS positioning for long baselines with differential corrections transmitted through the BeiDou short message service, where the positioning accuracy is from subdecimeter to centimeter and the convergence time is several minutes without integer ambiguity resolution. In this paper, the ORTK method is improved based on the dual-frequency global positioning system and triple-frequency BeiDou navigation satellite system. The convergence time is shortened to a few seconds using the following modifications/innovations. First, the uncombined corrections are used instead of the ionosphere-free corrections. A more efficient encoding strategy is proposed to compress the uncombined corrections. Second, the ultrarapid precise ephemeris provided by the Tongji BeiDou Analysis Center is assimilated in the corrections to mitigate the orbit errors, and a long-baseline ionosphere-weighted model is applied to estimate the ionospheric delays. Third, an asynchronous and time-differenced positioning filter is employed to address the time-delays and time-correlations of the corrections. Finally, the float solutions in our earlier study are upgraded to fixed solutions by partially fixing the ambiguities. Experiments on a 320 km baseline indicate that the ambiguities can be correctly fixed within 10 s and that the positioning accuracy is approximately 1.1 cm for both horizontal components and 5 cm for the vertical component. [ABSTRACT FROM AUTHOR]