Study On The Combination Algorithm Of GNSS Station’s Multi-day Solutions

The direct goal of station’s multi-day solutions is building the Terrestrial Reference Frame(TRF). And at the same time, it undertakes the task of maintaining and refining the TRF. The TRF is the realization of terrestrial reference system. It is composed of a series of physical points whose position and speed are precisely known corresponding to terrestrial reference system. Global coordinate datum is one of the most important infrastructure for developing Global Navigation Satellite System(GNSS). Building, maintaining and refining coordinate datum can not only serve satellite navigation systems directly, but also be the urgent need of spatial information infrastructure. With the efforts of geodesy scholars of national administration of surveying mapping and geoinformation and Headquarters of the General Staff of surveying and mapping bureau, CGCS2000 has been already realized. However, the maintaining and refining of coordinate datum are a long-term and continuous work. So it will be necessary to study on the algorithm of station’s multi-day solutions. This paper mainly research on how to use normal equation stack algorithm to calculate weekly-solutions based on daily-solutions through SINEX files and use multi-day solutions combination algorithm based on TRF to combine multi-day solutions. The main content of the paper includes the following aspects:(1)Gauss-Markoff model with constrains on paramete rs is given. The process of parameter pre-elimination is derived to reduce the dimension of normal equation. Least square solution using all observations and combining multiple steps least square solution are conducted. The consistency of these two ways is illustrated by comparison, thus integral adjustment at normal equation level is raised. According to the need of adjustment at normal equation level, the algorithm of parameter transformations is deduced. The process of the transcendent constrains for nor mal equation is researched.(2)Related content about SIN EX files is introduced so that using the information provided by SINEX files to reconstruct normal equation systems. Formulas of elimination of transcendent restriction are deduced. The changes of solutions before and after the elimination of transcendent restriction are showed by experiment. The algorithm of parameters rearrangement is designed. Then parameters in SINEX files are rearranged for use. The different kinds of restriction of datum are researched. The feasibility of datum transformation at normal equation level is illustrated by experiment. The experiment of using daily-solutions to calculate weekly-solutions based on normal equation stack algorithm is performed, and the results show that the precision of tracking station coordinates calculated by program is about 1cm.(3)The model of similarity transformation is researched. The process of coordinates transformation of two reference frames is deduced. For solving the problem of rank defect of normal equation in the situation of guaranteeing that the datum information of control network is not impacted, the minimal constrain is introduced. Then formulas of combining coordinate solutions at different reference epochs are deduced, and the datum is introduced in combining solutions for completing the process of combination. The experiment of multi-day solutions is performed, and the results show that the precision of tracking station coordinates calculated by program is about 1.5cm.(4)The estimation model of velocity parameter on station is researched, and the process of introduction of velocity parameter is deduced based on parameter transformation. For the situation of discontinuous coordinates, the algorithm of sleek Chebyshev Polynomial fitting is presented to fit unknown coordinates. The experiment of time series analysis of tracking station coordinates is performed for testing the reasonableness o f taking velocity parameter as fixed parameter. And the results show that the changes of tracking station weekly-solutions are not entirely linear.