Theory And Algorithms Of Terrestrial Reference Frame

Terrestrial reference frame (TRF) is the realization of terrestrial reference system, customarily called geodetic coordinate system or geodetic datum. TRF is the foundation of geodesy. Also, it has always been the fundamental problem of geodesy. The main task of geodesy is to deal with the measurement and representation of the Earth. Geodetic coordinate system is indispensable to represent and analyze the results of surveying. This paper reviews the nature of establishment of TRF, constraint types and their processing methods in establishing modern TRF. The nature of origin, scale, orientation, and their time evolution of current ITRF is discussed in order to understand it better. In addition, the maintenance of TRF is researched. Some suggestion is given on how to establish reference frame of GNSS of China.The conclusions of this paper are as follows:1. The nature of establishment TRF is to realize the positioning of geodetic control network. The positioning of a control network requires seven parameters, three translation components, one scale factor, and three rotation angles. If a dynamic reference frame is to be established, another seven parameters is needed, i.e., seven rates of the above components. From a geodetic point of view, the 14 parameters should be viewed as relative values between two TRFs, their selection should correspond to the adopted TRS definition that one wants to satisfy.2. Free network adjustment is a method that can conserve the best shape of control network only determined by observations. Loose constraint, as a method of free network adjustment, is suitable and convenient for spatial geodetic technique. A simple example has approved that there is a quite wide range of value, in which loose constraint solution is identical to free network solution. Various methods conserving the best shape of control network can be classified as minimum constraint. Minimum constraint provides sufficient and essential data for adjustment, which conserves the properties of the observing technique. Generally speaking, any solution can be identified into two parts: an internal noise in an observation and the reference system effect.3. The realized nature of the ITRF2000 origin becomes CM in the long term, but CF on seasonal and short timescales. Before ITRF2000, the realized nature of previous ITRF origins was not CM but approximately CF on all timescales due to an incomplete kinematic model under a CF frame. ITRF2000 is aligned with NNR-NUVEL1 A at 1 mm/a level, i.e., it satisfies NNR condition. An elaborate and scientific global plate kinermatic model is very important for realizing NNR condition, which states that the integral over the Earth's surface of all plate motions should be zero. Plate boundary model, being a more elaborate model than ever, inspires us to give some considerations on establishment of plate boundary model in China.4. Simply speaking, the maintenance of terrestrial reference frame is to provide coordinates of points varying with time, taking the form of velocity model or of coordinate time series in general. As for as the maintenance of regional reference frame, the latter is preferred.5. The reference frame must be recognized as the foundation of everything the GNSS does and therefore deserving of special attention. IGS00, the IGS long-term frame realization, is a frame of more accuracy than ITRF and is the basis of IGS products. GGSP (Galileo Geodetic Service Provider Prototype) is researching to realize Galileo TRF based on Galileo system. There is some experience for the design and construction of Beidou?reference frame.